1. (a) State and prove the second theorem of Castigliano. 10 (b) A mi…

Question

1. (a) State and prove the second theorem of Castigliano. 10

(b) A mild steel bar $100\text{ mm}$ diameter is bent as shown in fig. It is fixed horizontally at $A$ and a load of $500\text{ N}$ hangs at $D$. Draw the bending moment diagram for the parts $AB$, $BC$ and $CD$ indicating the maximum values. Find the maximum bending stress. Find the deflection at $D$. Take $E = 2 \times 10^5\text{ N/mm}^2$. 10