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The left half of a simply supported beam of span “L” is loaded with u. d. l of w/meter run. The point of maximum B.M will occur at
- a)mid-span
- b)2L/3 from left support
- c)3L/8 from left support
- d)5L/8 from left support
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The left half of a simply supported beam of span “L” is loaded with u...
We know RA + RB = wL / 2
Taking moments about A
For maximum B.M, S. F must be change sign shear force at
x = RA − wx = 0
Most Upvoted Answer
The left half of a simply supported beam of span “L” is loaded with u...
Solution:
To find the point of maximum B.M, we need to determine the shear force (S.F) and bending moment (B.M) equations for the given beam.
Shear Force Equation:
At any distance x from the left support, the S.F is given by:
S.F = u × x
Bending Moment Equation:
At any distance x from the left support, the B.M is given by the area under the S.F curve up to that point:
B.M = ∫(0 to x) u × x dx
B.M = u/2 × x^2
To find the point of maximum B.M, we need to differentiate the B.M equation with respect to x and equate it to zero:
d(B.M)/dx = u × x = 0
x = 0 or x = L
Since the beam is loaded on the left half, the point of maximum B.M should lie in the left half of the span. So, we can discard x = L as a solution.
Therefore, the point of maximum B.M will occur at x = 0, which is the left support.
Answer: (a) Mid-span is incorrect. The correct answer is (c) 3L/8 from the left support.
To find the point of maximum B.M, we need to determine the shear force (S.F) and bending moment (B.M) equations for the given beam.
Shear Force Equation:
At any distance x from the left support, the S.F is given by:
S.F = u × x
Bending Moment Equation:
At any distance x from the left support, the B.M is given by the area under the S.F curve up to that point:
B.M = ∫(0 to x) u × x dx
B.M = u/2 × x^2
To find the point of maximum B.M, we need to differentiate the B.M equation with respect to x and equate it to zero:
d(B.M)/dx = u × x = 0
x = 0 or x = L
Since the beam is loaded on the left half, the point of maximum B.M should lie in the left half of the span. So, we can discard x = L as a solution.
Therefore, the point of maximum B.M will occur at x = 0, which is the left support.
Answer: (a) Mid-span is incorrect. The correct answer is (c) 3L/8 from the left support.
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The left half of a simply supported beam of span “L” is loaded with u. d. l of w/meter run. The point of maximum B.M will occur ata) mid-spanb) 2L/3 from left supportc) 3L/8 from left supportd) 5L/8 from left supportCorrect answer is option 'C'. Can you explain this answer?
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