Truss Analysis MCQ with answer and solution

Concept

At a pinned support joint with only one horizontal member, that member alone balances the horizontal reaction.

Formula

ΣF_x = 0, ΣF_y = 0 at each joint

Step-by-step solution

1. Support A is a hinge and B is a roller, so only A gives a horizontal reaction. 2. Whole truss: ΣF_x = 0 gives H_A + 4 = 0, so H_A = 4t acting to the left. 3. Joint A has two members: AD (vertical) and AC (horizontal). 4. ΣF_x = 0 at joint A: -4 + F_AC = 0, so F_AC = +4t. 5. F_AC acts away from joint A (towards C), so AC is in tension. 6. Force in AC = 4t tension.

Explanation

The 4t horizontal load at D must be resisted by the hinge at A, because the roller at B takes only vertical force. The reaction at A is 4t to the left. At joint A, only member AC is horizontal, so it must pull A to the right with 4t. This means AC is in 4t tension.

Shortcut

Horizontal reaction at the hinge = 4t to the left, so the only horizontal member at A carries 4t, and it pulls A, so it is in tension.