Question $3$

Consider a rectangular pad footing of length $L=2\mathrm{.}5m,$ breadth $B=1\mathrm{.}5m,$ and depth $D_f=0\mathrm{.}5m,$ which is required to carry an imposed permanent action $V_{Gk}=800kN$ and an imposed variable action $V_{Qk}=450kN,$ both of which are applied at the centre of the foundation as shown in Figure $2.$ The footing is founded on dry sand with characteristic angle of shearing resistance ${}_k=35,$ effective cohesion $c_k^{\text{'}}=0$kPa, and weight density ${}_k=18k\frac{N}{m^3}.$ The weight density of the reinforced concrete is ${}_{ck}=25k\frac{N}{m^3}.$ Design for the resistance and determine the degree of utilization to satisfy the ultimate limit state using design DA$-1$ combination $1$&$2$ of EC$-7.$

$B=1\mathrm{.}5m$

$L=2\mathrm{.}5m$

Figure $2$ Cross$-$section of a rectangular pad footing

$[25$ marks$]$

$3$ of $4$