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(c) Dr. Khaled Galal Dept. of BCEE Concordia University CIVI 453  2007 DESIGN OF TWOWAY SLABS
CSA A23.304 defines three categories of twoway slabs as follows: A1 Flat plates and slabs A2 Twoway slabs with beams B Twoway slabs with stiff supports on four sides CSA A23.304, Appendix B Supports are: • Walls • Stiff supporting beams 2 DESIGN OF CATEGORIES A1 AND A2 TWOWAY SLABS
General: 1. Design Procedures for Flexure 13.5.1 13.5.4 Any procedures satisfying equilibrium and compatibility Gravity load analysis combined with lateral load results Four selected methods are: 13.6 Elastic plate theory 13.7 Theorems of plasticity 13.8 Slab systems as elastic frames 13.9 Direct design method (default or normal method): • Gravity loads only • Regular system with certain limitations 3 DIRECT DESIGN METHID  LIMITATIONS
1. Regular twoway slabs are defined in (13.1) as follows: • Ratio of longer to shorter panel lengths (CL. to CL.) not greater than 2 • For category A2 (slab with beams): α 1.l22 ≤ 5 .0 0 .2 ≤ α 2 .l22
α = Ratio of moment of inertia of beam section to moment of inertia of a width of slab bounded laterally by centerlines of adjacent panels (if any) on each side of the beam = I b / I S α 1 = α in direction of l1 α 2 = α in direction of l 2 l1 = Length of span in direction that moments are being determined, measured centertocenter of supports l 2 = Length of span transverse to l1 , measured centertocenter of supports 2. Minimum of 3 continuous spans in each direction (13.9.1.2) 3. Successive span lengths (CL. to CL.) do not differ by more than 1/3 of the longer span (13.9.1.3) 4. All loads due to gravity and uniformly distributed over an entire panel should satisfy (13.9.1.4): α D .wL ≤ 2α D .wD 4 DESIGN STEPS
Step1: Select slab thickness Step2: Moment (Flexural) design Step3: Select slab reinforcement Step4: Check shear Capacity Note: Same general design procedure for categories A1 and A2 (twoway slabs), but some details differ. 5 STEP1: SELECT SLAB THICKNESS
13.2.1 hs ≥ 120 (mm) 1. Deflection Criterion: 13.2.2 For regular twoway slabs, do not need to calculate deflections if slab thickness meets requirements in sections 13.2.3, 13.2.4, and 13.2.5: 13.2.3 Slabs without drop panels The minimum thickness of flat plates and slabs with column capitals shall be:
hs ≥ l n (0.6 + f y / 1000) 30 ( l n = The longer clear span) (131) At discontinuous edges, an edge beam shall be provided with a stiffness ratio, α , of not less than 0.80 or the thickness required by equation (131) shall be multiplied by 1.1 in the panel with the discontinuous edge. 13.2.4 Slabs with drop panels The minimum thickness of slabs with drop panels shall be:
hs ≥ l n (0.6 + f y / 1000) 30 − 2X d ∆h ln (132) where l n is the longer clear span and ∆ h is the additional thickness of the drop panel below the soffit of the slab and shall not be taken larger than hs . In equation (132), (2 X d / l n ) is the smaller of the values determined in the two directions and X d shall not be greater than ( l n /4). At discontinuous edges, an edge beam shall be provided with a stiffness ratio, α , of not less than 0.80 or the thickness required by equation (132) shall be multiplied by 1.1 in the panel with the discontinuous edge or edges. 6 13.2.5 Slabs with beams between all supports The minimum thickness, hs , shall be:
hs ≥ l n (0.6 + f y / 1000) 30 + 4 βα m (133) Where l n is the longer clear span, α m shall not be greater than 2.0, and the value α may be determined by taking I b equal to:
Ib = bw h 3 h [2.5(1 − s )] h 12 (134) β = ratio of clear spans in long to short directions α m = average value of α for beams on the four sides of a panel l n is clear span = ∑ α i / 4 where; α = where; I s =
E b .I b E s .I s the longer hs3 × (width of slab ⊥ to the considered beam) 12 7 2. Preliminary shear check criterion: To check if the determined hs is sufficient to develop shear resistance without shear reinforcement, or not. (Shear reinforcement can be used for thick slabs, i.e. hs > 300 mm, but is not recommended for thinner slabs) Critical sections for shear: a) Case of slabs without beams (category A1): • Check punching shear: rectangular perimeter around column ( face) or drop panel (
d2 from drop panel face) 2
d1 from column 2 8 • check oneway shear: (beam shear); critical section is at d1 from column face b) Case of slabs with beams (category A2): Check oneway shear (beam shear): critical section is at d v from beam edge, where d v is equal to bigger value of 0.9d or 0.76hs 9 13.3.4 Maximum shear stress resistance of a slab without shear reinforcement For twoway shear: 13.3.4.1 The factored shear stress resistance, v r , shall be the smallest of: (a) v r = vc = (1 +
2 βc )0.19λφ c f c' (135) where: β c = the ratio of long side to short side of the column (b) v r = vc = (
αsd
bo + 0.19)λφ c f c' (136) where: α s = 4 for interior columns, 3 for edge col., and 2 for corner col. (c) v r = vc = 0.38λφ c f c' For oneway shear:
V r = βφ c f c' bw d v (137) where; β = 0.21 and bw = 1000 mm If vr ≥ v f then proceed to step 2 in the design For category A1: if v r < v f then drop panel is needed Size and thickness will be determined by trial and error; must also check for minimum thickness:
hs ≥ l n (0.6 + f y / 1000) − 30 2X d ∆h ln (132) For category A2: if Vr < V f then need to increase slab thickness Note:
If considering shear reinforcement, there is an upper limit to v f as follows: 13.3.9.2 When stirrups are provided, the factored shear stress, v f , shall not be greater than 0.55λφ c f c' 13.3.8.2 When headed shear reinforcement is provided, the factored shear stress, v f , shall not be greater than 0.75λφ c f c' ...
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 Winter '07
 DrGala

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