Practice Question: Maximum Bending Stress for a Cantilever Beam
NCEES Civil PE Specification IV.D.: Bending
Problem
Approximate the maximum bending stress experienced by the 8 inch wide by 16 inch deep cantilever beam in the following loading and support condition:
CORRECT 😃
INCORRECT 😟
% Students Correctly Answered:
50.5%
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 fb:
$$ f_b=\frac{50,977.8\ kip-in\ast\left(\frac{16\ in}{2}\right)}{\frac{1}{12}\ast\left(8\ in\right){\ast\ \left(16\ in\right)}^3} $$
$$ f_b\approx149\ ksi $$
