Reinforced Concrete Structures : Design according to CSA A23.3-04

10. Two-Way Slabs: Direct-Design Method

Chapter 10 Two-Way Slabs Direct-Design Method 10.1 Notations Used in This Chapter Ag Gross cross-sectional area Asb Area of shear reinforcement crossing one face of the column and providing structural integrity As,min Minimum area of tension reinforcement required Avs Cross-sectional area of stirrup on a line parallel to the perimeter of the column CAB Distance between the centroidal axis of the critical section and at face AB of the critical section D Diameter of column circular section Ecb Modulus of elasticity of beam concrete Ecs Modulus of elasticity of slab concrete Ib Moment of inertia about centroidal axis of beam Is Moment of inertia about centroidal axis of gross section of slab Jc Property of the critical shear section analogous to the polar moment of inertia 302 Chapter 10 La Short span of slab measured between beam faces Lb Long span of slab measured between beam faces M– Negative moment M+ Positive moment Mf Factored unbalanced moment Mfb Portion of Mf transferred to the column Mfv Portion of Mf assumed by punching shear Mo Total factored moment for isostatic span Vc Shear resistance provided by the concrete Vse Shear force from specified loads Vf Factored shear stress Vr Shear stress resistance a Large side of the support ad Drop-panel dimensions b Small side of the support bb Band width of slab extending a distance of 1.5 hs or 1.5 hd past the sides of the column or column capital bo Perimeter of critical section for punching shear force bw Width of T-section web c1 Length of the side of the column in direction 1 c2 Length of the side of the column in direction 2 d Effective depth of a reinforced-concrete section fy Specified yield strength of steel reinforcement hd Overall depth of drop panel ho Depth of beam under slab hs Overall slab thickness l1 Length of span in direction where moments are being determined, measured centre to centre l2 Transverse span at l1, measured centre to centre l′ 2a Average span of adjacent spans l2 relative to the short span ln Clear span between supports in the long direction l′ n Clear span between supports in the short direction s Spacing of longitudinal or transverse reinforcement, as the case may be vc Shear stress resisted by the concrete alone vs Shear stress resisted by the steel stirrups wDf Factored dead load w′Df Factored dead load for the short span wf Total factored load Two-Way Slabs: Direct-Design Method 303 wLf Factored live load xd Distance from face of column to edge of drop panel α Ratio of moment of inertia of beam section to moment of inertia of a width of slab bounded laterally by centrelines of adjacent panels on each side of the beam α1 α in direction 1 α2 α in direction 2 αm Average value of α for beams bounded by panels β Ratio of a two-way slab’s long span to its short span measured between beam faces (Lb/La) βc Ratio of the long side to the short side of a column or support γv Fraction of moment transferred by eccentric shear λ Factor to account for concrete density (λ = 1 for plain concrete) φc Resistance factor for concrete φs Resistance factor for steel reinforcing bars 10.2 Basis for the Method In the case of two-way slabs not resting on rigid supports, as defined in Chapter 9, the direct-design method can be a wise choice. This method, described in Clause 13.9 of the standard, is a simplified version of the equivalent-frame method. It is based on empirical moments that approximate those obtained using the equivalent-frame method. The direct-design method can be used for two-way slabs: a) supported by beams and b) with or without drop panels, capitals, or both. ■ ■ Principle of the Method The slab system is converted into a frame consisting of a floor and columns above and below the floor. Generally, two frames are considered for each of the two orthogonal directions: a) an exterior frame comprising the column strip and half the middle strip and b) an interior frame comprising the column strip and half the middle strip on both sides of the column strip (see Figure 10.5). The positive and negative moments for each frame along the column and middle strips are determined using the tributary-area method. The reinforcement required...