Question

A fixed beam AB of span 10 m is subjected to a concentrated load of 72 kN acting at mid span C. The maximum bending moment in the beam is

• A. 60 kNm
• B. 90 kNm
• C. 120 kNm
• D. 180 kNm

Hint:

Memorize the key formulas for fixed beams:
- Point Load at Center: Max Moment = $PL/8$ (at center and supports).
- UDL over entire span: Max Moment = $wL^2/12$ (at supports). The center moment is $wL^2/24$.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the maximum bending moment in a fixed-end beam with a concentrated load at the center.

Step 2: Key Formula or Approach:
For standard loading cases on fixed beams, there are standard formulas for the fixed-end moments and the mid-span moment. For a fixed beam of span $L$ with a concentrated load $P$ at the center:
1. The fixed-end moments (hogging) at the supports (A and B) are:
\[ M_A = M_B = -\frac{PL}{8} \] 2. The bending moment at the mid-span (C) under the load (sagging) is:
\[ M_C = +\frac{PL}{8} \] The maximum bending moment in the beam is the maximum of the absolute values of the moments at the supports and at mid-span. In this symmetric case, they are equal in magnitude.

Step 3: Detailed Explanation:
We are given the following values:

• Load ($P$) = 72 kN

• Span ($L$) = 10 m


Now, calculate the magnitude of the moments:
\[ |M| = \frac{PL}{8} = \frac{(72 \text{ kN}) \times (10 \text{ m})}{8} \] \[ |M| = \frac{720}{8} \text{ kNm} \] \[ |M| = 90 \text{ kNm} \] The bending moment at the supports is -90 kNm (hogging) and at the center is +90 kNm (sagging). The maximum magnitude is therefore 90 kNm.

Step 4: Final Answer:
The maximum bending moment in the beam is 90 kNm.