Question 7.139: Determine the internal normal force, shear force, and the mo...

Determine the internal normal force, shear force, and the moment as a function of 0° ≤ θ ≤ 180° and 0 ≤ y ≤ 2 ft for the member loaded as shown.

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For 0^{\circ} \leq \theta \leq 180^{\circ}:

+\nearrow \Sigma F_x=0 ; \quad V+200 \cos \theta-150 \sin \theta=0

V=150 \sin \theta-200 \cos \theta

+\nwarrow \Sigma F_y=0 ; \quad N-200 \sin \theta-150 \cos \theta=0

N=150 \cos \theta+200 \sin \theta

\hookrightarrow +\Sigma M=0 ; \quad-M-150(1)(1-\cos \theta)+200(1) \sin \theta=0

M=150 \cos \theta+200 \sin \theta-150

At section B, \theta=180^{\circ}, thus

V_B=200  \mathrm{lb}

N_B=-150  \mathrm{lb}

M_B=-300  \mathrm{lb} \cdot \mathrm{ft}

For 0 \leq y \leq 2  \mathrm{ft}:

\overset{+}{\longrightarrow } \Sigma F_x=0 ; \quad V=200  \mathrm{lb}

 

+↑ \Sigma F_y=0 ; \quad N=-150  \mathrm{lb}

 

\hookrightarrow +\Sigma M=0 ; \quad-M-300-200  y=0

M=-300-200  y

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