Question 5.89: The uniform rod of length L and weight W is supported on the...

\hookrightarrow + \Sigma M_B=0 ; \quad-W\left(\frac{L}{2} \cos \theta\right)+N_A \cos \phi(L \cos \theta)+N_A \sin \phi(L \sin \theta)=0

N_A=\frac{W \cos \theta}{2 \cos (\phi-\theta)}          (1)

+→ \Sigma F_x=0 ; \quad N_B \sin \psi-N_A \sin \phi=0          (2)

+↑ \Sigma F_y=0 ; \quad N_B \cos \psi+N_A \cos \phi-W=0

N_B=\frac{W-N_A \cos \phi}{\cos \psi}            (3)

Substituting Eqs. (1) and (3) into Eq. (2):

\left(W-\frac{W \cos \theta \cos \phi}{2 \cos (\phi-\theta)}\right) \tan \psi-\frac{W \cos \theta \sin \phi}{2 \cos (\phi-\theta)}=0