A cantilever beam with inverted T cross-section carries uniformly distributed load. Where does the maximum magnitude of the bending stress occur?
- AAt the top of cross-sectionCorrect
- BAt the mid-depth joint
- CAt the junction of flange and web
- DAt the bottom of the section
Solution
Concept
Maximum Bending Stress in Beams
Formula
σ = (M × y) / I
Step-by-step solution
1. Use the bending stress formula σ = (M \* y) / I, where σ is proportional to the distance from the neutral axis (y). 2. For an inverted T-section, the neutral axis is closer to the bottom flange, making the top fiber the farthest distance (y\_max) from the neutral axis. 3. Since maximum bending stress occurs at the maximum distance y\_max, the maximum magnitude of bending stress occurs at the top of the cross-section.
Explanation
For a cantilever beam under a downward load, the beam bends upwards, causing the top fibers to experience maximum tensile stress. In an inverted T-section, the neutral axis is closer to the bottom (where the wide flange is located), making the top fiber (the top of the stem) the farthest point from the neutral axis. Since bending stress increases with distance from the neutral axis, the maximum magnitude of bending stress occurs at the top of the cross-section.
Shortcut
Max stress occurs at the farthest fiber from the neutral axis. An inverted T has its mass (flange) at the bottom, shifting the neutral axis down, making the top the farthest point.
Common mistake
Many students incorrectly select "At the bottom of the section" because they assume the wide flange carries the maximum stress or forget that the neutral axis shifts downward toward the flange, making the top fiber the farthest point from the neutral axis where maximum bending stress occurs.
Correct answer: A) At the top of cross-section