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Question

Difficulty: MediumStructural Shapes and Profiles

A horizontal steel I-beam is supporting a heavy downward load from a factory roof. If a small hole must be drilled through the beam to route an electrical cable, where is the safest location on the beam's cross-sectional profile to remove material in order to minimize the loss of bending strength?

  1. A
    Through the bottom horizontal flange, because it primarily experiences compressive forces
  2. Directly through the middle of the vertical webAnswer
  3. C
    An I-beam cannot be safely drilled; a solid rectangular steel beam of equal weight must be used instead
  4. D
    Through the top horizontal flange, because it primarily experiences tensile forces

Answer

The safest location is directly through the middle of the vertical web.
When a horizontal beam bends under a downward load, the material at the top is compressed, and the material at the bottom is stretched (placed in tension). The exact horizontal center of the profile, called the neutral axis, experiences neither tension nor compression from bending. Because the vertical web at this midpoint is doing no work to resist bending forces, removing a small amount of material there has the smallest possible impact on the beam's overall structural strength.

Step-by-Step Solution

1
Analyze the stresses on a simply supported horizontal beam with a downward load.
The beam bends downward, causing the top to squeeze together (compression) and the bottom to stretch apart (tension).
Understanding load distribution is required to identify areas of high and low stress.
2
Locate the point of minimum bending stress on the cross-sectional profile.
The transition point between compression (top) and tension (bottom) occurs at the exact center of the vertical web, known as the neutral axis.
The neutral axis is the zone where structural material does the least amount of work resisting bending forces.
3
Determine the optimal location to drill a hole.
Drilling through the middle of the vertical web removes material from the neutral axis, preserving the highly-stressed flanges.
Removing material from areas of zero bending stress minimizes the overall loss of strength.

Key Concept

Stress Distribution and the Neutral Axis in Beams
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Topics

Structural Shapes and Profiles

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