Question $3$

Yield Line Analysis

$20$ marks

Figure Q$3$ shows a beam and slab layout of a concrete floor composed of four slabs. The slabs are $225$ mm thick and the characteristic variable action $($imposed load$)$ is $q_k=3k\frac{N}{m^2}.$ The density of concrete is $25k\frac{N}{m^3}.$ The whole floor is reinforced uniformly and isotropically with equal hogging and sagging moments of resistance.

a$)$ Sketch the yield line patterns for the individual slabs in Figure Q$4,$ showing positive and negative yield lines.

$[4$ marks$]$

b$)$ Determine the minimum required plastic moment of resistance, $m_p,$ for the floor.

$[10$ marks$]$

c$)$ Calculate the area of reinforcement per metre in the slab, taking $m_p=A_{s}0\mathrm{.}9h{f}_p,$ where $A_s$ in the area of reinforcement per metre, $h$ is the depth of the slab and the steel strength $f_p=500\frac{N}{m}{m}^2.$