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Difficulty: HardTypes of Stress and Strain

A heavy machine is placed directly in the center of a horizontal steel beam that is supported only at its far left and right ends. The downward force of the machine causes the beam to bend slightly downward in the middle. Based on this load distribution, which of the following best describes the primary mechanical stresses acting on the extreme top and bottom surfaces of the beam at its midpoint?

  1. A
    The top surface experiences tension, and the bottom surface experiences compression.
  2. B
    The top surface experiences compression, and the bottom surface experiences shear.
  3. C
    Both the top and bottom surfaces experience uniform shear stress.
  4. The top surface experiences compression, and the bottom surface experiences tension.Answer

Answer

The top surface experiences compression, and the bottom surface experiences tension.
When a beam is supported at its ends and loaded in the center, it undergoes bending. This physical bending forces the top layers of the beam's material to crush together, generating compressive stress. Simultaneously, the bottom layers of the material are forced to stretch outward, generating tensile stress. The very center of the beam (neutral axis) experiences zero bending stress, but the extreme top and bottom surfaces experience maximum compression and tension, respectively.

Step-by-Step Solution

1
Analyze the deformation of the beam under the external load.
The central downward load causes the middle of the beam to sag, creating a slightly concave upward shape (like a shallow 'U').
Understanding the physical deformation dictates how the internal material layers are forced to move relative to one another.
2
Determine the stress on the top surface.
The top surface is on the inside of the bend, which forces its ends closer together, squeezing the material.
Forces that squeeze or crush a material generate compressive stress.
3
Determine the stress on the bottom surface.
The bottom surface is on the outside of the bend, forcing the material to elongate and stretch apart.
Forces that pull or stretch a material generate tensile stress.

Key Concept

Bending Stress Distribution in Beams
Estimated Time:45s
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Topics

Types of Stress and Strain

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