Question

Determine the design angle \( \theta (0°\leq\theta \leq90°) \) for strut AB so that the 400-lb horizontal force has a component of 500 lb directed from A towards C. What is the component of force acting along member AB? Take \( \phi \)= 40°.

Answer 1

solution

Parallelogram Law: The parallelogram law of addition is shown in Fig. (a).

Trigonometry: Using the law of sines [Fig.(b)] , we have

\( \frac{sin \theta}{500}=\frac{sin40°}{400}=>sin \theta=0.8035=>\theta=53.5° \)

So,  \( \psi \)=180°-53.5°=86.54°

Using law of sines [Fig. (b)]

\( \frac{F_{AB}}{sin86.54°}=\frac{400}{sin40°} \)

=>\( F_{AB}=621lb \)

Answer

Therefore, \( \psi \)=86.54° and \( F_{AB}=621 \)lb