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## Q. 1.1

Determine the support reactions of the pin-jointed truss shown in Figure 1.9 . End 1 of the truss has a hinged support, and end 2 has a roller support.

## Verified Solution

To ensure equilibrium, support 1 provides a horizontal and a vertical reaction, and support 2 provides a vertical reaction. Adopting the convention that horizontal forces acting to the right are positive, vertical forces acting upward are positive, and counterclockwise moments are positive, applying the equilibrium equations gives, resolving horizontally:

\begin{aligned}H_{1}+H_{3} &=0 \\H_{1} &=-H_{3} \\&=-10 \text { kips … acting to the left }\end{aligned}

Taking moments about support 1 and assuming that $V_{2}$ is upward:

$16 V_{2}-8 H_{3}-4 V_{3}-12 V_{4}=0$

$V_{2}$ = (8 × 10 + 4 × 20 + 12 × 20)/16

=25 kips … acting upward as assumed

Resolving vertically:

\begin{aligned}V_{1}+V_{2}+V_{3}+V_{4} &=0 \\V_{1} &=-25+20+20 \\ &=15 \text { kips … acting upward }\end{aligned}

The support reactions are shown at (ii).