Question

In the simple bending theory, the stress distribution assumed across the cross-section of a beam is

• A. Uniform
• B. Linear
• C. Parabolic
• D. Exponential

Hint:

In simple bending theory, the normal stress ($\sigma_x$) across the cross-section of a beam varies linearly with the distance from the neutral axis. The stress is zero at the neutral axis and reaches its maximum value at the outermost fibers of the beam.

Answer 1

The Correct Option is B

Step 1: Understand the assumptions of simple bending theory.
In the theory of simple bending (or pure bending), we assume:

• The material is homogeneous and isotropic.
• Plane sections remain plane before and after bending.
• The beam undergoes only bending (no shear force).

Step 2: Stress distribution in bending.
From the bending equation: \[ \sigma = \frac{My}{I} \] This indicates that the bending stress (\( \sigma \)) varies linearly with the distance \( y \) from the neutral axis.