Chapter 12, Problem 17P

Civil/Environmental Engineering

In the example for Fig. 12.4, where a 1000-lb downward force is applied at node 1, the external reactions $V_2$ and $V_3$ were calculated. But if the lengths of the truss members had been given, we could have calculated $V_2$ and $V_3$ by utilizing the fact that $V_2+V_3$ must equal 1000 and by summing moments around node 2. However, because we do know $V_2$ and $V_3$, we can work backward to solve for the lengths of the truss members. Note that because there are three unknown lengths and only two equations, we can solve for only the relationship between lengths. Solve for this relationship.