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If a uniform bar is supported at one end in a vertical direction and loaded at the bottom end by a load equal to the weight of the bar, the strain by a load equal to the weight of the bar, the strain energy as compared to that due to self-weight will be-
- a)Same
- b)Half
- c)Twice
- d)Thrice
Correct answer is option 'C'. Can you explain this answer?
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If a uniform bar is supported at one end in a vertical direction and ...
Strain energy (U)(=½(WΔ))
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Now, axil deformation due to load W is given by (Δ1=WL/AE)axial deformation due to self-weight W is given by (Δ2=WL/2AE)
(NowΔ1=2Δ2)(and U∞Δ)
Hence strain energy due to load W is given by (U1=(1/2)WΔ1)
(U1=2U2)
Hence strain energy as compared to that due to self-weight will be double.
Hence the option C is correct.
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If a uniform bar is supported at one end in a vertical direction and ...
Explanation:
- When a uniform bar is supported at one end in a vertical direction and loaded at the bottom end by a load equal to the weight of the bar, the bar undergoes deformation due to the applied load.
- The strain energy stored in the bar is a measure of the work done on the bar to deform it.
- The strain energy due to self-weight of the bar can be calculated using the formula U = (1/2)W^2L^3/3EI, where W is the weight of the bar, L is the length of the bar, E is the modulus of elasticity of the bar material, and I is the moment of inertia of the bar cross-section.
- The strain energy due to the applied load can be calculated using the formula U = PL/2, where P is the applied load and L is the length of the bar.
- Since the applied load is equal to the weight of the bar, P = W, and the strain energy due to the applied load is U = WL/2.
- The ratio of strain energies due to the applied load and self-weight is U_applied/U_self-weight = (WL/2)/(W^2L^3/3EI) = 3EI/2L^2.
- Since the modulus of elasticity and moment of inertia are constant for a given bar material and cross-section, the ratio of strain energies depends only on the length of the bar.
- When the bar length is doubled, the ratio of strain energies is multiplied by (2^2)/(3*1) = 4/3.
- Therefore, the strain energy due to the applied load is twice that due to self-weight when the bar length is reduced to half, and thrice that due to self-weight when the bar length is doubled.
Hence, the correct answer is option C, i.e., the strain energy due to the applied load is twice that due to self-weight when the bar length is reduced to half, and thrice that due to self-weight when the bar length is doubled.
- When a uniform bar is supported at one end in a vertical direction and loaded at the bottom end by a load equal to the weight of the bar, the bar undergoes deformation due to the applied load.
- The strain energy stored in the bar is a measure of the work done on the bar to deform it.
- The strain energy due to self-weight of the bar can be calculated using the formula U = (1/2)W^2L^3/3EI, where W is the weight of the bar, L is the length of the bar, E is the modulus of elasticity of the bar material, and I is the moment of inertia of the bar cross-section.
- The strain energy due to the applied load can be calculated using the formula U = PL/2, where P is the applied load and L is the length of the bar.
- Since the applied load is equal to the weight of the bar, P = W, and the strain energy due to the applied load is U = WL/2.
- The ratio of strain energies due to the applied load and self-weight is U_applied/U_self-weight = (WL/2)/(W^2L^3/3EI) = 3EI/2L^2.
- Since the modulus of elasticity and moment of inertia are constant for a given bar material and cross-section, the ratio of strain energies depends only on the length of the bar.
- When the bar length is doubled, the ratio of strain energies is multiplied by (2^2)/(3*1) = 4/3.
- Therefore, the strain energy due to the applied load is twice that due to self-weight when the bar length is reduced to half, and thrice that due to self-weight when the bar length is doubled.
Hence, the correct answer is option C, i.e., the strain energy due to the applied load is twice that due to self-weight when the bar length is reduced to half, and thrice that due to self-weight when the bar length is doubled.
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If a uniform bar is supported at one end in a vertical direction and loaded at the bottom end by a load equal to the weight of the bar, the strain by a load equal to the weight of the bar, the strain energy as compared to that due to self-weight will be-a)Sameb)Halfc)Twiced)ThriceCorrect answer is option 'C'. Can you explain this answer?
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If a uniform bar is supported at one end in a vertical direction and loaded at the bottom end by a load equal to the weight of the bar, the strain by a load equal to the weight of the bar, the strain energy as compared to that due to self-weight will be-a)Sameb)Halfc)Twiced)ThriceCorrect answer is option 'C'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about If a uniform bar is supported at one end in a vertical direction and loaded at the bottom end by a load equal to the weight of the bar, the strain by a load equal to the weight of the bar, the strain energy as compared to that due to self-weight will be-a)Sameb)Halfc)Twiced)ThriceCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a uniform bar is supported at one end in a vertical direction and loaded at the bottom end by a load equal to the weight of the bar, the strain by a load equal to the weight of the bar, the strain energy as compared to that due to self-weight will be-a)Sameb)Halfc)Twiced)ThriceCorrect answer is option 'C'. Can you explain this answer?.
If a uniform bar is supported at one end in a vertical direction and loaded at the bottom end by a load equal to the weight of the bar, the strain by a load equal to the weight of the bar, the strain energy as compared to that due to self-weight will be-a)Sameb)Halfc)Twiced)ThriceCorrect answer is option 'C'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about If a uniform bar is supported at one end in a vertical direction and loaded at the bottom end by a load equal to the weight of the bar, the strain by a load equal to the weight of the bar, the strain energy as compared to that due to self-weight will be-a)Sameb)Halfc)Twiced)ThriceCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a uniform bar is supported at one end in a vertical direction and loaded at the bottom end by a load equal to the weight of the bar, the strain by a load equal to the weight of the bar, the strain energy as compared to that due to self-weight will be-a)Sameb)Halfc)Twiced)ThriceCorrect answer is option 'C'. Can you explain this answer?.
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