Answer Happy

A reinforced concrete slab as shown in Figure 2(a) has fixed supports along AH, GH and FG. It is also simply supported along AB and EF. A uniform area load of q acts on the slab. The figure also indicates the pattern of plastic yield lines that represents one of the possible failure cases for the slab. The positions of some of the yield lines are defined by the value of a that measures from G, as shown in the figure. (a) Derive expressions for the total external work done by the load q and the total internal energy absorbed by the slab. Assume the following parameters in the analysis: m: unit ultimate bending moment in sagging that induces longitudinal stresses in the x direction m': unit ultimate bending moment in hogging that induces longitudinal stresses in the x direction um: unit ultimate bending moment in sagging that induces longitudinal stresses in the y direction um': unit ultimate bending moment in hogging that induces longitudinal stresses in the y direction If μ = 1 and m' = 1.2m, derive the expression for q/m. If q = 15 kN/m², find the maximum value for m. The same slab has been revised to have support conditions as shown in Figure 2(b), where only GH is fixed. Besides, there are square columns located near to A and F acting as supports. Sketch one possible yield line pattern for the slab. Comment briefly on whether shear will potentially control the slab failure, and how this should be considered in design. No calculation is needed to answer this. 0.5 2.5 1.0 2.5 0.5 ** 2.0 1.0 2.0 *10* um B E C D C D "um" All dimensions in metre All dimensions in metre (a) (b) 1.0 4.0 (b) (c) (d) H X a m m 0.5 4.5 U G