CIVI_453_-_Chapter_2_-_Design_of_Two-way_slabs_-_pages_1-9

CIVI_453_-_Chapter_2_-_Design_of_Two-way_slabs_-_pages_1-9...

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Unformatted text preview: Chapter 2 1 (c) Dr. Khaled Galal Dept. of BCEE Concordia University CIVI 453 - 2007 DESIGN OF TWO-WAY SLABS CSA A23.3-04 defines three categories of two-way slabs as follows: A1 Flat plates and slabs A2 Two-way slabs with beams B Two-way slabs with stiff supports on four sides CSA A23.3-04, Appendix B Supports are: • Walls • Stiff supporting beams 2 DESIGN OF CATEGORIES A1 AND A2 TWO-WAY 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 two-way 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 center-to-center of supports l 2 = Length of span transverse to l1 , measured center-to-center 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 (two-way slabs), but some details differ. 5 STEP1: SELECT SLAB THICKNESS 13.2.1 hs ≥ 120 (mm) 1. Deflection Criterion: 13.2.2 For regular two-way 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) (13-1) 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 (13-1) 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 (13-2) 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 (13-2), (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 (13-2) 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 (13-3) 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 (13-4) 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 one-way shear: (beam shear); critical section is at d1 from column face b) Case of slabs with beams (category A2): Check one-way 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 two-way 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' (13-5) 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' (13-6) 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 one-way shear: V r = βφ c f c' bw d v (13-7) 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 (13-2) 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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