Look at the load vs deflection diagram shown below for a bridge girder. For each of the following cases show using arrows the load$-$deflection path followed and also mark for each point the corresponding deflection on the $x$ axis. Finally, clearly show $A_4$ on the $x$ axis. Use ${}_d$ to indicate deflection due to dead load, ${}_{d+1}$ to indicate deflection due to dead$+$live load and ${}_1$ to indicate deflection due to live load $($difference between ${}_{d+1}$ and ${}_d)(10$ points$)$

a$.$ The construction has been completed and the structure is under dead load $W_0$ corresponding to point $1.$ Following this, the structure is loaded with live load, taking it to $W_{d+1}$ corresponding to point $2.$ Then, the live load is removed, taking it to point $3.$ Please figure out where point $3$ falls and place it on the figure.

b$.$ Before the application of any live load and usage of the structure, the structure is loaded with construction equipment which takes the load deflection for the bridge girder to point $4.$ Then, the construction equipment is removed so that only $W_d$ is acting. Following this live load is applied.

Case a