Question 11.9: A load P is supported at B by two uniform rods of the same c...
A load P is supported at B by two uniform rods of the same cross-sectional area A (Fig. 11.33). Determine the vertical deflection of point B.
The strain energy of the system under the given load was determined in Example 11.02. Equating the expression obtained for U to the work of the load, we write
U=0.364 \frac{P^{2} l}{A E}=\frac{1}{2} P y_{B}and, solving for the vertical deflection of B,
y_{B}=0.728 \frac{P l}{A E}Remark. We should note that, once the forces in the two rods have been obtained (see Example 11.02), the deformations d _{B / C} and d _{B / D} of the rods could be obtained by the method of Chap. 2. Determining the vertical deflection of point B from these deformations, however, would require a careful geometric analysis of the various displacements involved. The strain-energy method used here makes such an analysis unnecessary.