Practice Question: Moment Demand on a Cantilever Beam w/Triangular Load

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Solution

Answer: A) 23 kip - ft

As shown in Fig A, the trapezoidal distributed loading is segmented into a triangular and a uniform load. The areas under the triangle and rectangle represent the resultant forces. These forces act through the centroid of their corresponding areas.

\({{\stackrel{+}{\rightarrow}}}\mathrm{\Sigma }F_x=0\)

\({{\stackrel{+}{\rightarrow}}}\mathrm{\Sigma }F_y=0\)

\(A_x=0\)

\(\ A_y-4000-2000=0\)

\({\Rrightarrow A}_y=6000\ lb\)

\(\mathrm{\curvearrowleft }\mathrm{+}\mathrm{\Sigma }M_A=0;\)

\(-4000*\frac{10}{3}-2000*5+M_{A\ }=0\)

\({\Rrightarrow \ M}_{A\ }=\ 23,333.33\ lb-ft\cong 23\ kip - ft\)

 

 

 

 

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