Question

Determine the design angle ϕ (0∘≤ϕ≤90 ∘) between struts AB and AC so that the 400 lb horizontal force has a component of 600 lb which acts up to the left, in the same direction as from B towards A. Take θ = 30 ∘.

Answer 1

Answer:

design angle ∅ = 4.9968 ≈ 5⁰

Explanation:

First calculate the force Fac :

Fac = $\sqrt{400^2 + 650^2 - 2(400)(650)cos30}$

      = $\sqrt{160000 + 422500 - 80210}$

      = 708.72 Ib

using the sine law to determine the design angle

$\frac{sin}{400} = \frac{sin 30}{Fac}$

hence ∅ = $sin^{-1} (\frac{sin 30 *400}{708.72} )$

              = $sin^{-1} 0.0871$ =  4.9968 ≈ 5⁰