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, the stress distribution across the depth of the beam is linear—zero at the neutral axis and maximum at the outer fibers.

Answer 1

The Correct Option is B

Step 1: Understand simple bending theory assumptions.
The simple bending theory, also known as Euler–Bernoulli beam theory, assumes:
The material of the beam is homogeneous and isotropic.
The cross-section of the beam remains plane and perpendicular to the neutral axis after bending.
The stress is directly proportional to the distance from the neutral axis.
Step 2: Use the bending stress formula.
The bending stress at a distance \( y \) from the neutral axis is: \[ \sigma = \frac{My}{I} \] Where:
\( M \) is the bending moment,
\( y \) is the distance from the neutral axis,
\( I \) is the moment of inertia.
This clearly shows that stress varies linearly with \( y \).