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If a point load acting at the mid-span of a fixed beam of uniform section produces fixed end moments of 60 kN-m, then the same load spread uniformly over the entire span will produce fixed end moments equal to 
  • a)
    20 kN-m
  • b)
    30 kN-m
  • c)
    40 kN-m
  • d)
    45 kN-m
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If a point load acting at the mid-span of a fixed beam of uniform sect...
’Fixed end'momerit due to centra! point load,
M1 = PL/8 = 60 kNm
The fixed end moment due to uniformly distributed load is PL/12.  Thus it is equal to 40 kN-m.
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Most Upvoted Answer
If a point load acting at the mid-span of a fixed beam of uniform sect...
Explanation:

Given: Fixed end moments produced by a point load acting at mid-span of a fixed beam of uniform section = 60 kN-m

To find: Fixed end moments produced by the same load spread uniformly over the entire span.

Let us consider the beam AB of length L, which is fixed at both ends A and B. The point load P is acting at mid-span C of the beam.

Now, the fixed end moments produced by the point load P at A and B can be calculated as follows:

MA = MB = P × L/4 = P/2 × L/2

Given, MA = MB = 60 kN-m

Therefore, P/2 × L/2 = 60 kN-m

P = 120 kN

Now, the load P is spread uniformly over the entire span of the beam AB. Hence, the load per unit length w = P/L = 120/L kN/m

The fixed end moments produced by the uniformly distributed load w can be calculated as follows:

MA = MB = wL^2/12

MA = MB = (120/L × L^2)/12

MA = MB = 10 kN-m (cancelled L in denominator)

Therefore, the fixed end moments produced by the same load spread uniformly over the entire span = 10 × 4 = 40 kN-m

Hence, the correct option is (c) 40 kN-m.
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