CANADIAN CODE IMPLEMENTATION IN 1 ADAPT SOFTWARE

Transcription

1 Structural Concrete Software System TN4_Canadian_Code_implementation CNDIN CODE IMPLEMENTTION IN DPT SOFTWRE This details the implementation of the Canadian Code (CS ) in the Builder Platform programs. The implementation follows the Canadian Code s procedure of calculating a Demand, referred to as design value for each design section, and a Resistance, for the same section, referred to as design capacity. Design value and design capacity are generic terms that apply to displacements as well as actions. For each loading condition, or instance defined in Canadian Code, the design is achieved by making the resistance exceed the associated demand Design Value. Where necessary, reinforcement is added to meet this condition. The implementation is broken down into the following steps: Serviceability limit state Strength limit state Initial condition (transfer of prestressing) Reinforcement requirement and detailing In each instance, the design consists of one or more of the following checks: Bending of section o With or without prestressing Punching shear (two-way shear) Beam shear (one-way shear) Minimum reinforcement In the following, the values in square brackets [ ] are defaults of the program. They can be changed by the user. REFERENCES. CS MTERIL ND MTERIL FCTORS Concrete Cylinder strength at 8 days, as specified by the user f ck characteristic compressive cylinder strength at 8 days; Bilinear stress/strain curve with the horizontal branch at 0.9f c and maximum strain at Strain at limit of proportionality is not defined. Copyright 006 CS Section 0..3 & info@adaptsoft.com Woodside Road, Suite 0, Redwood City, California, 9406, US, Tel: (650) Fax (650)

2 σ 0.9f c E c ε ο ε Modulus of elasticity of concrete is automatically calculated and displayed by the program using f c, γc, and the following relationship 3 of the code. User is given the option to override the code value and specify a user defined substitute. ( c ) Ec 3300 f' γc 300 E c modulus of elasticity at 8 days f c characteristic cylinder strength at 8 days γ c density of concrete [400 kg/m 3 ] Nonprestressed Steel 4 Bilinear stress/strain diagram with the horizontal branch at f y Modulus of elasticity(e s ) is user defined [00000 MPa] No limit has been set for the ultimate strain of the mild steel in the code..5 σ f y MPa f y /E s ε Prestressing Steel bilinear stress-strain curve is assumed. Modulus of elasticity is user defined [90000 MPa] Material Factors Concrete Φ c 0.65 Nonprestressed steel Φ s 0.85 Prestressing steel Φ p CS Section CS Section

3 σ f p 90000MPa f p /E p ε LODING Self-weight determined based on geometry and unit weight of concrete, and other loads are user defined. SERVICEBILITY Load combinations Total load combinations: o.0 DL+.0 LL+.0 PT Sustained load combinations o.0 DL+0.3 LL+.0 PT The above combinations are the default settings of the program. User has the option to change them. Stress checks 5 Code stipulated stress limitations are used as default. However, user can edit the default values. Total load condition: o Concrete Maximum compressive stress 0.60 f c. If calculated stress at any location exceeds the allowable, the program identifies the location graphically on the screen and notes it in its tabular reports. The maximum allowable hypothetical tensile stress: For tensile zone exposed to corrosive environment : 0.5λ f c For others : 0.5λ f c DPT uses 0.50λ f c as its default value. o Nonprestressed Reinforcement None specified no check made o Prestressing steel None specified - no check made 5 CS Section

4 Sustained load condition: o Concrete Maximum compressive stress 0.45 f c. If stress at any location exceeds, the program displays that location with a change in color (or broken lines for black and white display), along with a note on the text output. The maximum allowable hypothetical tensile stress: For tensile zone exposed to corrosive environment : 0.5λ f c For others : 0.50λ f c DPT uses 0.50λ f c as its default value. o Nonprestressed Reinforcement None specified no check made o Prestressing steel None specified - no check made STRENGTH Load combinations 6 o. 4 D +.0 Hyp o (.5 D or 0.9 D)+.5 L + (0.5 S or 0.4 W)+.0 Hyp o (.5 D or 0.9 D)+.5 S + (0.5 L or 0.4 W)+.0 Hyp o (.5 D or 0.9 D)+.4 W + (0.5 L or 0.5 S)+.0 Hyp o.0 D+.0 E L+ 0.5 S +.0 Hyp Check for bending 7 o Plane sections remain plane. Strain compatibility is used to determine the forces on a section. o Maximum concrete strain in compression is limited to o Tensile capacity of the concrete is neglected. o Maximum allowable value for the neutral axis c 8 is determined based on yield strength of the steel f y. 700 c /d < 700+ fy Where necessary, compression reinforcement is added to enforce the above requirement. o If a section is made up of more than one concrete material, the entire section is designed using the concrete properties of lowest strength in that section. o Stress in nonprestressed steel is based on stress-strain relationship assumed o Stress in prestressing steel is calculated as: For bonded tendon, stress is calculated from stress-strain compatibility of the section For unbonded tendon 9 : 6 CS nnex C, Table C. 7 CS Section 0. 8 CS Section CS Section

5 8000 ff p pe+ ( dp cy) f py l0 n Where, f characteristic strength of tendon; p f pe effective prestress after all losses; d p distance from extreme compression fiber to centroid of the tendon; c y distance from extreme compression fiber to neutral axis calculated using factored material strengths and assuming a tendon force of Φ p p f py ; dp cy sum of the distance d p - c y for each of the plastic hinges in the span under n ( ) consideration. o Rectangular concrete stress block with maximum stress equal to α Φ c f c and the depth of stress block from the extreme compression fiber, a, equal to β c is used. α f c 0.67 β f c 0.67 o For flanged sections, the following procedure is adopted: If x u is within the flange, the section is treated as a rectangle If x u exceeds the flange thickness, uniform compression is assumed over the flange. The stem is treated as a rectangular section. o t every section of a flexural member, except post-tensioned two-way floor systems, the following will be satisfied 0 : One-way shear M r.m cr Where, M I y f + f ( ) cr ce r t The design is based on the following: f ce compression stress in the concrete due to effective prestress at the extreme fiber of a section where tensile stresses are caused by applied loads fr 0.6λ f' c V r V f V r V c +V s +V p v r,max v r,max 0.5φ cf'bd c w v + Vp 0 CS Section 8.7 CS Section.3 5

6 V r factored shear resistance; V f factored shear force due to design loads; V c shear resistance attributed to the concrete factored by Φ c ; V s shear resistance provided by shear reinforcement factored by Φ s ; V p component of the effective prestressing force in the direction of the applied shear factored by Φ p. DPT conservatively assumes it as zero; b w width of the web; d v effective shear depth max {0.9d, 0.7h} Design shear strength of concrete, V c : o For beams and one-way slabs: V φλβ f'bd c c c w v Where, β factor accounting for shear resistance of cracked concrete 0.8, if the section contains at least the minimum transverse reinforcement 30, if the section contains no transverse reinforcement 000+ d v f' c ( ) 8 MPa o In the vicinity of corner columns in two-way slabs without beams : Shear is checked along a critical section located at d/ from the column face. vc φλβ c f' c Shear reinforcement, v : If V f > V c + V p or h >750 mm vmin 0.06 f' bs w c y f v Vs s φsy fdcot v θ vmin 3 Where, V s V f - (V c +V p ) s longitudinal spacing of vertical stirrups. f y characteristic strength of the stirrup 400 MPa θ angle of inclination of diagonal compressive stresses to the longitudinal axis of the member 35 0 Maximum spacing of the links, s vmax 4 : CS Section CS Section CS Section.3.8 6

7 Two-way shear s vmax min { 0.70d v, 600 mm} if ( ) s vmax min { 0.35d v, 300 mm} if ( ) o Categorization of columns V φ V < 0.5λφ f'bd f p p c c w v V φ V 0.5λφ f'bd f p p c c w v No criterion is mentioned in CS regarding categorizations of columns for punching shear check. The program uses CI-38 criteria as detailed below. Based on the geometry of the floor slab at the vicinity of a column, each column is categorized into to one of the following options:. Interior column Each face of the column is at least four times the slab thickness away from a slab edge. Edge column One side of the column normal to the axis of the moment is less than four times the slab thickness away from the slab edge 3. Corner column Two adjacent sides of the column are less than four times the slab thickness from slab edges parallel to each 4. End column One side of the column parallel to the axis of the moment is less than four times the slab thickness from a slab edge In cases, 3 and 4, if the slab cantilevers beyond the exterior face of the support, based on the code 5, critical section may be assumed to extend into the cantilevered portion of the slab for a distance not exceeding d. But the program conservatively assumes that the columns are at the slab edge. Hence, the overhang of the slab beyond the face of the column is not included in the calculations. o Design Stress 6 Stress is calculated for several critical perimeters around the columns based on the combination of the direct shear and moment: v f Vf γ Mf e γ Mf c + + J J x y Where V f is the absolute value of the direct shear and M f is the absolute value of the unbalanced column moment about the center of geometry of the critical section. e is the distance of the point of interest to the center of the critical section, is the area of the 5 CS Section CS Section

8 critical section, γ is the ratio of the moment transferred by shear and J is the property of assumed critical section analogous to polar moment of inertia. The implementation of the above in DPT is extended with the option of allowing the user to consider the contribution of the moments separately. For a critical section with dimension of b and b and effective depth of d,, I, c, γ and M f are:. Interior column: b + b d b ( ) c 3 3 bd db b bd I γ b + 3 b M f abs Mf,direct. Edge column: (b is parallel to the axis of moment) ( ) b + b d b d c b d+ bd 3 3 bd db b I + + b d c bdc γ b + 3 b Mf abs Mf,direct V( f c) 3. Corner Column: ( ) b + b d b c b + b b 3 3 bd db b I + + bd c bdc + γ b + 3 b 8

9 Mf abs Mf,direct V( f c) b 4. End column: (b is parallel to the axis of moment) ( ) b + b d b c 3 3 bd db I + + bdc γ b + 3 b M u abs Mu,direct o llowable Stress For non-prestressed member, and prestressed member where columns are less than 4h s from a slab edge 7 : d b ( α s + 0.9) λφc fc 0 vc min ( + )0.9λφc fc βc 0.38λφc fc β c ratio of long side to short side of the column; α s 4 for interior columns, 3 for edge columns, and for corner columns. f c 8 MPa If d> 300 mm, v c will be multiplied by 300/ (300+d) For prestressed member where columns are more than 4h s from a slab edge 8 : φpcp f βλφ + + vc p c f' c 0.33λφc f' c v p bd 0 β p the smaller of 0.33 or( α sdb0+ 0.5) α s 4 for interior columns, 3 for edge columns, and for corner columns b 0 the perimeter of the critical section f cp the average value of f cp for the two directions 3.5 MPa 7 CS Section CS Section

10 V p the factored vertical component of all prestress forces crossing the critical section. DPT conservatively assumes it as zero. f c 35 MPa o Critical sections 9 The closest critical section to check the stresses is d/ from the face of the column where d is the effective depth of the slab/drop cap. Subsequent sections are 0.5d away from the previous critical section. If drop cap exists, stresses are also checked at 0.5d from the face of the drop cap in which d is the effective depth of the slab. Subsequent sections are 0.5d away from the previous critical section. o Stress check Stresses are calculated by combining the stresses in two directions and compared against the allowable stress. User has the option to consider the contribution of stress in each direction separately. If v f < v c If v f > v max If v max > v f > v c no punching shear reinforcement is required punching stress is excessive; revise the section provide punching shear reinforcement v max maximum allowable shear stress for a critical section including the contribution of shear reinforcement 0.75λφ f' For headed shear reinforcement 0 c c 0.55λφ c f' c For stirrup reinforcement Stress check is performed until no shear reinforcement is needed. Where drop caps exist, stresses are checked within the drop cap until the design stress is less than the permissible, then in a similar manner the stresses are checked outside the drop cap. If the shear reinforcement is required, then the layer outside the last layer of reinforcement will be checked against 0.9λφ c f' c o Shear reinforcement Where needed, shear reinforcement is provided according to the following : vs ( v -v ) f φ f c 0 s y bs v c 0.8λφ c f' c for headed shear reinforcement 3 9 CS Section CS Section CS Section CS Section

11 0.9λφ c f' c for stirrup reinforcement 4 Where v f is the maximum shear stress calculated based on the direct shear and moments in both directions using the equations shown earlier. If required, shear reinforcement will be extended to the section where v f is not greater than 0.9λ*Φ c * f c, but at least a distance d from the face of the column. o rrangement of shear reinforcements Shear reinforcement can be in the form of shear studs (headed shear) or shear stirrups (links). In case of shear links, the number of shear links (N shear_links ) in a critical section and distance between the links (Dist shear_links ) are given by: N shear_links Dist shear_links N vs shear _link b 0 shear_links The first layer of stirrups is provided at d/4 from the column face and the successive layers are at d/ from the previous layer. If shear studs are used, the number of shear studs per rail (N shear_studs ) and the distance between the studs (Dist shear_studs ) are given by: N shear_studs Dist INITIL CONDITION Load combinations shear _studs vs shear _stud N d slab N shear _studs rails CS does not specify a load combination for the initial condition. DPT uses the following default values. User can modify these values..0 DL +.5 PT llowable stresses 5 i. Tension: t ends of simply supported members: 0.5λ f ci ll others : 0.5λ f ci 3 CS Section CS Section CS Section 8.3..

12 The latter option is coded in DPT as default. ii. Compression : 0.6f ci If the tensile stress exceeds the threshold, program adds rebar in the tensile zone based on the following relationship: Nc s 0.5fy Nc tensile force in the concrete computed on the basis of uncracked section. Reinforcement Reinforcement will be provided for initial condition if tensile stress exceeds allowable stress. Rebar is provided based on CI code and will be placed on tension side: st/(0.5fy) Where: s: rea of reinforcement T: total tensile force on tension block Fy: Yield Stress of the steel but not more that 60 ksi DETILING Reinforcement requirement and placing Non-prestressed member Minimum tension rebar Beam 6 : smin 0. f'bh c t f y b t width of the tension zone of the section considered For T-beam with flange in tension, b t.5b w For L-beam with flange in tension, b t.5b w For flanged beams where flanges are in tension, minimum reinforcement over an overhanging flange equals times area of the overhanging flange. Minimum rebar requirement will be waived if M r >M f /3 Slab 7 : Prestressed member 8 smin 0.00 g s max min (5h, 500mm) 6 CS Section CS Section 7.8.

13 Minimum reinforcement for beams and slabs with bonded and unbonded tendons are based on Table 8.. PPENDIX This appendix includes additional information directly relevant to the design of concrete structures, but not of a type to be included in the program. Effective width of the flange 9 Effective flange width is not included in DPT_Floor Pro, because it is implicit in the finite element analysis of Floor Pro. But this is included in DPT_PT and calculated as follows: i. For T-Beams Effective overhanging flange width on each side is the smallest of: a. /5 th of the span length for a simply supported beam; b. /0 th of the span length for a continuous beam; c. times the flange thickness; d. ½ of the clear distance to the next web. ii. For L-Beams Effective overhanging flange width on each side is the smallest of: a. / th of the span length of the beam; b. 6 times the flange thickness; c. ½ of the clear distance to the next web. NLYSIS o rrangement of loads: Continuous beams and one-way slabs 30 : factored dead load on all spans with factored partition and live load on two adjacent spans; factored dead load on all spans with factored partition and live load on alternate spans; and factored dead and live load on all spans. Two-way slabs 3 : If the ratio of live over dead load exceeds 0.75, live load is skipped as in the following combination: factored dead load on all spans with 3/4 th of the full factored live load on the panel and on alternate panels; and factored dead load on all spans with 3/4 th of the factored live load on adjacent panels only. 8 CS Section CS Section & CS Section CS Section

14 Redistribution of moment 3 Percentage of redistribution (30-50c/d) % 0% c depth of neutral axis, and d effective depth Deflection Maximum permissible computed deflections are based on Table NOTTION t area of concrete in tension zone; D E f ck f p f cp f y h I L M r S s v v f v c W x u dead load; earthquake load; characteristic compressive cube strength at 8 days; characteristic tensile strength of prestressing steel [860 MPa]; average compressive stress in concrete due to effective prestress only; characteristic yield strength of steel, [460 MPa]; overall depth of the beam/ slab; moment of inertia of section about centroidal axis; live load; factored moment resistance; snow load; spacing of the stirrups; design shear stress; concrete shear strength; wind load; depth of neutral axis; and 3 CS Section CS Section

15 λ factor to account for low-density concrete;.0 for normal density; 0.85 for semi-low density; 0.75 for low-density 5