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U_{e}= work done by all external forces
U_{i} = internal work or strain energy
Δ = final elongation of bar
Θ = final angular deflection
U_{i} is not developed when:
Answer: d
Explanation: U_{i} is developed when structure deforms, which is happening in other three options.
What will be the value of Ue if material is linear elastic? Axial force is increased from 0 to P gradually.
Answer: c
Explanation: Due to linear elasticity, we can substitute force in terms of P and Δ and then integrate wrt x to get the final answer.
What will be the work done force P if another load external load F’ causes deflection Δ’ in the above question?
Answer: d
Explanation: Here, P will remain constant. So, it will be a simple integration from 0 to Δ’.
Answer: c
Explanation: Here, P will remain constant. So, it will be a simple integration from 0 to Δ’.
What will be the value of U_{e} if material is linear elastic? Moment is increased from 0 to m gradually.
Answer: c
Explanation: Due to linear elasticity, we can substitute moment in terms of M and θ and then integrate wrt x to get the final answer. Mdθ is done for moment to calculate work done.
What will be the work done force M if another load external load M’ causes deflection θ’ in the above question?
Answer: d
Explanation: Here, P will remain constant. So, it will be a simple integration from 0 to Δ’.
What will be the work done by M’ in above question?
Answer: c
Explanation: Due to linear elasticity, we can substitute moment in terms of M and θ and then integrate wrt x to get the final answer. Mdθ is done for moment to calculate work done.
If an axial force N is applied gradually to a bar which is linear elastic and has a constant cross sectional area A and length L, what will be Δ?
Answer: d
Explanation: Hooke’s law will be valid here as material is linear elastic.
In the above question, what will be the value of U_{i} ?
Answer: c
Explanation: Once deformation is known, we can calculate the work done using earlier equations and then U_{e} = U_{i}.
What will be the value of dU_{i} in terms of E and I?
Answer: c
Explanation: Relation between dθ and M/EI is known. So, we can use that to get results.
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