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Chapter 1

Q. 1.3

The pin-jointed truss shown in Figure 1.13 has a hinged support at support 1 and a roller support at support 2. Determine the forces in members 15, 35, and 34 caused by the horizontal applied load of 20 kips at joint 3.

The pin-jointed truss shown in Figure 1.13 has a hinged support at support 1 and a roller support at support 2. Determine the forces in members 15, 35, and 34 caused by the horizontal applied load of 20 kips at joint 3.

Step-by-Step

Verified Solution

The values of the support reactions were obtained in Example 1.2 and are shown at (i). The truss is cut at section A-A, and the free body diagram of the right-hand portion of the truss is shown at (ii).

Resolving forces vertically gives the force in member 35 as:

\begin{aligned}P_{35} &=V_{2} / \sin \theta \\&=10 / \sin 63.43^{\circ} \\&=11.18  \text { kips … compression } \end{aligned}

Taking moments about node 3 gives the force in member 15 as:

\begin{aligned}P_{15} &=12 V_{2} / 8 \\&=12 \times 10 / 8 \\&=15  \text { kips … tension } \end{aligned}

Taking moments about node 5 gives the force in member 34 as:

\begin{aligned}P_{34} &=8 V_{2} / 8 \\&=8 \times 10 / 8 \\&=10  \text { kips … compression } \end{aligned}