Mechanical Engineering Exam > Mechanical Engineering Questions > A horizontal bar, fixed at one end (x = 0), h...
Start Learning for Free
A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100mm2. Its elastic modulus varies along its length as given by E(x) = 100e-x GPa, Where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (x=1). The axial displacement of the free end is _______ mm.
Correct answer is between '1.70,1.72'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and c...
Given that
P=10kN =10x103N , A = 100mm2
Most Upvoted Answer
A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and c...
Elastic modulus variation along the length of the bar
The elastic modulus of the bar varies along its length according to the equation:
E(x) = 100e-x GPa
where x is the length coordinate along the axis of the bar.
Calculation of the axial force
The axial force applied at the free end of the bar is given as 10 kN (kiloNewtons), which is equivalent to 10,000 N (Newtons).
Calculation of the axial displacement
The axial displacement at the free end of the bar can be determined by integrating the strain along the length of the bar and then solving for the displacement.
The strain at any point x along the bar can be calculated using Hooke's Law:
ε(x) = σ(x) / E(x)
where ε(x) is the strain, σ(x) is the stress, and E(x) is the elastic modulus at that point.
The stress at any point x along the bar can be calculated using the formula:
σ(x) = F(x) / A(x)
where σ(x) is the stress, F(x) is the force acting on the cross-sectional area at that point, and A(x) is the cross-sectional area at that point.
Substituting the given values, we have:
σ(x) = 10,000 N / (100 mm2 / 1,000 mm2) = 100 N/mm2 = 100 MPa
Substituting the calculated stress and the given elastic modulus equation into the strain equation, we have:
ε(x) = 100 MPa / (100e-x GPa)
Integrating the strain equation for the length of the bar from 0 to 1 m, we get:
Δx = ∫01 ε(x) dx
Using numerical integration techniques or software, we find that the displacement Δx is approximately equal to 1.71 mm.
Conclusion
The axial displacement of the free end of the bar under a tensile load of 10 kN is approximately 1.71 mm.
Attention Mechanical Engineering Students!
To make sure you are not studying endlessly, EduRev has designed Mechanical Engineering study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Mechanical Engineering.
|
Explore Courses for Mechanical Engineering exam
|
|
Similar Mechanical Engineering Doubts
Top Courses for Mechanical EngineeringView all
A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100mm2. Its elastic modulus varies along its length as given by E(x) = 100e-xGPa, Where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (x=1). The axial displacement of the free end is _______ mm.Correct answer is between '1.70,1.72'. Can you explain this answer?
Question Description
A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100mm2. Its elastic modulus varies along its length as given by E(x) = 100e-xGPa, Where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (x=1). The axial displacement of the free end is _______ mm.Correct answer is between '1.70,1.72'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100mm2. Its elastic modulus varies along its length as given by E(x) = 100e-xGPa, Where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (x=1). The axial displacement of the free end is _______ mm.Correct answer is between '1.70,1.72'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100mm2. Its elastic modulus varies along its length as given by E(x) = 100e-xGPa, Where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (x=1). The axial displacement of the free end is _______ mm.Correct answer is between '1.70,1.72'. Can you explain this answer?.
A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100mm2. Its elastic modulus varies along its length as given by E(x) = 100e-xGPa, Where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (x=1). The axial displacement of the free end is _______ mm.Correct answer is between '1.70,1.72'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100mm2. Its elastic modulus varies along its length as given by E(x) = 100e-xGPa, Where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (x=1). The axial displacement of the free end is _______ mm.Correct answer is between '1.70,1.72'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100mm2. Its elastic modulus varies along its length as given by E(x) = 100e-xGPa, Where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (x=1). The axial displacement of the free end is _______ mm.Correct answer is between '1.70,1.72'. Can you explain this answer?.
Solutions for A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100mm2. Its elastic modulus varies along its length as given by E(x) = 100e-xGPa, Where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (x=1). The axial displacement of the free end is _______ mm.Correct answer is between '1.70,1.72'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100mm2. Its elastic modulus varies along its length as given by E(x) = 100e-xGPa, Where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (x=1). The axial displacement of the free end is _______ mm.Correct answer is between '1.70,1.72'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100mm2. Its elastic modulus varies along its length as given by E(x) = 100e-xGPa, Where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (x=1). The axial displacement of the free end is _______ mm.Correct answer is between '1.70,1.72'. Can you explain this answer?, a detailed solution for A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100mm2. Its elastic modulus varies along its length as given by E(x) = 100e-xGPa, Where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (x=1). The axial displacement of the free end is _______ mm.Correct answer is between '1.70,1.72'. Can you explain this answer? has been provided alongside types of A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100mm2. Its elastic modulus varies along its length as given by E(x) = 100e-xGPa, Where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (x=1). The axial displacement of the free end is _______ mm.Correct answer is between '1.70,1.72'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100mm2. Its elastic modulus varies along its length as given by E(x) = 100e-xGPa, Where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (x=1). The axial displacement of the free end is _______ mm.Correct answer is between '1.70,1.72'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering 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