Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > What will be the value of Ue if material is l...
Start Learning for Free
What will be the value of Ue if material is linear elastic? Axial force is increased from 0 to P gradually.
- a)1⁄4 P Δ
- b)1⁄3P Δ
- c)1⁄2P Δ
- d)P Δ
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
What will be the value of Ue if material is linear elastic? Axial forc...
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.
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.
Most Upvoted Answer
What will be the value of Ue if material is linear elastic? Axial forc...
If the material is linear elastic and the axial force is increased gradually from 0 to P, the value of Ue will depend on the material's stiffness or Young's modulus (E), the initial length of the material (L0), and the change in axial force (ΔP).
The formula for strain (ε) in a linear elastic material is given by:
ε = ΔL / L0
Where ΔL is the change in length and L0 is the initial length.
The formula for stress (σ) in a linear elastic material is given by:
σ = P / A
Where P is the axial force and A is the cross-sectional area.
Since the material is linear elastic, stress is directly proportional to strain:
σ = E * ε
Combining the above equations, we get:
P / A = E * ΔL / L0
Solving for ΔL, we get:
ΔL = (P * L0) / (E * A)
The value of Ue is equal to the change in potential energy, which is given by:
Ue = (1/2) * P * ΔL
Substituting the value of ΔL, we get:
Ue = (1/2) * P * (P * L0) / (E * A)
Therefore, the value of Ue when the axial force is increased gradually from 0 to P in a linear elastic material is:
Ue = (1/2) * (P^2 * L0) / (E * A)
The formula for strain (ε) in a linear elastic material is given by:
ε = ΔL / L0
Where ΔL is the change in length and L0 is the initial length.
The formula for stress (σ) in a linear elastic material is given by:
σ = P / A
Where P is the axial force and A is the cross-sectional area.
Since the material is linear elastic, stress is directly proportional to strain:
σ = E * ε
Combining the above equations, we get:
P / A = E * ΔL / L0
Solving for ΔL, we get:
ΔL = (P * L0) / (E * A)
The value of Ue is equal to the change in potential energy, which is given by:
Ue = (1/2) * P * ΔL
Substituting the value of ΔL, we get:
Ue = (1/2) * P * (P * L0) / (E * A)
Therefore, the value of Ue when the axial force is increased gradually from 0 to P in a linear elastic material is:
Ue = (1/2) * (P^2 * L0) / (E * A)
Attention Civil Engineering (CE) Students!
To make sure you are not studying endlessly, EduRev has designed Civil Engineering (CE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Civil Engineering (CE).
|
Explore Courses for Civil Engineering (CE) exam
|
|
Similar Civil Engineering (CE) Doubts
Top Courses for Civil Engineering (CE)View all
What will be the value of Ue if material is linear elastic? Axial force is increased from 0 to P gradually.a)1⁄4P Δb)1⁄3P Δc)1⁄2P Δd)P ΔCorrect answer is option 'C'. Can you explain this answer?
Question Description
What will be the value of Ue if material is linear elastic? Axial force is increased from 0 to P gradually.a)1⁄4P Δb)1⁄3P Δc)1⁄2P Δd)P ΔCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about What will be the value of Ue if material is linear elastic? Axial force is increased from 0 to P gradually.a)1⁄4P Δb)1⁄3P Δc)1⁄2P Δd)P ΔCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the value of Ue if material is linear elastic? Axial force is increased from 0 to P gradually.a)1⁄4P Δb)1⁄3P Δc)1⁄2P Δd)P ΔCorrect answer is option 'C'. Can you explain this answer?.
What will be the value of Ue if material is linear elastic? Axial force is increased from 0 to P gradually.a)1⁄4P Δb)1⁄3P Δc)1⁄2P Δd)P ΔCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about What will be the value of Ue if material is linear elastic? Axial force is increased from 0 to P gradually.a)1⁄4P Δb)1⁄3P Δc)1⁄2P Δd)P ΔCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the value of Ue if material is linear elastic? Axial force is increased from 0 to P gradually.a)1⁄4P Δb)1⁄3P Δc)1⁄2P Δd)P ΔCorrect answer is option 'C'. Can you explain this answer?.
Solutions for What will be the value of Ue if material is linear elastic? Axial force is increased from 0 to P gradually.a)1⁄4P Δb)1⁄3P Δc)1⁄2P Δd)P ΔCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free.
Here you can find the meaning of What will be the value of Ue if material is linear elastic? Axial force is increased from 0 to P gradually.a)1⁄4P Δb)1⁄3P Δc)1⁄2P Δd)P ΔCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
What will be the value of Ue if material is linear elastic? Axial force is increased from 0 to P gradually.a)1⁄4P Δb)1⁄3P Δc)1⁄2P Δd)P ΔCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for What will be the value of Ue if material is linear elastic? Axial force is increased from 0 to P gradually.a)1⁄4P Δb)1⁄3P Δc)1⁄2P Δd)P ΔCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of What will be the value of Ue if material is linear elastic? Axial force is increased from 0 to P gradually.a)1⁄4P Δb)1⁄3P Δc)1⁄2P Δd)P ΔCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice What will be the value of Ue if material is linear elastic? Axial force is increased from 0 to P gradually.a)1⁄4P Δb)1⁄3P Δc)1⁄2P Δd)P ΔCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
|
|
Explore Courses for Civil Engineering (CE) exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup