Practice Question: Maximum Bending Stress on Hollow Circular Section

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Solution

Answer: A) 4.6 ksi

The location of maximum bending stress corresponds to the location of the maximum moment which occurs at the support point of a cantilever beam. 

Determine the maximum moment:
\[M_{max}= \frac{wl^2}{2}\]
\[M_{max}= \frac{2 klf × (4 ft)^2}{2}=16 \ k \cdot ft\]

Maximum flexural stress is computed using the formula below:
\[f_{b-max}=\frac{M_{max} y}I\]

where: 

\(y\) is the distance to the extreme fiber from the centroid of the section. In our case, this is the outer radius.
\(I\) is the moment of inertia. 

The moment of inertia for a pipe section is calculated as follows:
\[I= \frac{π(R_o^4-R_i^4)}4\]
Inner Radius:

\[R_i=5 \ in\]
Outer Radius: 
\[R_o=5 \ in+0.5 \ in=5.5 \ in\]
Moment of Inertia:

\[I= \frac{π[(5.5 in)^4-(5in)^4]}4=227.8 in^4\]

Maximum Bending Stress:

\[f_{b-max}=\frac{16\ k \cdot ft ×12 × 5.5 in}{227.8 in^4}\]

\[f_{b-max}=4.6 \ ksi\]

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