Practice Question: Maximum Bending Stress for a Cantilever Beam

---

---

Solution

Answer: B) 149 ksi

The location of the maximum moment load in a cantilever beam is at the support. 

Solve for the moment at support:

$$ M=20\ kip\ast\ 60\ in+ \frac{1}{2} \ast (80\ \frac{kip}{ft} \ast \frac{(1\ ft)}{(12\ in)})\ast(80\ in\ )(160\ in+ \frac{(80\ in)}{3}) $$

$$ M=50,977.8\ kip-in $$

Maximum flexural stress is computed using the formula below:

$$ f_b=\frac{My}{I} $$

where:

$$ I\ =\ moment\ of\ inertia $$

$$ y\ =\ distance\ of\ the\ extreme\ fiber\ from\ the\ centroid\ of\ the\ section $$

Solve for f_b:

$$ f_b=\frac{50,977.8\ kip-in\ast\left(\frac{16\ in}{2}\right)}{\frac{1}{12}\ast\left(8\ in\right){\ast\ \left(16\ in\right)}^3} $$

$$ f_b\approx149\ ksi $$ 
 

---