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A concentrated load P acts on a simply supported beam of span L at a distance L/4 from the left end. The bending moment at the point of application of load is given by:
- a)PL/4
- b)3PL/9
- c)3PL/16
- d)PL/16
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A concentrated load P acts on a simply supported beam of span L at a ...
R1 + R2 = P
R2 × L = P × L/4
R2 = P/4
R1 = 3P/4
Bending moment at the point of applied load:
Most Upvoted Answer
A concentrated load P acts on a simply supported beam of span L at a ...
Bending Moment at the Point of Application of Load
Given:
- Concentrated load P acts on a simply supported beam of span L.
- The load acts at a distance L/4 from the left end.
To find: The bending moment at the point of application of the load.
Formula for Bending Moment in a Simply Supported Beam:
The bending moment (M) at any point in a simply supported beam is given by the equation:
M = (P * a * b) / L
Where:
- P is the load acting on the beam
- a is the distance from the left support to the point of application of the load
- b is the distance from the point of application of the load to the right support
- L is the span of the beam
In this case, the load P acts at a distance L/4 from the left end, so:
- a = L/4
- b = L - L/4 = 3L/4
Substituting these values into the equation for bending moment, we get:
M = (P * (L/4) * (3L/4)) / L
Simplifying the expression, we have:
M = (3P * L^2) / (16 * L)
Canceling out the common factors, we get:
M = (3P * L) / 16
Therefore, the bending moment at the point of application of the load is given by PL/16, which corresponds to option C.
Given:
- Concentrated load P acts on a simply supported beam of span L.
- The load acts at a distance L/4 from the left end.
To find: The bending moment at the point of application of the load.
Formula for Bending Moment in a Simply Supported Beam:
The bending moment (M) at any point in a simply supported beam is given by the equation:
M = (P * a * b) / L
Where:
- P is the load acting on the beam
- a is the distance from the left support to the point of application of the load
- b is the distance from the point of application of the load to the right support
- L is the span of the beam
In this case, the load P acts at a distance L/4 from the left end, so:
- a = L/4
- b = L - L/4 = 3L/4
Substituting these values into the equation for bending moment, we get:
M = (P * (L/4) * (3L/4)) / L
Simplifying the expression, we have:
M = (3P * L^2) / (16 * L)
Canceling out the common factors, we get:
M = (3P * L) / 16
Therefore, the bending moment at the point of application of the load is given by PL/16, which corresponds to option C.
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Community Answer
A concentrated load P acts on a simply supported beam of span L at a ...
R1 + R2 = P
R2 × L = P × L/4
R2 = P/4
R1 = 3P/4
Bending moment at the point of applied load:
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