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There are two beams of equal length L and a load P is acting on centre of both beams. One of them is simply supported at both ends while the other one is fixed at both ends. Deflection of centre of simply supported beam will be __________ times that of defection of centre of fixed beam.
- a)1
- b)2
- c)3
- d)4
Correct answer is option 'D'. Can you explain this answer?
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There are two beams of equal length L and a load P is acting on centre...
Answer: d
Explanation: Maximum moment developed in simply supported beam will be twice that of fixed supported and hence, we can find deflections.
Explanation: Maximum moment developed in simply supported beam will be twice that of fixed supported and hence, we can find deflections.
Most Upvoted Answer
There are two beams of equal length L and a load P is acting on centre...
For simply supported beam deflection WL*3 /48EI and for Fixed beam WL*3 /192 EI
Then ratio is 4
Then ratio is 4
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There are two beams of equal length L and a load P is acting on centre...
Two beams of equal length L are subjected to a load P acting at their centers. One beam is simply supported at both ends, while the other beam is fixed at both ends. We need to determine the ratio of deflection at the center of the simply supported beam to the deflection at the center of the fixed beam.
The deflection of a beam under a load depends on several factors, including the beam's length, support conditions, and the magnitude and distribution of the load. In this case, the length of both beams is given as L, and the load is acting at the center of each beam. We can analyze the deflection using basic concepts of beam bending theory.
1. Deflection of a Simply Supported Beam:
A simply supported beam is supported at both ends and can freely rotate at the supports. When a load is applied at the center of the beam, the beam bends into a concave shape. The maximum deflection occurs at the center of the beam.
2. Deflection of a Fixed Beam:
A fixed beam is rigidly supported at both ends and cannot rotate. When a load is applied at the center of the beam, the beam undergoes a combination of bending and axial deformation. The maximum deflection also occurs at the center of the beam.
Now, let's compare the deflection of the center of the simply supported beam to that of the fixed beam.
- The deflection of a simply supported beam can be calculated using the formula:
δ_s = (P * L^3) / (48 * E * I)
where δ_s is the deflection at the center of the simply supported beam, P is the load, L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia of the beam's cross-sectional shape.
- The deflection of a fixed beam can be calculated using the formula:
δ_f = (P * L^3) / (192 * E * I)
where δ_f is the deflection at the center of the fixed beam.
Comparing the two formulas, we can see that the deflection of the fixed beam (δ_f) is four times smaller than the deflection of the simply supported beam (δ_s). Therefore, the deflection of the center of the simply supported beam will be four times greater than the deflection of the center of the fixed beam.
So, the correct answer is option 'd) 4'.
The deflection of a beam under a load depends on several factors, including the beam's length, support conditions, and the magnitude and distribution of the load. In this case, the length of both beams is given as L, and the load is acting at the center of each beam. We can analyze the deflection using basic concepts of beam bending theory.
1. Deflection of a Simply Supported Beam:
A simply supported beam is supported at both ends and can freely rotate at the supports. When a load is applied at the center of the beam, the beam bends into a concave shape. The maximum deflection occurs at the center of the beam.
2. Deflection of a Fixed Beam:
A fixed beam is rigidly supported at both ends and cannot rotate. When a load is applied at the center of the beam, the beam undergoes a combination of bending and axial deformation. The maximum deflection also occurs at the center of the beam.
Now, let's compare the deflection of the center of the simply supported beam to that of the fixed beam.
- The deflection of a simply supported beam can be calculated using the formula:
δ_s = (P * L^3) / (48 * E * I)
where δ_s is the deflection at the center of the simply supported beam, P is the load, L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia of the beam's cross-sectional shape.
- The deflection of a fixed beam can be calculated using the formula:
δ_f = (P * L^3) / (192 * E * I)
where δ_f is the deflection at the center of the fixed beam.
Comparing the two formulas, we can see that the deflection of the fixed beam (δ_f) is four times smaller than the deflection of the simply supported beam (δ_s). Therefore, the deflection of the center of the simply supported beam will be four times greater than the deflection of the center of the fixed beam.
So, the correct answer is option 'd) 4'.
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There are two beams of equal length L and a load P is acting on centre of both beams. One of them is simply supported at both ends while the other one is fixed at both ends. Deflection of centre of simply supported beam will be __________ times that of defection of centre of fixed beam.a)1b)2c)3d)4Correct answer is option 'D'. Can you explain this answer?
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