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A cantilever beam of span 6m carries a point load of 100 kN at its free end and another point load 'W' at the
mid of its length. If the maximum bending moment is stated to be 900 kNm, the load 'W' will have the value
mid of its length. If the maximum bending moment is stated to be 900 kNm, the load 'W' will have the value
- a)50kN
- b)100kN
- c)150kN
- d)200kN
Correct answer is option 'B'. Can you explain this answer?
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A cantilever beam of span 6m carries a point load of 100 kN at its fre...
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Given data:
- Span of cantilever beam = 6m
- Point load at free end = 100 kN
- Point load at mid of length = W
- Maximum bending moment = 900 kNm
To find: Value of load W
Solution:
1. Free body diagram of cantilever beam:
- Point load of 100 kN at free end
- Point load of W at mid of length
- Reaction force at fixed end
2. Calculation of reaction force at fixed end:
- Taking moments about the fixed end:
∑M = 0
100 kN x 6m + W x 3m - Rf x 6m = 0
Rf = 150 kN
3. Calculation of bending moment at mid of length:
- Using the equation for bending moment at any point on the beam:
M = (Rf x a) - (w x a/2) - (w x a/2)
where,
a = distance of point from fixed end
M = bending moment at the point
- At mid of length, a = 3m
M = (150 kN x 3m) - (W x 3m/2) - (W x 3m/2)
M = 450 kNm - 1.5W
4. Calculation of load W:
- Maximum bending moment occurs at the fixed end of the beam
- Given, maximum bending moment = 900 kNm
- Therefore, at the fixed end:
M = (Rf x L) - (W x L/2)
900 kNm = (150 kN x 6m) - (W x 6m/2)
W = 100 kN
Therefore, the value of load W is 100 kN.
Answer: Option B (100 kN)
- Span of cantilever beam = 6m
- Point load at free end = 100 kN
- Point load at mid of length = W
- Maximum bending moment = 900 kNm
To find: Value of load W
Solution:
1. Free body diagram of cantilever beam:
- Point load of 100 kN at free end
- Point load of W at mid of length
- Reaction force at fixed end
2. Calculation of reaction force at fixed end:
- Taking moments about the fixed end:
∑M = 0
100 kN x 6m + W x 3m - Rf x 6m = 0
Rf = 150 kN
3. Calculation of bending moment at mid of length:
- Using the equation for bending moment at any point on the beam:
M = (Rf x a) - (w x a/2) - (w x a/2)
where,
a = distance of point from fixed end
M = bending moment at the point
- At mid of length, a = 3m
M = (150 kN x 3m) - (W x 3m/2) - (W x 3m/2)
M = 450 kNm - 1.5W
4. Calculation of load W:
- Maximum bending moment occurs at the fixed end of the beam
- Given, maximum bending moment = 900 kNm
- Therefore, at the fixed end:
M = (Rf x L) - (W x L/2)
900 kNm = (150 kN x 6m) - (W x 6m/2)
W = 100 kN
Therefore, the value of load W is 100 kN.
Answer: Option B (100 kN)
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