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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'moment due to central 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...
Given:
- A point load is acting at the mid-span of a fixed beam of uniform section.
- The point load produces fixed end moments of 60 kN-m.

To find:
- The fixed end moments produced when the same load is spread uniformly over the entire span.

Solution:
When a point load is applied at the mid-span of a fixed beam, it creates fixed end moments. These fixed end moments are calculated based on the formula:

M = (wL^2) / 8

Where:
M = Fixed end moment
w = Load per unit length (uniformly distributed load)
L = Span length

In this case, the fixed end moments produced by the point load at the mid-span is given as 60 kN-m. We need to find the load per unit length (w) that will produce the same fixed end moments when spread uniformly over the entire span.

Step 1: Calculate the span length (L)
Since the point load is acting at the mid-span, it divides the beam into two equal parts. Therefore, the span length (L) is twice the distance from the support to the mid-span.
L = 2 * (distance from support to mid-span)

Step 2: Calculate the load per unit length (w)
Using the formula for fixed end moments:
M = (wL^2) / 8

We can rearrange the formula to solve for w:
w = (8M) / L^2

Substituting the given values:
w = (8 * 60) / L^2

Step 3: Calculate the load per unit length for the entire span
Since the load is spread uniformly over the entire span, the load per unit length is the same throughout the span. Therefore, the load per unit length for the entire span is equal to the load per unit length for half the span (w).

So, the load per unit length for the entire span is:
Load per unit length = w = (8 * 60) / L^2

Step 4: Calculate the fixed end moments produced by the uniformly distributed load
Using the formula for fixed end moments:
M = (wL^2) / 8

Substituting the calculated value of w and L:
M = [(8 * 60) / L^2] * L^2 / 8

The L^2 terms cancel out, and we are left with:
M = 60 kN-m

Therefore, the fixed end moments produced when the same load is spread uniformly over the entire span is 60 kN-m, which corresponds to option C.
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