A steel I-beam is supported at both ends and subjected to a heavy downward load in the center of its span. Which of the following statements correctly identifies where the maximum compressive stress occurs, and correctly explains the structural efficiency of the I-beam's profile?
- AThe compressive stress is distributed evenly; however, the open I-shape is fundamentally less rigid against bending than a solid rectangular bar of the exact same weight.
- BThe vertical web experiences the maximum compressive stress; the shape requires a highly brittle material to absorb the downward bending force without fracturing.
- The top flange experiences the maximum compressive stress; the shape is efficient because it concentrates material far from the neutral axis where bending stresses peak.Answer
- DThe bottom flange experiences the maximum compressive stress; the shape is efficient because the downward load naturally compresses the lowest part of the span.
Answer
The maximum compressive stress occurs in the top flange. The I-beam's profile is efficient because it places the most material (the flanges) far from the neutral axis, exactly where bending stresses are highest.
When a beam supported at both ends bends downward, it forms a curve. The top edge of the curve becomes shorter, meaning it is under compression. The bottom edge becomes longer, meaning it is under tension. The I-beam is highly efficient because it concentrates its material in the top and bottom flanges—exactly where these compressive and tensile stresses are at their maximum—while minimizing material in the center (the neutral axis) where bending stress is nearly zero.
Step-by-Step Solution
Key Concept
Bending Moments and I-Beam Efficiency