VERIFICATION MANUAL. for. MERLIN-DASH (LFD and LRFD Steel)

Transcription

1 VERIFICATION MANUAL for MERLIN-DASH (LFD and LRFD Steel) Computer Program for Design and Analysis of Straight Highway Bridge System THE BRIDGE ENGINEERING SOFTWARE AND TECHNOLOGY (BEST) CENTER DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING UNIVERSITY OF MARYLAND COLLEGE PARK, MD November 2006

2 I. Introduction In order to fully verify the LFD and LRFD versions of MERLIN-DASH (Design, Analysis, and Rating of Straight Highway Bridge System), three examples from Four LRFD Design Examples of Steel Highway Bridges published by AISC was adopted. In this publication only one verification problem (Examples 2: Two-Span Continuous Composite I-Girder 90 ft 90 ft) is listed. Section II Bridge Information presents the following four subsections, with the information adopted from the AISC publication:. Bridge description 2. Bridge cross section, framing plan and elevation 3. AISC LRFD Dead- and live-load moment envelopes & Dead- and live-load shear envelopes 4. AISC LRFD Fatigue-load moment & Fatigue-load shear For verification, graphs and calculations based on MERLIN-DASH and hand calculations are given for both LFD and LRFD. Section III LRFD Verifications presents. LRFD unfactored moments and the graph 2. LRFD factored moments and the graph 3. LRFD unfactored shears and the graph 4. LRFD factored shears and the graph 5. Verification of LRFD code checks Section IV LFD Verifications presents. LFD moments and the graph 2. LFD shears and the graph 3. Verification of LFD code checks Appendix A lists the LRFD output and Appendix B lists the LFD output. 2

3 II. Bridge Information. Bridge description Ref: AISC Four LRFD Design Examples of Steel Highway Bridges, U.S. Unit Example: Two-Span Continuous Composite I Girder Specifications: () AASHTO Standard Specifications (7 th Edition with 2003 Interim) (2) AASHTO LRFD Bridge Design Specifications (2 nd Edition 998 with 2003 Interim) Structural steel: AASHTO M270, Grade 50W, F y =50 ksi Concrete: f c Z = 4.0 ksi; modular ratio n=8 Reinforcing steel: AASHTO M3, Grade 60, F y =60 ksi DC: Slab =.063 K/ft (DL for LFD) Concrete Haunch = K/ft (DL for LFD) Stay-in-place forms = 0.35 K/ft (DL for LFD) Detail factor =.2 (to match the steel weight) DC2: Barriers = K/ft (DL2 for LFD) DW: Wearing surface = 0.23 K/ft (DL2 for LFD) Live load: HL-93 (HS20 for LFD) Design factor: η = 0.95 (default; LRFD only) 3

4 2. Bridge cross section, framing plan and elevation 4

5 3. AISC LRFD Dead- and live-load moment envelopes & Dead- and live-load shear envelopes 5

6 4. AISC LRFD Fatigue-load moment & Fatigue-load shear 6

7 III. LRFD Verifications. LRFD unfactored moments and the graph Span No Increm No Dist from Left DC DW DC2 LL+ LL- LL tr + LL tr - LL Range (ft) (k-ft) (k-ft) (k-ft) (k-ft) (k-ft) (k-ft) (k-ft) (k-ft) LRFD Unfactored Moment Moment Panel Pt DC DW DC2 LL+ LL- LLtr+ LLtr Distance 7

8 2. LRFD factored moments and the graph Span No Increm No Dist from Left Service I Service II Strength I Strength II Strength IV Fatig Range (ft) (k-ft) (k-ft) (k-ft) (k-ft) (k-ft) (k-ft) LRFD Factored Moment Moment Panel Pt Service I Service II Strength I Strength II Strength IV Fatigue Range 8

9 3. LRFD unfactored shears and the graph Span No Increm No Dist from Left DC DW DC2 LL+ LL- LL tr + LL tr - LL Range (ft) (kip) (kip) (kip) (kip) (kip) (kip) (kip) (kip) LRFD Unfactored Shear 50 Shear r- DC DW DC2 LL+ LL- LLtr+ LLtr- -50 Panel Pt 9

10 4. LRFD factored shears and the graph Span No Increm No Dist from Left Service I Service II Strength I Strength II Strength IV Fatig Range (ft) (kip) (kip) (kip) (kip) (kip) (kip) LRFD Factored Shear Shear Panel Pt Panel Pt Service I Service II Strength I Strength II Strength IV Fatigue Range 0

11 5. Verification of LRFD code checks Various tables of the DASH LRFD output are verified by hand calculation using Excel. Those are Verification of: DASH LRFD Table Depth/Thickness Ratio (N=n, Composite Case) 2 Verification of: DASH LRFD Table A Depth/Thickness Ratio (N=infinite, Noncomposite Case) 3 Verification of: DASH LRFD Table Bending Capacity for Noncomposite Dead Load Case 4 Verification of: DASH LRFD Table Bending Capacity for Composite Live Load Case 5 Verification of: DASH LRFD Table LRFD Service II Check 6 Verification of: DASH LRFD Table Compression Flange Slenderness Check 7 Verification of: DASH LRFD Table Unbraced Length Check 8 Verification of: DASH LRFD Table A Bending Capacity Reduction for Unbraced Section 9 Verification of: DASH LRFD Table Unstiffened Section Shear Capacity

12 Verification of: DASH LRFD Table Depth/Thickness Ratio (N=n, Composite Case) Span Increment Distance Long. Composite DL +LL 2Dcp/tw 2Dcp/tw No. No. (ft) Stiffener Stress () (2) (3) (Ksi) 4 36 No Yes < No Yes < Satisfy compact () From Table.2.9.5C Strength I Total stress Summary f = 27.7 Ksi Check OK f pier = Ksi Check OK (2) AASHTO Eq. ( b-) for M + section fc' = 4 Ksi AASHTO Eq. ( b-2) for M - section Tension D (in.) tw (in.) A slab (in 2 ) A ten (in 2 ) A comp (in 2 ) A web (in 2 ) F y (Ksi) A reinf (in2) F yr (Ksi) Dcp (in.) 2D cp /t w Bottom Top N/A Check OK (3) AASHTO Eq. ( ) or Eq. ( a-) 3.76 * sqrt(e/f yc ) = Check OK 2

13 Verification of: DASH LRFD Table A Depth/Thickness Ratio (N=infinite, Noncomposite Case) Span Increment Distance Long. Composite DL 2D cp /t w 2D cp /t w 2D c /t w 2D c /t w No. No. (ft) Stiffener Stress () (2) (3) (4) (5) (Ksi) 4 36 No No > < No No < < 96.9 () From Table.2.9. &.2 multiplied by factors f = Ksi Check OK f pier = Ksi Check OK (2) AASHTO Eq. ( ) fc' = 4 Ksi Tension D (in.) tw (in.) A slab (in 2 ) A ten (in 2 ) A comp (in 2 )A web (in 2 ) F y (Ksi) A reinf (in2) F yr (Ksi) Dcp (in.) 2D cp /t w Bottom N/A Top N/A Check OK (3) AASHTO Eq. ( ) or Eq. ( a-) 3.76 * sqrt(e/f yc ) = Check OK (4) From Table D c /t 2*(D-(Y b -B t ))/t w = Check OK 2D c /t 2*(Y b -B t )/t w = 6.36 Check OK (5) AASHTO Eq. ( ) 6.77*sqrt(E/f c ) = > 200 Use 200 Check OK Check OK 3

14 Verification of: DASH LRFD Table Bending Capacity for Noncomposite Dead Load Case Span Increment Distance DL M n No. No. (ft) Moment (K-Ft) () (K-Ft) (2) > < () From Table.2.5. &.2 multiplied by factors (2) AASHTO Eq. ( a- or or a-,2,3) From Table Strength Category for max M + is # 3 (Lateral Torsional Buckling) Strength Category =3, and 2D c /t w <= λ b X sqrt(e/f yc ) use Eq. ( a-) From Table A, M n = K-Ft From Table Strength Category for max M- is #0 (compact) AASHTO Appendix A for M p D (in.) tw (in.) A slab (in 2 ) A ten (in 2 ) A comp (in 2 ) A web (in 2 ) F y (Ksi) A reinf (in2) F yr (Ksi) Y (in.) M p (K-Ft) Top t ten (in) t comp (in) t haunch (in) d slab (in) d t (in) d c (in) d reinf (in) t slab (in) d top (in)

15 Verification of: DASH LRFD Table Bending Capacity for Composite Live Load Case Span Increment Distance Compact M+ M- M+ M- Mn No. No. (ft) ID before before after after (K-Ft) () (K-Ft) () (K-Ft) (2) (K-Ft) (2) (K-Ft) (3) 4 36 Compact < Compact > () From Table (2) AASHTO Art Moment redistribution From Table Strength Category for max M - is #0 (Compact), redistribution allowed M - (after) = x 0.9 = Check OK M + (after) = = Check OK (0.4* reduced M - ) (3) From Table Strength Category for max M + or M - is #0 (Compact) AASHTO Appendix A for M p Tension D (in.) tw (in.) A slab (in 2 ) A ten (in 2 ) A comp (in 2 )A web (in 2 ) F y (Ksi) A reinf (in2) F yr (Ksi) Y (in.) M p (K-Ft) Bottom t ten (in) t comp (in) t haunch (in) d slab (in) d t (in) d c (in) d w (in) fc' (Ksi) d reinf (in) t slab (in) d top (in) D (in.) tw (in.) A slab (in 2 ) A ten (in 2 ) A comp (in 2 ) A web (in 2 ) F y (Ksi) A reinf (in2) F yr (Ksi) Y (in.) M p (K-Ft) Top t ten (in) t comp (in) t haunch (in) d slab (in) d t (in) d c (in) d reinf (in) t slab (in) d top (in) From Table C D p / D ' =.28 at.4l (st span) For < D p / D ' <= 5 Use AASHTO Eq a-2 M y = Min (F yt *S t, F yb *S b )= M p = M n = Check OK 5

16 Verification of: DASH LRFD Table LRFD Service II Check Span Increment Distance Section f+ f- f+ f- Allow. No. No. (ft) ID before before after after Stress (Ksi) () (Ksi) () (Ksi) (2) (Ksi) (2) (Ksi) (3) 4 36 Composite < Noncomp > 47.5 () From Table.2.9.5B (2) AASHTO Art Moment redistribution for stress From Table Strength Category for max M - is #0 (Compact), redistribution allowed f - (after) = 53.5 x 0.9 = Check OK f + (after) = = Check OK (0.4* reduced f - ) (3) For Shear connector specified in the negative moment region, allowable stress 0.95Fy is used. 6

17 Verification of: DASH LRFD Table Compression Flange Slenderness Check Span Increment Distance b f t f Dc b f /Dc b f /2t f No. No. () (2) (ft) (in) (in) (in) Satisfy compact () AASHTO Eq. ( ) * sqrt(e/f yc ) = 9.2 Check OK (2) AASHTO Eq. ( ) 2 Check OK 7

18 Verification of: DASH LRFD Table Unbraced Length Check Span Increment Distance I yf A f r t L p No. No. () (2) (ft) (in 4 ) (in 2 ) (in) (ft) () r t = sqrt(i yf /A f )= 3.5 M + region Check OK 4.6 M - region Check OK (2) AASHTO Eq. ( a-5) L p =.76 r t * sqrt(e/f yc ) = 2.24 M + region Check OK 6.3 M - region Check OK 8

19 Verification of: DASH LRFD Table A Bending Capacity Reduction for Unbraced Section Span Increment Distance C b J I yc L r M r M y No. No. () (2) (3) (4) (ft) (in 4 ) (in 4 ) (ft) (K-FT) (K-FT) (DL CASE) (LL CASE) () AASHTO Eq. ( a-4) C b = (P l /P h ) (P l /P h ) <= K b.75 M + region Check OK.44 M - region Check OK.38 M - region Check OK (2) Lr = 4.44 sqrt(i yc *d*e/(s xc *F yc )) = 27.2 M + region Check OK 4.30 M - region Check OK 38.8 M - region Check OK (3) AASHTO Eq. ( a-3) M + region Check OK L b < L p M - region Check OK AASHTO Eq. ( a-) M - region Check OK (4) M y = F y * S 9

20 Verification of: DASH LRFD Table Unstiffened Section Shear Capacity Span Increment Distance D/t w k C V n No. No. () (2) (3) (4) (ft) (KIPS) () k = 5 M + region Check OK 5 M - region Check OK (2).0 sqrt(ek/f yw ) = 59.2 M + region Check OK 59.2 M - region Check OK (3).38 sqrt(ek/f yw ) = 74.3 M + region Check OK 74.3 M + region Check OK (4) If D / t w >.38 sqrt(ek/f yw ), then C =.52 (Ek/F yw )/(D/t w ) 2 = 0.65 M + region Check OK If.0 sqrt(ek/f yw ) <= D/t w <=.38 sqrt(ek/f yw ), then C =.0 sqrt(ek/f yw )/(D/t w ) = M + region Check OK V n = CV p = C (0.58 F yw D t w ) = M + region Check OK M + region Check OK 20

21 IV. LFD Verifications. LFD moments and the graph Span No Increm No Dist from Left DL DL2 LL+ LL- LL Range Total + Total - (ft) (k-ft) (k-ft) (k-ft) (k-ft) (k-ft) (k-ft) (k-ft) LFD Moment 6000 MOment Panel Pt DL DL2 LL+ LL- LL Range Total + Total Panel Pt 2

22 2. LFD shears and the graph Span No Increm No Dist from Left DL DL2 LL+ LL- LL Range Total + Total - (ft) (kip) (kip) (kip) (kip) (kip) (kip) (kip) LFD Shear 400 Shear DL DL2 LL+ LL- LL Range Total + Total Panel Pt 22

23 3. Verification of LFD code checks Various tables of the DASH LFD output are verified by hand calculation using Excel. Those are Verification of: DASH LFD Table Depth/Thickness Ratios (N=n, Composite Case) 2 Verification of: DASH LFD Table Bending Capacity for Noncomposite Dead Load Case 3 Verification of: DASH LFD Table Bending Capacity for Composite Live Load Case 4 Verification of: DASH LFD Table Overload Check 5 Verification of: DASH LFD Table Compression Flange Element Check 6 Verification of: DASH LFD Table Unbraced Length Check 7 Verification of: DASH lffd Table A Bending Capacity Reduction for Unbraced Section 8 Verification of: DASH LFD Table Unstiffened Section Shear Capacity 23

24 Verification of: DASH LFD Table Depth/Thickness Ratios (N=n, Composite Case) Span Increment Distance Long. Composite D / t w Eq Eq.0-04 Eq No. No. (ft) Stiffener () 4 36 No Yes No Yes Satisfy compact D / t w = at.4l Check OK at pier 72 Check OK AASHTO Eq. (0-94) 9230/sqrt(F y ) = Check OK () AASHTO b 50 Check OK AASHTO Eq. (0-04) 36500/sqrt(F y ) = AASHTO Eq. (0-09) 73000/sqrt(F y ) = Check OK Check OK 24

25 Verification of: DASH LFD Table Bending Capacity for Noncomposite Dead Load Case Span Increment Distance DL M n No. No. (ft) Moment (K-Ft) () (K-Ft) (2) < < () From Table.2.5. (2) AASHTO Eqs. (0-03c-g) From Table Strength Category for max M + is # 3 (Lateral Torsional Buckling) Strength Category =3, and D c / t w <= λ / sqrt(f y ) use Eq. (0-03c) From Table A, M n = K-Ft From Table Strength Category for max M- is #0 (compact) LRFD AASHTO Appendix A for M p D (in.) tw (in.) A slab (in 2 ) A ten (in 2 ) A comp (in 2 ) A web (in 2 ) F y (Ksi) A reinf (in2) F yr (Ksi) Y (in.) M p (K-Ft) Top t ten (in) t comp (in) t haunch (in) d slab (in) d t (in) d c (in) d reinf (in) t slab (in) d top (in)

26 Verification of: DASH LFD Table Bending Capacity for Composite Live Load Case Span Increment Distance Compact M+ M- M+ M- Mn No. No. (ft) ID before before after after (K-Ft) () (K-Ft) () (K-Ft) (2) (K-Ft) (2) (K-Ft) (3) 4 36 Compact < Compact < () From Table (2) AASHTO Art Moment redistribution From Table Strength Category for max M - is #0 (Compact), redistribution allowed M - (after) = x 0.9 = Check OK M + (after) = = Check OK (0.4* reduced M - ) (3) From Table Strength Category for max M + or M - is #0 (Compact) LRFD AASHTO Appendix A for M p Tension D (in.) tw (in.) A slab (in 2 ) A ten (in 2 ) A comp (in 2 )A web (in 2 ) F y (Ksi) A reinf (in2) F yr (Ksi) Y (in.) M p (K-Ft) Bottom t ten (in) t comp (in) t haunch (in) d slab (in) d t (in) d c (in) d w (in) fc' (Ksi) d reinf (in) t slab (in) d top (in) D (in.) tw (in.) A slab (in 2 ) A ten (in 2 ) A comp (in 2 ) A web (in 2 ) F y (Ksi) A reinf (in2) F yr (Ksi) Y (in.) M p (K-Ft) Top t ten (in) t comp (in) t haunch (in) d slab (in) d t (in) d c (in) d reinf (in) t slab (in) d top (in) From Table C D p / D ' =.36 at.4l (st span) For < D p / D ' <= 5 Use AASHTO Eq a-2 M y = Min (F yt *S t, F yb *S b )= M p = M n =

27 Verification of: DASH LFD Table Overload Check Span Increment Distance Section f+ f- f+ f- Allow. No. No. (ft) ID before before after after Stress (Ksi) () (Ksi) () (Ksi) (2) (Ksi) (2) (Ksi) (3) 4 36 Composite > Noncomp > 47.5 () Stresses from Table divided by.3 (2) AASHTO Art Moment redistribution for stress From Table Strength Category for max M - is #0 (Compact), redistribution allowed f - (after) = x 0.9 = Check OK f + (after) = = Check OK (0.4* reduced f - ) (3) For Shear connector specified in the negative moment region, allowable stress 0.95Fy is used. 27

28 Verification of: DASH LFD Table Compression Flange Element Check Span Increment Distance b t b/t Eq Eq Eq No. No. (ft) (in) (in) Satisfy compact AASHTO Eq. (0-93) 40 / sqrt(f y ) = Check OK AASHTO Eq. (0-00) 24 Check OK AASHTO Eq. (0-74) 4400 / sqrt(f dl ) = 28 > 24 use 24 Check OK 28

29 Verification of: DASH LFD Table Unbraced Length Check Span Increment Distance A f L b Eq. 0-0 No. No. (ft) (in 2 ) (ft) (ft) AASHTO Eq. (0-0) L b <= A f / F y d = M + region Check OK M - region Check OK 29

30 Verification of: DASH lffd Table A Bending Capacity Reduction for Unbraced Section Span Increment Distance C b J S xc L r L b L p M r M y No. No. () (2) (3) (4) (ft) (in 4 ) (in 3 ) (ft) (ft) (ft) (K-FT) (K-FT) (DL CASE) (LL CASE) () C b = (P l /P h ) (P l /P h ) <= M + region Check OK.44 M - region Check OK.36 M - region Check OK (2) Lr = sqrt(572* 0 6 * I yc *d*/(s xc *F y )) = 27.2 M + region Check OK M - region Check OK 38.8 M - region Check OK (3) AASHTO Eq. (0-03c) M + region Check OK For L b <= L p, M r = M y M - region Check OK For L b <= L p, M r = M y M - region Check OK (4) M y = F y * S 30

31 Verification of: DASH LFD Table Unstiffened Section Shear Capacity Span Increment Distance D/t w k C V u No. No. () (2) (3) (4) (ft) (KIPS) () k = 5 M + region Check OK 5 M - region Check OK (2) 6000 sqrt(k/f y ) = 60 M + region Check OK 60 M - region Check OK (3) 7500 sqrt(k/f y ) = 75 M + region Check OK 75 M + region Check OK (4) If D / t w > 7500 sqrt(k/f y ), then C = 4.5E0 7 * k / F y / (D/t w ) 2 = M + region Check OK If 6000 sqrt(k/f y ) <= D/t w <= 7500 sqrt(k/f y ), then C = 6000 sqrt(k/f y ) / (D/t w ) = M + region Check OK Eq. (0-3) V u = CV p = C (0.58 F y D t w ) = M + region Check OK M + region Check OK 3

32 Appendix A LRFD output AISC Four LRFD Design Examples of Steel Highway Bridges, U.S. Unit Example: Two-Span Continuous Composite I Girder

33 INPUT PAGE INPUT PAGE 2 TABLE PROJECT DATA ************ TABLE STRUCTURAL DETAILS ****************** DESCRIPTION DATE TWO SPAN CONTINUOUS COMPOSITE I GIRDER CONTRACT NUMBER STR NO STR UNIT DES CHK SPECS. USED BY- -BY BEAM WIDTH EDGE OF COMPOSITE STEEL POSITION BETWEEN OVERHANG SLAB TO HAUNCH PERCENTAGE LOAD NUMBER CURBS OR WIDTH CURB AT NEG MOM DETAIL OF =INT. BARRIER DEPTH WIDTH. REGION FACTOR GIRDERS 2=EXT. (ft) (ft) (ft) (in) (in) (%) >= TABLE GENERAL PROGRAM OPTIONS *********************** OUTPUT SPAN CONSTRUCTION CODE PROGRAM LEVEL INTERVAL FLOW (0,) (MAX=20) = COMPOSITE CODE YEAR UNIT DESIGN CONTROL 2= NONCOMP. ID TYPE OPTION * WIDTH BETWEEN CURBS OR BARRIERS (ROAD WIDTH) is used for the determination of traffic lanes * The section properties with composite percentage at negative moment region is calculated by using the linear interpolation between the noncomposite section (N=Inf.) and 00% composite for the analysis at negative moment region. * DETAIL FACTOR is used for the steel dead load only 0 AASHTO * output level : 0 = basic output = detailed output * span interval : maximum = 20 default = 0 TABLE SPAN LENGTHS --- in feet ************************ SPAN- SPAN-2 SPAN-3 SPAN-4 SPAN-5 SPAN-6 SPAN-7 SPAN-8 SPAN-9 SPAN ,------,------,------,------,------,------,------,------,------, * structural type : = composite (default) 2 = noncomposite 3 = reinforced concrete 4 = prestressed concrete TABLE BEAM SPACING --- in feet ************************ * type of unit : 0 = English (default) = Metric 2 = Metric input English output 3 = English input Metric output SPAN- SPAN-2 SPAN-3 SPAN-4 SPAN-5 SPAN-6 SPAN-7 SPAN-8 SPAN-9 SPAN ,------,------,------,------,------,------,------,------,------, * design option : 0 = WSD (default) = LFD 2 = LRFD * program flow : 0 = DL analysis only = DL + LL analysis 2 = code check 3 = rating 4 = design 5 = design + code check 6 = design + recycle + code check 7 = DL stage only 8 = DL stage + LL INPUT PAGE 3 TABLE DEFINITION OF SECTIONS ********************** ROLLED SECTIONS WITH STANDARD SECTN PLATE GIRDER COVER PLATES OR REINFORCED PLATE GIRDERS... (in) CONCRETE SECTION SECTION NOMINAL WEIGHT WEB WEB DEPTH DEPTH THICK. TOP PLATE BOT. PLATE AREA Ix NO. ID. (in) (lb/ft) (in) WIDTH THICK. WIDTH THICK. (in**2) (in**4) PG PG NOTE: [] maximum allowable section number is 70 2 [2] For design option (flow 4, 5 or 6) this card need not be input

34 INPUT PAGE 4 INPUT PAGE 6 TABLE DEFINITION OF MEMBERS ********************* TABLE SLAB LOAD DEFINITION ******************** MEMBER MEMB END MEMBER DESCRIPTN PARAMETERS FOR YIELD STRESS NUMBER SECT ID NONPRISMATIC MEMB (KSI) LNGTH -->TYPE< (IN ORDER) LEFT RIGHT (ft) 0=PRISMAT S(0) S() WEB TOP BOT NOTE: [] maximum allowable member number is 70. [2] For design process (flow 4, 5 or 6) this card need not be input [3] For hybrid section, yield stress defined here will override DATA TYPE 302 for code checking INPUT PAGE 5 TABLE AASHTO LIVE LOADING - LOAD TYPE (A) ************************************ SLAB MODULAR RATIO SLAB LOAD DATA LOAD IDENTIFICATION DESIGN DEPTH POUR DAY N=3n N2=n INTENSITY POSITION LOAD POUR DESCRIPTION INITIAL FINAL FROM TO NO NO (in) (in) N N2 (k/ft) (ft) (ft) DECK SLAB AASHTO Art or LRFD Art b The ratio of the moduli of elasticity of steel (29000 ksi) to those of normal weight concrete (W=45 pcf) of various design strength shall be as follows: fc' = unit ultimate compressive strength of concrete as determined by cylinder tests at the age of 28 days in pounds per square inch. n = ratio of modulus of elasticity of steel to that of concrete. INPUT PAGE 7 AASHTO LOADING TANDEM LIVE LOAD AASHTO ROAD TYPE SIDEWALK ,2,3 OR LIVE LOAD--- HL - 93 =YES : 0=NO ADTT (k/ft) HL HL-93 VEHICLE X FACTOR OF NOTE: * Road types, 2, 3 and 4 are used for fatigue check. * Road type is Rural Interstate. 2 is Urban Interstate. 3 is Other Rural. 4 is Other Urban. truck on the bridge distributed to the girders as designated in AASHTO LRFD Art for one traffic lane loading. For Fatigue, Fraction of Truck, p, is based on the Road Types. Ref. AASHTO LRFD Table C * Default road type = * Sidewalk live loading is assumed taken by exterior girder only * HL-93 is for both truck + lane and tandem + lane loading, TABLE DEFINITION OF UNIFORM AND CONCENTRATED LOADS ******************************************** LOAD IDENTIFICATION UNIFROM LOAD DATA CONCENTRATED LOAD DATA LOAD DESCRIPTION INTENSITY POSITION INTENSITY DISTANCE NO. TYPE FROM TO FROM L SUPT (k/ft) (ft) (Kips) (ft) HAUNCH STAY IN PLAC FUTURE WS BARRIER NOTE: LOAD TYPE, 0 = (Default) Loads for noncomposite construction or Superimposed Loads for composite construction (In LRFD, it is for DW load) = Superimposed Loads (In LRFD, it is for DC2 load) 2 = Noncomposite Loads,(In LRFD, it is for DC load) where N = modulus ratio = Es/Ec 3

35 INPUT PAGE 8 INPUT PAGE 9 TABLE SHEAR CONNECTOR AND SLAB REINFORCEMENT DATA ******************************************* SHEAR CONNECTOR Qn VALUE Zr VALUE SLAB REINFORCEMENT CONCRETE CONNECTOR AASHTO ART. AASHTO ART. REBAR BAR AREA DIST. COMP. COMP. NO. DIA.IN NEGAT YIELD PER FOOT FROM STRENG. ALLOW PER M. REGION (kip / per STRESS OF SLAB TOP AT 28 -ABLE TRAN. 0=NO (kip / per connector) Fy DAYS SEC (in) =YES connect.) Truck Lane (ksi) (in**2) (in) (ksi) (ksi) TABLE DESIGN OPTION () ---- DESIGN METHOD & STIFFENER OPTION ******************************** TRANSVERSE AND LONGITUDINAL STIFFENER OPTION SECTION ID. DESIGN METHOD TRANSVERSE/LONGITUDINAL BEARING STIFFENER ,4=PLATE GIRDER 0=MIN. WEIGHT 0 = DO NOT USE 0= A709-36, = -50,2=WIDE FLANGE =MIN. COST = USE IF NECESSARY 2= BEST OF 0, 3= -50W NOTE: Qr = nominal resistance of the shear connector = (phi)sc x Qn... see AASHTO LRFD Eqs ,4.3- or NOTE: Design method: 0 = minimum weight objective function = cross-sectional area = minimum cost objective function = cost function Zr = shear fatigue resistance of an individual shear connector... see AASHTO LRFD Eqs & -2 fc' = unit ultimate compressive strength of concrete as determined by cylinder test at the age of 28 days = 4 ksi (default) fc = allowable compressive strength of concrete = 0.85fc' (default) * default number of shear connector per trans. section = 3 * If the shear connectors and slab reinforcements are supplied in the negative moment region, the contribution of rebar on the section properties in the negative moment region (for N = 3n & N = n) will be considered. Section ID : 0 = Plate Girder design with constant flange only in the pos. mom. area = Wide Flange compact design 2 = Wide Flange braced noncompact design 3 = Plate Girder design with constant flange across ** All supports are assumed to have bearing stiffener regardless the stiffener option INPUT PAGE 0 DESIGN OPTION (4) ---- MATERIAL AND FABRICATION COST ---- (2072) ***************************** * If Zr left blank, Road type input in Data 0602 and 7/8"-diameter studs are assumed * default rebar yield stress = 60 ksi MATERIAL COST FABRICATION COST M A T E R I A L S EXTRAS UNIT UNIT BASE (SIZE/WIDTH) PRICE ADJUSTMENT PRICE ASTM Fy PRICE ADJUSTMENT ID. DESINATION (ksi) ($/lb) (%) ($/lb) (%) ($/lb) A NOTE: [] ASTM = American Society for Testing and Materials [2] ASTM DESINATION... A-36, A-572, or A-588 [3] If the cost data are not input, all the built-in cost data will be used for the design processes [4] The default material is ASTM A-36 (Fy = 36 ksi). The maximum no. of allowable materials is 3. [5] Without inputing 2082, field splice location will be determined by the program according to contra-flexure points, and the first material property listed here will be used along the whole bridge 4

36 INPUT PAGE F A C T O R S U S E D B Y L R F D GAMMA for Load DC maximum =.25 4 GAMMA for Load DC minimum = 0.90 TABLE YIELD STRESS (Fy) AND LATERAL BRACING DATA (lb) *********************************************** 5 GAMMA for Load DW minimum =.50 6 GAMMA for Load DW minimum = 0.65 L O C A T I O N YIELD SPACING STRESS OF LATERAL BRACING DISTANCE DISTANCE FROM TO Fy Fy (WEB) Lb (ft) (ft) (ksi) (ksi) (ft) GAMMA for LL Load Strength I =.75 8 GAMMA for LL Load Strength II =.35 9 GAMMA for LL Load Service I = GAMMA for LL Load Service II = GAMMA for LL Load Fatigue = ETA for Service Limit State = ETA for Strength Limit State = NOTE: [] default Fy = 36 ksi [2] default spacing of lateral bracing = 25 feet Please refer to AASHTO LRFD Art for requirement. [3] The spacing of lateral bracing is also assumed to be the diaphragm spacing which is used for the calculation of wind effect (code check only). PAGE 2 TABLE.2..=PROGRAM ASSUMPTIONS ******************* PAGE 3 TABLE.2.2.=LOADING INFORMATION ******************* AVERAGE DEAD LOAD INTENSITIES ***************************** SPAN SLAB + STEEL = TOTAL NO. (K/FT) (K/FT) (K/FT) NO. D E S C R I P T I O N S Small deflection theory 2 Material is elastic 3 Beam length is much greater than lateral dimensions 4 Torsional effects are neglected SUPERIMPOSED DEAD LOADS *********************** 5 Shear deformations are neglected 6 Two kinematic degree-of-freedom are assumed 'at each joint (vertical deflection and bending rotation) 7 Concentrated joint loads 8 Uniform member loads 9 Transformed sections are used for composite sections... see AASHTO Art or LRFD Art b 0 Sections symmetrical about vertical, principal axis LOAD INTENSITY DIST DIST FROM TO (K or K/Ft) (Ft) (Ft) DW DC Unshored construction 2 Hinged bridge ends

37 PAGE 4 TABLE..3.=BRIDGE SUPERSTRUCTURE QUANTITIES ******************************** C O N C R E T E D E C K S T E E L SUPERSTRUCTURE TOTAL WEIGHT V O L U M E TOTAL TOTAL UNIT WEIGHT WEIGHT WEIGHT (kip) (pcf) (ft**3) (yard**3) (kip) (kip) NOTE: [] Concrete unit weight assumed to be 50 lb/ft**3 [2] Superimposed dead load not included [3] Dead load detail factor for steel beam =.05 is included. PAGE 5 TABLE..3.2=DISTRIBUTION OF LRFD LIVE LOADS ******************************** SPAN AASHTO DUMP MAXIMUM SPECIAL NO. LOADING TRUCK TRUCK TRUCK (A) (D) (M) (G,C) FOR STRENGTH POSITIVE MOMENT FOR STRENGTH POSITIVE SHEAR FOR STRENGTH NEGATIVE MOMENT FOR STRENGTH NEGATIVE SHEAR FOR FATIGUE POSITIVE MOMENT FOR FATIGUE POSITIVE SHEAR FOR FATIGUE NEGATIVE MOMENT FOR FATIGUE NEGATIVE SHEAR FOR STRENGTH POSITIVE MOMENT FOR STRENGTH POSITIVE SHEAR FOR FATIGUE POSITIVE MOMENT FOR FATIGUE POSITIVE SHEAR PAGE 6 TABLE.2.4.=NONCOMPOSITE SECTION PROPERTIES FOR N=INFINITY ********************************************** MOMENT OF WEB LOCATION OF N.A. ELASTIC SECTION MODULUS SP IN D FROM INERTIA DEPTH FROM BOT OF STEEL NO NO L SUPT STEEL (ft) Ix D Y(BS) BOT. TOP. (in**4) (in) (in) (in**3) NOTE: For rolled section, the 5th column is the depth d (inch) 6

38 PAGE 7 PAGE 8 TABLE.2.4.2=COMPOSITE SECTION PROPERTIES FOR N = ****************************************** MOMENT OF Q/Ix ELASTIC SECTION MODULUS,(in**3) SP IN D FROM INERTIA NO NO L SUPT Q=ST. MOMENT STEEL CONCRETE(SLAB) (ft) Ix OF INERTIA (in**4) (/in) BOT. TOP. TOP TABLE.2.4.3=COMPOSITE SECTION PROPERTIES FOR N = 8.00 ****************************************** MOMENT OF Q/Ix ELASTIC SECTION MODULUS,(in**3) SP IN D FROM INERTIA NO NO L SUPT Q=ST. MOMENT STEEL CONCRETE(SLAB) (ft) Ix OF INERTIA (in**4) (/in) BOT. TOP. TOP Please read NOTE on the following page PAGE 9 NOTE [] If the section modulus for the top flange indicates overflows (***), the neutral axis may be very closed to the top of the top flange. [2] The section properties shown in this table are used for the calculation of stresses. 7 [3] AASHTO Art or LRFD Art Composite sections in simple spans and the positive moment regions of continuous spans should preferably be proportioned so that the neutral axis lies below the top surface of the steel beam. Concrete 'on the tension side of the neutral axis shall not be considered in calculating resulting moments. In the negative moment regions of continuous spans, only the slab reinforcement can be considered to act compositely with the steel beams in calculating resisting moments. Mechanical anchorages shall be provided in the composite regions to develop stresses on the plane joining the concrete and the steel. Concrete on the tension side of the neutral axis may be considered in computing moments of inertia for deflections and for determining stiffness factors used in calculating moments and shears

39 PAGE 20 PAGE 2 TABLE.2.5.=NONCOMPOSITE DEAD LOAD MOMENTS FOR N=INFINITY (UNFACTORED) ********************************************* DEAD LOAD TOTAL (k-ft) SP IN D FROM CONCENTRATED UNIFORM NO NO L SUPT BEAM SLAB LOADS LOADS NONCOMPOSITE (ft) (k-ft) (k-ft) (k-ft) (k-ft) DEAD LOAD TABLE.2.5.2=COMPOSITE DEAD LOAD MOMENTS FOR N = (UNFACTORED) ***************************************** UNIFORM OTHER TOTAL (k-ft) SP IN D FROM SUPERIMPOSED CONCENTRATED UNIFORM -- NO NO L SUPT DEAD LOAD LOADS LOADS COMPOSITE (ft) (k-ft) (k-ft) DEAD LOAD DW DC2 DW DC

40 PAGE 22 PAGE 24 TABLE.2.5.3=COMPOSITE LIVE LOAD MOMENTS FOR N = 8.00 (UNFACTORED) ***************************************** SIDEWALK (MAXIMUM) LL+I,(k-ft), LOAD TYPE= HL -93 SP IN D FROM NO NO L SUPT POSITIVE NEGATIVE MAXIMUM GOVERN. MAXIMUM GOVERN. (ft) (k-ft) (k-ft) POSITIVE LOAD TYPE NEGATIVE LOAD TYPE HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL PAGE 23 TABLE.2.5.3A=LIVE LOAD MOMENT RANGE FOR N = 8.0 (k-ft) (UNFACTORED) ****************************************** TABLE.2.5.4=MOMENT SUMMARY FOR COMPOSITE CONSTRUCTION (UNFACTORED) ***************************************** DEAD LOAD LL+I:N= 8.0 LOAD TYPE= HL - 93 TOTAL MAXIMUM SP IN D FROM NON COMP. COMP. MAXIMUM GOVERN MAXIMUM GOVERN POSITIVE NEGATIVE NO NO L SUPT N=Infin. N=24.0 POSITIVE LOAD NEGATIVE LOAD (ft) (k-ft) (k-ft) (k-ft) TYPE (k-ft) TYPE (k-ft) (k-ft) HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL HL SP IN D FROM TRUCK ONLY NO NO L SUPT (ft) POS NEG RANGE