DESIGN GUIDE for midas Civil

Transcription

1 DESIGN GUIDE or midas Civil AASHTO LRFD restressed Concrete Girder Design Steel Composite Girder Design Steel Composite Bridge Load Rating

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3 analysis and design system. The guide aims to provide eatures and to provide relevant reerences to the clauses in the Design standards. The design guide covers prestressed concrete girder design, steel composite girder design and steel composite It is recommended that you read this guide and review corresponding tutorials, which are ound on our web site, the program s main menu. DISCLAIMER Developers and distributors assume no responsibility or the use o MIDAS Family rogram (midas Civil, midas FEA, midas FX+, midas Gen, midas Drawing, midas SDS, midas MIDAS package ) or or the accuracy or validity o any results obtained rom the MIDAS package. Developers and distributors shall not be liable or loss o caused directly or indirectly by the MIDAS package, when used or any purpose or use, due to any deect or ully understand the bases o the program and become amiliar with the users manuals. The user shall also independently veriy the results produced by the program.

4 Foreword eatures and to provide relevant reerences to the clauses in the Design standards. The design guide covers prestressed concrete girder design, steel It is recommended that you read this guide and review corresponding help available in the program s main menu. Organization

5 Contents Chapter 1. restressed Concrete Girder Design Strength Limit States 1. Flexural resistance 2. Shear resistance 3. Torsion resistance Serviceability Limit States Tensile stress or restressing tendons rincipal stress at service loads rincipal stress at service loads Check crack 52 Steel Composite Girder Design 55 Modeling and Design Variables 1. Modeling Design Variables Shear Connector (2007) and 6th(2012)

6 Span Checking Total Checking 149 Chapter Modeling and Design Variables 1. Modeling Design Variables

7 Chapter 1. restressed Concrete Girder Design AASHTO LRFD 7 th (2014)

8 Chapter 1. restressed Concrete Girder Design restressed concrete box girders and composite girders need to be designed to Serviceability Limit States Tensile stress or restressing tendons rincipal stress at service loads Check crack

9 Chapter 1. restressed Concrete Girder Design:AASHTO-LRFD 7 th (2014) Strength Limit States 1. Flexural resistance The actored lexural resistance shall satisy the ollowing condition, M u ΦM n. M u : Factored moment at the section due to strength load combination ΦM n : Factored lexural resistance 1.1. Resistance Factor Resistance actor Φ shall be taken as ollow. AASHTO LRFD14 ( ) [Fig.1. 1] Resistance Factor 0.75 i dt i t c 1.0 i t t (1.1) d t : Distance rom extreme compression iber to the centroid o the extreme tension steel element c : Distance rom the extreme compression iber to the neutral axis ε t : Net tensile Strain In midas Civil, ε t is applied as strain o a reinorcement which is entered at the extreme tensile iber. Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

10 Input reinorcements to be used in the calculation o resistance in the dialog box below. Model>roperties>Section Manager>Reinorcements Rebar coordinate at the section Entered rebar data [Fig.1. 2] Input Longitudinal reinorcement Once reinorcement is entered at the SC section, the rebar which is placed at the closest position to the extreme compression iber will be used to calculate the strain. In short, the rebar at the bottom most is used under the sagging moment. And the rebar at the top most is used under the hogging moment. Input tendon proile to be used in SC design in the dialog box below. Load>Temp./restress>Section Manager >Tendon roile Tendon position which is placed at the closest position to the extreme tensile iber will be used to calculate the strain. [Fig.1.3] Tendon roile 4 Design Guide or midas Civil

11 1.2 Calculate neutral axis depth Neutral axis is determined by the iteration approach as shown in the igure below. Assume neutral axis depth, c Initial c = H/2 (H=Section Height) Calculate C c (Concrete) (1) Calculate T s, C s (Reinorcement) (2) Calculate T ps (Tendon) (3) C c +C s -(T s +T ps )=0? YES Get neutral axis depth, c (4) NO [Fig.1. 4] Flow chart to calculate neutral axis depth, c (1) Calculate orce o concrete, C c. In midas Civil, the natural relationship between concrete stress and strain is considered as the equivalent rectangular concrete compressive stress block.(compressive strain limit o concrete, ε cu = 0.003) [Fig.1. 5] Calculate orce o concrete, C c C 0.85 ' A c c c (1.2) ' c : Speciied compressive strength o concrete or design Compressive strength to be used in SC design is deined in SC Design Material dialog box i ' c 4.0ksi ( ' 4.0) 0.65 i ' 4.0ksi c A c : Concrete area o compressive zone 1 c ( c) width Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

12 SC>SC Design Data> SC Design Material Concrete [Fig.1. 6] SC Design Material Enter the concrete and reinorcement grade to be used in SC design. The strength can be checked or the selected material grade according to the selected material code. When None is selected in Code ield, the strength o concrete and reinorcement can be directly entered. AASHTO LRFD14 ( ) Fig.1. 3 SC Design Material (Composite) For the composite type SC sections, the Design Material window changes to allow users to deine the material properties o the slab. The concrete and rebar material properties entered or slab are used or every calculation such as the neutral axis calculation. 6 Design Guide or midas Civil

13 (2) Calculate orce o reinorcement, T s, C s. Tensile resistance due to longitudinal reinorcement (T s )and compression resistance due to concrete (C s ) is calculated as shown in the ollowing equation. T A, C A ' ' (1.3) s s s s s s A s, A s : the cross sectional area o tensile and compressive reinorcement It is entered in Section Manager>Reinorcements as shown in the Fig1. 2. s, s : the stress o tensile and compressive reinorcement In order to calculate the tensile stress o reinorcement, midas Civil calculate the corresponding strains as per the strain compatibility condition. And then the related tensile stresses are calculated by the stress-strain relationship. The equation is shown as ollows. Strain d c c c d c t c s cu, s' (1.4) cu ε s : the strain o tensile reinorcement. ε s : the strain o compressive reinorcement. ε cu : the ultimate compressive strain in the concrete. (ε cu = 0.003) c : the neutral axis depth. d t : Distance rom the compression iber o concrete to the extreme tensile iber o reinorcement d c : Distance rom the compression iber o concrete to the extreme compressive iber o reinorcement Stress I the tensile stress o reinorcement reaches its yield stress limit, tensile stress will be applied as yield stress. I not, the tensile stress will be calculated as ε s x E s. ses ( s y) s, y ( s y) s' Es ( s' y) s ' y ( s' y) (1.5) E s : Modulus o elasticity in reinorcement F y : Yield tensile stress in reinorcement (3) Calculate orce o tendon, T ps. Tensile resistance o prestressing steel, T ps, is calculated as shown in the ollowing equation. T A ps p ps (1.6) A p : the cross sectional area o tendon. ps : the stress o tendon. Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

14 SC> Design arameter> arameters [Fig.1. 7] SC Design parameter Dialog - Flexural Strength Tensile stress o prestressing steel ps can be calculated by code or strain compatibility as speciied in SC design arameter dialog box. When code is selected in lexural strength option, the tensile stress ps is calculated by the equation as per AASHTO-LRFD or bonded and unbounded tendon respectively. When strain compatibility is used, the tensile stress ps is calculated by the stress-strain relationship. Load>Temp./restress>Section Manager>Tendon roperty Tendon Type Total Tendon Area pu py Bond Type Tendon Type Internal(re-Tension) Internal(ost-Tension) External [Fig.1. 8] Tendon roperty Dialog Bond Type Bonded: Section properties relect the duct area ater grouting. When tendon type is speciied as Internal (re-tension), bond type will be taken as Bonded Type. Unbonded: Section properties exclude the duct area. 8 Design Guide or midas Civil

15 When tendon type is speciied as external, bond type will be taken as Unbonded Type. [Table1. 1] Applicable Bond Type by Tendon Types Tendon Type Internal (re-tension) Internal (ost-tension) External Bond Type Bonded Bonded Unbonded Unbonded Total Tendon Area Enter the tendon area (A p ). Click to select the number o strands and diameter in order to calculate the tendon area automatically. pu, py Enter the ultimate strength pu and yield strength py o prestressing steel. Tensile stress o prestressing steel ps will be calculated as shown in the ollowing table. [Table1. 2] Calculation o tensile stress o prestressing steel Flexure Strength option Bond Type Tensile Stress Code Bonded ps or Bonded Type Unbonded ps or Unbonded Type Strain compatibility Bonded Strain compatibility Unbonded* ps or Unbonded Type * When lexure strength option is entered as strain compatibility and bond type is entered as unbonded type, tensile stress will be calculated using the code equation o unbonded tendon instead o strain compatibility method. It is because strain compatibility method is valid or ully bonded tendons. Tensile stress o prestressing steel ps is calculated as ollows. Code equation or bonded type tendon c ps pu 1k d p (1.7) AASHTO LRFD14 ( ) (Eq ) k py pu (1.8) AASHTO LRFD14 ( ) (Eq ) py : Yield strength o prestressing steel pu : Speciied tensile strength o prestressing steel d p : Distance rom extreme compression iber to the centroid o the prestressing tendons c: Distance between the neutral axis and the compressive ace Code equation or unbonded type tendon dp c 900 le ps pe py 2li le 2 N s (1.9) (1.10) AASHTO LRFD14 ( ) (Eq ) AASHTO LRFD14 ( ) (Eq ) Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

16 l i : length o tendon between anchorages N i : number o support hinges crossed by the tendon between anchorages or discretely bonded point. It is always applied as 0 in midas Civil. ps by Strain compatibility When lexure resistance is calculated by strain compatibility method, tensile stress o prestressing tendon is calculated by the stress-strain relationship. [Fig.1. 9] Stress-strain model o prestressing tendon (4) Determination o neutral axis position In order to ind the neutral axis, the iteration analysis will be perormed until compressive strength (C=C c +C s ) becomes equal to the tensile strength (T=T s +T ps ). The convergence criterion is applied as shown in the ollowing equation. Convergence condition: C ( Tolerance) (1.11) T 1.3 Calculate moment resistance M n Once the neutral axis is determined, lexural resistance is calculated by multiplying the distance rom the neutral axis. ' (1.12) M C a C a Ta T a n c c s s s s ps pi where, a c, a s, a s, a pi : the distance rom neutral axis depth, c to concrete, reinorcement rebar, tendon. 10 Design Guide or midas Civil

17 A s 0.85 c c a ac C s C c as' A p as ap T ps A s [Fig.1. 10] Forces and distances rom neutral axis depth or Mn T s I a tendon in tension is located at the upper part rom the neutral axis under the sagging moment, the lexural resistance will have (-) sign and it will reduce the total moment resistance. M C a C a Ta T a T a ' ' n c c s s' s s ps pi ps pi (1.13) 1.4 Factored Flexural Resistance M r M (1.14) n AASHTO LRFD14 ( ) (Eq ) where, M n : nominal resistance Φ : resistance actor 1.5 Minimum Reinorcement The moment resistance with considering entered reinorcements or tendons shall satisy the ollowing condition. M max(1.33 M, M ) (1.15) r u cr AASHTO LRFD14 ( ) Cracked Moment ( M cr ) For composite sections, the equation 1.16 is used to calculate the cracked moment (M cr ). S c Mcr 3( 1r 2cpe) Sc Mdnc 1 Snc (1.16) AASHTO LRFD14 ( ) (Eq ) The M dnc is taken rom the Muy caused by the dead load o girder section during the construction stage analysis. The S nc value is obtained rom the section modulus o the pre-composite section under the tensile stress. The S c value is taken rom the section modulus o the post-composite section Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

18 under the tensile stress. In midas Civil, cracked moment shall be calculated as per the ollowing equation. (For the composite type sections, the equation 1.16 is used; or the non-composite type sections, the equation 1.17 is used. Mcr 3 ( 1r 2cpe) Sc (1.17) γ 1 : lexural cracking variability actor 1.2 or precast segmental structures 1.6 or all other concrete structures γ 2 : prestress variability actor 1.1 or bonded tendons 1.0 or unbounded tendons I both bonded and unbonded type tendons are assigned in a section, 2 will be applied as 1.0 which is more conservative value. γ 3 : ratio o speciied minimum yield strength to ultimate tensile strength o the reinorcement 0.67 or A615,Grade 60 reinorcement 0.75 or A706, Grade 60 reinorcement 1.00 or prestressed concrete structures In midas Civil, 3 wil be applied as 1.0. r : modulus o rupture o concrete speciied in Article In midas Civil, r will be always applied as 0.37 ' c. S c : section modulus or the extreme iber o the composite section where tensile stress is caused by externally applied loads (in 3 ) In midas Civil, section modulus under tension is applied. AASHTO LRFD14 ( ) (C ) cpe : compressive stress in concrete due to eective prestress orces only (ater allowance or all prestress losses) at extreme iber o section where tensile stress is caused by externally applied loads (ksi) It is obtained in elastic state (uncracked section) and the ollowing equation has been applied in midas Civil. cpe Aps e Aps eep (1.18) A g S : Eective prestress orces o prestressing tendons e e p : Distance rom the neutral axis to the centroid o the prestressing tendons A : Area o prestressing tendon ps A g : Gross area o cross-section S : Sectional modulus in compression In midas Civil, construction type o SC section is determined in SC design parameter dialog box. 12 Design Guide or midas Civil

19 SC> Design arameter> arameters [Fig.1. 4] SC Design parameter Dialog - Construction Type Construction type: Segmental, Non-Segmental The selected construction type will aect the calculation o cracked moment, shear and torsional resistance, and tensile stress limit o concrete. 1.6 Check moment resistance In midas Civil, actored moment is obtained rom load combinations speciied in Load Combinations dialog box. In AASHTO LRFD speciication, load combinations need to be generated as shown in the ig AASHTO LRFD14 (3.4.1) [Fig.1. 5] Load Combinations and Load actors or strength limit state Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

20 Results>Load combinations>concrete Design tab Active: Strength/Stress Active: Serviceability [Fig.1. 6] Load Combinations dialog In midas Civil, load combinations can be automatically generated by clicking [Auto Generation ] button. The load combinations need to be generated in concrete design tab. The most critical load combination among Strength/Stress type load combinations will be used to obtain actored moment, actored shear orce, and actored torsional moment. The Service type load combinations will be used to veriy the serviceability limit state. The veriication o lexural moment obtained rom Strength/Stress type load combination can be divided into two ollowing cases. 1) No need to satisy minimum reinorcement M r M u (1.19) 2) Need to satisy minimum reinorcement M r M and u Mr Mcr (1.20) 1.7 Moment resistance veriication by Result Tables The results can be checked as shown in the table below. Design>SC Design>SC Design Result Tables>Check Flexural Strength [Fig.1. 7] Result table or moment resistance 14 Design Guide or midas Civil

21 Elem : Element number art : Check location (I-End, J-End) o each element. ositive/negative : ositive moment, negative moment. LCom Name : Load combination name. Type : Displays the set o member orces corresponding to moving load case or settlement load case or which the maximum stresses are produced. CHK : Flexural strength check or element Muy : Design moment Mcr : Crack Moment Mny : Nominal moment resistance. himny : Design moment resistance. Ratio : Muy/ himny : Flexural resistance ratio, The veriication is satisied when it is less than 1.0. himny /min(1.33muy, Mcr) : Veriication o minimum reinorcement. The veriication is satisied when it is less than 1.0. I the veriication o minimum reinorcement is not required, it will be displayed as by Excel Report Detail veriication results can be checked in MS Excel report as shown in the igure below. Design>SC Design>SC Design Calculation [Fig.1. 8] Excel report or moment resistance Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

22 2. Shear resistance Shear resistance without consideration o eects o torsion shall be veriied to satisy the ollowing condition. M u V (1.21) n AASHTO LRFD14 ( ) strength reduction actor, Φ=0.9. Reer to the clause 2.3 Torsion Resistance or the veriication o shear resistance where the eects o torsion are required to be considered. In AASHTO-LRFD (2012), the design or shear and torsion will be perormed or segmental and non-segmental box girders. 2.1 Classiication o Segmental Box Girder The program will consider a section is segmental box girder when the ollowing 2 conditions are satisied. 1. In SC Design arameter dialog box, Construction Type is speciied as Segment. 2. When a section is deined with SC box section (ex. SC-1CELL, 2CELL, 3CELL, ncell, ccell2, LAT, and Value type) roperty > Section roperty > Section >SC [Fig.1.16] SC section data dialog 2.2 arameters or shear Eective web width (b v ) b v : eective web width taken as the minimum web width within the depth d v as determined in Article (in.) Eective web width (b v ) is taken as web thickness. For SC multi-cell girder, web thickness can be automatically taken as a summation o thickness or all webs. Also this value can be entered by the user directly as shown in the igure below. AASHTO LRFD14 ( ) 16 Design Guide or midas Civil

23 roperty > Section roperty > Section >SC [Fig 1.17] Consideration o eective web width 1) When the user directly enters values or web thickness Apply the minimum value among the entered web thickness values. 2) When Auto option is selected Apply the minimum web thickness among t1, t2, and t3. These values are automatically taken as a summation o thickness or both webs at the stress point, Z1, Z2, and Z Eective shear depth (d v ) Non-Segmental Box Girder d v : eective shear depth takem as the distance, measured perpendicular to the neutral axis, between the resultants o the tensile and compressive orces due to lexure; it need not be taken less than the greater o 0.9d e or 0.72h(in.) In midas Civil, the value o eective shear depth, dv, is calculated as shown in the equation below. AASHTO LRFD14 ( ) M n dv min, 0.9 de, 0.72h A s s Aps ps (1.22) d e A d A d ps ps p s s s A A ps ps s s (1.23) d p : Distance rom extreme compression iber to the centroid o the prestressing tendons d s : Distance rom extreme iber to the centroid o nonprestressed tensile reinorcement Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

24 [Fig.1.18] Eective shear depth Segmental Box Girder dv : 0.8h or the distance rom the extreme compression iber to the centroid o the prestressing reinorcement, whichever is greater (in.) In midas Civil, the value o eective shear depth, dv, is calculated as shown in the equation below. AASHTO LRFD14 ( ) d v max 0.8 h, d t (1.24) h = Total height o a section d t = Distance rom extreme compression iber to the centroid o the prestressing tendons Net longitudinal tensile strain (ε s ) s is the net longitudinal tensile strain in the section at the centroid o the tension reinorcement s M d v u 0.5N V V A EA u u p ps po EA s s p ps (1.25) AASHTO LRFD14 ( ) (Eq ) po s 0.7 pu M V V d u u p v A s and A p are taken as area o nonprestressing and prestressing steel on the lexural tension side o the member respectively. d v : 0.8h or the distance rom the extreme compression iber to the centroid o the prestressing reinorcement, whichever is greater (in.) In midas Civil, the value o eective shear depth, dv, is calculated as shown in the equation below. d v max 0.8 h, d t (1.26) 18 Design Guide or midas Civil

25 h : Total height o a section d t : Distance rom extreme compression iber to the centroid o the prestressing tendons [Fig 1.19] Net longitudinal tensile strain 2.3 The nominal shear resistance, V n V n (Non-Segmental Box Girder) For non-segmental box girders, the nominal shear resistance, V n, shall be determined as the lesser o: Vn Vc Vs Vp (1.27) V 0.25 bd V (1.28) ' n c v v p AASHTO LRFD14 ( ) (Eq ) (Eq ) V c : shear resistance component that relies on tensile stresses in the concrete V s : shear resistance component that relies on tensile stresses in the transverse reinorcement V p : shear resistance component in the direction o the applied shear o the eective prestressing orce. In midas Civil, shear resistance due to prestressing orce, Vp, includes primary prestress orce. The secondary eects rom prestressing shall be included in the design shear orce obtained rom the load combinations. b v : Eective web width taken as the minimum web width within the depth, dv (reer to the clause Eective web width) d v : Eective shear depth (Reer to the clause Eective shear depth) V n (Segmental Box Girder) For segmental box girders, the nominal shear resistance, V n, shall be determined as the lesser o: Vn Vc Vs Vp (1.29) V bd V (1.30) ' n c v v p AASHTO LRFD14 ( ) (Eq ) (Eq ) V c : shear resistance component that relies on tensile stresses in the concrete V s : shear resistance component that relies on tensile stresses in the transverse reinorcement V p : shear resistance component in the direction o the applied shear o the eective prestressing orce. In midas Civil, shear resistance due to prestressing orce, Vp, includes primary prestress orce. The secondary eects rom prestressing shall be included in the design shear orce obtained rom the Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

26 load combinations. b v : Eective web width taken as the minimum web width within the depth, dv (reer to the clause Eective web width) d v : Eective shear depth (Reer to the clause Eective shear depth) 2.4 The nominal shear resistance by concrete, V c Design or shear may utilize any o the two methods (simpliied and general procedure) or prestressed sections identiied in AASHTO-LRFD12. In midas Civil, sections can be designed as per the general procedure V c (Non-Segmental Box Girder) V ' bd (1.31) c c v v AASHTO LRFD14 ( ) AASHTO LRFD14 ( ) (Eq ) b v : Eective web width taken as the minimum web width within the depth, dv (reer to the clause Eective web width) d v : Eective shear depth (Reer to the clause Eective shear depth) β : Factor indicating ability o diagonally cracked concrete to transmit tension and shear as speciied in Article For the sections containing at least the minimum amount o transverse reinorcement : AASHTO LRFD14 ( ) 4.8 (1 750 ) s (1.32) When sections do not contain at least the minimum amount o shear reinorcement: (1 750 ) (39 S ) 1.38 Sxe Sx ag 0.63, s xe 12.0( in.) S 80.0( in.) x (1.33) S x : The lesser o either d v or the maximum distance between layers o longitudinal crack control reinorcement, where the area o the reinorcement in each layer is not less than 0.003bvsx, as shown in Figure (in.). In midas Civil, it is applied as dv. a g : maximum aggregate size(in.)in midas Civil, it is applied as 1in.. ε s : net longitudinal tensile strain in the section at the centroid o the tension reinorcement.reer to the clause Net longitudinal tensile strain Vc (Segmental Box Girder) V K ' bd (1.34) c c v v AASHTO LRFD14 ( ) (Eq ) b v : Eective web width taken as the minimum web width within the depth, dv (reer to the clause Eective web width) d v : Eective shear depth (Reer to the clause Eective shear depth) K: Stress variable K shall not be taken greater tham 1.0 or any section where the stress in the extreme tension iber, calculated on the basis o gross section properties, due to actored load and eective prestress orce ater losses exceeds 0.19 c in tension 20 Design Guide or midas Civil

27 pc K 1 (1.35) ' c AASHTO LRFD14 ( ) (Eq ) In midas Civil, the value o K is calculated as below. 1) Calculate the tensile stress o tendon, t, ater losses Tendon based on the uncracked section. 2) I 0.19 ', K = min(k, 1.0) t c I 0.19 ', K = min(k, 2.0) t c AASHTO LRFD14 ( ) pc : Unactored compressive stress in concrete ater prestress losses have occured either at the centroid o the cross-section resisting transient loads or at the junction o the web and lange where the centroid lies in the lange (ksi) In midas Civil, pc is calculated as ollows. When the centroid lies in the lange, veriy the stress at a junction o the web and lange. pc A A e N A I A ps e ps e p u yjoint g g g (1.36) y joint is a distance rom the centroid to the junction o the web and lange When the centroid lies in the web, veriy the stress at the centroid o the cross-section. pc Aps e Nu (1.37) A g A g 2.5 The nominal shear resistance by shear reinorcement, Vs The nominal shear resistance by shear reinorcement, Vs, is calculated as ollows: Vs (Non-Segmental Box Girder) V s Ad v y v (cot cot )sin (1.38) s AASHTO LRFD14 ( ) (Eq ) d v :Reer to Eective shear depth (or Non-Segmental Box Girders) θ: angle o inclination o diagonal compressive stresses as determined in Article (degrees) ; i the procedures o Article are used, cotθ is deined therein. Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

28 [Fig.1.20] angle o inclination o transverse Compressive stress The ollowing equation is incorporated in midas Civil: s (1.39) AASHTO LRFD14 ( ) (Eq ) s :Reer to Net longitudinal tensile strain α: Angle o inclination o transverse reinorcement to longitudinal axis (degrees) Enter the Angle o transverse reinorcement as shown in Fig1.22. s : Spacing o transverse reinorcement Enter the itch o transverse reinorcement as shown in Fig1.22. Model>roperties>Section Manager>Reinorcements Transverse Reinorcement [Fig.1.21] Transverse Reinorcement The required input data or transverse reinorcement are as ollows: - itch: Enter the spacing o transverse reinorcement - Angle: Enter the angle o inclination o transverse reinorcement - Aw: Enter the total area o all transverse reinorcements in the web Vs (Segmental Box Girder) midas Civil applies the ollowing equation where the angle o inclination (α) o transverse reinorcement is taken into account: 22 Design Guide or midas Civil

29 V s Ad v y v (sin cot ) (1.40) s AASHTO LRFD14 ( ) ((Eq ) d v : reer to Eective shear depth (or Segmental Box Girders) α: angle o inclination o transverse reinorcement to longitudinal axis (degrees) Enter the Angle o transverse reinorcement as shown in Fig Maximum spacing or transverse reinorcement (s max ) The maximum spacing o transverse reinorcement can be checked by the ollowing steps: 1) Calculate the shear stress (v u ) acting on the concrete. AASHTO LRFD14 ( ) v u Vu Vp (1.41) bd v v AASHTO LRFD14 ( ) (Eq ) Φ = Use the shear strength reduction actor o 0.9. b v : reer to Eective web width d v : reer to Eective shear depth (or Non-Segmental Box Girders) 2) Calculate s max dierently, depending on whether the section is Segmental Box Girder or not and on the range o v u. 3) Compare the entered spacing o transverse reinorcement with s max s max (Non-Segmental Box Girder) I v u < c s max = 0.8d v 24.0 in. I v u c s max = 0.4d v 12.0 in. AASHTO LRFD14 ( ) d v : reer to Eective shear depth (or Non-Segmental Box Girders) s max (Segmental Box Girder) I v u < 0.19 c s max = 0.8d v 36.0 in. I v u 0.19 c s max = 0.4d v 18.0 in. d v : reer to Eective shear depth (or Segmental Box Girders) AASHTO LRFD14 ( ) AASHTO LRFD14 ( ) midas Civil calculates v u using Eq or the shear check and using Eq or the torsion check. Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

30 2.7 Minimum required transverse reinorcement (A v,min ) The minimum required transverse reinorcement can be checked according to the ollowing steps: 1) Calculate the minimum required reinorcement, A v,min, dierently dependng on whether the section is Segmental Box Girder or not. For Non-Segmental Box Girders ' bs v Av,min c (1.42) For Segmental Box Girders A v,min 0.05 w y y bs (1.43) AASHTO LRFD14 ( ) (Eq ) (Eq ) In midas Civil b w =b v. 2) Calculate the shear strength o the section, and then veriy the transverse reinorcement using the ollowing equations: For V u < 0.5Φ(V c +V p ) Skip the transverse reinorcement checks. For V u 0.5Φ(V c +V p ) A A vreq, 1 Vu 0.5 ( Vc Vp) s d(sin cot ) A y vreq, 2 v,min A min( A, A ) v, req v, req1 v, req2 v (1.44) I the area o transverse reinorcement (A v ) is greater than or equal to A v,req, it says OK. The area o transverse reinorcement (A v ) is Aw which is entered rom Fig Design Guide or midas Civil

31 2.8 Interace Shear For the composite sections, the Shear Friction caused during construction sequences needs to be considered. Thereore, the Interace Shear check unction is activated or the precomposite section design check Calculate Vni The V ni value is calculated based on the above calculation. The A cv is the Interacial Shear section area. The A c value is the cross section o the shear reinorcement o the Interacial Shear section. The ollowing equation ( ) needs to be satisied about the minimum shear reinorcement rea. The c value is the compressive orce acting on the interace. In the program, the c value is calculated based on the selweight o slab. The program suggests the actors used in design. In midas Civil, they are applied as shown below: Table. The design actors used in midas Civil AASHTO-LRFD12 Standard In Acv = bci x Lvi, bci value is taken rom the Bvi input by the user and the Lvi value is taken rom the girder length o the program model. Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

32 The Av is the cross section o the reinorcement rebars in the interacial shear plane (Acv). The calculator is activated when the button is clicked. So that the cross section is calculated based on the rebar diameter, number and gap inputted by the user. The Vri value is calculated based on the above equation ( ). Also, the Vri value should be equal to or greater than Vui. For SC design check, the is taken as 1.0. The Interace Shear calculation can be reviewed in the MS Excel Report. The Interace Shear check result can be also checked in the Shear Resistance Results table. 2.9 Check shear resistance midas Civil checks the shear strength limit state or the V max and V min cases among the Active: Strength/Stress load combinations, which are deined in Fig.1.12 Load Combinations dialog Check the shear resistance results by Result Tables The results can be checked as shown in the table below. Design>SC Design>SC Design Result Tables>Check Shear Strength [Fig.1.22] Result table or shear resistance Elem : Element number art : Check location (I-End, J-End) o each element Max./Min. : Maximum shear, minimum shear LCom. Name : Load combination name. Type : Displays the set o member orces corresponding to moving load case or settlement load case or which the maximum stresses are produced. CHK : Shear strength check or element Vu : Maximum shear orce among Strength/Stress load combinations Mu : Bending moment or the LCom which has Vu Vn : Nominal Shear resistance. hi : Resistance actor or shear Vc : Shear resistance o concrete. 26 Design Guide or midas Civil

33 Vs : Shear resistance o shear reinorcement. Vp : Shear orce o the eective prestressing orce. hivn : Design Shear resistance. de : Eective web width dv : Eective depth or shear ex : Longitudinal Strain theta : Angle o inclination o transverse compressive stresses beta : Factor indicating ability o transversely cracked concrete to transmit tension and shear Avs : Area o shear reinorcement Ast : Area o longitudinal reinorcement Al : Area o longitudinal torsional reinorcement bv : Eective width Avs_min : Minimum required transverse reinorcement Avs_req : Required transverse reinorcement Al_min : Minimum longitudinal torsional reinorcement bv_min : Minimum eective web width Vri : Nominal interace shear resistance Vui : actored interace shear orce due to total load based on the applicable strength and extreme event load combinations by Excel Report The detailed results, which contain the calculations, are produced in the Excel Report. Design>SC Design>SC Design Calculation [Fig.1.23] Excel Report or shear resistance Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

34 3. Torsion resistance Check the combined shear and torsional resistance. 3.1 Dimension o section or torsion The dimensions o section that are required or checking torsion are as ollows: Ao : Area enclosed by the shear low path, including any area o holes therein (in2) midas Civil uses the area o the closed section enclosed by the torsion reinorcement, instead o the shear low path. h : erimeter o the centerline o the closed transverse torsion reinorcement (in) Acp : Total area enclosed by outside erimeter o the concrete section (in2) : The length o the outside perimeter o concrete section (in) [Fig.1.24] Dimension o section or torsion **Additional inormation or the torsional area Ac and circumerence h calculation o the composite section. In midas Civil, when Ao section is applied or the composite section, the girder and slab sections (section areas with the Torsion Thk Oset applied in the Section Manager) are calculated separately and then added. The h circumerence is calculated based on the same approach but the value o bw*2 is substracted in order to consider the contact area between the girder and slab. ex) 3.2 Calculate torsional resistance Torsional resistance can be checked according to the ollowing steps: 1) Calculate the torsional cracking moment (T cr ) dierently, depending on whether the section is Segmental Box Girder or not. 2) Compare the actored torsional moment (T u ) with the limit, which diers depending on the type o girder (segmental box girder or non-segmental box girder), in order to decide whether the eect o torsion should be considered or not. 3) In case where the torsional eect should be considered, calculate the design torsional strength and compare it with T u. 28 Design Guide or midas Civil

35 3.2.1 Torsional cracking moment (T cr ) For Non-Segmental Box Girders T cr 2 A ' cp pc c 1 p (1.45) c ' c AASHTO LRFD14 ( ) (Eq ) pc : compressive stress in concrete ater prestress losses have occurred at either the centroid o the cross-section resisting transient loads or at the junction o the web and lange where the centroid lies in the lange (ksi) midas Civil calculates pc as ollows: I the centroid lies in the lange: calculate at the junction o the web and lange. pc Aps e Aps eep y (1.46) joint Ag Ig y joint is the distance rom the centroid to the junction o the web and lange. I the centroid lies in the web: calculate at the centroid o the corss-section. pc Aps e (1.47) A g A 2 cp p shall be less than or equal to 2A ob v or a box section. c For Segmental Box Girders T K Ab ' cr c o e K : Reer to the value o K speciied in b e : eective width o shear low path, but not exceeding the minimum thickness o the webs or langes comprising the closed box section (in.). be shall be adjusted to account or presence o ducts as speciied in Article midas Civil uses bv. (1.48) AASHTO LRFD14 ( ) (Eq ) Condition or torsion check For Non-Segmental Box Girders T u 0.25T cr (1.49) AASHTO LRFD14 ( ) (Eq ) For Segmental Box Girders T u 1/3T cr Φ = resistance actor or torsion(=0.9) (1.50) AASHTO LRFD14 ( ) (Eq ) Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

36 3.2.3 Torsional resistance In accordance with AASHTO-LRFD12, the torsional resistance should meet the condition T u ΦT n or the cases o segmental box girders and non-segmental box girders. AASHTO LRFD14 ( ) For Non-Segmental Box Girders T n 2AA o t ycot s (1.51) AASHTO LRFD14 ( ) (Eq ) A t : area o one leg o closed transverse torsion reinorcement in solid menbers, or total area o transverse torsion reinorcement in the exterior web o cellular members (in. 2 ). Awt o Torsional Reinorcement entered in Fig will be used. s :itch o Torsional Reinorcement entered in Fig will be used. Θ: angle o crack as determined in accordance with provisions o Article with the modiications to the expressions or v and V u herein (degrees). The same equation, which was used or the shear check, will be used: s s : Reer to Net longitudinal tensile strain. (1.52) AASHTO LRFD14 ( ) (Eq ) For Segmental Box Girders 2AA o t y Tn s (1.53) AASHTO LRFD14 ( ) (Eq ) A t : Awt o Torsional Reinorcement entered in Fig will be used. s : itch o Torsional Reinorcement entered in Fig will be used. The reinorcement data used or the torsion check are as ollows: Model>roperties>Section Manager>Reinorcements Torsional Reinorcement [Fig.1.25] Transverse Reinorcement - itch : spacing o transverse torsional reinorcement - Awt : area o transverse torsional reinorcement 30 Design Guide or midas Civil

37 (the area o a single stirrup among the outer closed stirrups) - Alt : area o longitudinal torsional reinorcement (the area o all reinorcing steels which are close against the outer closed stirrups) 3.3 Check longitudinal reinorcement Check the longitudinal reinorcement to resist torsion. Check it or box sections and or solid sections, respectively. For Solid sections A ps is the area o tensile tendon and A s is the area o tensile reinorcement. 2 2 Mu 0.5N u V u 0.45phT u Aps ps As y cot Vp 0.5Vs dv 2Ao (1.54) AASHTO LRFD14 ( ) (Eq ) d v : reer to Eective shear depth (or Non-Segmental Box Girders) For Box sections The Code suggests that the reinorcement or resisting torsion is limited to the ollowing equation or box sections: A l Tp n h 2A o y (1.55) AASHTO LRFD14 ( ) (Eq ) midas Civil incorporates the above equation to check the longitudinal torsional reinorcement. The Alt o Torsional Reinorcement entered in Fig will be used. Alt is only or resisting warping torsion and is used only or box sections. A lt ( Tu / ) p 2A o y h (1.56) AASHTO LRFD14 ( ) (Eq ) 3.4 Check combined torsional and shear stress For Segmental Box Girders, check the combined shear and torsional stress. V u T u bd v v 2Ab o e ' c (1.57) AASHTO LRFD14 ( ) (Eq ) b v : reer to Eective web width d v : reer to Eective shear depth (or Segmental Box Girders) b e : eective thickness o the shear low path o the elements making up the space truss model resisting torsion calculated in accordance with Article (in). midas Civil uses b v. midas Civil calculates the maximum combined stress using the equation below. Vu bd Tu ' (1.58) c 2Ab v v o e Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

38 3.5 Check torsional moment resistance midas Civil checks the combined shear and torsional strength limit state or the V max, V min and T max cases among the Active: Strength/Stress load combinations, which are deined in Fig.1.12 Load Combinations dialog. 3.6 Check the torsional resistance results by Result Tables The results can be checked as shown in the table below. Design>SC Design>SC Design Result Tables>Check Combined Shear and Torsion Strength [Fig.1.26] Result table or torsional resistance Elem : Element number art : Check location (I-End, J-End) o each element Max./Min.: Maximum torsion/shear, minimum torsion/shear LCom Name: Load combination name. Type: Displays the set o member orces corresponding to moving load case or settlement load case or which the maximum stresses are produced. CHK: Shear and torsion strength check or element Vu : shear orce or the corresponding LCom Mu : bending moment or the corresponding LCom Tu : torsional moment or the corresponding LCom Vn : Nominal Shear resistance. Tn : Nominal Torsional resistance. hi : strength reduction actor or shear hi_t : strength reduction actor or torsion Vc : Shear resistance o concrete. Vs : Shear resistance o shear reinorcement. Vp : Shear orce o the eective prestressing orce. hivn : Design Shear resistance. hi_ttn : Design Torsional resistance. de : Eective web width dv : Eective depth or shear ex : Longitudinal Strain theta : Angle o inclination o transverse compressive stresses beta : Factor indicating ability o transversely cracked concrete to transmit tension and shear Avs : Area o shear reinorcement Ast : Area o longitudinal reinorcement Al : Area o longitudinal torsional reinorcement bv : Eective width Avs_min : Minimum required transverse reinorcement Avs_req : Required transverse reinorcement Al_min : Minimum longitudinal torsional reinorcement bv_min : Minimum eective web width At : Area o transverse torsional reinorcement At_req : Required transverse torsional reinorcement 32 Design Guide or midas Civil

39 3.6.2 by Excel Report Detail veriication results can be checked in MS Excel report as shown in the igure below. Design>SC Design>SC Design Calculation [Fig.1.27] Excel report or torsional resistance Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

40 Chapter 1. restressed Concrete Girder Design:AASHTO-LRFD 7 th (2014) Serviceabiltiy Limit States 1. Stress or cross section at a construction stage The allowable stress at a construction stage diers depending on the generated stress because the precompressed tensile zone is deined dierently depending on the generated stress. Thereore, the generated stress at every stage and step is compared to the corresponding allowable stress, and the most unavorable ratio o the generated stress to the allowable stress is searched and checked against the criteria. That is to say, calculate the ratio o generated stress to allowable stress or every stage and see i the highest ratio meets the criteria. 1.1 Allowable stress o concrete (1) Allowable compressive stress o concrete σ ca = 0.60 ci (1.59) AASHTO LRFD14 ( ) the deinition o ci is stated in (2) Allowable tensile stress o concrete AASHTO LRFD14 ( ) [Fig.1.28] Allowable tensile stress o concrete 34 Design Guide or midas Civil

41 Midas Civil calculates the allowable tensile stress o concrete using Table , as stated in the table below: Non-Segment Segment recompressed Tensile Zone Other Than recompressed Tensile Zone Joint Non Joint [Table 1.3] Allowable tensile stress o concrete Case Without bonded reinorcement bonded and I reinorcement nt stress min(0.5y, 30ksi) With bonded reinorcement or bonded tendon I reinorcement nt stress > min(0.5y, 30ksi) Without bonded reinorcement bonded and I reinorcement nt stress With bonded reinorcement or bonded d tendon min(0.5y, 30ksi) I reinorcement nt stress > min(0.5y, 30ksi) re ) i) Allowable stress(ksi) = 0.0 ta ta = 0.24*SQRT(' ci ) = 0.0 ta ta = ' ci 0.2 ta = 0.24*SQRT(' ci ) ta = 0.0 With bonded Reinorcement stress 0.5y = *SQRT(' ta ci ) recompressed tensile Zone reinorcement or bonded Reinorcement nt stress s> 0.5y tendon ta = 0.0 ta = 0.0 ta = 0.19*SQRT(' ci ) With bonded reinorcement or bonded tendon ta I reinorcement nt stress min(0.5y, 30ksi) I reinorcement nt stress > min(0.5y, 30ksi) = 0.0 ta = 0.0 ) Description on each item is as ollows: recompressed Tensile Zone: According to the Code, recompressed Tensile Zone is deined as Any region o a prestressed component in which prestressing causes compressive stresses and service load eects cause tensile stresses. midas Civil calculates the concrete stress in cross-section using the ollowing methods and deines the recompressed Tensile zone at Beore Loss (construction stage). I it is compressive stress or Tendonrimary(CS)+Tendon Secondary(CS), and i it is tensile stress or Summation(CS)-(Tendon primary+tendon secondary). AASHTO LRFD14 (5.2) Joint/non-Joint: In midas Civil, joints can be deined in the dialog below: SC> SC Segment Assignment AASHTO LRFD14 ( ) [Fig.1.29] SC Segment Assignment As shown in Fig.2.2, i elements 1, 2 and 3 are assigned as one segment, i-end o element 1 and j-end o element 3 become the joints and the rest become the non-joints. Bonded reinorcement It is assumed that the tensile reinorcement or the tendon deined as Bond Type in Fig.1. 7 are bonded reinorcement. Based on the aorementioned, i tensile reinorcement or bonded tendon is present in the tension zone, it is assumed that bonded reinorcement exists. AASHTO LRFD14 (C ) Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

42 Check the stress in reinorcement The Code states that the bonded reinorcement, which retains a speciic stress value (0.5y or 30ksi), shall resist the tensile orce on the tension zone. midas Civil applies the above regulation as ollows: Compute the concrete triangular stress block on the tension zone, using the extreme iber tension stress and the extreme iber compression stress o concrete. Compute the tension orce o concrete by multiplying the compression stress by the area o the concrete triangular stress block. Compute the tension orce o reinorcement by multiplying the area o reinorcement and tendon, which are included in the triangular stress block, by the speciic stress (0.5y or 30ksi). I the tension orce o reinorcement is larger than that o concrete, it is concluded that the tensile stress o reinorcement satisies the regulation. [Fig.1.30] Check the tension orce o reinorcement 1.2 Compressive strength o concrete at time o loading, ci The Code deines ci as: ci is speciied compressive strength o concrete at time o initial loading or precompressing; nominal concrete strength at time o application o tendon midas Civil computes the compressive strength o concrete ( ci ) during the construction stages according to the construction days deined in Fig.2.4 and the unction o concrete strength deined in Fig.2.5. The days or each construction stage can be deined in Fig2.4. AASHTO LRFD14 (5.3) Load> Construction Stage> Compose construction Stage Stage Additional Steps Activation [Fig.1.31] Compose construction Stage dialog Stage>Duration: Enter the duration o the construction stage. It is the basic unit where elements become active or inactive, boundary conditions become active or inactive and loads are applied or removed. 36 Design Guide or midas Civil

43 Additional Step>age: Deine the speciic days or the analysis steps within the construction stage. Within a construction stage where the model and boundary conditions remain unchanged, changes in load application timing or additional loads may be incorporated through additional steps. Activation>Group List>age: Select relevant element groups, which are applicable to the current stage, in the Group List and activate the selected groups by moving them to Activation Group List. Speciy the Age o the selected element groups. The age entered here will be used to relect the eects o creep and shrinkage that took place prior to the current construction stage. The age o the element, which is casted at the start o the current construction stage, is zero. The age typically represents the time span rom the time o concrete casting to the time o removal o ormwork during which the concrete is considered as a structural element, that is to say the curing period o concrete. Based on the inputs shown in Fig.2.4, midas Civil takes the ollowing days or the construction stage analysis: The duration o the construction stage CS1 is 30 days, the duration o the additional step within CS1 is 15 days, and the Activation age is 5 days. The actual duration o CS1 is 35 days (Stage Duration + Activation age). The compressive strength o concrete is computed at 5 days, 20 days and 35 days or CS1. I the next stage CS2 is deined with the duration o 20 days, CS2 starts at 35 days and ends at 55 days. The development o concrete compressive strength with days is deined in the dialog below. AASHTO LRFD14 ( ) roperties> Time Dependent Materials>Comp. Strength [Fig.1.32] Time Dependent Materials dialog Development o Strength: Deine the unction to compute the compressive strength o concrete during the construction stages. Deine a unction by selecting ACI, CEB-FI or Structural Concrete Design Code, or directly deine the values. The compressive strength o concrete is computed by relecting the variation o the modulus o elasticity with concrete ages. For CS1 the compressive strengths o concrete are computed at 5 days, 20 days and 35 days, and they are compared to the corresponding stresses. Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

44 1.3 Check stress or cross section at a construction stage c ca, t ta (1.60) 1.4 Check the stress results or cross section at a construction stage by Result Tables The results can be checked as shown in the table below. Design>SC Design >SC Design Result Tables>Check stress or cross section at a construction stage [Fig.1.33] Result table or stress at a construction stage Elem : Element number art : Check location (I-End, J-End) o each element Comp./Tens.: Compression or Tension Stress Stage : Construction stage at which stresses are maximum at the corresponding section. CHK : Combined stress check or construction stages FT : Combined Stress due to My and axial orce at Top iber FB : Combined Stress due to My and axial orce at Bottom iber FTL : Combined Stress due to My, Mz and axial orce at Top Let iber FBL : Combined Stress due to My, Mz and axial orce at Bottom Let iber FTR : Combined Stress due to My, Mz and axial orce at Top Right iber FBR : Combined Stress due to My, Mz and axial orce at Bottom Right iber FMAX : Maximum combined stress out o the above six components. ALW : Allowable stress o cross section at construction stage. Girder/Slab : The girder o the composite section is indicated as Girder(composite); the slab o the composite section is indicated as Slab(composite); the non-composite SC section is indicated as Girder(SC). Right click on mouse >> Context Menu >> Activate Records The results can be iltered and selected or the Girder and Slab. The results can be output separately or the Girder(Composite) and Slab(Composite). For the non-composite SC sections, the results are ouput or the Girder(SC). For the non-composite SC sections, even i the Slab part is selected, the results are not output or the Slab(Composite). 38 Design Guide or midas Civil

45 1.4.2 by Excel Report Veriication results can be checked in MS Excel report as shown in the igure below. Design>SC Design >SC Design Calculation [Fig.1.34] Result table or stress at a construction stage **The stress result is output or the girder and slab separately with the addition o the composite section design check. Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

46 2. Stress or cross section at service loads The element stress at service loads ater losses should meet the ollowing conditions: The maximum compressive stress at service loads ater losses allowable compressive stress o concrete: σ c σ ca The maximum tensile stress at service loads ater losses allowable tensile stress o concrete: σ t σ ta The Code suggests that the stresses in SC structures ater losses shall be checked or the ollowings: Check compressive stress: or the load combinations o Service Limit state 1 Check tensile stress: or the load combinations o Service Limit state 3 AASHTO LRFD14 ( ) ( ) [Fig.1.35] Load Combination or Service Limit state In midas Civil, the Load Cases to check compressive stress and tensile stress ater losses can be selected via the dialog box shown in Fig.2.9. The Load Cases in Service Limit1 will be used to check compressive stress, and the Load Cases in Service Limit3 will be used to check tensile stress. [Fig.1.36] Concrete Allowable Stress Load Case dialog 40 Design Guide or midas Civil

47 2.1 Allowable stress o concrete (1) Allowable compressive stress o concrete AASHTO LRFD14 ( ) [Fig.1.37] Allowable compressive stress o concrete The ollowing ormula is incorporated in midas Civil: σ ca = 0.45 c (1.61) (2) Allowable tensile stress o concrete AASHTO LRFD14 ( ) [Fig.1.38] Allowable tensile stress o concrete midas Civil calculates the allowable tensile stress o concrete using Fig.2.11, as stated in the table below: Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

48 [Table1.4] Allowable tensile stress o concrete Non-Segment Segment Case With bonded reinorcement or bonded corrosion condition - not Worse tendon recompressed corrosion condition -severe Tensile Zone Without bonded reinorcement bonded d and Other Than recompressed Tensile Zone (recompressed Tensile Zone) and I reinorcement nt stress 0.5y, Joint (With bonded reinorcement or bonded I reinorcement nt stress s > 0.5y, tendon ) With bonded reinorcement or bonded I reinorcement nt stress min(0.5y, 30ksi), tendon Non Joint I reinorcement nt stress > min(0.5y, 30ksi) Allowable stress(ksi) ta = 0.19*sqrt(ck) ta = *sqrt(ck) ta = 0.0 ta = 0.0 ta = *SQRT('c) ta = 0.0 ta = 0.0 ta = 0.19*SQRT('c) ta = 0.0 ta = 0.0 Description on each item is as ollows: recompressed Tensile Zone According to the Code, recompressed Tensile Zone is deined as Any region o a prestressed component in which prestressing causes compressive stresses and service load eects cause tensile stresses. midas Civil calculates the concrete stress in cross-section using the ollowing methods and deines the recompressed Tensile zone at Ater Loss (construction stage). -I it is compressive stress or Tendonrimary(CS)+Tendon Secondary(CS), and -i it is tensile stress or Service Limit State load combination(sls)-(tendon primary+tendon secondary). AASHTO LRFD14 (5.2) Corrosion Condition The data or Corrosion Condition can be entered in the dialog box below: SC> Design arameter> arameters [Fig.1.39] SC Design parameter Dialog -corrosion condition The input parameters and the corresponding terms deined in the Code are listed in the table below: 42 Design Guide or midas Civil

49 [Table1.5] corrosion condition Input parameter Severe Moderate/Mild Term o the Code Severe Not worse Joint/non-Joint : reer to Bonded reinorcement : reer to Check the stress in reinorcement : reer to Check stress or cross section at service loads c ca, t ta (1.62) 2.3 Check the stress results or cross section at service loads by Result Tables The results can be checked as shown in the table below. Design>SC Design>SC Design Result Tables>Check stress or cross section at service loads [Fig.1.40] Result table or stress at service loads Elem: Element number art: Check location (I-End, J-End) o each element Comp./Tens.: Compression or Tension Stress LCom Name: Load Combination Name Type: Displays the set o member orces corresponding to moving load case or settlement load case or which the maximum stresses are produced CHK: Combined stress check or Service loads FT: Combined Stress due to My and axial orce at Top iber FB: Combined Stress due to My and axial orce at Bottom iber FTL: Combined Stress due to My, Mz and axial orce at Top Let iber FBL: Combined Stress due to My, Mz and axial orce at Bottom Let iber FTR: Combined Stress due to My, Mz and axial orce at Top Right iber FBR: Combined Stress due to My, Mz and axial orce at Bottom Right iber FMAX: Maximum combined stress out o the above six components. ALW: Allowable stress in concrete at service limit state. Girder/Slab : The output is presented separately or the Composite Section as the Girder(composite) and Slab(Composite). Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

50 2.3.2 by Excel Report Veriication results can be checked in MS Excel report as shown in the igure below. Design>SC Design>SC Design Calculation [Fig.1.41] Excel report or stress at service loads **The stress result is output separately or the Girder/Slab with the addition o the Composite Section Design. 3. Tensile stress or restressing tendons Compare the stress in tendon with the allowable stress or each tendon group. Ater immediate losses at anchorages, the maximum stress in tendon allowable stress. Elsewhere away rom anchorages, the maximum stress in tendon allowable stress. Ater all losses, the maximum stress in tendon allowable stress. 3.1 Allowable stress o tendon The Code presents the ollowing stress limits or tendons depending on the tendon types: AASHTO LRFD14 (5.9.3) [Fig.1.42] Stress Limit or restressing Tendons 44 Design Guide or midas Civil

51 Tendon Type can be speciied rom the Design parameters dialog. SC> Design arameter> arameters [Fig.1.43] SC Design parameter Dialog Tendon Type The input parameters o the dialog and the corresponding terms deined in the Code are listed in the table below: [Table1.6] Tendon Type Input parameter Low Relaxation Tendons Stress Relieved Tendons restressing Bar Term o the Code Low Relaxation Strand Stress Relieved Strands dl Hi h t thb Deormed Hige-strength Bar re/ost tensioning can be speciied as showin in Fig.1. 8 Tendon roperty Dialogue. Midas Civil applies the stress limits or tendons dierently, depending on the Tendon Type and whether it is re/ost tensioning. Allowable stress in tendon immediately ater anchor set at anchorages(afdl1) The maximum allowable stress in tendon at anchorages ater immediate losses. The values or At anchorages and couplers immediately ater anchor set o Table are set as the limits. Allowable Stress in Tendon immediately ater anchor set elsewhere(afdl2) The maximum allowable stress in tendon elsewhere along length o member away rom anchorages. The values or Elsewhere along length o member away rom anchorages o Table are set as the limits. This is not applicable to retension. Allowable stress in tendon at service limit state ater losses(afll1) The maximum allowable stress in tendon at service limit state ater all losses. The values or At service limit stage ater losses o Table are set as the limits. 3.2 Check the stress in restressing tendons by Result Tables The stress results o tendon can be checked as shown in the table below. Design>SC Design>SC Design Result Tables>Check tensile stress or restressing tendons Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

52 [Fig.1.44] Result table or tensile stress or prestressing tendon Tendon: Tendon proile name. For ost-tensioned: FDL1: Stress in tendon at anchorages. The maximum stress in tendon at anchorages ater immediate losses FDL2: Maximum stress in tendon along the length o the member away rom anchorages, immediately ater anchor set. The maximum stress in tendon elsewhere along length o member away rom anchorages immediately ater anchor set FLL1: Maximum stress in tendon ater all losses at the last stage. The maximum stress in tendon at service limit state ater all losses AFDL1: Allowable stress in tendon immediately ater anchor set at anchorages. The allowable stress or FDL1 AFDL2: Allowable stress in tendon immediately ater anchor set elsewhere. The allowable stress or FDL2 AFLL1: Allowable stress in tendon at service limit state ater losses. The allowable stress or FLL1 For re-tensioned: FDL1: Stress in tendon. FDL2: - FLL1: Maximum stress in tendon ater all losses at the last stage. AFDL1: Allowable stress in tendon prior to transer. AFDL2: - AFLL1: Allowable stress in tendon at service limit state ater losses Tendon Time-dependent Loss Graph The stress in each tendon or each construction stage can be checked rom the dialog below: Result > Bridge> Tendon Loss Graph [Fig.1.45] Tendon Time-dependent Loss Graph In the graph above the stress at the beginning represents the stress in tendon at anchorage ater immediate losses (FDL1), and the largest stress in the graph represents the maximum stress in tendon elsewhere along length o member away rom anchorages immediately ater anchor set (FDL2) by Excel Report Veriication results can be checked in MS Excel report as shown in the igure below. Design>SC Design>SC Design Calculation 46 Design Guide or midas Civil

53 [Fig.1.46] Excel Report or tensile stress or prestressing tendons 4. rincipal stress at a construction stage Find the maximum principal tensile stress among the stress check points 1~10 o the crosssection at a construction stage and compare it to the allowable stress. In other words, maximum principal tensile stress allowable stress. 4.1 Allowable tensile stress The Code presents the ollowing equation o allowable tensile stress or Segmentally Constructed Bridges: AASHTO LRFD14 ( ) ta ' ci (1.63) ci is identical to that o midas Civil applies the above equation or both Segment and Non-segment. 4.2 Maximum principal stress The maximum principal tensile stress or each point at a constructions stage is computed as ollows: ps x z x z s t p (1.64) where, σ x : Sum o axial stresses in ECS x-direction σ z : Sum o axial stresses in ECS z-direction τ s : Shear stress due to shear. τ t : Shear stress due to torsion. τ p : Shear stress due to shear reinorcement. Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

54 4.2.1 Beam stresses o SC The stress components to compute the maximum principal tensile stress can be checked rom the Result Table below: Results>Result Tables>Beam>Stress(SC) [Fig.1.47] Beam stresses o SC Sig-xx (Axial): Axial stress due to the axial orce (Fx) in the ECS x-direction Sig-xx (Moment-y): Stress due to My (moment about the ECS y-axis) in ECS x-direction Sig-xx (Moment-z): Stress due to Mz (moment about the ECS z-axis) in ECS x-direction Sig-xx (Bar): Axial stress due to shear steel bars in the ECS x-direction Sig-xx (Summation): Sum o the axial stress in the ECS x-direction and the axial stress due to shear steel bars in the ECS x-direction Sig-zz: Stress in the ECS z-direction Sig-xz (shear): Sum o shear stresses due to shear orce and shear steel bars Sig-xz (torsion): Shear stress due to torsion Sig-xz (bar): Shear stress due to shear steel bars Sig-Is (shear): Transverse stress due to shear orce Sig-Is (shear+torsion): Transverse stress due to torsion and shear orce Sig-s1: Maximum principal stress Sig-s2: Minimum principal stress 4.3 Check principal stress at a construction stage ps ta (1.65) 4.4 Check the principal stress results at a construction stage by Result Tables The results can be checked as shown in the table below. Design>SC Design>SC Design Result Tables>rincipal stress at a construction stage [Fig.1.48] Result table or principal stress at a construction stage Elem: Element number. art: Check location (I-End, J-End) o each element. Comp./Tens.: Compression or Tension Stress. Stage: Construction stage. CHK: rincipal stress check or construction stages. Sig_1: rincipal Stress at the let top o top lange. Sig_2: rincipal Stress at the right top o top lange. Sig_3: rincipal Stress at the right bottom o bottom lange. 48 Design Guide or midas Civil

55 Sig_4: rincipal Stress at the let bottom o bottom lange. Sig_5: rincipal Stress at the top o let web.(at Z1 Level) Sig_6: rincipal Stress at the top o right web.(at Z1 Level) Sig_7: rincipal Stress at the neutral axis in let web.(at Z2 Level) Sig_8: rincipal Stress at the neutral axis in right web.(at Z2 Level) Sig_9: rincipal Stress at the bottom o let web.(at Z3 Level) Sig_10: rincipal Stress at the bottom o right web.(at Z3 Level) Sig_MAX: The maximum rincipal stress among Sig_A: Allowable principal stress at neutral axis in the web by Excel Report Veriication results can be checked in MS Excel report as shown in the igure below. Design>SC Design>SC Design Calculation [Fig.1.49] Excel Report or principal stress at a construction stage 5. rincipal stress at service loads (Excluding torsional shear stress) Find the maximum principal tensile stress among the stress check points 1~10 o the crosssection at service loads and compare it to the allowable stress. In other words, maximum principal tensile stress allowable stress. Here the shear eect due to torsion is excluded Allowable tensile stress The Code (Table ) presents the ollowing equation o allowable tensile stress or Segmentally Constructed Bridges: ta ' c (1.66) AASHTO LRFD14 ( ) midas Civil applies the above equation or both Segment and Non-segment Maximum principal stress The maximum principal tensile stress or each point at a construction stage is computed as ollows: ps x z where, σ x : Sum o axial stresses in ECS x-direction σ z : Sum o axial stresses in ECS z-direction τ s : Shear stress due to shear. τ t : Shear stress due to torsion. τ p : Shear stress due to shear reinorcement. x z s t p (1.67) Beam stresses o SC The stress components to compute the maximum principal tensile stress can be checked rom the Result Table below: Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

56 Reer to Beam stresses o SC. 5.3 Check principal stress at service loads ps ta (1.68) 5.4 Check the principal stress results at service loads by Result Tables The results can be checked as shown in the table below. Design>SC Design>SC Design Result Tables > Result table or principal stress at service loads(excluding torsional shear stress) [Fig.1.50] Result table or principal stress at service loads (excluding torsional shear stress) Elem: Element number. art: Check location (I-End, J-End) o each element. Comp./Tens.: Compression or Tension Stress. Stage: Construction stage. CHK: rincipal stress check or construction stages. Sig_1: rincipal Stress at the let top o top lange. Sig_2: rincipal Stress at the right top o top lange. Sig_3: rincipal Stress at the right bottom o bottom lange. Sig_4: rincipal Stress at the let bottom o bottom lange. Sig_5: rincipal Stress at the top o let web.(at Z1 Level) Sig_6: rincipal Stress at the top o right web.(at Z1 Level) Sig_7: rincipal Stress at the neutral axis in let web.(at Z2 Level) Sig_8: rincipal Stress at the neutral axis in right web.(at Z2 Level) Sig_9: rincipal Stress at the bottom o let web.(at Z3 Level) Sig_10: rincipal Stress at the bottom o right web.(at Z3 Level) Sig_MAX: The maximum rincipal stress among Sig_A: Allowable principal stress at neutral axis in the web by Excel Report Veriication results can be checked in MS Excel report as shown in the igure below. Design>SC Design>SC Design Calculation [Fig.1.51] Excel report or principal stress at service loads (excluding torsional shear stress) 50 Design Guide or midas Civil

57 6. rincipal stress at service loads Find the maximum principal tensile stress among the stress check points 1~10 o the crosssection at service loads and compare it to the allowable stress. Here both shear and torsion will be relected in the stress calculation. In other words, maximum principal tensile stress allowable stress. 6.1 Allowable tensile stress The Code (Table ) presents the ollowing equation o allowable tensile stress or Segmentally Constructed Bridges: ta ' c (1.69) AASHTO LRFD14 ( ) midas Civil applies the above equation or both Segment and Non-segment. 6.2 Maximum principal stress The maximum principal tensile stress or each point at a construction stage is computed as ollows: ps x z x z s t p (1.70) where, σ x : Sum o axial stresses in ECS x-direction σ z : Sum o axial stresses in ECS z-direction τ s : Shear stress due to shear. τ t : Shear stress due to torsion. τ p : Shear stress due to shear reinorcement Beam stresses o SC The stress components to compute the maximum principal tensile stress can be checked rom the Result Table below: Reer to Beam stresses o SC. 6.3 Check principal stress at service loads ps ta (1.71) 6.4 Check the principal stress results at service loads by Result Tables The results can be checked as shown in the table below. Design>SC Design>SC Design Result Tables>rincipal stress at service loads [Fig.1.52] Result table or principal stress at service loads Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

58 Elem: Element number. art: Check location (I-End, J-End) o each element. Comp./Tens.: Compression or Tension Stress. Stage: Construction stage. CHK: rincipal stress check or construction stages. Sig_1: rincipal Stress at the let top o top lange. Sig_2: rincipal Stress at the right top o top lange. Sig_3: rincipal Stress at the right bottom o bottom lange. Sig_4: rincipal Stress at the let bottom o bottom lange. Sig_5: rincipal Stress at the top o let web.(at Z1 Level) Sig_6: rincipal Stress at the top o right web.(at Z1 Level) Sig_7: rincipal Stress at the neutral axis in let web.(at Z2 Level) Sig_8: rincipal Stress at the neutral axis in right web.(at Z2 Level) Sig_9: rincipal Stress at the bottom o let web.(at Z3 Level) Sig_10: rincipal Stress at the bottom o right web.(at Z3 Level) Sig_MAX: The maximum rincipal stress among Sig_A: Allowable principal stress at neutral axis in the web by Excel Report Veriication results can be checked in MS Excel report as shown in the igure below. Design>SC Design>SC Design Calculation [Fig.1.53] Excel report or principal stress at service loads 7. Check crack The limit state or crack can be checked by comparing the applied spacing o tensile reinorcement with the maximum spacing o reinorcement. In accordance with AASHTO-LRFD, the crack limit shall be checked or the mild steel reinorcement. The applied spacing o tensile reinorcement shall be compared to the computed maximum spacing o reinorcement. In other words, applied spacing o reinorcement maximum spacing o reinorcement 7.1 Maximum spacing o reinorcement The maximum spacing o reinorcement is computed as ollows: s max 700 e 2d (1.72) c s ss AASHTO LRFD14 ( ) (Eq ) dc s 1 0.7( h d ) c (1.73) d c : thickness o concrete cover measured rom extreme tension iber to center o the lexural reinorcement located closest thereto (in.) ss : tensile stress in steel reinorcement at service limit state (ksi) ss is computed according to the ollowing steps: 1) Compute the concrete stress (cs) at the location o tensile reinorcement using 52 Design Guide or midas Civil

59 the extreme iber tension stress and the extreme iber compression stress. 2) Compute the strain o concrete (εcs=cs/ec) with regard to cs. 3) Compute ss (ss = Es εcs). γ e :exposure actor 1.00 or Class 1 exposure condition 0.75 or Class 2 exposure condition Exposure condition can be entered in the SC Design parameters dialog. SC> Design arameter> arameters [Fig.1.54] SC Design parameter Dialog - Exposure Factor 7.2 Spacing o reinorcement The spacing o Longitudinal reinorcement entered rom Section Manager>Reinorcements shall be used as the applied spacing o tensile reinorcement. Model>roperties>Section Manager>Reinorcements Spacing o reinorcements Top and bottom reinorcement data [Fig.1.55] Input Longitudinal reinorcement When the positive moment is checked, the spacing o bottom reinorcements will be used. When the negative moment is checked, the spacing o top reinorcements will be used. Chapter 1. restressed Concrete Girder Design - AASHTO LRFD

60 7.3 Check the crack width at service loads by Result Tables The results can be checked as shown in the table below. Design>SC Design>SC Design Result Tables>Check crack width at service loads [Fig.1.56] Result table or crack width at service loads Elem: Element number art: Check location (I-End, J-End) o each element Top/Bottom: At top o element, at bottom o element LCom. Name: Load combination name. Type: produce maximum and minimum member orce components or the load combinations including moving load cases or settlement load cases. Check : OK/NG FT : Stress at the top (+ compression, - tension) FB : Stress at the bottom (+ compression, - tension) s_use : The spacing o tensile reinorcement in use. s_max : The calculated maximum spacing o reinorcement. I the compressive stress is applied at the design check location, the crack check is omitted. For the Composite Section, the deck crack is ignored. Thereore, the crack check at the slab top o the composite section is not provided in midas Civil. **Degree o Continuity at Various Limit States( ) by Excel Report Veriication results can be checked in MS Excel report as shown in the igure below. Design>SC Design>SC Design Calculation [Fig.1.57] Excel report or crack width at service loads 54 Design Guide or midas Civil

61 Chapter 2. Steel Composite Girder Design AASHTO LRFD 6 th (2012)

62 Steel Composite Girder Design Steel Composite I-Girder Bridge Check Constructability Check Shear Connector

63 Chapter 2. Steel Composite Girder Design : AASHTO-LRFD 4 th and6 th (2007 & 2012) Introduction 1. AASHTO LRFD 07 and 12 Steel Composite 1.1 Check List o AASHTO LRFD 07 and 12Steel Composite For AASHTO LRFD 07 and 12 Steel Composite Design, Limit State Design is applied. The criteria that Steel Composite Section must ollow or Limit State Design is as ollows. (1) Cross-Section roportion Limit State Review on section properties, e.g. width-thickness ratio (2) Strength Limit State Review on lexure strength, shear strength and torsional strength (3) Service Limit State Review on permanent deormation (4) Constructibility Review on shear and lexure occurring rom load combinations during construction stages (5) Fatigue Limit State Review on atigue in steel and concrete materials in Steel Composite girder 1.2 Classiication o Steel Composite Steel Composite section can be categorized by the ollowing classiication groups. (1) Section Shape Type There are three main section shape types in midas Civil; I, Box and Tub shapes. In the case o box and tub sections, there are two more cases, single or multiple box section. [Table2. 1] Section Shape Type I Box Tub (2) Moment Type : ositive / Negative For continuous beams, negative moments may occur around interior supports. Design code may apply dierent ormulas or these cases. Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 57

64 (3) Bridge Type : Straight / Curved Based on the horizontal alignment o a bridge, it can be classiied as either straight or curved. The program recognizes curved bridges based on the input o the girder radius or each component. (4) Compact Type : Compact / Noncompact / Slender Compact Type (6.2) [Table2.2] Steel Section Classiication Type Compact Noncompact Slender Description A composite section in positive lexure, which satisies speciic steel grade, web slenderness, and ductility requirements, is capable o developing a nominal resistance exceeding the moment at irst yield, but not to exceed the plastic moment. A composite section in positive lexure or which the nominal resistance is not permitted to exceed the moment at irst yield. Cross-Section o a Compression member composed o plate components o suicient slenderness such that local buckling in the elastic range will occur. 1.3 Stieners o Steel Composite The program considers transverse and longitudinal stieners. [Table2 3] Types o Stieners Type Transverse Stieners Longitudinal Stieners Description Transverse stieners are usually provided to increase shear resistance by tension ield action. These work as anchors or the tension so that post buckling shear resistance can be developed. It should be noted that elastic web shear buckling cannot be prevented by transverse stieners. Longitudinal stieners may be provided to increase lexural resistance by preventing local buckling. These work as restraining boundaries or compression elements so that inelastic lexural buckling stress can be developed in a web. It consists o either a plate welded longitudinally to one side o the web, or a bolted angle. [Fig.2.1] Longitudinal Stiener and Transverse Stiener 58 Design Guide or midas Civil

65 2. Considerations Steel Composite Design 2.1 Construction Stage or steel composite During the construction o a steel composite bridge, the steel girder is constructed beore the construction o the concrete deck o the upper part o the structure. The steel composite section is divided into three major steps. [Table2.4] Construction Stage or Steel Composite Section Construction stage or steel composite section Description Only Steel Girder (non-composite) Only the steel girder has been constructed. Steel girder and concrete deck as load (non-composite) Although the concrete deck has been constructed, it has not hardened yet. Thereore, the weight o the wet concrete is applied as a load condition. Steel girder and concrete deck as member (composite) Ater concrete is hardened, the strength and stiness are ormed. Hereater, the steel girder and concrete deck work as a complete composite section. In order to ind and portray the Steel Composite Section Design rocess within the program, utilize the Construction Stage unction. 2.2 Time Dependent Material Steel composite section is composed o steel and concrete. Concrete is a time dependent material and transorms due to creep and shrinkage. Also, the restraints imposed by the shear connectors cause additional stresses within the composite section. Thereore, time dependent characteristics (creep and shrinkage) must be taken into consideration. Modular ratio is the ratio o modulus o elasticity o steel to that o concrete. The short-term modular ratio "n" is used or transient loads in the program. Long-term modular ratio "3n" is used or permanent loads acting ater composite action. For normal-weight concrete, AASHTO-LRFD 07 and 12 recommend the values o the short-term modular ratio. 3. Calculation o lastic Moment and Yield Moment The plastic moment M p or a composite section is deined as the moment that causes yielding in steel section and reinorcement and uniorm stress distribution o 0.85 in compression concrete slab. In positive lexure regions, the contribution o reinorcement in concrete slab is small and can be neglected. The yield moment, M y, or a composite section is deined as the moment that causes the irst yielding in one o the steel langes or the moment at which an outer iber irst attans the yield stress. M y is the sum o the moments applied to the pre-composite steel section, the short-term composite concrete and steel section, and the long-term composite concrete and steel section. Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 59

66 3.1 lastic Moment(M p ), Yield Moment( M y ) in ositive Flexure (1) Cross section proportions I section and Box/Tub steel composite sections must satisy the ollowing criteria regarding cross section proportions. I the conditions have not been met ater the design has been completed, it will be indicated as an NG on the design report generated. 1) Web roportions [Table 2.5] Web roportions Case Condition Web with longitudinal stiener 150 Web without longitudinal stiener 300 2) Flange roportions [Table 2.6] Flange roportions Section Type D t w D t w WEB For I section ( ) ( ) For Box/Tub Section ( ) ( ) b 2t I b 12.0 D 6 t 1. 1 t w I yc I yt Box / Tub b 2t b 12.0 D 6 t 1. 1 t w Flange For I section ( ) ( ) ( ) ( ) For Box/Tub Section ( ) ( ) ( ) Iyc : moment o inertia o the compression lange o the steel section about the vertical axis in the plane o the web Iyt : moment o inertia o the tension lange o the steel section about the vertical axis in the plane o the web 3 t cb c I yc, 12 3 t tbt I yt (2.1) Design Guide or midas Civil

67 (2) Section Classiication Section Classiication o ositive Flexure Moment Section Classiication ( ) Yes Straight Bridge? min( d / t D 2 t cp w w F yc, F yt ) 70.0 ksi E F s yc No No :Curved Bridge Yes Compact Section Noncompact Section [Fig.2.2] Section Classiication o Negative ositive Moment : depth o the web in compression at the plastic moment determined as per Article D6.3.2 End The Section Classiications o I, Box, Tub are all the same. In a positive moment, the ollowing ductility conditions must be met at all times. I not, the program will show NG. Dp 0. 42D t (2.2) Ductility ( ) : Distance rom the top o the concrete deck to the neutral axis o the composite section at the plastic moment : Total depth o the composite section (3) lastic Moment in ositive Moment (M ) I the positive moment is applied on a compact section, M should be calculated as shown in Table 2.7. lastic Moment (D6.1) [Fig.2.3] Case o calculation o Mp in positive moment Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 61

68 62 Design Guide or midas Civil [Table 2.7] Calculation o and M p or section in ositive Flexure Case NA Condition and p M In Web t w rt rb s c 1] [ 2 w rb rt s c t D Y ] ) ( [ Y t Y D M w ] [ t t w w rb rb rt rt s s d d d d d In Top lange c w t rt rb s ] ) ( [ Y t Y t M c c ] [ t t w w rb rb rt rt s s d d d d d Concrete Deck, Below rb c w t rt rb s s rb t c s s t Y M 2 2 ] [ t t w w c c rb rb rt rt d d d d d Concrete Deck, at rb rb c w t rt s s rb t c C rb Y s s t Y M 2 2 ] [ t t w w c c rt rt d d d d Concrete Deck, Above rb Below rt rb c w t rt s s rt t c s rb rt t w c s t Y ) ( s s t Y M 2 2 ] [ t t w w c c rb rb rt rt d d d d d Concrete Deck, at rt rt rb c w t s s rt t c C rt Y s s t Y M 2 2 ] [ t t w w c c rb rb d d d d Concrete Deck, Above rt rt rb c w t s s rt t c s rt t w c rb s t Y ) ( s s t Y M 2 2 ] [ t t w w c c rb rb rt rt d d d d d M p or section in ositive Flexure (Table D6.1-1)

69 : Distance rom the plastic neutral axis to the centerline o the top layer o longitudinal concrete deck. : Distance rom the plastic neutral axis to the centerline o the bottom layer o longitudinal concrete deck. : Distance rom the plastic neutral axis to the midthickness o the tension lange. : Distance rom the plastic neutral axis to middepth o the web. : Distance rom the plastic neutral axis to midthickness o the compression lange. : Distance rom the plastic neutral axis to midthickness o the concrete deck. (by reinorcement) (by reinorcement) (by steel girder) (by steel girder) (by steel girder) (by concrete slab) (4) Yield Moment in ositive Moment (M y ) When a positive moment is applied on a compact section, M y is calculated as shown in Equation 2.3. M Min M, M ) (2.3) y ( ytop ybot MyTop : Yield Moment o Top Flange MyBot : Yield Moment o Bottom Flange F y M M S D1 Top M S D2 Top(3n) ytop M D1 M D2 M S M AD Top( n) AD (2.4) My (D6.2.2) Fy (Eq. D ) F M M M M D1 D2 AD y (2.5) SBot SBot(3n) SBot( n) ybot M D1 M D2 M AD M_ytop (Eq. D ) : Non-composite section modulus : Long-term composite section modulus : Short-term composite section modulus : Moment o non-composite section : Moment o long-term composite section : Additional yield moment o short-term composite section 3.2 lastic Moment(M p ), Yield Moment(M y ) in Negative Flexure For I sections in negative lexure, M p and M y are calculated. (1) Cross Section roportions For negative lexure, cross section proportions must meet the ollowing requirements. I the program does not meet the requirements, NG will be reported ater the design. Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 63

70 1) Web roportions [Table 2.8] Web roportions Case Condition Web with longitudinal stieners 150 Web without longitudinal stieners 300 D t w D t w 2) Flange proportions [Table 2.9] Flange roportions Section Type : b 2t I / Box / Tub 12.0 D b 6 t 1. 1 t w I yc I yt (2) Section Classiication Section Classiication ( ) [Fig.2.4] Section Classiication o Negative Flexure Moment Depth o the web in compression in the elastic range. Iyc : moment o inertia o the compression lange o the steel section about the vertical axis in the plane o the web Iyt : moment o inertia o the tension lange o the steel section about the vertical axis in the plane o the web 64 Design Guide or midas Civil

71 Minimum Negative Flexure Concrete Deck Reinorcement Under negative moment, concrete deck has to meet the minimum rebar ratio requirement. Once the requirements o Equation 2.6 are satisied, the next design step can be taken. Ars 0. 01A deck (2.6) (3) lastic Moment in Negative Moment (M p ) Under negative moment, M p is only calculated when Appendix A6 is used. M p is calculated by either o the two ollowing methods. lease reer to Table 2.10 or the equations. lastic Moment (D6.1) [Fig.2.5] Case o calculation o Mp in Negative Moment [Table 2.10] Calculation o and M p or section in Negative Flexure Case NA Condition and p In Web c w t rb rt M Mp or section in Negative Flexure (Table D6.1-2) In Top lange c w t rb rt (by reinorcement) (by reinorcement) (by steel girder) (by steel girder) (by steel girder) (4) Yield Moment in Negative Moment (M y ) When Appendix A6 is used or negative lexure, M y is calculated and utilized. M y is calculated as shown below in Equation 2.7. M y Min( M ytop, M ybot ) (2.7) MyTop : Yield Moment o Top Flange MyBot : Yield Moment o Bottom Flange My in Negative Moment (D6.2.3) Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 65

72 F M M M D1 D2 AD y (2.8) STop STop ( R) STop ( R) M F M ytop M D1 M D2 M AD (2.9) M S M S M S D1 D2 AD y Bot Bot( R) Bot( R) (2.10) ybot M D1 M D2 M AD (2.11) : Long-term composite section modulus with longitudinal reinorcements 66 Design Guide or midas Civil

73 Chapter 2. Steel Composite Girder Design : AASHTO-LRFD 4 th and6 th (2007/2012) Modeling and Design Variables 1. Modeling Design Variables In this chapter, the design variable values, the meaning behind the design requirements, and the design process or Steel Composite Design in midas Civil are explained Composite Section Data The steel composite section is mainly composed o steel girder and concrete slab. Stieners can be added to steel girder section while longitudinal reinorcement can be added to reinorce concrete slab. In this section, the input methods or these sections and the meaning and application o design variables are explained Composite Section (1) Composite Section Data roperties > Section > Section roperties> Add > Composite Tab Composite Section (1) Composite Section Data 1) Girder Num When the Girder Num is inputted as more than 1, the moment o inertia o area in transverse direction (I zz ) is increased assuming that slab behaves in consistence with each girder in analysis. When the number o girder is inputted as more than 1, it is excluded rom the consideration o design. For design, Girder Num must be inserted as 1. In such case, cross beams should be modelled to consider the transverse stiness instead o increasing the girder number. 2) The value o B c or the slab is used as the eective width o the concrete deck. [Fig.2.6] Section Data Dialog Box 3) Multiple Modulus o Elasticity Option To design the steel composite section, the modulus o elasticity or short-term and longterm eect in creep and shrinkage can be input. The modulus o elasticity input here is applied or construction stage analysis o Steel Composite section as shown in [Fig.2.7]. Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 67

74 [Fig.2.7] Elastic Modulus ratio or Construction Stage (2) Section Stiener roperties > Section > Section roperties> Add > Composite Tab > Stieners Button... (2) Section Stiener (Longitudinal) 1) Types o longitudinal stieners that are useable are Flat, Tee, and U-Rib. 2) For I sections, stieners can be added on either side o the web. For Box/Tub sections, upper and lower langes can be installed as well as the web panel. 3) When the check box under c column is checked on, the stiness value o the stiener is considered in analysis. Otherwise, the value is not considered or analysis. Regardless o whether or not the check box is checked on or o, longitudinal stieners are considered in design. Based on the assignment o longitudinal stiener, Rb, web load shedding actor varies or stiened web/unstiened web. It is also required or classiying the interior panels in shear check as stiener/unstiened. [Fig.2.8] Section Stiener Dialog Box Longitudinal Reinorcement Design > Composite Design > Longitudinal Reinorcement Longitudinal Reinorcement In a steel composite section, the longitudinal reinorcements are arranged within the concrete deck. The strength is calculated as shown in Table [Table 2.11] Applicability o material under the calculation o strength Case ositive Flexure Negative Flexure Figure [Fig.2.9] Longitudinal Reinorcement Dialog Box Concrete Slab Applied None Reinorce -ment None Applied 68 Design Guide or midas Civil

75 1.1.3 Transverse Stiener (1) Transverse Stiener Design > Composite Design > Transverse Stiener Transverse Stiener Figure 2.10 shows the window in which users can arrange transverse stieners in steel composite section. When the transverse stieners are installed, the existence and spacing between stieners determine whether the web is stiened or unstiened under strength limit state. Tension ield action in Shear check or Strength Limit State is considered only or stiened interior panels. [Fig.2.10] Transverse Stiener Dialog Box [Fig.2.11] Transverse Stiener arameters (1) Stiener Type 1) One / Two Stiener Option Button Choose between one or two stieners. The two stiener option is available or I/Box/Tub sections. [Fig.2.12] Stiener Type Dialog Box 2) itch (d o ) itch reers to transverse stiener spacing. At the strength limit state, this can be used to distinguish between stiened and unstiened webs or calculate shear strength o the web. Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 69

76 1.2. Design Material Data For the design o steel composite section, construction stage and time dependent material properties o concrete must be deined. In this section, the input method or concrete's time dependent properties and steel composite section material inormation is deined. Contents Explanation Time Dependent Material (1) Creep/Shrinkage roperties > Time Dependent Material > Creep/Shrinkage Time Dependent Material (1) Creep/Shrinkage The time dependent properties o concrete, such as creep and shrinkage, are deined. During construction stage analysis o bridges, these properties are utilized or concrete material. During analysis, they are relected in the calculation o member orces but not relected in the design o the steel composite section. [Fig.2.13] Add/Modiy Time Dependent Material Dialog Box (Creep/Shrinkage) (2) Comp. Strength roperties > Time Dependent Material > Comp. Strength... (2) Comp. Strength In order to relect the change in the modulus o elasticity o the time dependent property o concrete, the change in compressive strength or modulus o elasticity is deined. Aging eects may vary or each construction stage since concrete is poured at dierent locations. The varying aging eects are relected in the calculation o the member orce but not in the design o the composite sections. [Fig.2.14] Add/Modiy Time Dependent Material Dialog Box (Compression Strength) Modiy Composite Material (1) Modiy Composite Material Design > Composite Design > Design Material Modiy Composite Material The material utilized or steel composite sections are provided in the SRC material properties. The materials should be deined as SRC Type. (1) Modiy Composite Material Figure 2.15 shows the dialog box where users 70 Design Guide or midas Civil

77 Contents Explanation can type in material characteristics or the steel composite section design. The material property values entered will have a priority over the values entered in Material Data dialog box. 1) Steel Girder Section - Steel Hybrid Factor Hybrid actor is considered in the case where langes and web have dierent material properties. 2) Concrete o Concrete slab 3) Steel materials o Concrete slab [Fig.2.15] Modiy Composite Material Dialog Box (2) Hybrid Factor (2) Hybrid Factor(R h ) When the check box or Hybrid Factor is selected, icon on the right is activated. The dierent materials or the top and bottom langes and web o the steel girder can be deined. Hybrid Factor (R h ) is determined based on these material inormation. [Fig.2.16] Hybrid Factor Dialog Box Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 71

78 1.3. Design arameters or Composite Section Contents Design arameter Design > Composite Design > Design arameters Design arameter Explanation (1) Strength Resistance Factor Strength Resistance Factor is deined. By clicking, the resistance actors are automatically set to the deault values deined in. The values also may be modiied or entered manually. (2) Girder Type or Box/Tub Section Consider St.Venant Torsion and Distortion Stress I the Multiple Box Sections option is selected, lateral bending stress is considered in accordance with St.Venant Torsion and Distortion Stress. I the Single Box Sections option is selected, the lateral bending stress is always considered. [Fig.2.17] Composite Steel Girder Design arameter Dialog Box (3) Options For Strength Limit State Appendix A6 or Negative Flexure Resistance in Web Compact/Noncompact Sections I this option is checked, Appendix A6 is applied or the lexure strength o straight composite I- sections in negative lexure with compact/ noncompact webs. Use o Appendix A6 is optional in accordance with the code as shown below. [Fig.2.18] Negative Flexure Resistance in Web Compact/Noncompact Sections M n 1.3R h M y in ositive Flexure and Compact Sections( ) Beore deciding, whether to apply this check or not, ollowing conditions need to be manually veriied: 72 Design Guide or midas Civil

79 Contents Explanation - The span under consideration and all adjacent interior pier sections satisy the requirements o Article B6.2, - The appropriate value o θ RL rom Article B6.6.2 exceeds radians at all adjacent interior-pier sections - In which case the nominal lexural resistance o the section is not subject to the limitation o Eq I the above three conditions are not satisied or the compact sections under positive lexure in a continuous span, the M n value is restricted to 1.3R h M y. ost-buckling Tension-ield Action or Shear Resistance ( ) I this option is checked, post buckling resistance due to tension ield action is considered in the nominal shear resistance o an interior stiened web panel. I not, V n is taken as, CV. where, C = ratio o shear-buckling resistance to the shear yield strength V p = plastic shear orce. (4) Design arameters Design and result outputs are generated or the limit states checked in the Design arameters Unbraced Length Design > Composite Design > Unbraced Length Unbraced Length Unbraced length actor or steel composite section is considered. The value input here has higher priority than the value calculated rom Span Group. (1) L b Lateral Unbraced Length is used to calculate lateral torsional buckling resistance in compression lange o I Girder or top lange o Tub Girder. I the lateral unbraced length is not added, the program will use span lengths. I span lengths are not deined either, the lateral unbraced length is applied or the corresponding member length. [Fig.2.19] Unbraced Length Dialog Box Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 73

80 Contents Shear Connectors Design > Composite Design > Shear Connectors... Explanation Shear Connectors In this program, studs are used or shear connectors. The parameters used or calculation are shown below. (1) Category Category deined by 75yr-(ADTT) SL equivalent to Ininite Lie (Table ) (2) F u Shear Resistance o Shear Connector (3) Shear Connector arameters [Fig.2.21] Shear Connector arameters [Fig.2.20] Shear Connector Dialog Box (4) Length Between Maximum Moment and Zero Moment The Length between Maximum Moment and Zero Moment needs to be inputted by users to veriy pitch as per strength limit state. (5) Nominal Shear Force Calculation ( ) One o the two conditions needs to be selected or the calculation o the nominal shear orce, which is applied or the veriication o pitch at the strength limit state Fatigue arameter Design > Composite Design > Fatigue arameter Fatigue arameter (1) Category Category deined by 75ye-(ADTT) SL equivalent to ininite lie (Table ) (2) (ADTT) SL Number o trucks per day in a single-lane averaged over the design lie ( ) (ADTT) SL can be manually calculated as per (3) N Number o stress range cycles per truck passage Value can be taken rom Table (4) Longitudinal Warping Stress Range 74 Design Guide or midas Civil

81 Contents Explanation For the veriication o atigue, lexure stress is calculated as the summation o Longitudinal Bending Stress Range and Longitudinal Warping Stress Range. By choosing the Auto-Calculation option, atigue vertical bending moment is simply increased by 10% or the longitudinal warping stress. Longitudinal warping stress range can be manually calculated as per BEF (Beam on Elastic Foundation) analogy presented by Wright and Abdel-Samad. The designer guide to Box Girder by Bethlehem Steel Corporation also presents this method. Detailed calculations can be seen in Design Example 5: Three Span Continuous Curved Composite Tub-Girder Bridge (page 85-94). [Fig.2.22] Fatigue arameters Dialog Box Sotware calculations do not account or Transverse Bending Stress due to Distorsion. Thereore, transverse bending stress range at the top or bottom corners o the tub section need to be manually checked with the nominal atigue resistance. I the User Input option is selected, longitudinal bending stress range is summated with the inputted value o the Longitudinal Warping Stress Range or top or bottom lange depending upon the lexure condition at the section. These distorsion stresses are considered only or the sections having box lange as those are the section in which the torsion is considered Span Inormation Structure > Wizard > Composite Bridge > Span Inormation Span Inormation The elements o composite sections are deined as one Span Group. The Span Group will serve the ollowing unctions. (1) Finding the most critical parts o the group unit and providing the corresponding results in the Span Checking table. Reer to Chapter 7 o "Steel Composite Design Result" or more inormation. (2) Calculation o Unbraced Length When assigning a span group, support properties are considered or calculating the unbraced length. The unbraced length can also be manually inputted once the corresponding support conditions under the support column are selected. Using the span parameters inputted, the unbraced length can be calculated automatically. However, i the unbraced length is inputted in Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 75

82 Contents Explanation Section 1.3.2, this value will be applied as the unbraced length irst. (3) End web panels For each element, location o support, i any, can be identiied as i or j. The stiened webs with supports are identiied as end panels. Also, the elements that are assigned with i or j or the support are considered as end panels. Tension ield action is not considered or the end panel in Shear Check. [Fig.2.23] Span Inormation Dialog Box Curved Bridge Inormation Design > Composite Design > Curved Bridge Ino Curved Bridge Inormation Once the girder radius value o the element units in the steel composite section is entered, the corresponding elements are categorized as curved bridges. (1) Radius is used or the review o shear connectors' pitch and the moment o inertia o area or the longitudinal stiener attached to web. The curve type needs to be determined as convex or concave so the program determines whether the longitudinal stiener is on the side o the web away or toward rom the center o the curvature. Lateral bending stress due to curvature is obtained rom the analysis results and not using V-Load equation. [Fig.2.24] Curved Bridge Inormation Dialog Box (2) I convex, let stiener is on the side o the web away rom the center o curvature and right stiener is on the side o the web toward the center o curvature. I concave, the opposite case o the convex is applied. lease reer to the table below or the equations applied to each case. 76 Design Guide or midas Civil

83 Contents Explanation [Table 2.12] Curvature Correction Factor or Longitudinal Stiener Case Let Stiener Z 6 1 ( ) Convex Right Stiener Z 12 1 ( ) Let Stiener Z 12 1 ( ) Concave Right Stiener Z 6 1 ( ) where, β : Curvature correction actor or longitudinal stiener rigidity Z : Curvature arameter Deck Overhang Loads Deck Overhang Loads Design parameters or the Deck Overhang load can be entered. The l value obtained rom F(Distributed orce) and (Concentrated orce) is not applied to Box section, but only or I-section and top stiener o Tub section. The l value or deck overhang is considered only or the constructibility limit state. Distributed Force, F (1) Distributed Force, F Distributed orce values are inputted F l = F tan α (2) Concentrated Force, Concentrated orce values are inputted l = tan (3) Eccentricity o Overhang Loads, e Eccentricity o overhang loads are inputted α = tan -1 (e/d) [Fig.2.25] Deck Overhang Loads Dialog Box [Fig.2.26] Deck Overhand Bracket The l value is generated by combining the values produced rom the analysis and the value inputted in this dialog box. I this eature is not used, l value only rom the analysis results will be used. Lateral bending moment due to uniormly distributed lateral bracket orce (F l ) is estimated as: where, 2 Fl Lb M l (c ) 12 Ml : lange lateral bending moment due to the eccentric loadings rom the orming brackets F l : uniormly distributed lateral orce L b : unbraced length Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 77

84 Contents Explanation Lateral bending moment due to concentrated lateral bracket orce (F l ) assumed to be placed at the middle o the unbraced length is estimated as: l Lb M l (c ) 8 where, Ml : lange lateral bending moment due to the eccentric loadings rom the orming brackets l : concentrated lateral orce L b : unbraced length and F are the dead loads and construction loads such as Deck Overhang Weight, Screed rail load, Railing load, Walkway load, Machine Load, etc. considered or the constructability check only. The load coeicient applied to Erection (DC) Load Case is applied to calculate the load in this case Design Force/Moment Design > Composite Design > Design Tables > Design Force/Moment Design Force/Moment This eature displays design member orces (strong axis moment, M y ), weak-axis moment (M z ) and shear stress (V U ) or the local axis o elements under selected load combination o steel composite section or each construction stage. For explanation regarding design member orces under construction stages, please reer to Section 1.5 in this chapter. [Fig.2.27] Design Force/Moment Dialog Box 78 Design Guide or midas Civil

85 1.4 Load Combination or steel composite section Application o load combination in midas Civil or (1) Application o load combinations and actors in midas Civil or The load combinations used or the review o each limit state as per Table , are shown below. [Fig.2.28] Load Combinations and Load Factors Using the Auto Generation eature o the program, the load combinations regulated by the design code can be automatically generated. Load actors are considered or each load combinations in this program. Load actors are considered only within the program, and γ p value can be designated by Auto Generation eature. [Fig.2.29] Load Factors or ermanent Loads, γ p Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 79

86 (1) Auto Generation o Load Combinations Result > Combination > Load Combination > Composite Steel Girder Design > Auto Generation... (1) Auto Generation o Load Combinations This eature automatically generates load combinations under provision o. 1) Design Code When load combinations are generated, they strictly ollow the design code selected by the user. 2) Load Modiier (η i ) Load modiier is a actor relating to ductility, redundancy, and operational classiication. It is deined by the ollowing equations. For loads or which a maximum value o γ i is appropriate: η i = η D η R η I 0.95 For loads or which a minimum value o γ i is appropriate: η i = 1/(η D η R η I ) 1.0 η D : a actor relating to ductility as per η R : a actor relating to redundancy as per η I : a actor relating to operational classiication as per ) Load Factors or ermanent Loads (γ p ) Load Factors or ermanent Loads are as per Table Each option button or γ p value is activated when the corresponding static load case is deined. [Fig.2.30] Automatic Generation o Load Combinations Dialog Box I a user wishes to review limit states based on the load combinations deined manually, it can be done by selecting the load combination o interest in Load Combination Type as in Section Design Guide or midas Civil

87 1.4.2 Used load combination or steel composite design Load combinations used in the steel composite section design are deined under Load Combination Type. (1) Load Combination Type Contents Design > Composite Design > Load Combination Type... Explanation (1) Load Combination Type 1) Strength Limit State Choose load combinations or use under review o strength limit state. 2) Service Limit State Choose load combinations or review o usability limit state. 3) Fatigue 1 Limit State Choose load combinations or review in atigue limit state (Fatigue Load Combination is or ininite lie design; (ADTT) SL inputted in the sotware > (ADTT) SL, equivalent to ininite lie as per Table ). 4) Fatigue 2 Limit State Similarly, choose load combinations or review in atigue limit state (Conversely to Fatigue I, Fatigue Load Combination is or inite lie design). [Fig.2.31] Load Combination Type Dialog Box 1.5 Modeling Steel Composite Sections or Construction Staged Analysis In this section, methods o construction stage modeling, implementation o concrete's time-dependent material properties in steel composite section and 3 types o design member orces applied to steel composite section design are explained. Construction stages o steel composite section can be implemented dierently or case 1 to 3 as in table [Table 2.13] Modeling Construction Stage Cases or Steel Composite Design Case Construction Stage Time Dependent Material(Creep / Shrinkage) Case 1 Deined Deined Case 2 Not Deined (Apply modular ratio o 3n) Case 3 Not Deined Not Deined (Apply modular ratio o 3n) Member orces and stresses used in steel composite section design (1) Member orces For design o steel composite section, member orces per construction stage o steel composite section must be calculated. The program considers two main actors or design and review o construction stage o steel composite section. Construction stages o steel composite section Time dependent material properties o Concrete (Creep, Shrinkage and Compression Strength) Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 81

88 Design member orces used or design o steel composite section are divided into three main categories. [Table 2.14]Design Force and Moment or Steel Composite Design Design Force/Moment Description Dead (Beore) Dead (Ater) Short Term Member orces beore the concrete deck is activated. Only steel section properties are used. Member orces occurring due to erection load cases deined by user with the time dependent material properties (Creep & Shrinkage) o concrete Long term section properties are used. Member orces rom the post-construction state and load cases not included in the above categories. Short term section properties are used. (2) Stress Bending stress ( bu ) used or design o steel composite section is calculated as in equation M M D1 D2 bu SNC SLT M S AD ST Md1 : moment o non-composite section Md2 : moment o long-term composite section MAD : additional yield moment o short-term composite section SNC : non-composite section modulus SLT : long-term section modulus SST : short-term section modulus bu : largest value o the lexural stress in the langes at the section under consideration (2.12) On the other hand, lateral bending stress ( l ) is calculated as in equation M M uz lat l 0. 6 Sl F (2.13) y l : lange lateral bending stress S l : lateral section modulus o the langes about z-axis Muz : lexural moment about z-axis Mlat : lateral bending moment in the lange calculated rom the overhang loads Fy : speciied minimum yield strength o a lange Case 1 In Case 1, construction stages and time dependent material properties o concrete (Creep/Shrinkage) are deined. Composite sections or Construction Stages unction must be deined as well; otherwise, the sections shall be excluded rom design. I time dependent material property inormation is inputted as well as long-term modulus o elasticity, long-term modulus o elasticity has higher priority in consideration o calculation. 82 Design Guide or midas Civil

89 Deine Composite Section or Construction Stage Contents Composite Section or Construction Stage Load >Load Type> Construction Stage > Composite Section or C.S... Explanation Composite Section or Construction Stage For deinition o construction stage, inormation in this window must be deined. (1) Active Stage Construction stage where steel composite section should be activated is inserted. (2) Construction sequence 1) "Material Type" column By choosing Element, material property o the element is used. By selecting Material, material inormation chosen under "Material" Column is applied with higher priority. [Fig.2.32] Add/Modiy Composite Section or Construction Stage Dialog 2) Composite Stage column Construction stages where steel girder and concrete slab should be activated are chosen. 3) Age column Age inormation when each part is activated is input. Inormation in this column has higher priority over the age input during deinition o construction stage. (1) Member orces under Dead (Beore composite) Member orces beore activation o Concrete Deck are applied. (Reer to Table 2.4 in "Introduction") For design purposes, Dead (Beore) member orces are applied ater multiplying the load actors applied in Dead Load (CS) in Load Combination dialog box. (2) Member orces under Dead (Ater composite) For the member orces under Dead (Ater), in post-composite stages, the long-term modulus o elasticity is determined by the time dependent material properties deined by users. Member orces under Dead (Ater) consist o static load cases and construction stage load cases. I Dead Load o Component and Attachments (DC2), Dead Load o Wearing Suraces and Utilities (DW), Creep (CH), and Shrinkage (SH) are deined as erection loads, they are accounted or the Dead (Ater). Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 83

90 Deine Erection Load (1) Deine Erection Load Analysis > Analysis Control > Construction Stage > Load Cases to be Distinguished rom Dead Load or C.S Output >Add (Modiy/delete)... 1) Deine Erection Load Erection Load is deined. 1) Load Type or C.S Determine the Load Type or the construction stages o the composite section. Load types are considered by the sotware or auto generation o load combinations. 2) Assignment Load Cases Deine Erection Load by selecting and moving the Load Cases desired rom the List o Load Case panel to the Selected Load Case panel. [Fig.2.33] Deine Erection Load Dialog (3) Calculation o the short-term member orces Short-term modulus o elasticity o the composite section is calculated based on the DB value inputted. All load cases are considered as the short-term loads except the ones deined as Dead (Beore) and Dead (Ater) Case 2 In Case 2, construction stages are deined without the time dependent material property (Creep/Shrinkage) inormation. Long term eects are considered using the long term modular ratio entered in the Section Data dialog box. Sections or dierent construction stages must be deined and dierentiated using the Composite Section or Construction Stage deinition. Otherwise, they will not be considered or the design check. (1) Member orces under Dead (Beore) Dead (Beore) is applied beore the concrete deck is activated. (Reer to Table 2.4 in the "Introduction") For the design, the Dead (CS) multiplied by the load actor is applied as the member orce under Dead (Beore). (2) Member orces under Dead (Ater) The eects o Creep/Shrinkage are relected by applying the ratio o elastic modulus that is inputted in the Section Data (Reer to Section (1)) or the long-term stage. In other words, the Creep/Shrinkage eects are relected by using the section inormation with the ratio o elastic modulus that considers the time dependent material property or the analysis and design. These long term modular ratios deined or considering creep and shrinkage, auto generate Section Stiness Scale Factors or the sections in which these are inputted. Section Stiness Scale Factors need to be activated in the construction stages in accordance with the Composite Section or Construction Stage deinition, i.e. the section stiness scale actors are activated when the corresponding section becomes composite as per the deinition o composite section or CS. I users compose construction stages and deine Dead Load o Component and Attachments (DC2), Dead Load o Wearing Suraces and Utilities (DW), Creep (CH), and Shrinkage (SH) as Erection Load, the load cases will be included in the Dead (Ater). (3) Short term member orces The ratio o elastic modulus o the composite section is calculated using the DB value inputted. All the load cases which are not activated in the Construction Stage are considered as the short-term loads. 84 Design Guide or midas Civil

91 1.5.4 Case 3 In case the construction stages are not deined, users can model and deine steel composite sections by using the Load Case or re-composite Section unction at Load > Load Type > Settlement/Misc. > Misc. > re-composite Section. For this case, short- and long-term ratios o elastic modulus deined in the section data (Reer to Section (1)) are used. In this case, instead o member orces per construction stages, member orces under Dead (Beore) is used to check the constructibility o the model. (1) Member orce under Dead (Beore) In the Load Cases or re-composite Section dialog box, users can deine which load cases to account or the member orces and apply as Dead (Beore) in design. Since this is or pre-composite state, the steel only section properties are used (Reer to Section (1)). Dead Load (Beore) [Fig.2.34] Load Cases or re-composite Section (2) Member orces under Dead (Ater) Member orces under Dead (Ater) use the long term section properties. These loads should be separated rom the short term member orces by the use o Analysis > Analysis Control > Boundary Change Assignment. 1) Data Selection Check the box corresponding to Section Stiness Scale Factor. As explained earlier, Section Stiness Scale Factors are used or considering the long term section properties. 2) Boundary Group Combination Create a boundary group combination considering the appropriate boundary groups rom the boundary group list. The created boundary group combinations need to be selected or the post composite long term load cases. For the static load cases assigned with the section stiness scale actor boundary groups, long term section property will be used. Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 85

92 Dead Load (Ater) [Fig.2.35] Load Cases or ost-composite Section (3) Short-term member orces The ratio o elastic modulus rom the database is used or the short-term loads o the composite section. All load cases are considered or the short-term loads except the ones considered or the Dead (Beore) and Dead (Ater). 86 Design Guide or midas Civil

93 Chapter 2. Steel Composite Girder Design : AASHTO-LRFD 4 th and6 th (2007/2012) Application o AASHTO LRFD I Girder Section 1.1. Introduction The program designs I-girder sections according to the orders in the low chart below. This chapter demonstrates how the is applied in the program. [Fig.2.36] Flow chart o Composite I-girder bridge Typical I-Sections have a cross section as shown below: [Fig.2.37] I-Section in positive lexure Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 87

94 1.2 Strength Limit State The program checks the strength limit states or the lexure, shear, and ductility o the composite sections. Strength Limit States Check Ductility Check lexural resistance & Check shear resistance [Fig.2.38] Flow chart o Strength Limit States Ductility Ductility shall be checked to prevent premature crushing o concrete. For the veriication o a web section that is under positive lexure, the ductility shall be veriied as: D (2.14) p D t Dp :distance rom the top o the concrete deck to the neutral axis o the composite section at the plastic moment Dt : total depth o the composite section Ductility (Eq ) Flexural Resistance There are our cases or checking lexural resistance o I Sections as shown below. Check lexural resistance & Yes ositive Moment? No Check Ductility sd ks D M c, Ed ( zc, bar / I y, c, bar ) p d t No :Curved Bridge Straight Bridge? Yes Yes Straight Bridge? No :Curved Bridge Yes Slender Section? No :Compact or Noncompact Compact Section? No No Use Optional AENDIX A6? Yes Yes Case 1 : Check lexural resistance o ositive Flexure Moment in Compact Section Case 2 : Check lexural resistance o ositive Flexure Moment in Noncompact Section Case 3 : Check lexural resistance o Negative Flexure Moment Case 4 : Check lexural resistance o Negative Flexure Moment by using AENDIX A6 AENDIX A6 ositive Flexure Moment Negative Flexure Moment End [Fig.2.39] Flow chart o lexural resistance (1) Case 1: Compact Section in ositive lexural moment 88 Design Guide or midas Civil

95 The lexural resistance shall be checked according to the low chart below i the section is under positive lexural moment, satisies the ductility requirement and is a compact web. I the ductility requirement is not satisied, the program will display NG in the design result page. Case 1 ( ) [Fig.2.40] Case 1 : Flow chart o lexural resistance o ositive Flexure Moment in Compact Section I a section is compact and under positive lexural moment, lexural resistance shall be checked according to the ollowing equation: Flow chart o Case 1 ( ) M u 1 S 3 l xt M n l : Flange lateral bending stress M n : Nominal lexural resistance o the section. M u : Bending moment about the major-axis o the cross-section. : Resistance actor or lexure. (2.15) Flexural Resistance (Eq ) 1) Nominal Flexural Resistance(M n ) [Table 2.15]Calculation o Nominal Flexural Resistance(M n ) Case D 1 M n M M p 0. D t n p Otherwise Dp M n M p Dt Mn (Eq ) (Eq ) Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 89

96 M p : lastic moment o the composite section determined as per Article D6.1. D p : distance rom the top o the concrete deck to the neutral axis o the composite section at the plastic moment D t : total depth o the composite section 2) Strength Resistance Factor or lexure (ϕ ) The design code deines the lexural reduction actor as However, the program primarily considers the actor that is inputted by users in the design parameters. [Fig.2.41] Composite Steel Girder Design arameter 3) Especially, the ollowing requirement regarding the nominal lexural resistance must be satisied when " M 1. 3R M in ositive Flexure and Compact Sections" is checked at n h y Composite Steel Girder Design arameters>options or Strength Limit State. (Fig.2.41) M 3R n 1. hm y (2.16) Nominal lexural resistance (Eq ) (2) Case 2 : ositive lexural moment in noncompact section 90 Design Guide or midas Civil

97 The lexural resistance shall be checked according to the below low chart i a section is under positive lexural moment, satisies the ductility requirement and is noncompact. Curved bridges are considered as noncompact sections. Case 2 ( ) Case 2 : Check lexural resistance o ositive Flexure Moment in Noncompact Section Check Compression lange F bu nc R b F R nc h F , yc Check Tension lange 1 bu l Fnt 3 Fnt R h F yt , End [Fig.2.42] Case 2 : Flow chart o lexural resistance o ositive Flexure Moment in Noncompact Section 1) Compression lange At the strength limit state, the compression lange shall satisy the below criteria regarding the lexure: bu Fnc (2.17) F R R F (2.18) nc b h yc bu : Flange stress calculated without consideration o lange lateral bending. F nc : Nominal lexural resistance o the compression lange. Compression lange (Eq ) (Eq ) Tension lange The tension lange shall satisy the below criteria regarding the lexure: 1 F 3 bu nt h l yt nt (2.19) F R F (2.20) Tension lange (Eq ) (Eq ) l : Flange lateral bending stress, F nt : Nominal lexural resistance o the tension lange. R b : Web load-shedding actor. (3) Case 3: Negative lexural moment in composite section and noncomposite section Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 91

98 The lexural resistance shall be checked according to the below low chart i a section is under negative lexural moment and is one o the ollowing cases: Curved bridge Straight Bridge but slender section Straight Bridge and compact or noncompact, but Appendix A6 is not applied [Fig.2.43] Case 3 : Flow chart o lexural resistance o Negative Flexure Moment 1) Discretely Braced Compression Flange For a compression lange, the ollowing requirement shall be satisied at the strength limit state: 1 F (2.21) 3 bu l nc Compression Flange (6.10.8) (Eq ) F Min F, F ) (2.22) nc ( nc( FLB) nc( LTB) : Local Buckling Resistance based on Discretely Braced Compression Flange : Lateral Torsional Buckling Resistance based on Discretely Braced Compression Flange 92 Design Guide or midas Civil

99 [Table 2.16] Calculation o F nc(flb) Case F nc(flb ) Fnc ( FLB ) Rb RhFyc p Fyr p p Fnc FLB ( ) 1 1 Rb RhF yc R F h yc r p F nc(flb) (Eq ) (Eq ) in which: : Slenderness ratio or the compression lange : Limiting slenderness ratio or a noncompact lange R b : web load-shedding actor determined as speciied in Article R h : hybrid actor determined as speciied in Article b c (2.23) 2t c E p 0.38 (2.24) F yc E r 0.56 (2.25) F yr F yr : compression-lange stress at the onset o nominal yielding within the cross-section, including residual stress eects, but not including compression-lange lateral bending, taken as the smaller o 0.7F yc and F yw, but not less than 0.5F yc. (Eq ) (Eq ) (Eq ) [Table 2.17] Calculation o F nc(ltb) L p Case F nc(ltb) L Fnc ( LTB ) Rb RhFyc b L p yr b p L L Fnc LTB Cb ( ) 1 1 Rb RhFyc Rb RhFyc b b L r r F R F h yc L L Lr L p L Fnc ( LTB) Fcr Rb RhFyc C b : Moment gradient modiied F nc(flb) ( ) (Eq ) (Eq ) (Eq ) [Table 2.18] Calculation o C b Case Unbraced cantilevers and or members where mid / 2 >1 or 2 =0 L b : Unbraced length. 1 1 For all other cases C b Calculation o Cb (Eq ) (Eq ) Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 93

100 L p : Limiting unbraced length to achieve the nominal lexural resistance o R b R h F yc under uniorm bending. E Lp 1. 0r (2.26) t F yr yc E Lr r (2.27) t F F cr 2 CbRb E (2.28) 2 L / r ) ( b t 1 Dctw rt bc / 12(1 ) (2.29) 3 b t c c (Eq ) (Eq ) (Eq ) (Eq ) L r : Limiting unbraced length to achieve the onset o nominal yielding in either lange under uniorm bending with consideration o compression lange residual stress eect (in). : Elastic lateral torsional buckling stress. r t : eective radius o gyration or lateral torsional buckling F yr : compression-lange stress at the onset o nominal yielding within the cross-section, including D c : depth o the web in compression in the elastic range determined as per D6.3.1 mid : Stress without consideration o lateral bending at the middle o the unbraced length o the lange under consideration, calculated rom the moment envelope value that produces the largest compression at this point, or the smallest tension i this point is never in compression 2) Continuously braced Tension Flange At the strength limit state, the ollowing requirement shall be satisied or the continuously braced tension lange: bu RhFyt (2.30) (4) Case 4 : Flexural resistance o Negative Flexure Moment by using Appendix A6 The optional provisions o Appendix A6 shall apply to the sections in negative lexural and straight bridges and compact and noncompact web I-sections according to the low chart below. Tension Flange ( ) (Eq ) 94 Design Guide or midas Civil

101 Check lexure resistance o Negative Flexure Moment by using Appendix A6 AENDIX A6 Yes : Compact web 2 D t w cp pw ( D cp ) No : Noncompact web Calculate Web plastiication Factor R R pc pt M M M M p yc p yt R R pc pt RhM 1 1 M p RhM 1 1 M p yc yt w rw w rw pw( Dc ) pw( Dc ) pw( Dc ) pw( Dc ) M M M M p p yc yt M M M M yc p p yc R Yes No : Noncompact lange No :Rolled section Discretely Braced Compression Flange? Built-up Section? Local Buckling Resistance Yes No :continuously braced M R M u pc yc M R M u pt yt Yes : Compact lange 0.76 k c k 4/ D/ t c 0.35k 0.76 c w M R nc ( FLB ) pc M yc M nc( FLB) FyrS 1 1 RpcM xc yc p R r p pc M yc Yes Lb L p No L p L L b r No Yes M R nc ( LTB ) pc M yc Lateral Torsional Buckling Resistance M nc( FLB) FyrS xc Lb L p Cb 1 1 RpcM RpcM yc Lr L p M min M, M nc ncflb ncltb yc R M pc yc M nc( LTB) F S R M cr xc pc yc Check Flexural Resistance 1 M S M 3 u xc 0. 6 l l F yc nc End [Fig.2.44] Case 4: Flow chart o lexural resistance o Negative Flexure Moment by using Appendix A6. I Appendix A6 is applied at the strength limit state, the ollowing our requirements regarding lexure shall be satisied. The design veriication is done or the compression and tension langes. Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 95

102 [Table 2.19] Limit State deined by Appendix A6 Case Limit State Discretely-Braced Flange Section Compression Tension M M u u 1 S 3 l 1 S 3 l xc xt M M nc nt Limit State by A6 (A ) (A ) Continuously-Braced Flange Section Compression Tension M M u u R R pc pt M M yc yt (A ) (A ) : Resistance actor or lexure. l : Flange lateral bending stress, M nc : Nominal lexural resistance based on the compression lange. M u : Bending moment about the major-axis o the cross-section. M yc : Yield moment with respect to the compression lange. M nt : Nominal lexural resistance based on the tension lange. M yt : Yield moment with respect to the tension lange. S xc : Elastic section modulus about the major axis o the section to the compression lange taken as M yc /F yc R pc : Web plastiication actor or the compression lange. R pt : Web plastiication actor or the tension lange. [Table 2.20] Calculation o R pc and R pt 2D t w 2D t w cp cp ( D pw pw cp ( D & w < rw cp Case ) ) Compact web Noncompact web R R 1 1 R M RhM 1 1 M p Web lastiication Factor M Rpc M M Rpt M h yc w pw Dc pc ( ) M p rw pw ( Dc) p yc p yt yt w pw( Dc) pt rw pw( Dc) M M M M p yc p yt M M M M p yc p yt R pc and R pt (A ) (A ) (A ) (A ) in which: M p : lastic moment D c : Depth o the web in compression in the elastic range determined as per D D cp : Depth o the web in compression in the plastic moment. M y : Yield moment taken as the smaller o M yc and M yt. : Limiting slenderness ratio or a noncompact web E rw 5.7 (2.31) F yc λ w : Slenderness ratio or the web based on the elastic moment. 2D c w (2.32) tw (A ) (A ) 96 Design Guide or midas Civil

103 E Fyc M p RhM y pw( Dcp ) 2 D rw D cp c (2.33) (A ) Discretely braced Compression Flange For the discretely braced compression langes, the minimum o the local buckling resistance and lateral torsional buckling resistance is used to perorm the design check as: M nc Min[ M nc( FLB), M nc( LTB) ] (2.34) Local buckling Resistance (M nc(flb) ) The local buckling resistance shall be calculated as shown in the ollowing table: Compression Flange (A6.3.2) [Table 2.21] Calculate M nc(flb) Case p (Compact lange) k M c nc(flb) M R - nc( FLB) pc yc M (A ) p (Noncompact lange) Rolled k Built-up c c k 4 / D t w 0.35 k 0.76 c : Slenderness ratio or the compression lange. c M nc(flb) Fyr S 1 1 R pcm xc yc p r p R b c (2.35) 2t : Limiting slenderness ratio or a compact lange. E p 0.38 (2.36) F yc Ek c r 0.95 (2.37) Fyr : Flange local buckling coeicient determined as per A or built-up sections and 0.76 or rolled shapes. F yr : compression-lange stress at the onset o nominal yielding within the cross-section, including residual stress eects, but not including compression-lange lateral bending, taken as the smaller o 0.7Fyc, RhFyt Sxt/Sxc and Fyw, but not less than 0.5Fyc S xc : Elastic section modulus about the major axis o the section to the compression lange taken as M yc /F yc S xt : Elastic section modulus about the major axis o the section to the tension lange taken as M yt /F yt pc M yc (A ) (A ) (A ) (A ) Lateral Torsional Buckling Resistance (M nc(ltb) ) The lateral torsional buckling resistance is calculated as shown in the ollowing table: M nc(ltb) (A6.3.3) Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 97

104 [Table 2.22] Calculation o L p Case M nc(ltb) Lb L p L b b L r L r M nc( LTB) F Cb 1 1 R M R nc( LTB) yr pc S M xc yc pc M yc Lb L p Lr L p R L M nc( LTB) Fcr Ssc RpcM yc pc M yc R pc M yc (A ) (A ) (A ) L p : Limiting unbraced length to achieve the nominal lexure resistance R pc M yc under uniorm bending L 1. 0r p t E F yc (2.38) Lp (A ) L r : Limiting unbraced length to achieve the nominal onset o yielding in either lange under uniorm bending with consideration o compression lange residual stress eects 1 E J Fyr S xch L r rt Fyr S xch E J 2 (2.39) Lr (A ) C b : moment gradient modiier, is divided into two cases and calculated according to either A or A o. For the detailed calculations, please reer to the section "3.2 Strength Limit State > (1) Flexural Resistance > Case 3". F cr : Elastic lateral torsional buckling stress F cr C rt 2 2 b E J L (2.40) b L S b xch rt F cr (A ) J : St. Venant torsional constant Dt J 3 3 w b 3 ct c 3 t ( b c c b tt ) 3 3 t t ( b r t : Eective radius o gyration or lateral torsional buckling r b t c 1 D ctw / bct c t t ) (2.41) (2.42) J (A ) r t (A ) : compression-lange stress at the onset o nominal yielding within the cross-section, including residual stress eects, but not including compression-lange lateral bending, taken as the smaller o 0.7,, / and, but not less than 0.5. h : Depth between the centerline o the langes. : Major-axis bending moment at the middle o the unbraced length, calculated rom the moment envelop value that produces the largest compression at this point in the lange under consideration, or the smallest tension i this point is never in compression. shall be due to the actored loads and shall be taken as positive when it causes compression and negative when it causes tension in the lange under consideration. : moment at the brace point opposite to the one corresponding to, calculated rom the moment envelope value that produces the largest compression at this point in the lange under consideration, or the smallest tension i this point is never in compression(kip-in). M0 shall be due to the actored loads and shall be taken as positive when it causes compression and negative when it cause tension in the lange under consideration. 98 Design Guide or midas Civil

105 : moment at the brace point opposite to the one corresponding to, calculated as the intercept o the most critical assumed linear moment variation passing through and either or, whichever produces the smaller value o. may be calculated as ollows - When the variation in the moment along the entire length between the brace points is concave in shape M 1 M 0 (2.43) - Otherwise M mid (2.44) 1 2M M 2 M 0 (A ) (A ) : Except as noted below, largest major-axis bending moment st either end o the unbraced length causing comrpession int the lange under consideration, calculated rom the ciritical moment envelop value. shall be taken as positive. I the moment is zero or cause tension in the lange under consideration at both ends i the unbraced length, shall be taken as zero. : Yield moment with respect to the compression lange. : Yield moment with respect to the tension lange Shear resistance Shear resistance o an I-web Steel Composite Section is checked as shown in the low chart below. Check shear resistance Shear resistance (6.10.9) No Stiened web? Yes Unstiened webs No :Stiened End panel Interior Web anel? Yes :Stiened Interior Web anels Stiened Web anels V V n p Calculate V cr V n CV 0.58 F yw p Dt w V V n p Calculate V cr V n CV 0.58 F yw p Dt w No 2Dtw b t b c c ttt 2.5 Yes Calculate V n Calculate V n V n V p C 0.87 ( C ) 2 d 0 d 0 D D V V n p 0.87 (1 C ) C 2 d 0 1 D V n Check V u V V n End [Fig.2.45] Flow chart o shear resistance The program distinguishes Unstiened and Stiened webs according to the ollowing criteria: Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 99

106 [Table 2.23] Classiication o Unstiened web and Stiened Web Case Without a longitudinal stiener and with transverse stiener spacing not exceeding 3D With one or more longitudinal stieners and with a transverse stiener spacing not exceeding 1.5D Classiication Stiened web Otherwise Unstiened web However, even stiened webs are classiied as unstiened web i the check box is not checked at Composite Steel Girder Design arameters >Options or Strength Limit State>ost-buckling Tension-ield Action or Shear Resistance. (Fig.2.41) (1) Shear Resistance Check Shear resistance shall be checked as: Vu vvn (2.45) : Resistance actor or shear. V n : Nominal shear resistance. V u : Shear in the web at the section under consideration due to the actored loads Shear resistance (Eq ) 1) Unstiened Webs The nominal shear resistance o unstiened webs shall be taken as: V n p V CV (2.46) cr yw p V 0. 58F Dt (2.47) w : Shear -buckling resistance : plastic shear orce C : Ratio o shear-buckling resistance to shear yield strength [Table2.24] Calculation o Ratio o shear-buckling resistance to shear yield strength, C Case C D Ek 1.12 t C 1. 0 w F yw Ek D F t yw w Ek F yw 1.12 C D t 1.57 Ek D 1.40 Ek C 2 D Fyw t Fyw w t w : Shear-buckling coeicient 5 k 5 2 do D Stiened Webs w Ek F yw (2.48) The nominal shear resistance is calculated dierently or the two types o stiened webs: Unstiened Webs ( ) (Eq ) (Eq ) C (Eq ) (Eq ) (Eq ) (Eq ) 100 Design Guide or midas Civil

107 interior web panels and end web panels. All webs with a support assigned on its i or j node in the Span Inormation (Fig.2.22) are considered as end panels and the others are considered as interior web panels. Stiened Webs ( ) [Fig.2.46] Classiication o End anel and Interior anel End panels The nominal shear resistance, V n, o a web end panel shall be taken as: V n p V CV (2.49) cr V 0. 58F (2.50) yw p Dt w Interior web panels There are two cases o an interior web panel as shown in the ollowing table: [Table 2.25] Calculation o V n and V p o Interior web panel Case ( b 2Dtw t b t c c t t 2.5 ) V V n p p V, V n p 0.87(1 C) C 2 do 1 D V 0. 58F yw Dt w End panels ( ) (Eq ) (Eq ) Interior web panel ( ) (Eq ) Otherwise : Transverse stiener spacing : Nominal shear resistance o the panel V V n p C V 0. 58F p 0.87(1 C) 2 do do 1 D D yw Dt w (Eq ) User's option Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 101

108 Users need to speciy that the web is stiened by checking the check box at: Composite Steel Girder Design arameters >Options or Strength Limit State >'ost-buckling Tension - Field Action or Shear Resistance ( )'. Depending on the user's veriication, the calculation will dier as shown in the ollowing table: User's option (Eq ) [Table 2.26] User's option: ost-buckling Tension-ield Action or Shear Resistance Check ( b 2Dtw t b t c c t t 2.5 ) V, V n p V V n p 0.87(1 C) C 2 do 1 D (Eq ) On Otherwise V 0. 58F p V V n p p yw Dt w 0.87(1 C) C 2 do 1 D V 0. 58F yw Dt w O V n V cr V 0. 58F p CV yw p Dt w 1.3 Service Limit State Flange stress or permanent deormation and web bend-buckling are veriied at the service limit state. The program does not check elastic deormation. Elastic deormation can be reviewed manually ater moving load analysis at: Results > Deormation Service Limit State ( ) At the completion stage o the construction, the program applies Service II load combination, speciied in Article , and reviews the permanent deormation. Thereore, the permanent deormation is reviewed only or the composite section since the section cannot be non-composite in the completed state. But, the sotware can assume the concrete deck in the composite section to be ineective as per , which states that the concrete deck may be assumed to be ineective or both positive and negative lexure, provided that the maximum tensile stresses in concrete deck at the section under consideration caused by Service II loads are greater than 2 r. Sotware perorms this check and determines whether to consider the concrete deck to be eective or not. The service limit state is reviewed as shown in the low chart ollows: 102 Design Guide or midas Civil

109 Service Limit State Check Flexure Yield in lange Check Top lange o Composite Section 0. 95R h F y Check Bottom lange o Composite Section l R h F y Check Nominal Bend-buckling Resistance or web D ositive Flexure and 150? t w No Check Web Bend-buckling resistance or webs c F crw Yes End [Fig.2.47] Flow chart o Service Limit State Flexure Flange shall satisy the ollowing requirements at the service limit state or the top and bottom langes o the composite sections: (1) Top Flange The top steel lange o composite section shall satisy the ollowing requirement R F (2.51) h y (2) Bottom Flange The bottom steel lange o composite section shall satisy the ollowing requirement. l 0. 95RhF (2.52) y 2 : Flange stress at the section under consideration due to the Service II loads calculated without consideration o lange lateral bending : Flange lateral bending stress at the section under consideration due to the Service II loads determined, :speciied minimum yield strength o a lange Top Flange (Eq ) Bottom Flange (Eq ) Nominal Bend-buckling Resistance or webs I composite section is in positive lexure and the web section property satisies D/t w 150, Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 103

110 use the service limit state shall be veriied according to: (2.53) c F crw : Compression-lange stress at the section under consideration due to the Service II loads calculated without consideration o lange lateral bending Fcrw : Nominal bending-buckling resistance or webs with or without longitudinal stieners Nominal Bendbuckling Resistance (Eq ) 0.9Ek (2.54) Fcrw Min( R, / 0.7) 2 hfyc Fyw D t w k : bend- buckling coeicient 9 k (2.55) 2 ( D / D) c Concrete Deck The program veriies the stress o the concrete deck or shored construction cases in positive lexure as per Article Fcrw (Eq ) k (Eq ) (2.56) deck r deck : longitudinal lexure stresses in the concrete deck with short-term modular ratio,n Φ r : Φ shall be taken as 0.9 and r shall be taken as the modulus o rupture o the concrete, 0.24 c as per Article Check Constructibility Constructibility shall be veriied or the three categories as shown in the ollowing chart: Check Contructibility Check lexural resistance , Check longitudinal stresses In concrete deck Check Shear requirement or webs [Fig.2.48] Flow chart o Constructibility limit stage The constructibility is checked based on the design member orces under Dead (Beore) Flexure The program shall veriy lateral bending stress in discretely braced compression and tension langes during the construction stages, or when slabs are not delected yet. Thereore, the program considers all langes as discretely braced langes or the design check. Constructibility is veriied in terms o lexural resistance according to the ollowing low chart: 104 Design Guide or midas Civil

111 [Fig.2.49] Flow chart o lexural resistance in Constructibility Limit State (1) Section classiication [Table 2.27] Section classiication 2D t w w c 2D t c Case Section E 5.7 Compact or non-compact Web F yc E 5.7 Slender Web F yc Section classiication ( ) (2) Discretely braced langes in Compression Discretely braced langes in compression are veriied according to the ollowing three equations. Check lange nominal lexure yielding For the critical stages o construction, the ollowing equation shall be satisied. However, the requirement does not need to be checked i a section has slender web and its is l equal to 0. in compression ( ) Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 105

112 R F (2.57) l h yc nominal yielding (Eq ) Check local buckling and lateral torsional buckling as per Article and Article respectively 1 F (2.58) 3 l nc Check web bend buckling as per Article Only or the sections with slender webs, the ollowing equation shall be checked. bu F (2.59) crw ϕ : resistance actor or lexure speciied in : lange stress calculated without consideration o lange lateral bending. : lange lateral bending stress, : nominal bending-buckling resistance or webs. : nominal lexure resistance o the lange. lexural resistance (Eq ) web bend buckling (Eq ) (3) Discretely braced langes in Tension The ollowing equation shall be checked or discretely braced tension langes. l RhFyt (2.60) in Tension ( ) (Eq ) Concrete Deck I the longitudinal tensile stress in concrete deck determined as per Article d, exceeds r then the minimum one percent longitudinal reinorcement determined as per Article is required at the section. Code recommends that the minimum reinorcement should be No. 6 bars or smaller spaced at not more than 12 inches. Concrete Deck ( ) The total tensile orce in the concrete deck is transmitted rom the deck through the shear connectors to the top lange. Sotware assumes the shear connectors to be suiciently present at this location to resist the orce and prevent potential crushing o concrete. Sotware doesn t calculate the length over which this orce must be transmitted. Shear connector pitch calculations are as per Fatigue and Strength Limit State only. F (2.61) deck r r 0.24 ' modulus o rupture o the normal-weight concrete c ϕ : 0.9 F deck : Longitudinal tensile stress in the concrete deck My F deck (2.62) In (Eq d) = Es /Ec 106 Design Guide or midas Civil

113 1.4.3 Shear The program shall use the load combinations deined in the Load Combination Type (Reer to Section in this chapter) or the veriication o the shear strength. Webs shall satisy the ollowing requirement during critical stages o construction. V V (2.63) u v cr : shear in the web at the section under consideration due to the actored loads ϕ v : resistance actor or shear, (Fig.2.41) : shear buckling resistance determined rom Eq (Eq ) The program checks the nominal resistance or unstiened webs and stiened webs with the same ormula as the tension ield action is not considered or Constructibility check. (1) Unstiened/Stiened web 1) The nominal shear resistance o unstiened/stiened webs shall be taken as: V V CV (2.64) n p cr yw p V 0. 58F Dt (2.65) w Unstiened/ Stiened web (Eq ) (Eq ) 2) Calculation o Ratio o shear-buckling resistance to shear yield strength, C lease reer to Section in this chapter or the calculation o C. 1.5 Fatigue Limit State For horizontally curved I-girder bridges, the range o atigue stress due to major-axis bending plus lateral bending shall be investigated. Article also mentions the requirements or Fracture. But Fracture Limit State is not considered in midas Civil. Code speciies the atigue live load in Article or the Fatigue check. But in the sotware, atigue check is perormed only or the moving load deined or the analysis. Fatigue Limit State (6.10.5) For considering the atigue live load as speciied in code, user will have to deine a user deined vehicle and then manually edit the auto generated load combinations, so that the atigue moving vehicle is the only vehicle considered or atigue check and is only included in atigue combination. For atigue limit state, sotware assumes the shear connector to be provided along the entire length o the girder, ensuring composite action. Thereore, the concrete deck is assumed to be eective in computing all stresses and stress ranges applied to the composite section in the subsequent atigue calculations Load Combinations Used or Fatigue Limit State Check For this part o design check, AASHTO LRFD 07 and 12 are applied dierently in the program. lease reer to Section 5.1 in this chapter or more inormation. Fatigue limit shall be veriied according to the two paths. Fatigue limit shall be veriied according to Section 1.5.3(1) or the load combinations that are inputted as Fatigue 1 Limit State Load Combination Type (Section in Chapter "Modeling and Design Variables"). For the load combinations that are inputted as Fatigue 2 Limit State, Section 1.5.3(2) shall be ollowed. The program veriies the load combinations deined in the Load Combination Type. I users deine '(ADTT) SL 75 year (ADDTT)SL' Equivalent to Ininite Lie, the veriication shall consider the Fatigue II Load Combination. Otherwise, this combination o atigue limit state shall be skipped and Fatigue I Load Combination shall be considered or veriication. Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 107

114 [Fig.2.50] Flow chart o Fatigue Limit Stage Fatigue Limit State For the compression lange, compressive stress due to unactored dead load is compared with the tensile stress due to actored live load beore perorming the atigue check. I two times the tensile stress due to actored live load is greater than the compressive stress due to unactored dead load, then only the atigue check is perormed. For the tension lange, atigue check is always perormed. (1) The atigue limit state shall be veriied according to the ollowing. ( ) ( F) (2.68) n : Load actor or the atigue load combination. : Force eect, live load stress range due to the passage o the atigue load. : Nominal atigue resistance. Fatigue Limit State (Eq ) (2) The load actor,, speciied in the table below, shall be applied or the atigue load combination. These actors are automatically considered by the sotware, while auto generating the load combinations. [Table 2.28] Load combination and Load Factor Load Combination Limit State Fatigue I - LL, IM &CE only Fatigue II - LL, IM &CE only DC, DD, DW, EH, EV, ES, EL, S, CR, SH LL, IM, CE, BR,L, LS WA WS WL Load Factor (Table ) Nominal Fatigue Resistance The nominal atigue resistance is calculated dierently or the load combinations in the Service 1 Limit State and the Service 2 Limit State. 108 Design Guide or midas Civil

115 (1) Nominal Fatigue Resistance Due to the Load Combinations or Fatigue I Limit State The program shall calculate the nominal atigue resistance according to the input categories made in the atigue dialog box (Fig.2.22). ( F ) ( F) (2.69) n TH The program shall apply the nominal atigue resistance according to Categories A, B, B', C, C', D, E, and E', speciied in the table below. For all other cases, the nominal atigue resistance shall be considered as 24.0 ksi (165.0 Ma). Nominal atigue resistance (Eq ) [Table 2.29] Constant-Amplitude Fatigue Thresholds, Detail Threshold Category US Unit(ksi) SI Unit(Ma) A B B' C C' D E E' Fatigue Thresholds For US Unit, (Table ) For SI Unit AASHTO LRFD 07 (Table ) (2) Nominal Fatigue Resistance due to the Load Combinations or Fatigue II Limit State I Fatigue Resistance is veriied or Fatigue Load Combination 2, the below equation shall be used. For the veriication, the program uses the design parameter values inputted by users in the Fatigue dialog box (Fig.2.22). A ( ) N 1 3 F n (2.70) N (365)(75) n( ADTT) (2.71) SL Fatigue (Eq ) (Eq ) A : Constant taken rom Table 2.30 n : Number o stress range cycles per truck passage taken rom Table 2.31 [Table 2.30] Detail Category Constant, A Detail Category US Unit (x 10 8 (ksi 3 )) Constant, A! SI Unit (x10 11 (Ma 3 )) A B B' C C' D E E' A For US Unit, (Table ) For SI Unit AASHTO LRFD 07 (Table ) Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 109

116 [Table 2.31] Cycles per Truck assage, n Span Length Longitudinal Members >40.0 t 40.0 t Simple span Girders Cycles per Truck assage (Table ) Continuous Girders Near interior support Elsewhere Cantilever Girders 5.0 Orthotropic Deck plate Connections Subjected to Wheel Load Cycling 5.0 Trusses 1.0 Spacing Transverse Members > 20.0 t 20.0 t The n value inputted in the Fatigue arameter dialog box (Fig.2.22) according to Table 2.31 is used or the calculation. (ADTT)SL : ADTT or single lane Special Fatigue Requirement or Webs The atigue limit state shall be veriied in terms o shear buckling resistance as: Vu V cr (2.72) Vu : shear in the web at the section under consideration due to the unactored permanent loads plus the actored atigue load Vcr CV p (2.73) V 58F p 0. ywdtw (2.74) or Webs ( ) (Eq ) (Eq ) (Eq ) 110 Design Guide or midas Civil

117 2. Box / Tub Girder Section 2.1 Introduction Design o Box/Tub steel composite sections ollow the same procedure as or I-Girders. Box/tub 2.2 Strength Limit State The program checks the strength limit states or the lexure, shear and ductility o the composite sections. Strength Limit States Check Ductility Check lexural resistance & Check shear resistance & [Fig.2.51] Flow Chart o Strength Limit State Ductility Ductility shall be checked to prevent premature crushing o concrete. I a section is under positive lexure, ductility shall be veriied as: D (2.75) D t Ductility (Eq ) Flexure (1) Classiication o Composite Section or Flexure There are our cases or checking lexural resistance o Box/Tub composite sections as shown below. Check lexural resistance & Yes ositive Moment? No Yes Compact Section? Straight Bridge? No No :Curved Bridge Yes Compression lange? No :Tension Yes Case 1 : Check lexural resistance o ositive Flexure Moment in Compact Section Case 2 : Check lexural resistance o ositive Flexure Moment in Noncompact Section Case 3 : Check lexural resistance o Negative Flexure Moment & Compression lange Case 4 : Check lexural resistance o Negative Flexure Moment & Tension lange ositive Flexure Moment Negative Flexure Moment End [Fig.2.52] Strength Limit State or Flexure The webs that are under positive lexure and satisy the ollowing requirements shall be Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 111

118 considered as compact sections. Otherwise, they shall be considered as non-compact sections or the positive lexure design check. Sections o a curved bridge are considered to be noncompact. Flange and web yield strength do not exceed 70 ksi (485 Ma) Web satisies the requirements in Article as shown below. Webs without longitudinal stieners: D/t w 150 Webs with longitudinal stieners: D/t w 300 Web slenderness limit satisies the requirements in Article D cp /t w 3.76 (E/F yc ) ( ) The classiication o the section under negative lexure, as compact /noncompact /slender is not required or the design checks. (2) Case 1 : ositive Flexural Moment in Compact Section Case 1 : Check lexural resistance o ositive Flexure Moment in Compact Section Yes Dp 0. 1D t No Calculate M n Dp M n M p Dt Check Flexural Resistance M u M n Calculate M n M n M p Case 1 ( ) End [Fig.2.53] Case 1 : Flow Chart o Flexural resistance or Compact Section in ositive Flexure Moment For compact sections, lexure at the strength limit state shall be veriied as: M u Mn (2.76) (Eq ) 1) Bending moment about the major-axis( M u ) M u is the bending moment about the major axis due to the actored loads. The maximum bending moment rom the load combinations, applied to Strength Limit State in the Load Combination Type (Reer to Chapter "Modeling Design Variable" Section 1.4.2) is applied as M u. 2) Nominal lexure resistance(m n ) [Table 2.32] Calculation o M n o Compact Section in ositive Flexure Case D 1 M n p 0. D t M n M p M n (Eq ) 112 Design Guide or midas Civil

119 Otherwise Dp M n M p Dt (Eq ) I a section is under positive lexure, plastic moment is calculated or the location o the plastic neutral axis. For more inormation, please reer to Chapter "Introduction" Section ) Flexural resistance actor are taken as 1.00 in. However, i the actor is deined by users in the design parameter dialog box, the user deined value is utilized as a priority. (3) Case 2 : Non-compact Section in ositive Moment For non-compact sections, lexural strength limit state is veriied as shown in the low chart ollows. Webs o a curved bridge is considered to be non-compact sections. Flexural resistance actor ( ) Case 2 ( ) Case2 : Check lexural resistance o ositive Flexure Moment in Noncompact Section Yes Compression lange? No :Tension lange Yes Tub Section? No :Box Section Calculate Fnc nc b h yc Calculate Fnc F F R F F F R F nc b h yc Calculate F nt R F h yt F nt Check Flexural Resistance bu F nc Check Flexural Resistance bu F nt [Fig.2.54] Case 2 : Flow Chart o Flexural Resistance or Non-compact Section in ositive Flexure Moment End 1) Compression Flange At the strength limit state, compression langes shall satisy the ollowing in terms o lexure. bu Fnc (2.77) The nominal lexural resistance o the compression lange, Fnc, is taken dierently or box and tub sections as: Compression Flange (Eq ) Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 113

120 [Table 2.33] Calculation o F nc Section Type Box Tub F nc nc F nc F R F b b h h yc F F R F yc F nc (Eq ) (Eq ) 1 3 F v yc 2 in which : T v (2.78) 2A t o c and v (Eq ) (Eq ) Δ : a actor dependent on St. Venant torsional shear stress in the bottom lange od the tub section. Rb : Web load shedding actor [Table 2.34] Calculation o R b Case R b Constructibility Limit State is reviewed Composite web under positive lexure satisies Article & One or more longitudinal stiener & D Ek 0.95 t w F yc 2D t w c rw Otherwise, 1 a 2 wc DC R b rw awc tw 1.0 R b (Eq ) (Eq ) Rh : Hybrid Factor [Table 2.35] Calculation o R h Case Hybrid Section Non-Hybrid or Web strength > lange strength R h R h 3 12 (3 ) 12 2 in which: 1.0 2D t A n w n Hybrid Factor, R h ( ) 114 Design Guide or midas Civil

121 2) Tension Flange At the strength limit state, tension langes shall satisy: bu Fnt (2.79) For both box and tub type composite sections, the nominal lexure resistance o tension lange, F nt shall be calculated as: F nt RhFyt (2.80) Tension Flange (Eq ) (Eq ) 1 3 F v yt 2 in which : v T (2.81) 2A t o t (Eq ) (Eq ) I, consider so that (4) Case 3&Case 4 : Negative Flexure Flexural resistance o negative lexure moment shall be veriied as shown in the low chart below. Check lexural resistance o Negative Flexure Moment & & Case 3 and 4 ( ) ( ) ( ) Yes Compression lange? No :Tension lange Yes Stiened web? No :Unstiened Web Yes Tub Section? No :Closed-Box Section Check lexural resistance O Longitudinal Stiened Flange Check lexural resistance o Unsiened Flange Check lexural resistance o Tension Flange o Tub Section Check lexural resistance o Tension Flange Closed-box Compression lange End Tension lange [Fig.2.55] Case 3 & Case 4 : Flow Chart o Flexural Resistance or Negative Flexural Moment (5) Case 3 : Compression Flange in Negative Flexural Moment For this part o design check, AASHTO LRFD 07 and 12 are applied dierently in the program. lease reer to Section 5.4 in this chapter or more inormation. Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 115

122 (Eq ) [Fig.2.56] Case 3 : Flow Chart o Flexural Resistance or Compression Flange in Negative Flexure The program shall distinguish unstiened and longitudinally stiened elements depending on whether the longitudinal stiener is applied on the compression langes in the section property dialog box. At the strength limit state, the ollowing requirement shall be satisied in terms o lexure: bu Fnc (2.82) Unstiened Flange (Eq ) 1) Unstiened Flange For unstiened langes, the ollowing requirement shall be satisied: 116 Design Guide or midas Civil

123 F nc F cb 1 v vfcv [Table 2.36] Calculation o F cb p Case p 2 F R R F r r F cb R R F b h yc cb F cb Fcb 2 λ : slenderness ration or the compression lange b c, t c Ek p 0.57 and F For unstiened langes, and. 1 3 F (2.85) v yc 2 yc in which : v 2 T A t o b h yc 0.3 p Rh r p yr 0.9ER k b (2.83) Ek r 0.95 (2.84) F c Fyr : smaller o the compression-lange stress at the onset o nominal yielding, with consideration o residual stress eects, or the speciied minimum yield strength o the web F cb (Eq ) (Eq ) (Eq ) (Eq ) (Eq ) (Eq ) (Eq ) (Eq ) F yr ( 0.3) F F (2.86) yc yw (Eq ) [Table 2.37] Calculation o F cv Case F cv 1.12 Ek s 1.12 Fyc 1.40 Ek F s yc Ek F s yc 1.40 Ek F s yc F 0. 85F cv yc 0.65 FycEk Fcv 0.9Ek s Fcv 2 s F cv (Eq ) (Eq ) (Eq ) 2) Longitudinally Stiened Flange Also or longitudinally stiened langes, the ollowing requirement shall be satisied as or unstiened langes. However, the plate-buckling coeicients, and, shall no longer be constant but calculated to account or F nc. 2 1 v F nc Fcb (2.87) vfcv For longitudinally stiened compression langes, and are determined depending on the number and location o stieners applied to the langes. 1late-Buckling Coeicient or Uniorm Normal Stress(k) Depending on the number o uniormly spaced stieners, shall be taken as: F nc (Eq ) Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 117

124 [Table 2.38] Calculation o k Case n 1 n 2 k k 8I wt s 3 c k I k wt s 3 c 1 3 K (Eq ) (Eq ) 2 late-buckling Coeicient or Shear Stress (k s ) I wt k s 2 n 1 s 3 c (2.88) Is : moment o inertia o a single longitudinal lange stiener about an axis parallel to the lange and taken at the base o the stiener n : number o equally spaced longitudinal lange stieners w : larger o the width o the lange between longitudinal lange stieners or the distance rom a web to the nearest longitudinal lange stiener k s (Eq ) [Fig.2.57] Deinition o w (6) Case 4 : Tension Flange in Negative Flexural Moment For tension langes, lexural resistance limit state shall be veriied as shown in the low chart: The lexural resistance o negative lexure moment and tension lange will be checked by the process indicated in the low chart below. Case 4 : Check lexural resistance o Negative Flexure Moment & Tension lange Tub Section? F R F nt h yt Check Flexural Resistance F bu nt Fnt RhFyt End [Fig.2.58] Case 4 : Flow Chart o Flexural Resistance or Tension Flange in Negative Moment The tension langes shall be veriied according to: Tension langes (Eq ) 118 Design Guide or midas Civil

125 bu Fnt (2.89) F nt shall be taken as: [Table 2.39] Calculation o F nt Section Type Tub Closed-Box nt F nt F R F F 1 3 F v yt h yt nt RhFyt 2 in which : v T 2A t o t F nt (Eq (Eq ) (Eq ) (Eq ) Shear Box and tube type steel composite sections shall be veriied or its shear strength as shown in the low chart: Check Shear resistance Yes Stiened Web? Yes Interior Web anel? No :End panel No :Unstiened Web Case 1 : Check Shear resistance o Stiened & Interior Web anel Case 2 : Check Shear resistance o Stiened & End Web anel Case 3 : Check Shear resistance o Unstiened Web Stiened Web Unstiened Web End [Fig.2.59] Flow Chart o Shear Resistance The program classiies stiened and unstiened webs as shown in the table below: [Table 2.40] Classiication o Stiened Web and Unstiened Web Case Without a longitudinal stiener and with transverse stiener spacing not exceeding 3D With one or more longitudinal stieners and with a transverse stiener spacing not exceeding 1.5D Otherwise Classiication Stiened web Unstiened web Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 119

126 (1) Shear Strength Veriication Shear strength shall be veriied as shown in the low chart: Check shear resistance No Stiened web? Yes Unstiened webs No :Stiened End panel Interior Web anel? Yes :Stiened Interior Web anels Stiened Web anels V V n p Calculate V cr V n CV 0.58 F yw p Dt w V V n p Calculate V cr V n CV 0.58 F yw p Dt w No 2Dtw b t b c c ttt 2.5 Yes Calculate V n Calculate V n V n V p C 0.87 (1 C ) 2 d 0 d 0 1 D D V V n p 0.87 (1 C ) C 2 d 0 1 D V n Check V u V V n End [Fig.2.60] Flow Chart o Strength Limit State or Shear Shear strength shall be veriied as: V V (2.90) u v n ϕv: resistance actor or shear Vu : shear in the web at the section under consideration due to the actored loads 1) Unstiened web For unstiened webs, the nominal shear resistance (V n ) shall be taken as: V n Vcr CVp (2.91) in which: Vp 0. 58FywDtw (2.92) C : ratio o the shear-buckling resistance to the shear yield strength Vp : plastic shear orce Shear strength (Eq ) Unstiened web (Eq ) (Eq ) 120 Design Guide or midas Civil

127 2) Stiened Web Shear Strength rogram shall determine whether a stiened web belongs to an end panel or interior panel depending on whether its nodes are supported or not in the span inormation. The web shall be irst identiied as an end panel or an interior panel and, then, its shear strength shall be veriied. I a web is supported at its nodes, the web belongs to an end panel; i not supported, it belongs to an interior panel. 1 End panels For end panel webs, the nominal shear resistance shall be taken as: V n Vcr CVp (2.93) in which: Vp 0. 58FywDtw (2.94) End panels (Eq ) (Eq ) 2 Interior panels For interior panels, the nominal shear resistance shall be taken as: [Table 2.41] Calculation o V n or Interior anel Case Nominal shear resistance (V n ) ( b 2Dtw t b t c c t t Otherwise, 2.5 ) V V n V V n p p 0.87(1 C) C 2 do 1 D C 0.87(1 C) 2 do do 1 D D Interior panels (Eq ) (Eq ) [Table 2.42] Calculation o Ratio o the shear buckling resistance to the shear yield strength, C D t Case Ek 1.12 C 1. 0 w F yw Ek D F t yw w Ek F yw w C 1.12 C D t Ek F 1.57 Ek D 1.40 Ek C 2 D Fyw t Fyw w t w k: shear-buckling coeicient yw C (Eq ) (Eq ) (Eq ) k (Eq ) Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 121

128 5 k 5 2 do D (2.95) (2) Check or Inclination For box and tube composite sections, inclination o webs shall be considered. Shear orce on each section shall be evenly applied to its two webs ater the consideration o the incline angle as: Vu Vui (2.96) cos Inclination (Eq ) [Fig.2.61] Inclination o Web V ui : shear on each web due to the actored loads V u : vertical shear due to the actored loads on one inclined web θ: the angle o inclination o the web plate to the vertical(degrees) 2.3 Service Limit State For box and tub composite sections, lexure and web bend-buckling at the service limit state are veriied as shown in the low chart below. The program shall veriy service limit state or the composite sections at the completion stage o construction. Load combinations deined in the Load Combination Type (lease Reer to Chapter "Modeling Design Variable" Section 1.4.2) shall be used or the veriication o the service limit state. 122 Design Guide or midas Civil

129 Service Limit State Check Flexure Yield in lange Check Top lange o Composite Section 0. 95R h F y Top steel lange (Eq ) Check Bottom lange o Composite Section l R h F y Check Nominal Bend-buckling Resistance or web F crw Calculate Fcrw and 0.9Ek Min( R, / 0.7) 9 2 hfyc Fyw k D ( Dc / D) t w k 2 Bottom steel lange (Eq ) Check Web Bend-buckling resistance or webs c F crw End Bend-buckling (Eq ) [Fig.2.62] Flow Chart o Service Limit State Flexure Flexure shall be veriied at top and bottom langes. As per Article C6.11.4, Eq and are checked only or compact sections in positive lexure. Thus in midas Civil, these equations are not checked or negative lexure and noncompact sections in positive lexure. (1) Veriication o Top steel lange o composite sections or lexure Serviceability o top steel langes shall be veriied by comparing the stress as: Fcrw (Eq ) k (Eq ) 0. 95R F (2.97) h y (2) Veriication o Bottom steel lange o composite sections or lexure Serviceability o bottom steel langes shall be veriied by examining lexure as shown in the equation below. I a web is under positive lexure and satisies the requirements in AASHTO LRFD 12 Article , its strength shall be determined to be satisactory and veriication shall be skipped. For box and tub composite sections, lange lateral bending stress shall be assumed as 0 or the design check. l 0. 95RhFy 2 (where, = 0) (2.98) l Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 123

130 Web Bend Buckling Except or sections in positive lexure in which the web satisies the requirement o Article , all sections shall satisy Eq shown below. Webs shall be veriied in terms o bend-buckling as: (2.99) c F crw c : compression-lange stress Fcrw : nominal bend-buckling resistance or webs F crw 0.9Ek Min( RhF D t w, F 2 yc yw / 0.7) (2.100) in which: k : bend-buckling coeicient 9 k (2.101) 2 ( D / D) c Dc : Depth o the web in compression in the elastic range 2.4 Check Constructibility For box and tub composite sections, constructibility shall be veriied in terms o lexure and shear. Member orce under Dead (Beore) shall be used as the design member orce or the veriication o constructibility limit strength Flexure The program shall veriy lexural strength by assuming that concrete hardening has not occurred yet and all section are discretely braced. The lexural veriication shall be done in three cases as shown in the igure ollows. Check Constructibility Tub Section (Eq ) (Eq ) (Eq ) Tub Section (Eq ) Yes Compression lange? No :Tension Yes Tub Section? No :Closed-Box Section Check Flange stress o Tub Section in Compression Check Flange stress o Closed-Box in Compression ~2 Check Flange stress o Closed-Box in Tension ~5 Comp. Box Flange (Eq ) (Eq ) End [Fig.2.63] Flow Chart o Flexural Resistance or Constructibility Limit State (1) Open Flange (top lange o tub section) in Compression and Tension Tension Box Flange (Eq ) 1) Open lange in compression For tub composite sections, compression top langes shall be veriied or yielding, lexure and bend buckling o webs, as shown in the equation below. I or slender webs, (Eq ) (Eq ) 124 Design Guide or midas Civil

131 Eq shall not be veriied. 1 R F and bu l Fnc 3 bu l h yc (2.102) For slender webs, bend-buckling shall be veriied as: F (2.103) bu crw 2) Open lange in tension For tub composite sections, tension top langes shall satisy the requirement o Eq which is same as that or I girder. Shear (Eq ) (Eq ) (Eq ) (2) Noncomposite box lange (top lange o box section and bottom lange o tub or box section) in Compression and Tension ( or constructability check, the top lange o box section is designed as a noncomposite box lange) 1) Noncomposite box lange in compression For box langes in compression, constructibility shall be examined based on the compressive stress due to lexure and bend buckling on webs. For sections with compact or noncompact webs, Eq shall not be checked as per Article Veriication o compression stress due to lexure : F (2.104) Veriication o bend buckling on webs : bu crw bu nc F (2.105) 2) Noncomposite box lange in tension and continuously braced box lange in tension or compression shall satisy the ollowing requirement: R F (2.106) bu h y 1 3 F (2.107) v y 2 in which : v 2 T A t o Shear For the veriication o constructibility, shear shall be veriied to prevent shear buckling at webs according to the ollowing requirement. The program shall distinguish end panel and interior panel or the veriication o shear-buckling resistance. V V (2.108) u v cr V in which: Vp 0. 58FywDtw cr CV p (2.109) Concrete Deck Constructibility o concrete deck shall not be veriied or the box and tub steel composite sections. 2.5 Fatigue Limit State Load combinations o Fatigue Limit State In this section, AASHTO LRFD 07 and 12 are applied dierently. For more inormation about the 07 edition, please reer to Section 5.1 in this chapter. For more inormation on basic considerations and assumptions or Fatigue Limit State, please reer to Section 1.5 in this chapter. Fatigue limit state shall be veriied as shown in the low chart: Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 125

132 Fatigue Limit State (Eq ) [Fig.2.64] Flow Chart o Fatigue Limit State or Flexure The veriication o atigue resistance shall ollow Section 2.5.3(1) or the load combinations o Fatigue 1 Limit State in Load Combination Type (Chapter "Modeling Design Variables" Section 1.4.2) and Section 2.5.3(2) or the load combinations o Fatigue 2 Limit State. However, i '(ADTT) SL 75year (ADTT) SL ' is inputted, Fatigue II Load Combination is veriied. Otherwise, the veriication needs not to be done Fatigue Limit State As per Article , one additional requirement speciied particularly or tub girders sections is in regard to longitudinal warping and transverse bending stresses. When tub girders are subjected to torsion, their cross-sections become distorted, resulting in secondary bending stresses. Thereore, longitudinal warping stresses and transverse bending stresses due to cross-section distortion shall be considered or: Single tub girder in straight or horizontally curved bridges Multiple tub girders in straight bridges that do not satisy requirements o Article Multiple tub girders in horizontally curved bridges Any single or multiple tub girder with a tub lange that is not ully eective according to the provisions o Article For consideration o these distorsion stresses in the sotware, Longitudinal Warping Stress Range input is required in the atigue parameters dialog box. (Fig.2.21) Fatigue limit state shall be veriied per stress unit as: Fatigue (Eq ) (Table ) Fatigue (Eq ) (Eq ) ( ) ( F) (2.110) n γ : load actor or atigue load combination ( ) : orce eect, live load stress range due to the passage o the atigue load ( F)n : nominal atigue resistance Nominal Fatigue Resistance (Table ) (Table ) Special Fatigue Requirement 126 Design Guide or midas Civil

133 The program s calculation o Nominal Fatigue Resistance will be dierent based on whether the load combinations are entered into Fatigue 1 Limit State or Fatigue 2 Limit State. Between the two values, the lower value will be applied and reviewed. (1) The Nominal Fatigue Resistance o Fatigue I Limit State due to load combinations The program will calculate the Nominal Fatigue Resistance based on the category selected in the Fatigue dialog window. ( F ) ( F) (2.111) n TH (Eq ) ASHTO LRFD 12 (Eq ) (Eq ) Within the program, categories o Nominal Fatigue Resistance, such as A, B, B', C, C', D, E, and E' are applied as shown in [Table2.29]. (2) The Nominal Fatigue Resistance o Fatigue II Limit State due to load combinations I atigue review is perormed with consideration to atigue load combination 2, the ollowing equation is used to calculate the resistance value o atigue. A ( ) N 1 3 F n in which: N (365)(75) n( ADTT) (2.112) SL Section roportion ( ) A : Constant taken rom Table n : Number o stress range cycles per truck passage taken rom Table (ADTT)SL : ADTT or single lane itch (Eq ) The value o the Detail Category Constant (A) and 75-yr (ADTT) SL Equivalent to Ininite Lie (n, truck per day) are each respectively applied in [Table2.30] and [Table2.31]. I, the n value is entered into the Fatigue arameter, this value will be applied irst Special Fatigue Requirement or Webs The program will perorm the review o the atigue due to the shear buckling o the web. Vu V cr (2.113) Vcr : shear in the web at the section under consideration due to the unactored permanent loads plus the actored atigue load Vcr CV p in which: Vp 0. 58FywDtw (2.114) 3. Shear Connector When the shear connector is deined in the steel composite sections, the review o the shear connectors is perormed. The shear connector perorms review o itch, Transverse spacing, Cover and enetration, Fatigue, Special Requirement or point, and strength limit state. Center-to-Center itch ( ) Vsr (Eq ) V at (Eq ) F ar (Eq ) (Eq ) 3.1 Section roportion For the ratio o height to diameter o the stud type shear connector, ollowing equation is used. h 4.0 (2.115) d 3.2 itch The pitch is reviewed using the below equation. Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 127

134 nz p V sr r Zr : shear atigue resistance o an individual shear connector determined as per Article n : number o shear connector in a cross section Vsr : horizontal atigue shear range per unit length (2.116) Also, the program checks i and are satisied as well as Equation k (Eq ) (Eq ) V sr V F 2 2 at at (2.117) in which : Vat: longitudinal atigue shear range per unit length V Q V at (2.118) I Fat : radial atigue shear range per unit length taken as the largest o either Abot lgl Frc Fat 1 or Fat2 wr w (2.119) in which : σlg: range o longitudinal atigue stress in the bottom lange without consideration o lange lateral bending Abot: area o the bottom lange Frc : net range o cross-rame o diaphragm orce at the top lange l : distance between brace point R : minimum girder radius within the panel w : eective length o deck (in.) taken as 48.0 in., except at end supports where w may be taken as 24.0 in. eective length o deck distance I it is straight members, the value o F at1 is 0. I it is a Box/Tub section, regardless o whether it is straight or curved, the value o F at1 is 0. The program will consider the value o F at2 as 0. The center-to-center distance o the shear connectors cannot exceed 24inches and 6 times the diameter o the stud. 3.3 Transverse spacing (1) The transverse spacing o the shear connector must be more than 4 times the diameter o the stud. (2)The shear connectors must be located 1 inch inwards rom the edge. [Table 2.43] Calculation o plate-buckling coeicient or uniorm normal stress, k Case n = 1 n=2 Z r (Eq ) α (Eq ) Z r (Eq ) K 8I k wt s 3 c k I k wt s 3 c 1 3 minimum number o shear connector (Eq ) 3.4 Cover and penetration The ollowing conditions must be met or the cover and penetration o the shear connector. (1)The clear depth o concrete cover over the tops o the shear connector must not be at least 2.0 inches. (2) The shear connector must penetrate at least 2.0 inches into the concrete slab. Qr (Eq ) 128 Design Guide or midas Civil

135 3.5 Fatigue Shear Resistance, Z r This part is applied dierently in the AASHTO LRFD 07 and 12. For the 07 conditions, ollow Section 5.2 o this chapter. The atigue shear resistance o the shear connector is calculated as shown in the ollowing table. [Table 2.44] Calculation o Fatigue Shear Resistance, Z r Shear Connector Type Stud Case Fatigue shear resistance ( Z ) r 75 year ( ADTT) 960 SL 75 year ( ADTT) 960 SL Case 2 Z r d N N log N Z r 5.5d 2 Calculate (Eq ) 3.6 Strength Limit State (1) Strength Limit State Ater the strength limit state is calculated, the minimum number o shear connector (n) Is calculated as shown in the equation below. n (2.120) Q r : total nominal shear orce (2) Factored shear resistance o a single shear connector The resistance o the shear connector is calculated as shown in the equation below. 1p, 2p (Eq ) (Eq ) (Eq ) Q r scqn (2.121) Qn : nominal shear resistance o a single shear connector determined as in Article ϕsc: resistance actor or shear connectors inputted by the user in Composite Steel Design arameter (Fig.2.17) Calculate (Eq ) (3) Total Nominal Shear Force, 1) Calculate the Total Nominal Shear Force,, or the veriication o the shear connectors under positive moment. 2 2 (2.122) p F p T (Eq ) p : total longitudinal orce in the concrete deck p Max( 1 p, 2 p) (2.123) in which : 0.85 ' b t 1p s s s (2.124) 2 p F yw Dt w F yt b t t t F yc b c t c 1n, 2n (Eq ) (Eq ) Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 129

136 Fp : total radial orce in the concrete deck I I (2.125) t1 t2 in which : Lp : arc length between an end o the girder and an adjacent point o maximum positive live load plus impact moment F T (Eq ) For straight bridges, the value o F p is calculated as 0. 2) Calculate when the shear connector experiences a negative moment. 2 2 T F T (2.126) t : total longitudinal orce in the concrete deck between the point o maximum positive live load plus impact moment and the centerline o an adjacent interior support T p n (2.127) Q n (Eq ) in which : n : total longitudinal orce in the concrete deck over an interior support taken as: n Min( 1 n, 2 n) (2.128) in which : 1 n F 2n yw Dt c w F 0.45 ' b t s s yt b t t t F yc b c t c (2.129) Ft : total radial orce in the concrete deck between the point o maximum positive live load plus impact moment and the centerline o an adjacent interior support taken as: F T Ln (2.130) T R in which : Ln : arc length between the point o maximum positive live load plus impact moment and the centerline o an adjacent interior support inputted by the user in shear connector dialog box (Fig.2.19) For straight bridges, the value o F p is calculated as 0. (4) Nominal shear resistance, Q n [Table 2.45] Calculation o Nominal Shear Resistance, Q n Shear Connector Type Stud Q n 0.5A sc Q n ' E c c A Asc : cross-sectional area o a stud shear connector Ec : modulus o elasticity o the deck concrete Fu : speciied minimum tensile strength o a stud shear connector sc F u rojecting width (Eq ) (Eq ) 130 Design Guide or midas Civil

137 4. Stiener The Stiener calculates the transverse/longitudinal stiener attached to the web and the longitudinal stiener attached to the compression lange. Stieners Check Transverse Stieners Check Longitudinal Stieners Check Longitudinal Compression Flange Stieners Only Box Section [Fig.2.65] Flow Chart o Stiener 4.1 Web Transverse Stiener (1) rojecting Width rojecting width o transverse stiener attached to web panel shall satisy ollowing two conditions: [Table 2.46] rojecting Width Conditions o Web Transverse Stiener Check List I Section Tub Section Closed-Box Section Condition 1 16t p bt b / 4 16 t p bt Condition 2 b t D (Eq ) (Eq ) tp : thickness o the projecting stiener element b :or I-sections, ull width o the widest compression lange. or tub section, ull width o the widest top lange. For closed box section, the limit o b /4 does not apply. [Table 2.47] Deine b according to Section Type Section Type b (Eq ) (Eq ) (Eq ) I Tub Full width o the widest compression lange with in the ield section under consideration Full width o the widest top lange within the ield section under consideration ( ) (2) Moment o Inertia Check This part is applied dierently in the AASHTO LRFD 07 and 12. For the 07 conditions, ollow the section 5.3 o this chapter. The program will perorm the calculation o the vertical stieners attached to the web. (Eq ) 1) V u >V n I Min I, I ) (2.131) t ( t1 t2 Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 131

138 It : moment o inertia o transverse stiener [Table 2.48] Calculation o Moment o Inertia o the transverse stiener or I girder section, I t Case Single-sided vertical stieners t I t I t 2 Double-sided vertical stieners I t b t 0.5b 0.5t t b 12 p 3 b t 3 3 t 2 p t p t w (Eq ) (Eq ) I 3 t1 btw J D F t yw It 2 40 E (2.132) 2.5 J ( d / D) o (Eq ) J : stiener bending rigidity parameter Max F / F,1.0) (2.133) t ( yw crs Fcrs : local buckling stress or the stiener 0.31E Fcrs F (2.134) 2 ys b t t Fys : speciied minimum yield strength o the stiener do : the smaller o the adjacent web panel widths b : the smaller o do and D C : ratio o the shear-buckling resistance longitudinal stiener (Eq ) 2) V u V n [Table 2.49] Check or Transverse Stiener when V u V n Case I I t1 t 2 Otherwise Veriications u v vr Vn V cr I t It1 ( It 2 It1) vvn vvcr Otherwise It I t 2 It I t 2 V V projecting width (Eq ) 3) The ollowing is calculated when the transverse and longitudinal stieners attach to the web at the same time. I t b t D b l 3.0d o I bt : projecting width o the transverse stiener bl : projecting width o the longitudinal stiener l (2.135) (Eq ) (Eq ) 132 Design Guide or midas Civil

139 Il : moment o inertia o the longitudinal stiener 4.2 Web Longitudinal Stiener (1) Strength limit state The longitudinal stiener attached to the web is calculated as shown in the alling equation. s RhFys (2.136) s : the lexural stress in the longitudinal stiener Fys : speciied minimum yield strength o the stiener (2) rojecting width The projecting width o the Longitudinal stiener is limited as per the ollowing equation. As per Article C , or the structural tees, b l should be taken as one hal the width o the lange. E bl 0. 48t (2.137) s F ys ts: thickness o the stiener β (Eq ) (Eq ) Z (Eq ) (3) Moment o inertia and radius gyration Moment o inertia and radius o gyration are calculated using the dimensions inputted in the Section Stiener dialog box (Fig.2.8). The moment o inertia and the radius o gyration o the longitudinal stiener shall satisy: 2 3 do I Dtw D l and Fys 0.16do r E (2.138) Fyc R F do : transverse stiener spacing R : minimum girder radius in the panel r : radius o gyration o the longitudinal stiener including an eective width o the web equal to 18*tw taken about the neutral axis o the combined section Il : moment o inertia o the longitudinal stiener including an eective width o the web equal to 18*tw taken about the neutral axis o the combined section β :curvature correction actor or longitudinal stiener rigidity [Table 2.50] Calculation o β h ys projecting width (Eq ) Moment o inertia AASHTO LRFD 07&12 (Eq ) Case For cases where the longitudinal stiener is on the side o the web away rom the center o curvature For cases where the longitudinal stiener is on the side o the web toward the center o curvature Z : curvature parameter Z 6 1 Z 12 1 Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 133

140 0.95d Z Rt w 2 o 10 (2.139) 4.3 Longitudinal Compression Flange Stiener (or box compression lange) (1) The strength o the stieners must be greater than the yield strength o the compression langes. (2) rojecting Width The rojecting Width (b l ) o the Longitudinal Compression Flange Stiener is calculated as shown in the ollowing equation. E bl 0. 48t (2.140) s F yc t s : thickness o the projecting longitudinal stiener element (3) Moment o inertia Each Moment o inertia o the Longitudinal Compression Flange Stiener Is calculated as shown in the ollowing equation. 3 I (2.141) l wt c w : larger o the width o the lange between longitudinal lange stieners or the distance rom a web to the nearest longitudinal lange stiener [Table 2.51] Calculation o ψ Number o the longitudinal stiener attached to compression lange(n) k : plate-buckling coeicient or uniorm normal stress 3 n k 3 n k n 3 Equally applicable as n=2 134 Design Guide or midas Civil

141 5. Dierence Between AASHTO-LRFD 4 th (2007) and AASHTO- LRFD 6 th (2012) This section explains how the unctions o midas Civil are applied dierently in AASHTO-LRFD 4 th Edition (2007) and AASHTO-LRFD 6 th Edition (2012). 5.1 Fatigue Limit State In both standards, the atigue resistance is calculated dierently. AASHTO-LRFD 4 th Edition (2007) AASHTO-LRFD 6 th Edition (2012) The calculation only considers the Fatigue 2 Based on the conditions, the calculation Load Combination out o the user load considers the Fatigue 1 or 2 Load Combination. combinations. Fatigue Resistance (ΔF) n Calculation Fatigue 1 Load Case Combination Is not used in the calculation. Fatigue Resistance (ΔF) n Calculation When using the Fatigue 1 Load Case Combination, the value o ΔF) n Is calculated as such: AASHTO LRFD07&12 ( ) ( ) ( F ) ( F) n TH When using the Fatigue 2 Load Case Combination, the value o ΔF) n Is calculated as such: 1 3 F A 1 ( ) n ( F N 2 ) in which: TH N (365)(75) n( ADTT) SL When using the Fatigue 2 Load Case Combination, the value o ΔF) n Is calculated as such: A ( F) n N in which: 1 3 N (365)(75) n( ADTT) SL 5.2 Fatigue Limit State or Shear Connector In both standards, Fatigue resistance or Shear Connector (Z r ) is calculated dierently. AASHTO-LRFD 4 th Edition (2007) AASHTO-LRFD 6 th Edition (2012) The Fatigue resistance(z r ) o the stud type or The Fatigue resistance(z r ) o the stud type or the Shear Connector is calculated as such: the Shear Connector is calculated as such: Z r d d (in SI Unit) log N ( in SI Unit) 2 Z r d (in US Unit) log N ( in US Unit) AASHTO LRFD07&12 ( ) Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 135

142 5.3 Transverse Stiener In both standards, Transverse Stiener is calculated dierently AASHTO-LRFD 4 th Edition (2007) AASHTO-LRFD 6 th Edition (2012) Calculation o the Stiener bending rigidity parameter(j) D J 2.5 / do D When the Web post buckling or tension-ield When the Web post buckling or tension-ield resistance is considered, the ollowing is resistance is considered, the ollowing is calculated. calculated. I t I t2 Calculation o the Stiener bending rigidity parameter(j) I I (1) t1 t 2 1) n cr 2.5 J ( d / D) V V o Vu vv vr I t It1 ( It 2 It1) vvn vv 2) Other conditions I t I t2 cr AASHTO LRFD07&12 ( ) I I (2) t1 t 2 It I t2 136 Design Guide or midas Civil

143 5.4 Flexure Resistance o Box Flange in compression under Unstiened condition In both standards, the Flexure Resistance o Box Flange in compression under Unstiened condition is calculated dierently. AASHTO-LRFD 4 th Edition (2007) AASHTO-LRFD 6 th Edition (2012) (1) F nc 1) F 2) F R 1 ke F yc nc Rb RhFyc cb ke R1 R2 Fyc R R F b h Fyr RhF 3) R 2 F nc yc yc ke F R 1 sin 2 ke F yc 2 v k 2 s 0.9ERbk Rb 2 b 0.9Ek c t c yc 2 b t b c F c t c ke R2 R1 R 1 : constant which when multiplied by yields the slenderness ratio equal to ke/ F yc 0.6 times the slenderness ration or which F nc rom Eq.3 is equal to R R F R b h 2 v 4 Fyc 2 c c yc k k s 2 2 R 2 : constant which when multiplied by yields the slenderness ratio or ke/ F yc which F nc rom Eq.3 is equal to R F 2 yr F F yr yc ( 0.4) F F F yc 1.23 yr yc F 2 v 4 Fyc yw R bf yc 2 k k s 2 (1) F nc F nc F 1) F cb cb p 1 v vfcv F cb Rb RhFyc F cb p F cb 2) F cv R R F b r h b 2 yc 0.9ER k 1.12 r p 1 1 Rh r p Ek F s yc Fcv 0. 85F yc Eks F F cv 1.40 F cv yc 0.65 Ek F s yc 2 F 0.9Ek 0.57 p r F yr yc Ek F yc Ek F yr ( 0.3) F Ek yc s F yw Ek F s yc AASHTO LRFD07&12 ( ) Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 137

144 Chapter 2. Steel Composite Design : AASHTO-LRFD 4 th and6 th (2007/2012) Steel Composite Design Result 1. Strength Limit State Result 1.1 Flexure (1) by Result Table As shown in the table below, the results can be checked in the result table. Design > Composite Design > Design Result Tables > Strength Limit State (lexure) [Fig.2.66] Result Table or Strength Limit State o Flexure My : yield moment Mp : plastic moment Mu : moment due to the actored loads phimn : nominal lexural resistance o a section multiplied by resistance actor, phi, or lexure bu : largest value o the compressive stress throughout the unbraced length in the lange under condition, calculated without consideration o lange lateral bending phifn : nominal lexure resistance o a lange Dp :distance rom the top o the concrete deck to the neutral axis o the composite section at the plastic moment Dt : total depth o the composite section Based on the dierent search conditions, the result values which appear will vary, as shown in the table below. [Table 2.52] Result Case Table or Strength Limit State o Flexure Condition Output Items le xu re Section Applied Clause My Mp Mu phimn bu phifn Dp Dt (+) (-) compact 6.10 & 6.11 O O O O - - O O noncompact 6.10 & O O O O & O O Appendix A6 O O O O Design Guide or midas Civil

145 (2) by Excel Report The results can be viewed in an Excel Report as shown below. 1) ositive Flexure [Fig.2.67] Excel Report or Strength Limit State o ositive Moment Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 139

146 2) Negative Flexure [Fig.2.68] Excel Report or Strength Limit State o Negative Moment 1.2 Shear (1) Result Table As shown in the table below, the results can be checked in the result table. Design > Composite Design > Design Result Tables > Strength Limit State (shear) [Fig.2.69] Result Table or Strength Limit State o Shear Vu : shear due to the actored load phivn : nominal shear resistance multiplied by resistance actor, phi, or shear bt_lim1 : projecting width limit or transverse stiener, 2.0+(D/30), as per Eq bt_lim2 : projecting width limit or transverse stiener, 16tp, as per Eq bt_lim3 : projecting width limit or transverse stiener, b/4, as per Eq bt : projected width o transverse stiener as per Article lt_lim : limiting moment o inertia o transverse stiener as per Eq &4 lt : Moment o Inertia o transverse stiener as per Article Design Guide or midas Civil

147 (2) by Excel Report The results can be viewed in an Excel Report as shown below. [Fig.2.70] Excel Report or Strength Limit State o Shear 2. Service Limit State Result (1) by Result Table The results can be viewed in an Excel Report as shown below. Design > Composite Design > Design Result Tables > Service Limit State [Fig.2.71] Result Table or Service Limit State c : compression-lange stress crw: nominal bending buckling resistance or webs as per Eq c : compression-lange stress c_lim : limit o compression-lange stress t : tension-lange stress t_lim : limit o tension-lange stress Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 141

148 (2) by Excel Report The results can be viewed in an Excel Report as shown below. [Fig.2.72] Excel Report or Strength Limit State o Shear 3. Constructibility Result 3.1 Flexure (1) by Result Table The results can be viewed in a result table as shown below. Design > Composite Design > Design Result Tables > Constructibility (lexure)... [Fig.2.73] Result Table or Constructibility Limit State o lexure buw : lange stress calculated without consideration o lange lateral bending phicrw : nominal bend-buckling resistance or webs buc : compression-lange stress with consideration o lange lateral stress phic : limit o compression-lange stress but : tension-lange stress with consideration o lange lateral stress phit : limit o tension -lange stress deck : longitudinal tensile stress in a composite section deck phir : limit o concrete deck tensile stress. r shall be taken as the modulus o rupture as per the Article Design Guide or midas Civil

149 (2) by Excel Report The results can be viewed in an Excel Report as shown below. [Fig.2.74] Excel Report or Constructibility o ositive Moment Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 143

150 2) Negative Flexure [Fig.2.75] Excel Report or Constructibility o Negative Moment 3.2 Shear (1) by Result Table The results can be viewed in a result table as shown below. Design > Composite Design > Design Result Tables > Constructibility (shear)... [Fig.2.76] Result Table or Constructibility o Shear Vu : shear in the web due to the actored load phivcr : shear-buckling resistance multiplied by resistance actor, phi, or shear 144 Design Guide or midas Civil

151 (2) by Excel Report The results can be viewed in an Excel Report as shown below. [Fig.2.77] Excel Report or Constructibility o Shear 4. Fatigue Limit State Result (1) by Result Table The results can be viewed in a result table as shown below. Design > Composite Design > Design Result Tables > Fatigue Limit State... [Fig.2.78] Result Table or Fatigue Limit State γ(δ) : Range o Fatigue Limit State (ΔF)n : Nominal Fatigue Resistance Lcom : Load combinations used in the calculation Vu : shear in the web due to the unactored permanent load plus the actored atigue load Vcr : shear buckling resistance as per Eq Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 145

152 (2) by Excel Report The results can be viewed in an Excel Report as shown below. 5. Shear Connector Result [Fig.2.79] Excel Report or Fatigue Limit State (1) by Result Table The results can be viewed in a result table as shown below. Design > Composite Design > Design Result Tables > Shear Connector... [Fig.2.80] Result Table or Shear Connector H/D : height to diameter ratio (H/D)lim : limit value o height to diameter ratio (=4.0) p : pitch o shear connectors speciied by the user p_lim1: pitch limit value, nzi/(vsr), as per Eq p_lim2: pitch limit value, 6d s : transverse spacing o shear connectors spacing (Transverse Cross Section) edge : distance o the top compression lange edge_lim (=1.0 in) Cover : clear depth o concrete cover over the tops o the shear connectors (> 2.0 in) enetration : depth o penetration o the shear connector(>2.0in) n : number o shear connectors entered in transverse direction n_req : required number o shear connectors 146 Design Guide or midas Civil

153 (2) by Excel Report The results can be viewed in an Excel Report as shown below. [Fig.2.81] Excel Report or Shear Connector 6. Stiener Result (1) by Result Table The results can be viewed in a result table as shown below. Design > Composite Design > Design Result Tables > Longitudinal Stiener... [Fig.2.82] Result Table or Stiener bl : projecting width bl_lim : limit o projecting width as per Eq I : Moment o inertia o cross-section I_lim : limit o moment o inertia o cross-section as per Eq r : radius o gyration r_lim : limit o radius o gyration as per Eq s : lexure stress o longitudinal stiener phirhfys : limit o lexure stress as per Eq Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 147

154 (2) by Excel Report The results can be viewed in an Excel Report as shown below. [Fig.2.83] Excel Report or Stiener 7. Span Checking (1) by Result Table Design > Composite Design > Design Result Table... Most critical member results in each span can be viewed in a result table as shown below. [Fig.2.84] Result Table or Span Group 148 Design Guide or midas Civil

155 (2) by Span Result Graph Design > Composite Design > Design Result Diagram... The results o the span group deined by the span inormation can be checked here. The lexure and shear results based on distance or node can be checked here. The current applied member orce or elasticity is marked in red while the strength or elasticity is marked in green. [Fig.2.85] Span Result Graph 8. Total Checking (1) by Result Table Design > Composite Design > Design Result Table... Summary results or each member can be viewed in a result table as shown below. [Fig.2.86] Result Table or Toal Checking Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012) 149

156 Chapter 3. Steel Composite Bridge Load Rating AASHTO LRFD 2 nd (2011)

157 Chapter 3. Steel Composite Bridge

158 Chapter 3. Steel Composite Bridge Load Rating : AASHTO-LRFR 2 nd (2011) Introduction 1. AASHTO LRFR 2011 Bridge Load Rating 1.1 Deinition o Load Rating The NBIS (National Bridge Inspections Standards Regulation) regulations deine load rating as The determination o the live load carrying capacity o a bridge using as-built bridge plans and supplemented by inormation gathered rom the latest ield inspection. Load ratings are expressed as a rating actor (RF) or as a tonnage or a particular vehicle. Emphasis in load rating is on the live-load capacity and dictates the approach o determining rating actors instead o the design approach o satisying limit states. 1.2 urpose o bridge rating Bridge load rating provides a measure o a bridge's ability to carry a given live load in terms o a simple actor, reerred to rating actor. These bridge rating actors can be used to aid in decisions about the need or (1) load posting, (2) bridge strengthening, (3) overweight load allowances, (4) and bridge closers. [Table3.1] urpose o bridge rating Load osting Bridge Strengthening Bridge Closers 1.3 Dierence between Bridge Design and Load Rating Bridge design and rating, though similar in overall approach, dier in important aspect. (1) hilosophy o Bridge Design Bridge Design may adopt a conservative reliability index and impose checks to ensure serviceability and durability without incurring a major cost impact. (2) hilosophy o Bridge Load Rating Bridge ratings generally require the Engineer to consider a wider range o variables than is typical in bridge design. In rating, the added cost o overly conservative evaluation standards Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR

159 can be prohibitive as load restrictions, rehabilitation, and replacement become increasingly necessary. The rating procedures presented LRFR recognize a balance between saety and economics. In most cases, a lower target reliability than design has been chosen or load rating at the strength limit states to rating is done on a more selective basis than is prescribed or design in the AASHTO LRFD Bridge Design Speciications. 1.4 Application o Load Rating (1) New Construction When designing a new structure, it is required that RF1 or the HL-93 vehicle at the Inventory Level; thereore, a Legal Load Rating will never be required on a newly designed structure. (2) Changes in the below category in the existing building: Live loads Dead loads hysical condition Speciications, Laws [Table3.2] Dierent Cases or The Load Rating New Bridges Change in the live loads Change in the hysical condition 154 Design Guide or Midas Civil

160 2. Load Rating Levels The LRFR methodology consists o three distinct levels o evaluation: (1) Design load rating (2) Legal load rating (3) ermit load rating The result o each evaluation serve speciic purpose and also inorm the need or urther evaluations. The important actors o each load rating level are summarized as shown below. [Fig.3.1] Load Rating Levels Each o these three levels o rating are discussed in detail in immediately ollowing sections. 2.1 Design Load Rating Design load rating is a irst level assessment o bridges. It is a measure o the perormance o existing bridge to current LRFD bridge design standards. (1) Live Load At Design load rating level, the HL-93 live-load model o the LRFD is applied, using dimensions and properties o the bridge in its present as inspected condition. (2) Limit States Under this check, bridges are screened or the strength limit state at the LRFD design level o reliability. Evaluation at a second lower evaluation level o reliability is also an option. The rating also considers all applicable LRFD serviceability limit states (3) purpose Design load rating can serve as a screening process to identiy bridges that should be load rated or legal loads. Bridges the pass the design load check (RF1) at the Inventory level will have satisactory load rating or all legal loads that all within the LRFD exclusion limits. (4) Level o Design Load Rating There are two levels o the Design Load Rating: 1) Inventory Rating level The Inventory rating level generally corresponds to the rating at the design level o reliability or new bridges in the AASHTO LRFD Bridge Design Speciications, but relects the existing bridge and material conditions with regard to deterioration and loss o section. Load ratings based on the Inventory level allow compressions with the capacity or new structures and, thereore, result in a live load, which can saely utilize an existing Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR

161 structure or an indeinite period o time. 2) Operation Rating level Load rating based o the Operation rating level generally describe the maximum permissible live load to which the structure may be subjected. Generally corresponds to the rating at the Operating level may shorten the lie o the bridge. 2.2 Legal Load Rating This second level rating provides a single sae load capacity (or a given truck coniguration) applicable to AASHTO and State legal loads. The revious distinction o Operating and Inventory level ratings is no longer maintained when load rating or legal loads. Legal load rating provides a level o reliability, corresponding to the operating level reliability or redundant bridges in good condition. (1) Live Load Live load is categorized into the two types according to AASHTO LRFR 2011 as: 1) AASHTO Legal loads, as speciied in Article 6A a 2) The Notional Rating Load as speciied in Article 6A b or State legal loads. (2) Limit States Strength is the primary limit state or load rating; service limit states are selectively applied. (3) purpose Bridges that do not have suicient capacity under the design-load rating shall be load rated or legal loads to establish the need or load posting or strengthening. 2.3 ermit Load Rating This third level o rating should only be applied to bridges having suicient capacity or legal loads. In other words, ermit load rating should be used only i the bridge has a rating actor greater than 1.0 when evaluated or AASHTO legal loads. (1) Live Load The actual permit vehicle s gross vehicle weight and axle coniguration will be the live load used in the permit-load evaluation. The MBE(Manual or Bridge Evaluation) categorizes permit loads into two classes: 1) Routine/annual permits, and 2) Special permits. (2) Limit States ermits are checked using the Strength II limit-state load combination with the Service II limit-state load combination optional or steel bridges to limit potential permanent deormations. (3) purpose ermit load rating checks the saety and serviceability o bridges in the review o permit application or the passage o vehicles above the legally established weight limitations. 156 Design Guide or Midas Civil

162 3. rocess o Load Rating Flow Chart AASHTO LRFR 11 ( AENDIX A6A) [Fig.3.2] Flow Chart o Load Rating The process starts with a bridge irst being rated at the Design Inventory level under HL- 93 load model. I the bridge is ound to be satisactory at this level o rating, it s considered not to require posting or AASHTO legal loads and state legal loads within the LRFD exclusion limits, and hence the bridge can be evaluated directly or permit load vehicles. However i the rating actor at the Design Inventory level is ound to be less than 1.0, the bridge must be evaluated under either the Design Operating level or the Legal load level. At these levels o rating i the bridge is ound to be satisactory it is considered not to require posting or AASHTO legal loads and state legal loads having only minor variations orm the AASHTO legal loads, and the bridge can be evaluated or permit load vehicles. I, however, the bridge is ound to be not satisactory, load posting will be required or legal loads and no permit analysis is allowed. There is however the option or higher orms o evaluation, such as load testing o the bridge or the use o inite element modeling, or when a bridge is ound to be unsatisactory at the Legal load level and the engineer eels the bridge may not require posting. Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR

163 Chapter 3. Steel Composite Bridge Load Rating : AASHTO-LRFR 2 nd (2011) Modeling and Design Variables 1. Modeling Design Variables In this chapter, the design variables, the meaning behind the design requirements, and the design process or Steel Composite Load Rating in midas Civil are explained. 1.1 Design arameters or Steel Composite Load Rating In this section, the application o load rating and input method and meaning o the related variables are explained Rating Design Code Rating > Bridge Rating Design > Steel Design> Rating Design Code Rating Design Code The program perorms the load rating based on the code selected in this dialog box. [Fig.3.3] Rating Design code Steel Bridge Load Rating arameters Rating > Bridge Rating Design > Steel Design> Rating arameters Steel Bridge Load Rating arameters (1) The system actor is inputted according to the System Factor,, provided in AASHTO LRFR 2011 (Table 3.6). The system actor is multiplied to the lexural strength (M n ) and shear strength (V n ) and, thereore, applied to all elements. (2) Strength Resistance Factor Strength Resistance Factor is deined. The resistance actors are automatically set to the deault values deined in AASHTO LRFR 12. The values also may be modiied or entered manually. (3) Girder Type or Box/Tub Section I the Single Box Section option is selected, the 158 Design Guide or Midas Civil

164 sections are considered as noncompact section; i the Multiple Box Section option is selected, the sections are considered as compact sections. Consider St.Venant Torsion and Distortion Stress I the Multiple Box Section option is selected, lateral bending stress is considered in accordance with St. Venant Torsion and Distortion Stress. I the Single Box Section option is selected, the lateral bending stress is not considered. (4) Options For Strength Limit State Appendix A6 or Negative Flexure Resistance in Web Compact/Noncompact Sections I this option is checked, Appendix A6 is applied or the lexural strength o straight composite I- sections in negative lexure with compact/noncompact webs. M n 1.3R h M y in ositive Flexure and Compact Sections( ) I this option is checked, M n value is restricted to 1.3R h M y under positive lexure. ost-buckling Tension-ield Action or Shear Resistance ( ) I this option is checked, post buckling resistance due to tension ield action is considered in the nominal shear resistance o an interior stiened web panel according to. I not, V n is taken as CV p. (5) Service Limit State Service Limit State I this option is checked, the service limit is veriied according to AASHTO LRFR A.6.4. [Fig.3.4] Load Rating arameters Dialog Box I Auto-Calculation is selected, the RF is calculated automatically according to LRFR standards. For more details, please reer to "Application o in Midas Civil" Section 3.3. I User Input is selected, the capacities, parameters calculated or the veriication o the RF, can be manually inputted. The allowed compressive stress and tensile stress o the concrete need to be inputted. The compressive and tensile stresses inputted or Design Load and Legal Load are applied or the veriication o the Design Load Rating and Legal Load Rating, respectively. (6) Fatigue Limit State Fatigue Limit State Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR

165 I this option is checked, the program checks the Fatigue Limit State according to AASHTO LRFR 11 6A.6.4. Also, the Load Test Measurement or the Application o Diagnostic Test Result can be selected between Strain and Displacement Unbraced Length Rating > Bridge Rating Design > Steel Design> Unbraced Length Unbraced Length The Unbraced Length or steel composite section is considered. The value input here has higher priority than the value calculated rom Span Group. (1) L b The Lateral Unbraced Length is used to calculate the lateral torsional buckling resistance or the compression lange o I-Girders. I the Lateral Unbraced Length is not applied, the span inormation, i deined, is used or the calculation. I the span inormation is not deined, element lengths are applied as the lateral unbraced length. [Fig.3.5] Unbraced Length Dialog Box Shear Connectors Rating > Bridge Rating Design > Steel Design> Shear Connectors Shear Connectors Studs are used as shear connectors and the ollowing parameters are used or the calculation: (1) Category Category deined by 75yr-(ADTT) SL equivalent to Ininite Lie. (2) F u Shear Resistance o Shear Connector (3) Shear Connector ane meters 160 Design Guide or Midas Civil

166 [Fig.3.7] Shear Connector arameters (4) Length between Max.Moment and Zero Moment The length o the sections where shear connectors need to be considered is inputted or the calculation o the pitch at the strength limit state Fatigue arameter [Fig.3.6] Shear Connector Dialog Box Rating > Bridge Rating Design > Steel Design> Fatigue arameter... (5) Nominal Shear Force Calculation The type o nominal shear orce calculation is determined or the calculation o the Nominal Shear Force,, which his used to calculate the minimum number o shear connector, n, at the strength limit state. Based on the calculation type selected, the equations used to calculate are diered Fatigue arameter (1) Category Category deined by 75yr-(ADTT) SL equivalent to ininite lie (Table ). (2) (ADTT) SL Number o trucks per day in a single-lane averaged over the design lie ( ) Value can be manually calculated as per (3) n Number o cycles per truck passage Value can be taken rom Table (4) Longitudinal Warping Stress Range For the veriication o atigue, lexure stress is calculated as the summation o Longitudinal Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR

167 Bending Stress Range and Longitudinal Warping Stress Range. By choosing the Auto-Calculation option, atigue vertical bending moment is simply increased by 10% or the longitudinal warping stress. I the User Input option is selected, longitudinal bending stress range is summated with the inputted value o the Longitudinal Warping Stress Range or top or bottom lange depending upon the lexure condition at the section. [Fig.3.8] Fatigue arameters Dialog Box Curved Bridge Inormation Rating > Bridge Rating Design > Steel Design> Curved Bridge Ino Curved Bridge Inormation Once the girder radius value o the element units in the steel composite section is entered, the corresponding elements are categorized as curved bridges. The inputted girder radius is used or the ollowing equations. [Fig.3.9] Curved Bridge Inormation Dialog Box (1) Radius is used or the review o lange lateral bending moment caused due to the curvature. (N is taken as 10.) 2 Ml M lat (LRFD 2012 c b-1) NRD where, Mlat : lange lateral bending moment M : major-axis bending moment l : unbraced length R : girder radius D : web depth N : a constant taken as 10 or 12 in past practice 162 Design Guide or Midas Civil

168 [Table3.3] Convex and Concave Convex Concave (2) Radius is used or the review o shear connector's pitch and the moment o inertia o area or the longitudinal stiener attached to web. (3) Curve Type - Convex, Concave I Convex is selected, Let Stiener is on the side o the web away rom the center o curvature and Right Stiener is on the side o the web toward the center o curvature. I Concave is selected, the opposite case o the convex is applied. The Let and Right are determined based on the progressing direction o the cross section. lease reer to the table below or the equations applied to each case. [Table3.4]Curvature Correction Factor or Longitudinal Stiener Case Equation Convex Concave Let Stiener Right Stiener Let Stiener Right Stiener Z 6 1 ( Z 12 1 ( Z 12 1 ( Z 6 1 ( : Curvature correction actor or longitudinal stiener : Curvature arameter Diagnostic Test Result Rating > Bridge Rating Design > Steel DesignDiagnostic Test Result Diagnostic Test Result Variables that are used to veriy the load carrying capacity or the diagnostic test result are inputted in this dialog box. (1) Auto calculation Delection and impact actor are inputted or the diagnostic test. (2) User Input The Adjustment Factor, K, is inputted by users. K is used to calculate the load-rating actor or the live-load capacity based on the load test result, RF T. Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR

169 K 1 K a K b ( ) where, K a : accounts or both the beneit derived rom the load test, i any, and consideration o the section actor (area, section modulus, ect.) resisting the applied test load K b : accounts or the understanding o the load test results when with those predicted by theory [Fig.3.10] Diagnostic Test Result Dialog Box 1.2 Design Material Data In this section, the material property inormation input method or the Steel Composite Load Rating is explained Rating material Rating > Bridge Rating Design > Steel Design> Rating material... (1) Rating material Rating material In this dialog box, the Material roperties can be modiied or the calculation o the structure capacity. The material utilized or composite sections are provided in the SRC material properties. The material should be deined as SRC Type. (1) Modiy Composite Material This dialog box is used to input material characteristics or the steel composite section design. The material property values entered will have a priority over the values entered in Material Data dialog box. 1) Steel o the Steel Girder Section Hybrid Factor Hybrid Factor is considered in the case where langes and web have dierent material properties. 164 Design Guide or Midas Civil

170 2) Concrete o the Concrete slab 3) Steel Rebar o the Concrete slab [Fig.3.11] Rating Material Dialog Box (2) Hybrid Factor (2) Hybrid Factor(R h ) When the check box or Hybrid Factor is selected, icon on the right is activated. The dierent materials or the top and bottom langes and web o the steel girder can be deined. Hybrid Factor (R h ) is determined based on these material inormation. [Fig.3.12] Hybrid Factor Dialog box Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR

171 1.3 Settings or Load Rating In this section, how to deine which part o the structure the load rating is perormed and actors and rating levels or each part are explained Rating Group Setting Rating > Bridge Rating Design > Steel Design> Rating Group Setting Rating Group Setting The Bridge Rating Group Setting Dialog allows users to apply Condition Factors per dierent groups deined already and i- and j-end check positions. (1) Inputting dierent Condition Factors and other design eatures are aster with the elements deined in Groups. Selected Groups are targeted or the design o the Rating Factor. Structure Group is deined in Deine Structure Group at: Tree Menu > Group> Structure Group>New... [Fig.3.13] Rating Group Setting Dialog Box [Fig.3.14] Structure Group Dialog Box (2) Dierent values o Condition Factor,, can be applied to dierent Structure Groups o elements. In the program, the Condition Factor is internally multiplied to Nominal Flexural Strength, Nominal Flexural Resistance, Nominal Shear Strength and Nominal Fatigue Resistance to calculate the Road Factor. For more details, please reer to [Table 3.7] and [Table 3.8]. (3) The Check osition, i- and/or j- end, is considered and selected or the Groups selected or the design. 166 Design Guide or Midas Civil

172 1.3.2 Deine Rating Case Rating > Bridge Rating Design > Steel Design> Deine Rating Case Deine Rating Case In Deine Rating Case Dialog, Load Factor is deined or each o the Service Limit State, Strength Limit State and Fatigue Limit State. (1) For the Fatigue Limit State calculation, Unactored dead load should be selected. (2) Deault Load Factors are automatically inputted or each Load Type (DC, DW,...) as per LRFR 2012 and can be manually modiied by users. Maximum and Minimum Load Factors are inputted or DC(Beore), DC(Ater), and DW. The deault maximum and minimum values are provided according to LRFR 2011 Table 6A and LRFD 2012 Table Only one load actor is inputted or the Temperature Load, but the load actor is used as positive and negative (+, -) or the calculation. DC(Beore) is or the state beore the concrete deck is activated. DC(Ater) is or the state ater the concrete deck is activated. DC(Ater) considers the Erection load case, i deined by user, and the stress caused by the time dependent material property, Creep & Shrinkage. er dierent Load Type, Load Cases can be additionally inputted per dierent Load Type and relected in the Load Rating Factor calculation. [Fig.3.15] Deine Rating Case Dialog Box (3) For dierent Load Types, dierent Load Cases are selected. Member orces beore the composite state are applied to Dead Load (CS) and member orces ater the composite state are applied to Erection Load. Static Load case is deined at: Load > Load Type > Create Load Cases > Static Load Cases Inormation inputted in the Load case internally generates the 12 Types results (Fx-max,... Mymin) per nodes in the calculation. For each node, Max/Min orces are calculated per total 6 degree o reedom (DOF) or each node. (4) Live Load and Load Factor are inputted Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR

173 separately or the rimary Vehicle and Adjacent Vehicle. When is clicked, the load combinations and corresponding Load Factors are generated. When the load combination is clicked, the load combination and load actors are inputted in the Rating Case Dialog Box. Each Live Load should be inputted prior in Moving Load Cases at: Load > Load Type > Moving Load > Moving Load Analysis Data > Moving Load Cases) [Fig.3.16] Live Load Factor or Rating Dialog Box (5) Evaluation Live Load Model Load Rating low as per LRFR standard is explained in [Fig.3.2]. The program does not automatically ollow the low o [Fig.3.2]. In this Live Load Factors or Rating Dialog, rating level needs to be deined as well as the load cases. In the "Introduction" Chapter, Section 2.2 and Section 2.3, dierent purposes and applications o perorming Legal Load Rating level and ermit Load Rating level are explained. However, in this dialog box, the Legal Level and ermit Level both needs to be selected because the same LRFD Load Factors are used in the two level checks osition or Rating Output Rating > Bridge Rating Design > Steel Design osition or Rating Output osition or Rating Output In this Dialog, the osition or Rating Output is inputted. (1) Users can select Groups in the Filters or Load Rating Summary and deine the osition or Rating Output. (2) When Apply is clicked in this dialog box, the elements to be printed in the output is deined and saved. [Fig.3.17] osition or Rating output Dialog Box 168 Design Guide or Midas Civil

174 1.3.4 Rating Design Force/Moment Tables Rating > Bridge Rating Design > Steel DesignRating Design Tables > Design Force/Moment Rating Design Tables For the selected load combinations, design member orce (longitudinal-direction moment (M y ), transverse-direction moment (M z ), shear (V u )) are calculated at dierent part(s) o the elements per construction stages. [ig.3.18] Rating Design Force/Moment Tables Dialog Box 1.4 Composite Section Data Steel composite section is composed o steel girder and concrete slab. Additional stieners may be arranged in the steel girder; longitudinal and sub reinorcement rebars may be arranged in the concrete slab. In this section, Steel Composite Load Rating eatures and unctions and related section input method and design variables are explained Longitudinal Reinorcement Rating > Bridge Rating Design > Steel Design> Longitudinal Reinorcement Longitudinal Reinorcement In a steel composite section, the longitudinal reinorcements are arranged within the concrete deck. The strength is calculated as shown in the below table. [Table3.5] Material Application or Strength Calculation Case ositive Flexure Negative Flexure Figure [Fig.3.19] Longitudinal Reinorcement Dialog Concrete Slab Reinorce -ment Apply None None Applied Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR

175 1.4.2 Transverse Stiener Rating > Bridge Rating Design > Steel Design> Transverse Stiener Transverse Stiener Figure 3.20 shows the dialog box in which users can arrange transverse stieners in steel composite section. When the transverse stieners are installed, the existence and spacing between stieners determine whether the web is stiened or unstiened under strength limit state. [Fig.3.20] Transverse Stiener Dialog [Fig.3.21] Transverse Stiener arameters (1) Stiener Type 1) One / Two Stiener Option Button Choose between one or two stieners. The two stiener option is available or I/Box/Tub sections. 2) itch (d o ) itch reers to the Transverse Stiener spacing. At the strength limit state, this can be used to distinguish between stiened and unstiened webs or calculate shear strength o the web. [Fig.3.22] Stiener Type Dialog 170 Design Guide or Midas Civil

176 Chapter 3. Steel Composite Bridge Load Rating : AASHTO-LRFR 2 nd (2011) Application o AASHTO LRFR 11 in midas Civil 1. Rating Factor Calculation The Bridge Load Rating unction o midas Civil calculates the Rating Factor (RF) at i/j nodes o elements or the Rating Cases according to AASHTO LRFR 2011 standard and inds the minimum RF. Rating load carrying papa city needs to be done at three dierent levels - Design Load Rating, Legal Load Rating, and ermit Load Rating - according to the AASHTO LRFR Midas Civil Bridge Load Rating calculates RF by using the equations (3.3) or Design Load Rating and Legal Load Rating or the load cases deined in Deine Load Case [ig.3.15]. The RF calculated in Midas Civil determines whether it is sae to carry the rimary Vehicle. I RF>1 it is sae and the larger RF, the greater the load carrying capacity o the bridge. 1.1 RF Calculation as per AASHTO LRFR The RF value shall be taken as below according to the LRFR standard: C ( RF DC )( DC) ( DW )( DW) ( )( ) ( )( LL IM ) L (3.1) RF AASHTO LRFR 11 (Eq. 6A ) RF : Rating actor C : Capacity Capacity, C, is calculated as shown in [Table 3.6] or the corresponding Limit State. [Table3.6] C (Capacity) in AASHTO LRFR 2011 Case Strength Limit States C c s n ( 0.85 ) Service Limit States : Allowable Stress speciied in the LRFD code DC : Dead-load eect due to structural components and attachments DW : Dead-load eect due to wearing suraces and utilities : ermanent loads other than dead loads LL : Live load eect C R C c R s C AASHTO LRFR 11 (Eq. 6A ) (Eq. 6A ) (Eq. 6A ) Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR

177 IM : Dynamic load allowance : LRFD load actor or structural components and attachments : LRFD load actor or wearing suraces and utilities : LRFD load actor or permanent loads other than dead loads : Evaluation live load actor : Condition actor : System actor : LRFD resistance actor R n : Nominal member resistance 1.2 Load Rating in Midas Civil Review Items In Midas Civil, load rating is reviewed based on the three dierent limit states or steel composite bridges. For more inormation about how to deine load cases or each limit state, please reer to "Modeling and Design Variables" Section and this chapter ("Application o AASHTO LRFR 11 in midas Civil") Section Load Rating o Steel Composite Bridge Strength Limit State Service Limit State Fatigue Limit State [Fig.3.23] Flow Chart o Load Rating o Steel Composite Bridge in midas Civil Calculation o RF Midas Civil's SC Bridge Load Rating unction uses the below equation [3.2] upon the request o the Caliornia Department o Transportation (Caltrans). C( DC )( DC) ( DW )( DW) ( T )( T) ( SEC )( SEC) ( )( ) ( USER )( USER) ( AV )( AV) RF ( )( V ) (3.2) V For the Steel Composite Load Rating, the equation [3.2] is modiied to relect the steel composite bridge characteristics. The equation [3.3] relects the member orce or beore and ater the concrete deck is activated and is used to calculate the RF value. DC DCA DW DW T T SEC SEC USER USER AV A V C ( DC )( DC B B) RF ( AV ) V (3.3) RF : Rating actor calculated by Midas Civil C : Capacity 172 Design Guide or Midas Civil

178 [Table3.7] C (Capacity) Calculated by Midas Civil Service Limit States Case Strength Limit States C c s Rn ( 0.85 ) Auto-Calculation User Input C C c R User-deined allowable stress in [Fig.3.4] Fatigue Limit State C c s Rn ( 0.85 ) c s s I user-deined and result, the program adjusts to be equal to 0.85 and calculate C. For calculating C, midas Civil uses dierent depending on the type o limit state. [Table3.8] Calculated by Midas Civil Load Rating State Calculated by Midas Civil Strength Limit State Flexural Strength M n or F n according to Shear Strength V n according to Fatigue Limit State calculated according to AASHTO LRFD 2012 DC : Dead load eect due to structural components and attachments DC B :Dead load eect due to structural components and attachments beore the concrete deck is activated DC A :Dead load eect due to structural components and attachments due to the erection load case, deined by users, and time dependent material property o concrete (Creep and Shrinkage) DW : Dead-load eect due to wearing suraces and utilities T : Temperature and Temperature Gradient SEC : In Deine Rating Case Dialog Box, Creep Secondary, Shrinkage Secondary and Tendon Secondary can be selected : ermanent loads other than dead loads USER : User-deined load AV : Adjacent Vehicle load V: rimary vehicle load : LRFD load actor or Dead load eect due to structural components and attachments : LRFD load actor beore the concrete deck is activated : LRFD load actor ater the Erection load case deined by user and time dependent material property o concrete are activated : LRFD load actor or wearing suraces and utilities : LRFD load actor or temperature : LRFD load actor or secondary : LRFD load actor or user-deined load : LRFD load actor or permanent loads other than dead loads : LRFD load actor or adjacent vehicle load : LRFD load actor or primary vehicle load The above actors may be explained in terms o the Deine Rating Case dialog box as ollows. Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR

179 The values input in the red-colored box are applied as the actors directed with the arrow. [Fig.3.24] Deine Rating Case dialog box where actors are inputted Load Rating Flow in Midas Civil (1) Load Rating Flow The low o load rating according to LRFR standard is explained in [Fig. 3.2]. In this section, how load rating is perormed in midas Civil is explained. In midas Civil, load rating is perormed or the load cases deined in Deine Rating Case dialog box [Fig. 3.15]. (2) Setting and Input Methods The two pictures in the below table are parts o Deine Rating Case dialog box. Limit State Rating Level [Fig.3.25] Limit State in Deine Rating Case dialog box [Fig.3.26] Rating Level in Deine Rating Case dialog box The Load Rating is perormed or the Limit State selected by user in the right picture above and the Rating Level selected in the let picture. Thereore, user can create and check load cases or maximum six dierent cases (3 Limit States x 2 Rating Levels = total 6 Cases). The below igure presents which choices need to be selected in Deine Rating Case dialog box and their order in accordance with LRFR Load Rating low chart. 174 Design Guide or Midas Civil

180 [Fig.3.27] Flow Chart o LRFR 11 and Deine Rating Case dialog box (3) Load Applied The vehicle load applied according to the rating level prescribed in the LRFR 2011 is explained in "Introduction" Section 2. To increase the lexibility o the users, vehicle load needs to be manually deined by users. ehicle loads can be deined at: Load > Load Type > Moving Load > Moving Load Analysis Data > Vehicles. I AASHTO LRFD Load is selected or the Standard Name, the vehicle loads are automatically inputted in accordance with LRFD. The below igure shows the Deine Standard Vehicular Load dialog box and the list o the vehicular load type supported in midas Civil when AASHTO LRFD Load is selected as the Standard. Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR

181 [Fig.3.28] Deine Standard vehicular load dialog box Condition Factor, The Condition Factor provides a reduction to account or the increased uncertainty in the resistance o deteriorated members and the likely increased uture deterioration o these members during the period between inspection cycles. The condition actor needs to be inputted in the Rating Group Setting Dialog Box [Fig.3.13] in midas Civil. Condition Factor AASHTO LRFR 11 ( 6A.4.2.3) [Table3.9] Condition Factor Structural Condition o Member c Good or Satisactory 1.00 Fair 0.95 oor 0.85 Condition Factor AASHTO LRFR 11 (Table. 6A ) System Factor, System actor relects the level o redundancy o the complete superstructure system. System actors that correspond to the load actor modiication in the AASHTO LRFD Bridge Design Speciications should be used. The system actors in [Table3.10] are more conservative than the LRFD. I the simpliied system actors presented in [Table3.10] are used, they should be applied only System Factor AASHTO LRFR 11 (6A.4.2.4) 176 Design Guide or Midas Civil

182 when checking lexural and axial eect at the strength limit state o typical spans and geometries. The system actor needs to be inputted in the Steel Bridge Load Rating arameters dialog box [Fig.3.4] in midas Civil. [Table3.10] System Factor Structural Type Welded Members in Two-Girder/Truss/Arch Bridges 0.85 Riveted Members in Two-Girder/Truss/Arch Bridges 0.90 Multiple Eyebar Members in Truss Bridges 0.90 Three-Girder Bridges with Girder Spacing 6t 0.85 Four-Girder Bridges with Girder Spacing 4t 0.95 All Other Girder Bridges and Slab Bridges 1.00 Floorbeams with Spacing >12 t and Noncontinuous Stringers 0.85 Redundant Stringer Subsystems between Floorbeams 1.00 s System Factor AASHTO LRFR 11 (Table. 6A ) A Constant value o ϕ s =1.0 is to be applied when checking shear at the strength limit state. 1.3 Load Combination AASHTO LRFR clariies the Load Factors or dierent Limit States and loads as shown in [Table 3.11]. The Load Factors are inputted in the Deine Rating Case Dialog (Chapter "Modeling and Design Variables" Article 1.3.2) [Table3.11] Limit States and Load Factors or Load Rating Load Combination AASHTO LRFR 11 (Table. 6A ) Shaded cells o the table indicate optional checks. Service I is used to check the 0.9 F y stress Limit in reinorcing steel. Load actor or DW at the strength limit stress may be taken as 1.23 where thickness has been ield measured. Fatigue limit state is checked using the LRFE atigue truck. (see LRFR Article 6A.6.4.1) Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR

183 1.4 I and Box Section In Load Rating, certain items need to be checked in accordance with AASHTO LRFD Design Article; while some do not. lease reer to the below table or the applicability o each case. [Table3.12] LRFD Design Articles applied per section type and review criteria I Section Box Section Case Straight Bridge Curved bridge Straight Bridge Curved bridge Flexural resistance and Shear resistance and Not considered in midas Civil constructability No need to be considered Fatigue requirements No need to be considered or webs I and Box Section AASHTO LRFR 11 ( 6A.6.9.1~6A.6.9.5) l AASHTO LRFR 11 ( 6A )) Composite sections are considered as unshored construction or the load rating in midas Civil according to LRFR A AASHTO LRFR 11 provides standards or box sections only but not tub sections. Thereore, the load rating or tub sections is done in accordance with the box section standards. 2. Strength Limit State The minimum RF is calculated or the Rating Cases inputted or the Strength Limit State. lease reer to [Table 3.12] or the LRFD Articles applied or dierent section types. 2.1 General Strength Limit State is reviewed or lexural strength and shear strength. Strength Limit States LRFR 11 6A and 6A Rating Factor or Flexural Strength Rating Factor or Shear Strength [Fig.3.29] Flow chart o Strength Limit State 178 Design Guide or Midas Civil

184 2.2 Load Combination Dierent load combinations are applied per load rating levels or the strength limit state check. [Table3.13] Load Combination Load Rating Level Design load level Legal load level ermit load level Load Combination Strength load combination Strength load combination Strength load combination 2.3 Rating Factor(RF) Calculation Rating Factor or Flexural Strength The RF is calculated or each Rating Case according to the equation (3.4). The minimum RF is calculated at the i- and j- ends or the positive and negative moments. Load Combination AASHTO LRFR 11 (6A.6.4.1) (6A ) DC DCA DW DW T T SEC SEC USER USER AV A V C ( DC )( DC B B) RF ( AV ) V (3.4) C :capacity, [Table3.14] C (Capacity) and C M n or F n calculated according to AASHTO LRFD 2012 [Table3.15] Cases M n and F n are calculated M n Compact Section in ositive lexural moment Flexural resistance o Negative Flexure Moment by using Appendix A6 ositive lexural moment in noncompact section Negative lexural moment and one o the ollowing cases: - Curved bridge - Straight Bridge but slender section -Straight Bridge and compact or noncompact, but Appendix A6 is not applied F n ( DC )( DCB ) DC DCA DW DW T T SEC SEC USER USER AV ( AV ) : B A My rom Load Case ( V : My rom rimary Vehicle(.V) V ) Rating Factor or Shear Strength The RF is calculated at i/j nodes or the rating cases inputted or the strength limit state according to the equation (3.5) and the minimum RF is ound. Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR

185 RF C ( DC )( DCB) DC DCA DW DW T T SEC SEC USER USER AV ( AV ) B A (3.5) V V C : Vn calculated by MIDAS-CIVIL depending on Code o AASHTO LRFD 2012 ( DC )( DCB ) DC DCA DW DW T T SEC SEC USER USER AV ( AV ) B A : Vz rom Load Case ( V : Vz rom rimary Vehicle(.V) V ) 3. Service Limit State The minimum RF is calculated according to the equation (3.5) or the Rating Cases inputted or the Service Limit State. Then, the minimum RF is determined. 3.1 General The below LRFD Design Article is applied or the Service Limit State check in Load Rating. [Table3.16] LRFD Articles applied or dierent section type Case LRFD Design Article I Section Box Section Service Limit State AASHTO LRFR 11 (6A ) 3.2 Load Combination For the Service Limit State check, Service II load combination is applied or all Load Rating level. [Table3.17] Load Combination Load Rating Level Design load level Legal load level ermit load level Load Combination Service load combination Load Combination AASHTO LRFR 11 (6A.6.4.1) (6A ) 3.3 Rating Factor(RF) Calculation The RF is calculated or the compressive and tensile stresses at i/j nodes. DC DCA DW DW T T SEC SEC USER USER AV A V C ( DC )( DC B B) RF V ( AV ) (3.6) C : Stress DC DW T SEC USER ( ) ( )( DC ) AV DCB B DCA : Stress rom Load Cases ( V : Stress rom rimary Vehicle(.V) V ) A DW T SEC USER AV 180 Design Guide or Midas Civil

186 The capacity, C, changes depending on whether the value is auto-calculated or user-deined in the Load Rating arameters dialog box shown in [Fig.3.4]. lease reer to the below table. [Table3. 18] C (Capacity) in Service Limit State Case Composite Section Auto-Calculation Noncomposite Section User Input c C R 0. 95F R h y C 0. 8R F Allowable Stress inputted in [Fig.3.4] y Capacity AASHTO LRFR 11 (6A ) In Which, F y : Yield Stress 4. Fatigue Limit State The RF is calculated using the equation (3.6) or the rating cases inputted or the Fatigue Limit State and the minimum RF is determined. 4.1 General The atigue requirements or webs speciied in LRFD Design Article does not need to be considered or the Fatigue Limit State veriication o the i- and box- type sections. AASHTO LRFR 2011 does not speciy the standards or the tub sections; however, the tub sections are veriied according to the box section veriication in midas Civil. Fatigue Limit State AASHTO LRFR 11 (Section 7) Fatigue Requirements AASHTO LRFR 11 (6A.6.9.1) 4.2 Load Combination (1) The Fatigue load combination is applied or the Fatigue Limit State veriication as shown in [Table 3.11]. (2) The Fatigue Limit state is only veriied or the Design Load Rating level. Legal Load Rating and ermit Load Rating levels are not veriied or the Fatigue Limit State. 4.3 Rating Factor(RF) Calculation DC DCA DW DW T T SEC SEC USER USER AV A V C ( DC )( DC B B) RF V ( AV ) (3.7) C: capacity [Table3.19] C (Capacity) and C calculated by MIDAS-Civil depending on Code o AASHTO LRFD 2012 DC DW T SEC USER ( ) ( )( DC ) AV DCB B DCA : Stress rom Load Case A DW T SEC USER AV Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR

187 ( V )( V ) :Stress rom rimary Vehicle(.V) is constant-amplitude atigue threshold. 4.3 Levels o Fatigue Limit State Category (1 )The two types o Fatigue damage are: Load-induced atigue damage Distortion-induced Fatigue damage Levels AASHTO LRFR 11 (7.1) (7.2.1) The Load-induced atigue damage is veriied in midas Civil. (2) The two levels o load-induced atigue damage are: The ininite-lie calculation The inite-lie calculation lease reer to [Table 3.20] or the LRFR Design Articles applied in each case. [Table3.20] LRFR Article applied or Fatigue cases Levels o Fatigue Evaluation LRFR Design Article Ininite - lie 7.2 and Load-induced Fatigue Finite - lie 7.2 and Distortion-induced Fatigue 7.3 Application o LRFR AASHTO LRFR 11 (7.2.1) Flow o Fatigue Limit State The ininite-lie calculation and inite-lie calculation are distinguished according to the low chart shown in [Fig.3.30]. Only bridge details that ail the ininite-lie check are subject to the more complex inite-lie evaluation. Fatigue Evaluation o Load-induced Fatigue damage and Yes max F TH No Ininite Fatigue Lie Y Y Finite Fatigue Lie R n( ADTT ) SL e R A Flow AASHTO LRFR 11 (7.2.4) (Eq ) (7.2.5) End Ininite Fatigue Lie AASHTO LRFR Design Guide or Midas Civil

188 [Fig.3.30] Flow Chart o Fatigue Evaluation o Load-induced Fatigue damage Y : total atigue lie o a atigue-prone detail in years : maximum stress range expected at the atigue-prone detail : Average member o trucks per day in a single lane averaged over the atigue lie is resistance actor speciied or evaluation, minimum, or mean atigue lie. A is Detail Category Constant. n is the number o stress-range cycles per truck passage estimated according to (in order o increasing apparent accuracy and complexity) (Eq ) Finite Fatigue Lie AASHTO LRFR 11 (Eq ) In midas Civil, dierent, and values are applied per the Fatigue category such as A, B, B', C, C', D, E, and E' inputted in the Fatigue parameters dialog [Fig.3.8]. is taken as 24.0 ksi (165.0 Ma) except the other cases deined in [Table 3.21]. For n, the n value user deined in the Fatigue arameters dialog box shown in [Fig.3.8] is used or the calculation. [Table3.21] Constant-Amplitude Fatigue Thresholds, Detail Threshold Category US Unit (ksi) SI Unit (Ma) A B B' C C' D E E' Fatigue Threshols (Table ) [Table3.22] Resistance actor speciied or evaluation, minimum, or mean atigue lie, Detail Category Evaluation Lie Minimum Lie Mean Lie A B B' C C' D E E' Resistnace Factor AASHTO LRFR 11 (Table ) [Table3.23] Detail Category Constant, A Detail Category US Unit (x 10 8 (ksi 3 )) Constant, A! SI Unit (x10 11 (Ma 3 )) A A Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR

189 B B' C C' D E E' (Table ) Eective Stress Ranges (1) Calculation o Eective Stress Range The Eective Stress Range,, is taken dierently or the two cases: 1) Calculating Estimated Stress Range and 2) Measuring Estimated Stress Range. lease reer to [Table 3.24] or the dierent calculations. [Table3.24] Eective Stress Range Case Calculating Estimated Stress Range Eective Stress Range ( ) R 3 Measuring Estimated Stress Range 1/ 3 e ( ) e Rs i i s Eective Stress Range AASHTO LRFR 11 (Eq ) (Eq ) In midas Civil, the Fatigue Limit State is veriied with the Calculating Estimated Stress Range method. Where : The stress-range estimate partial load actor. Unless otherwise speciied, : analysis partial load actor : truck-weight partail load actor : Measured eective stress range; or 75% o the calculated stress range due to the passage o the atigue truck as speciied in LRFD Design Article , or a atigue truck determined by a truck survey or weigh-in-motion study. : ercaentage o cycles at a particular stress range : The particular stress range Rs AASHTO LRFR 11 (Eq ) (2) stress-range estimate partial load actor For calculating, the and values are applied according to [Table 3.25]. Thereore, there is no uncertainty in the veriication. [Table3.25] artial Load Factor, Case For Evaluation or Minimum Fatigue Lie Stress range by simpliied analysis, and truck weight per LRFD Stress range by simpliied analysis, artial Load Factors AASHTO LRFR 11 (Table ) 184 Design Guide or Midas Civil

190 and truck weight estimated through weigh-in-motion study Stress range by reined analysis, and truck weight per LRFD Stress range by reined analysis, and truck weight estimated through weigh-in-motion study Stress range by ield-measured strains N/A N/A 0.85 For Mean Fatigue Lie All method N/A N/A Determining Fatigue-rone Details Bridge details are only considered prone to load-induced atigue damage i they experience a net tensile stress. Thereore, i the below requirement is satisied, the Fatigue Limit State needs to be veriied. 2 R ( ) (3.8) s tension deadloadcompression Fatigue-rone Details AASHTO LRFR 11 (7.2.3) (Eq ) Where : Factored tensile portion o the stress range due to the passage o a atigue truck : Unactored compressive stress at the detail due to dead load. Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR

191 Chapter 3. Steel Composite Bridge Load Rating : AASHTO-LRFR 2 nd (2011) Bridge Load Rating Result 1. Result Tables For the element o the worst case, capacity, demand and basis o demand can be reviewed per dierent rating cases. 1.1 Service Limit State Summary (1) by Result Table The results may be reviewed with the Result Table as shown below. Rating > Bridge Rating Design > Steel Design > Rating Design Result Tables > Service Limit State Summary [Fig.3.31] Result Table or Service Limit State Summary Rating Case: Rating Case combination with the minimum RF Component : Indicates the member type: compression/tension Minimum Rating Factor: The minimum RF Location: The Element number and its i/j nodes where the RF is calculated Relative Location: The relative location rom the starting point o the bridge (Reer to Span Inormation dialog box) Allowable Stress: C or allowable stress inputted by the user Demand: Stress demand oint : Design point at i/j nodes (e.g., Right Top, Right Bottom, Let Top, Let Bottom) DC(Beore) Factor : Load Factor or Load Case-DC(Beore) DC(Beore) Stress rom DC(Beore) DC(Ater) Factor : Load Factor or Load Case-DC(Ater) DC(Ater) Stress rom DC(Ater) DW Factor : Load Factor or Load Case-DW DW Stress : Stress rom DW Temperature Factor : Load Factor or Load Case-Temperature Temperature Stress : Stress rom Temperature ermanent Factor : Load Factor or Load Case- ermanent ermanent Stress :Stress rom ermanent Secondary Factor : Load Factor or Load Case-Secondary Secondary Stress :Stress rom Secondary User Deined Factor : Load Factor or Load Case-User Deined User Deined Stress : Stress rom User Deined 186 Design Guide or Midas Civil

192 ri. LL Factor : Load Factor or Load Case-rimary live load ri. LL Stress : Stress rom rimary live load Adj. LL Factor : Load Factor rom Load Case-Adjacent live load Adj. LL Stress : Stress rom Adjacent live load (2) by Excel Report The results may be reviewed in the orm o MS Excel Report as shown in [Fig.3.32]. [Fig.3.32] Excel Report or Service Limit State Summary 1.2. Strength Limit State Summary (1) by Result Table The results may be reviewed in the Result Table as shown below. Rating > Bridge Rating Design > State Summary Steel Design > Rating Design Result Tables > Strength Limit [Fig.3.33] Result Table or Strength Limit State Summary ositive/negative: ositive/negative moment LRFD Resistance Factor: Resistance Factor according to the standard selected or the Rating Design Code Demand, Mu: moment due to the actored loads Capacity, phimn: nominal lexural resistance o a section multiplied by phi o lexure Demand, bu: largest value o the compressive stress throughout the unbraced length in the lange under condition, calculated without consideration o lange lateral bending Capacity, phifn: nominal lexure resistance o a lange DC(Beore) Force : My rom DC(Beore) DC(Ater) Force: My rom DC(Ater) DW Force: My rom DW Temperature Force: My rom Temperature T.Gradient Force: My rom T.Gradient ermanent Force: My rom ermanent Secondary Force: My rom Secondary User Deined Force: My rom User Deined ri. LL Force: ri. My rom LL Adj. LL Force: My rom Adj. (2) by Excel Report The results may be reviewed in MS Excel report orm as shown in [Fig.3.34]. Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR

193 [Fig.3.34] Excel Report or Strength Limit State Summary 1.3. Flexure Strength Rating Factor The Rating Factor can be reviewed per rating cases. (1) by Result Table The results may be reviewed in the Result Table as shown below. Rating > Bridge Rating Design > Steel Design > Rating Design Result Tables > Flexure Strength Rating Factor [Fig.3.35] Result Table or Flexure Strength Rating Factor Group : Name o Element Group deined by user Elem. : Number o Element or which the Rating Factor is calculated art : i/j nodes and number o the elements used or design s System Factor: used to calculate RF o the element c Condition Factor: used to calculate RF o the element Rating Factor : Rating Factor calculated according to equation (2.1) Check : Whether the result is OK or NG (OK i RF>1) (2) by Excel Report The results may be reviewed in the MS Excel Report orm as shown in [Fig.3.36] [Fig.3.36] Excel Report or Flexure Strength Rating Factor 188 Design Guide or Midas Civil

194 1.4. Shear Strength Rating Factor The Rating Factor can be reviewed per rating cases and elements. (1) by Result Table The results may be reviewed in the Results Table as shown below. Rating > Bridge Rating Design > Steel Design > Rating Design Result Tables > Shear Strength Rating Factor [Fig.3.37] Result Table or Shear Strength Rating Factor (2) by Excel Report The results may be reviewed in the MS Excel Report orm as shown in [Fig.3.38]. [Fig.3.38] Excel Report or Flexure Strength Rating Factor 1.5. Steel Stress Rating Factor The Service Limit State veriication result can be viewed or the compressive and tensile stress per elements and rating cases. (1) by Result Table The results may be reviewed in the MS Excel Report orm as shown in [Fig.3.39]. Rating > Bridge Rating Design > Steel Design > Rating Design Result Tables > Steel Stress Rating Factor [Fig.3.39] Result Table or Steel Stress Rating Factor (2) by Excel Report The results may be reviewed in the MS Excel Report orm as shown in [Fig.3.40]. Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR

195 [Fig.3.40] Excel Report or Steel Stress Rating Factor 1.6. Fatigue Rating Factor (1) by Result Table The results may be reviewed in the Result Table as shown below. Rating > Bridge Rating Design > Steel Design > Rating Design Result Tables > Fatigue Rating Factor [Fig.3.41] Result Table or Fatigue Rating Factor (2) by Excel Report The results may be reviewed in the MS Excel Report orm as shown in [Fig.3.42]. [Fig.3.42] Excel Report or Fatigue Rating Factor 190 Design Guide or Midas Civil

196 2. Rating Detail Table The Rating Detail Table presents the rating actor, capacity, basis o demand calculation, and the amount o steel per load cases, elements and rating cases. 2.1 Flexure Strength Rating Detail The Flexure Strength Rating Detail may be viewed with the program Result Table or MS Excel Report document. (1) by Result Table The results may be reviewed in the MS Excel Report orm as shown in [Fig.3.43]. Rating > Bridge Rating Design > Steel Design > Rating Design Result Tables > Flexure Strength Rating Detail [Fig.3.43] Result Table > Flexure Strength Rating Detail phimn: nominal lexural resistance o a section multiplied by phi o lexure phifn: nominal lexure resistance o a lange Areas Rebar : Rebar Area Areas min :Minimum Rebar Area Reinorcement Requirement max: Maximum reinorcement requirement DC(Beore) Force : My rom DC(Beore) DC(Ater) Force: My rom DC(Ater) DW Force: My rom DW Temperature Force: My rom Temperature T.Gradient Force: My rom T.Gradient ermanent Force: My rom ermanent Secondary Force: My rom Secondary User Deined Force: My rom User Deined ri. LL Force: My rom ri. LL Adj. LL Force: My rom Adj. LL (2) by Excel Report The results may be reviewed in the MS Excel Report orm as shown in [Fig.3.44]. [Fig.3.44] Excel Report or Flexure Strength Rating Detail Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR

197 2.2 Shear Strength Rating Detail (1) by Result Table The results may be reviewed in the Result Table as shown below. Rating > Bridge Rating Design > Steel Design > Rating Design Result Tables > Shear Strength Rating Detail [Fig.3.45] Result Table > Shear Strength Rating Detail (delta F)n : Nominal Fatigue Limit State DC(Beore) Force : Vz due to DC(Beore) DC(Ater) Force: Vz due to DC(Ater) DW Force: DW Vz Temperature Force: Vz due to Temperature T.Gradient Force: Vz due to T.Gradient ermanent Force: Vz due to ermanent Secondary Force: Vz due to Secondary User Deined Force: Vz due to User Deined ri. LL Force: Vz due to ri. LL Adj. LL Force: Vz due to Adj. LL (2) by Excel Report The results may be reviewed in the MS Excel Report orm as shown in [Fig.3.46]. [Fig.3.46] Excel Report or Flexure Strength Rating Detail 2.3 Steel Stress Rating Detail The Steel Stress can be reviewed or all load cases and stress types. (1) by Result Table The results may be reviewed in the Result Table as shown below. Rating > Bridge Rating Design > Steel Design > Rating Design Result Tables > Steel Stress Rating Detail [Fig.3.47] Result Table or steel stress Rating Detail 192 Design Guide or Midas Civil

198 c : bending stress on web plate crw: bending stress limit on web plate Rating Factor Comp.: RF or the allowable compressive stress Rating Factor Tens: RF or the allowable tensile stress Allowable Stress Comp.: Allowable compressive stress user-deined Allowable Stress Tens.: Allowable tensile stress user-deined DC(Beore) -Let Top Stress : Stress at the Let Top due to the DC(Beore) Load Cases DC(Beore) -Right Top Stress : Stress at the Right Top due to the DC(Beore) Load Cases DC(Beore) -Right Bottom Stress: Stress at the Right Bottom due to the DC(Beore)Load Case DC(Beore) -Let Bottom Stress: Stress at the Let Bottom due to the DC(Beore) Load Case DW, Temperature, ermanent, Secondary, Adj. LL can be explained the same way as the above DC- XXXXXX bolded. (2) by Excel Report The results may be reviewed in the MS Excel Report orm as shown below. [Fig.3.48] Excel Report or Steel Stress Rating Detail 2.4 Fatigue Rating Detail The Fatigue Rating may be reviewed or all load cases and stress types. (1) by Result Table The results may be reviewed in the Result Table as shown below. Rating > Bridge Rating Design > Steel Design > Rating Design Result Tables > Fatigue Rating Detail [Fig.3.49] Result Table or Fatigue Rating Detail (delta F)n : Nominal Fatigue Limit State DC(Beore) Stress :Stress due to DC(Beore) DC(Ater) Stress : Stress due to DC(Ater) DW Stress :Stress due to DW Temperature Stress: Stress due to Temperature T.Gradient Stress: Stress due to T.Gradient ermanent Stress: Stress due to ermanent Secondary Stress: Stress due to Secondary User Deined Stress: Stress due to User Deined Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR

199 ri. LL Stress: Stress due to ri. LL Adj. LL Stress: Stress due to Adj. LL (2) by Excel Report The results may be reviewed in the MS Excel Report orm as shown below.. [Fig.3.50] Excel Report or Fatigue Rating Detail 3. Load Rating Report 2.1 Load Rating Summary Result Table The below table presents the moment and shear at the Strength Limit State and stress at the Service Limit State. The table indicates the worst cases load combination based on the 1) moment at the Strength Limit State, 2) Stress at the Service Limit State, and 3) Shear at the Strength Limit State. [Fig.3.51] Excel Report or Load Rating Summary Result Table 194 Design Guide or Midas Civil