Q$1.$ Fig. Q$-1$ shows a bridge pier with built$-$in corbels on both sides to support transverse beams. The depth of the corbel varies linearly from $500$ mm at the edge of the pier head to $1000$ mm at the face of the column. Each corbel is to carry four vertical concentrated loads, each of magnitude $P.$ Each load is applied on a bearing pad measuring $500$ mm by $250$ mm on plan with the longer dimension in the plane of the pier. Given that: $f_{ck}=40$MPa and $f_{yk}=500$ MPa $.$

$($a$)$ Construct a strut$-$and$-$tie model for the transfer of loads, and sketch the model on sections $x-x$ and $y-y.$ Consider nodes to be located at $100$ mm from the face, wherever possible. Also, show the strut members by broken lines, tie members by solid lines, and nodes by black dots.

$($b$)$ Assuming that the strut members and nodes are adequate in capacities, determine and sketch all the required reinforcement for the pier if $P=500kN.$

Front View

Side View

Fig. Q$-1$