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A concentrated load P acts on a simply supported beam of span L at a distance L/3 from the left support. The bending moment at the point of application of the load is given by
- a)PL/3
- b)2PL/3
- c)PL/9
- d)2PL/9
Correct answer is option 'D'. Can you explain this answer?
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A concentrated load P acts on a simply supported beam of span L at a d...
Solution:
To determine the bending moment at the point of application of the load, we can use the formula for the bending moment at any point on a simply supported beam subjected to a concentrated load. The formula is given by:
M = (P x a x b) / L
where M is the bending moment, P is the applied load, a is the distance of the load from the left support, b is the distance of the load from the right support, and L is the span of the beam.
In this case, we are given that the load is applied at a distance of L/3 from the left support. Therefore, a = L/3. The distance of the load from the right support is b = L - (L/3) = 2L/3.
Substituting these values into the formula, we have:
M = (P x (L/3) x (2L/3)) / L
Simplifying the expression, we get:
M = (2PL/9) / L
The L in the numerator cancels out with the L in the denominator, leaving us with:
M = 2P/9
Therefore, the bending moment at the point of application of the load is given by 2P/9, which corresponds to option D.
To determine the bending moment at the point of application of the load, we can use the formula for the bending moment at any point on a simply supported beam subjected to a concentrated load. The formula is given by:
M = (P x a x b) / L
where M is the bending moment, P is the applied load, a is the distance of the load from the left support, b is the distance of the load from the right support, and L is the span of the beam.
In this case, we are given that the load is applied at a distance of L/3 from the left support. Therefore, a = L/3. The distance of the load from the right support is b = L - (L/3) = 2L/3.
Substituting these values into the formula, we have:
M = (P x (L/3) x (2L/3)) / L
Simplifying the expression, we get:
M = (2PL/9) / L
The L in the numerator cancels out with the L in the denominator, leaving us with:
M = 2P/9
Therefore, the bending moment at the point of application of the load is given by 2P/9, which corresponds to option D.
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Community Answer
A concentrated load P acts on a simply supported beam of span L at a d...
For vertical equilibrium
R1 + R2 = P
Taking moment about R1, we have
The bending moment at the point of application of load = Area under OABC
R1 + R2 = P
Taking moment about R1, we have
The bending moment at the point of application of load = Area under OABC
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A concentrated load P acts on a simply supported beam of span L at a distance L/3 from the left support. The bending moment at the point of application of the load is given bya)PL/3b)2PL/3c)PL/9d)2PL/9Correct answer is option 'D'. Can you explain this answer?
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