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Chapter 2

Q. 2.1

Determine the forces produced by the applied loads in the members of the sawtooth truss shown in Figure 2.9.

Determine the forces produced by the applied loads in the members of the sawtooth truss shown in Figure 2.9.

Step-by-Step

Verified Solution

The support reactions are calculated, and the directions of the member forces are assumed as indicated.

Resolving forces at node 7:

\begin{aligned} P_{67} &=V_{7} / \sin 30^{\circ} \\ &=20 \text { kips … compression } \\ P_{57} &=V_{7} / \tan 30^{\circ} \\ &=17.32 \text { kips … tension } \end{aligned}

Resolving forces at node 6:

\begin{aligned} P_{46} &=P_{67} \\ &=20 \text { kips … compression } \\ P_{56} &=0 \end{aligned}

Resolving forces at node 5 :

\begin{aligned}P_{45} &=W_{5} / \sin 60^{\circ} \\&=11.55 \text { kips … tension } \\P_{35} &=P_{57}-W_{5} / \tan 60^{\circ} \\&=11.55 \text { kips … tension }\end{aligned}

Resolving forces at node 4 :

\begin{aligned}P_{34} &=P_{45} / \sin 30^{\circ} \\&=5.77 \text { kips … compression } \\P_{24} &=P_{46}-P_{45} \sin 60^{\circ} \\&=10 \text { kips … compression }\end{aligned}

Resolving forces at node 2 :

\begin{aligned}P_{23} &=P_{24} / \cos 49.11^{\circ} \\&=15.28 \text { kips … tension }\end{aligned}

Resolving forces at node 1 :

\begin{aligned}P_{12} &=V_{1} / \sin 60^{\circ} \\&=11.55 \text { kips … compression } \\P_{13} &=V_{1} / \tan 60^{\circ} \\&=5.77 \text { kips … tension }\end{aligned}