Question

Theory of simple bending equation is applicable for

• A. constant shear face and zero bending moment
• B. constant bending moment and zero shear force
• C. zero bending moment and zero shear force
• D. constant bending moment and constant shear force

Hint:

The ideal condition for the simple bending theory is called Pure Bending.
Pure Bending means:
- Bending Moment = Constant.
- Shear Force = Zero.
An example is the central portion of a beam loaded with two symmetric point loads.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the conditions under which the theory of simple bending (or pure bending) is strictly applicable.

Step 2: Detailed Explanation:
The

theory of simple bending, which leads to the flexure formula $\frac{M}{I} = \frac{\sigma}{y} = \frac{E}{R}$, is derived based on a set of assumptions. One of the most important is that the beam is subjected to

pure bending.
Pure bending is a loading condition where a beam is subjected to a constant bending moment and, consequently, zero shear force.
The relationship between bending moment ($M$) and shear force ($V$) is $V = dM/dx$.
If the bending moment $M$ is constant, then its derivative with respect to $x$ must be zero.
\[ \frac{dM}{dx} = 0 \implies V = 0 \] This condition (constant bending moment and zero shear force) ensures that the stresses in the beam are purely normal stresses due to bending, without any complicating shear stresses that would warp the cross-section. While the bending equation is often applied to cases where shear force is present, its theoretical derivation is based on the case of pure bending.

Step 3: Final Answer:
The theory of simple bending equation is strictly applicable for a condition of constant bending moment and zero shear force.