(a) Derive an expression for the elongation of a conical bar due to i…

Question

(a) Derive an expression for the elongation of a conical bar due to its self-weight.

(b) Two prismatic bars are rigidly fastened together and support a vertical load of 40 KN as shown in figure 1. The upper bar is of steel having unit weight $760\text{ kN/m}^3$, length $10\text{ m}$ and cross sectional area of $80.7\text{ cm}^2$. The lower bar is of brass having unit weight $800\text{ kN/m}^3$, length $6\text{ m}$ and cross – sectional area $64.5\text{ cm}^2$. For steel $E = 207\text{ GPa}$ and brass $E = 90\text{ GPa}$. Determine:

(i) Extension of free end due to self –weight only

(ii) Maximum stress in each material.