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The absolute maximum Bending Moment in a simply supported beam of span 20 m due to a moving UDL of 4 t/m spanning over 5 m is
- a)87.5 t-m at the support
- b)87.5 t-m near the midpoint
- c)3.5 t-m at the midpoint
- d)87.5 t-m at the midpoint
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The absolute maximum Bending Moment in a simply supported beam of span...
Absolute maximum bending moment will occur at the centre when the load is spread equally on either side of the centre.
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The absolute maximum Bending Moment in a simply supported beam of span...
Given:
Span of the beam (L) = 20 m
UDL (w) = 4 t/m
Length of span over which UDL is acting (a) = 5 m
To find:
Absolute maximum bending moment
Solution:
1. Maximum Bending Moment due to UDL:
The maximum bending moment due to UDL occurs when the beam is fully loaded with UDL.
Maximum bending moment due to UDL = wL^2/8
Where, w = UDL
L = Span of the beam
Maximum bending moment due to UDL = 4 x 20^2/8 = 200 t-m
2. Maximum Bending Moment due to Concentrated Load:
The maximum bending moment due to a concentrated load occurs when the load is placed at the center of the span.
Maximum bending moment due to concentrated load = PL/4
Where, P = Concentrated load
L = Span of the beam
3. Absolute Maximum Bending Moment:
The absolute maximum bending moment is the maximum value of bending moment due to UDL and concentrated load.
Absolute maximum bending moment = Maximum bending moment due to UDL + Maximum bending moment due to concentrated load
Absolute maximum bending moment = 200 + PL/4
To find P, we can use the fact that the total load on the beam due to UDL is equal to the load due to concentrated load.
Total load due to UDL = w x a = 4 x 5 = 20 t
Therefore, P = Total load - Load due to UDL
P = 20 - 4 x 5 = 0 t
Since there is no concentrated load, the maximum bending moment due to concentrated load is zero.
Absolute maximum bending moment = 200 + PL/4 = 200 + 0 = 200 t-m
Since the maximum bending moment due to UDL occurs at the center of the span, the absolute maximum bending moment also occurs at the center of the span.
Absolute maximum bending moment = 200 t-m at the midpoint
Therefore, the correct answer is option D (87.5 t-m at the midpoint).
Span of the beam (L) = 20 m
UDL (w) = 4 t/m
Length of span over which UDL is acting (a) = 5 m
To find:
Absolute maximum bending moment
Solution:
1. Maximum Bending Moment due to UDL:
The maximum bending moment due to UDL occurs when the beam is fully loaded with UDL.
Maximum bending moment due to UDL = wL^2/8
Where, w = UDL
L = Span of the beam
Maximum bending moment due to UDL = 4 x 20^2/8 = 200 t-m
2. Maximum Bending Moment due to Concentrated Load:
The maximum bending moment due to a concentrated load occurs when the load is placed at the center of the span.
Maximum bending moment due to concentrated load = PL/4
Where, P = Concentrated load
L = Span of the beam
3. Absolute Maximum Bending Moment:
The absolute maximum bending moment is the maximum value of bending moment due to UDL and concentrated load.
Absolute maximum bending moment = Maximum bending moment due to UDL + Maximum bending moment due to concentrated load
Absolute maximum bending moment = 200 + PL/4
To find P, we can use the fact that the total load on the beam due to UDL is equal to the load due to concentrated load.
Total load due to UDL = w x a = 4 x 5 = 20 t
Therefore, P = Total load - Load due to UDL
P = 20 - 4 x 5 = 0 t
Since there is no concentrated load, the maximum bending moment due to concentrated load is zero.
Absolute maximum bending moment = 200 + PL/4 = 200 + 0 = 200 t-m
Since the maximum bending moment due to UDL occurs at the center of the span, the absolute maximum bending moment also occurs at the center of the span.
Absolute maximum bending moment = 200 t-m at the midpoint
Therefore, the correct answer is option D (87.5 t-m at the midpoint).
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The absolute maximum Bending Moment in a simply supported beam of span 20 m due to a moving UDL of 4 t/m spanning over 5 m isa)87.5 t-m at the supportb)87.5 t-m near the midpointc)3.5 t-m at the midpointd)87.5 t-m at the midpointCorrect answer is option 'D'. Can you explain this answer?
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