218
7 Design
bending and a stress block according to Figure 7.2-12. For nonprestressed members z must not be less than 0.9d. For members containing mild steel reinforcement as well as prestressed tendons, the effective shear depth z can be taken as:
significant concentrated loads, or at sections near points of curtailment of reinforcement.
z=
zs2 As + z 2p Ap
(7.3-12) where zs and zp denote the distances between the centreline of the compressive chord and the reinforcement and tendon axes, respectively. zs As + z p Ap
Sections closer to supports than the distance d may be designed for the same shear force as at the control section provided that the member is directly supported. Unless more refined modelling techniques are used to consider loads taken directly to a support through strut or arch action (see subsection 7.3.6), the following rules apply: –– the contribution of point loads applied within a distance of d < av ≤ 2d from the face of the support to the design shear force VEd may be reduced by the factor:
β = av (2d ) (7.3-13) Figure 7.3-6: Definition of control section for sectional design
The effect of redistribution of internal forces in slabs with concentrated loads can result in higher shear capacities when compared to one-way slabs or beams subjected to uniformly distributed loading. This effect may be accounted for by assuming a uniform distribution of the shear force along a control width bw, as shown in Figure 7.3-7.
–– in the case of point loads applied as close as av < d from the face of the support, the design shear force VEd must be calculated with b = 0.5 as if the load was applied at av = d. Where a concentrated load is applied to a slab near a support line, its capacity must be checked for punching at the control perimeter around the loaded area, as described in subsection 7.3.5, and for shear at a control section taken parallel to the line of the support, as defined in Figure 7.3-7. The control section is taken at the lesser of the distances equal to d and av/2 from the face of the support. The load distribution angle must be taken as a = 45° for the case of clamped edges and a = 60° for simply supported edges.
Figure 7.3-7: Location and length of the control section, bw, for the determination of the shear resistance of slabs with point loads located near a support-line; (b) simple edge support; (c) clamped edge support
For determining VEd, the shear force from the sectional analysis V Ed0 may be reduced by favourable contributions resulting from any inclined tension chords (VEtd), compression chords (VEcd) and prestressing tendons (V Epd) – see Figure 7.3-8. In determining V Epd, an eventual reduction in prestress due to the development length must be considered. Any unfavourable contributions from inclined chord and prestressing tendon forces must be added to VEd0. Figure 7.3-8: Contributions of inclined chord forces to design shear force (M Ed0 , VEd0 and N Ed0 denote bending moment, shear and normal forces resulting from sectional analysis)
fib_MC_CS6.indb 218
11.09.2013 10:42:48