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A beam with length ‘l’ between the pinned supports overhangs by ‘a’ and both sides. Then mid-span bending moment in the beam is zero under uniformly distributed load covering the entire span, if
- a)l
- b)l = 2a
- c)l = 3a
- d)l = 4a
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A beam with length ‘l’ between the pinned supports overhangs by ‘a’ a...
RA + RB = w x (l + 2a)
RA = RB = 1 /2∙ w(l + 2a)
Mmid = 0
l = 2a
Most Upvoted Answer
A beam with length ‘l’ between the pinned supports overhangs by ‘a’ a...
Understand the problem:
We have a beam with a length 'l' that is supported by pinned supports. The beam overhangs on both sides by a distance 'a'. We need to determine the condition under which the mid-span bending moment in the beam is zero when a uniformly distributed load covers the entire span.
Analyze the problem:
To find the condition for zero mid-span bending moment, we need to consider the equilibrium of the beam. The bending moment at any point on the beam is given by the product of the load intensity and the distance from the point to the nearest support.
Apply equilibrium condition:
1. Consider a section of the beam at mid-span, where the bending moment is to be determined. Let's assume the uniform load intensity is 'w' and the distance from the mid-span to the nearest support is 'l/2'.
2. The bending moment at this section can be calculated as: M = w(l/2 - a)
3. For the bending moment to be zero, we need to have M = 0. Therefore, w(l/2 - a) = 0
4. Since we want to find the condition under which the bending moment is zero for any load intensity, we can conclude that (l/2 - a) must be equal to zero.
5. Simplifying the equation, we get: l/2 = a
Determine the correct option:
The equation l/2 = a tells us that the overhang 'a' should be equal to half the beam length 'l'. This condition is satisfied by option 'B', where l = 2a. Therefore, the correct answer is option 'B'.
Conclusion:
The mid-span bending moment in a beam will be zero under a uniformly distributed load covering the entire span when the overhang distance 'a' is equal to half the beam length 'l'. This condition ensures that the moments created by the load on both sides of the mid-span cancel each other out.
We have a beam with a length 'l' that is supported by pinned supports. The beam overhangs on both sides by a distance 'a'. We need to determine the condition under which the mid-span bending moment in the beam is zero when a uniformly distributed load covers the entire span.
Analyze the problem:
To find the condition for zero mid-span bending moment, we need to consider the equilibrium of the beam. The bending moment at any point on the beam is given by the product of the load intensity and the distance from the point to the nearest support.
Apply equilibrium condition:
1. Consider a section of the beam at mid-span, where the bending moment is to be determined. Let's assume the uniform load intensity is 'w' and the distance from the mid-span to the nearest support is 'l/2'.
2. The bending moment at this section can be calculated as: M = w(l/2 - a)
3. For the bending moment to be zero, we need to have M = 0. Therefore, w(l/2 - a) = 0
4. Since we want to find the condition under which the bending moment is zero for any load intensity, we can conclude that (l/2 - a) must be equal to zero.
5. Simplifying the equation, we get: l/2 = a
Determine the correct option:
The equation l/2 = a tells us that the overhang 'a' should be equal to half the beam length 'l'. This condition is satisfied by option 'B', where l = 2a. Therefore, the correct answer is option 'B'.
Conclusion:
The mid-span bending moment in a beam will be zero under a uniformly distributed load covering the entire span when the overhang distance 'a' is equal to half the beam length 'l'. This condition ensures that the moments created by the load on both sides of the mid-span cancel each other out.
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A beam with length ‘l’ between the pinned supports overhangs by ‘a’ and both sides. Then mid-span bending moment in the beam is zero under uniformly distributed load covering the entire span, ifa)lb) l = 2ac) l = 3ad) l = 4aCorrect answer is option 'B'. Can you explain this answer?
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