FE Civil Statics Practice Problems

The current FE Civil specification assigns 8-12 of the 110 exam questions to Statics. Form A contains 9 original problems in this area. The sample below is published in full, with the same worked-solution format used throughout the book.

A 500-N traffic signal head hangs from point A. Cable AB extends from A to a pole on one side and rises at $3 0^{\circ}$ above the horizontal; cable AC extends to a pole on the opposite side and rises at $4 5^{\circ}$ above the horizontal. The tension in cable AB is most nearly:

(A)366 N
(B)414 N
(C)448 N
(D)500 N

Show worked solution

Answer: (A)

Force balance at A in both directions yields $T_{A B} = 500/ (sin 3 0^{\circ} + cos 3 0^{\circ}) = 366$ N.

Three forces meet at A: the 500-N weight and the two cable tensions.

Σ F_{x} : T_{A B} cos 3 0^{\circ} = T_{A C} cos 4 5^{\circ}

Σ F_{y} : T_{A B} sin 3 0^{\circ} + T_{A C} sin 4 5^{\circ} = 500 N

With $tan 4 5^{\circ} = 1$ , the horizontal equation gives $T_{A C} sin 4 5^{\circ} = T_{A B} cos 3 0^{\circ}$ ; the vertical sum then contains only $T_{A B}$ .

T_{A B} (sin 3 0^{\circ} + cos 3 0^{\circ}) = 500

T_{A B} = \frac{500}{1.366} = 366 N

FE Reference Handbook — Statics: Equilibrium Requirements

Why the other choices appear

(B)Assumes the two cable tensions are equal and sums vertical components, $T (sin 3 0^{\circ} + sin 4 5^{\circ}) = 500$ , giving 414 N.
(C)Reports the tension in cable AC (448 N) instead of cable AB.
(D)Sets the cable tension equal to the full supported weight.