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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...
Understanding Bending Moments in Simply Supported Beams
In structural engineering, the bending moment at a point in a beam is crucial for analyzing the beam's strength and stability. For a simply supported beam with a concentrated load, we can calculate the bending moment at the point of application.
Given Conditions
- A simply supported beam of length L.
- A concentrated load P applied at a distance L/3 from the left support.
Calculating Reaction Forces
1. Determine the support reactions:
- Let the left support be A and the right support be B.
- The total load P causes a reaction at both supports.
- Using equilibrium equations, the reactions can be calculated.
2. Calculate Reaction at A (RA):
- RA = (2/3)P (as the load P is closer to B).
3. Calculate Reaction at B (RB):
- RB = (1/3)P.
Calculating Bending Moment at Load Application
To find the bending moment (M) at the point where the load P is applied (L/3 from A):
1. Use the moment equation:
- M = RA * distance from A to the load point.
- Distance = L/3.
2. Substituting the values:
- M = (2/3)P * (L/3) = (2PL)/(9).
Conclusion
Thus, the bending moment at the point of application of the load P, which is at a distance L/3 from the left support, is given by:
- Final Result: M = 2PL/9.
This confirms that the correct answer is option 'D', 2PL/9.
In structural engineering, the bending moment at a point in a beam is crucial for analyzing the beam's strength and stability. For a simply supported beam with a concentrated load, we can calculate the bending moment at the point of application.
Given Conditions
- A simply supported beam of length L.
- A concentrated load P applied at a distance L/3 from the left support.
Calculating Reaction Forces
1. Determine the support reactions:
- Let the left support be A and the right support be B.
- The total load P causes a reaction at both supports.
- Using equilibrium equations, the reactions can be calculated.
2. Calculate Reaction at A (RA):
- RA = (2/3)P (as the load P is closer to B).
3. Calculate Reaction at B (RB):
- RB = (1/3)P.
Calculating Bending Moment at Load Application
To find the bending moment (M) at the point where the load P is applied (L/3 from A):
1. Use the moment equation:
- M = RA * distance from A to the load point.
- Distance = L/3.
2. Substituting the values:
- M = (2/3)P * (L/3) = (2PL)/(9).
Conclusion
Thus, the bending moment at the point of application of the load P, which is at a distance L/3 from the left support, is given by:
- Final Result: M = 2PL/9.
This confirms that the correct answer is option 'D', 2PL/9.
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A concentrated load P acts on a simply supported beam of span L at a d...
For vertical equilibrium
Taking moment about R1 , we have
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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