Question

The slope at the end of a simply supported beam with a central point load is .........

• A. zero
• B. maximum at mid-span
• C. non-zero and symmetric at ends
• D. infinite at mid-span

Hint:

For simply supported beams: - Central load → Symmetric bending and slope - Slope is maximum at supports and zero at mid-span under central point load.

Answer 1

The Correct Option is C

For a simply supported beam subjected to a central point load, the following behavior is observed:
- Maximum deflection occurs at the mid-span.
- Slope at the supports (ends) is not zero, because the beam is free to rotate there.
- The load being central causes a symmetric bending moment diagram, hence the slope at both ends is equal in magnitude but opposite in direction.
The slope \( \theta \) at the supports is given by: \[ \theta = \frac{PL^2}{16EI} \] where:
\( P \) = central point load,
\( L \) = span of the beam,
\( E \) = modulus of elasticity,
\( I \) = moment of inertia.
So, the slope is:
- Non-zero at ends
- Symmetric