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bar a and b are made up of same material and are of same length but bar a has diameter d while bar b has diameter 2d.if both are subjected to same axial load ratio of strain energy of bar b to bar a?
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?bar a and b are made up of same material and are of same length but b...
Ratio of Strain Energy of Bar B to Bar A
Given Information
- Bar A and Bar B are made up of the same material and are of the same length
- Bar A has diameter d while Bar B has diameter 2d
- Both are subjected to the same axial load
Explanation
The strain energy stored in a body is given by the formula:
U = (1/2) x σ x ε x V
where U is the strain energy stored in the body, σ is the stress induced, ε is the strain produced, and V is the volume of the body.
From the given information, we know that:
- Bar A and Bar B are of the same length, so their volumes are the same
- Both are subjected to the same axial load
Therefore, the stress induced in both the bars will be the same.
The strain produced in Bar A is given by:
εA = σ / E
where E is the modulus of elasticity of the material of the bars.
The strain produced in Bar B is given by:
εB = εA / 2
since the diameter of Bar B is twice that of Bar A.
Therefore, the strain energy stored in Bar A is:
UA = (1/2) x σ x εA x V
The strain energy stored in Bar B is:
UB = (1/2) x σ x εB x V
Substituting the value of εB in the above equation, we get:
UB = (1/2) x σ x εA/2 x V
Cancelling out the common terms in the above equations, we get:
UB/UA = (1/2) x εA/2 = 1/4
Conclusion
The ratio of strain energy of Bar B to Bar A is 1:4.
Community Answer
?bar a and b are made up of same material and are of same length but b...
Steel bar 2 m in length elongates 1.5 mm when subjected to as your pull of 1100 kilo Newton the bar is 40 mm in diameter for a length of 1 m, 30 mm in diameter for a length of 0.6 m and 20 mm in diameter for the remaining length calculate the value of modules of elasticity
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?bar a and b are made up of same material and are of same length but bar a has diameter d while bar b has diameter 2d.if both are subjected to same axial load ratio of strain energy of bar b to bar a?
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?bar a and b are made up of same material and are of same length but bar a has diameter d while bar b has diameter 2d.if both are subjected to same axial load ratio of strain energy of bar b to bar a? 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 ?bar a and b are made up of same material and are of same length but bar a has diameter d while bar b has diameter 2d.if both are subjected to same axial load ratio of strain energy of bar b to bar a? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ?bar a and b are made up of same material and are of same length but bar a has diameter d while bar b has diameter 2d.if both are subjected to same axial load ratio of strain energy of bar b to bar a?.
?bar a and b are made up of same material and are of same length but bar a has diameter d while bar b has diameter 2d.if both are subjected to same axial load ratio of strain energy of bar b to bar a? 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 ?bar a and b are made up of same material and are of same length but bar a has diameter d while bar b has diameter 2d.if both are subjected to same axial load ratio of strain energy of bar b to bar a? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ?bar a and b are made up of same material and are of same length but bar a has diameter d while bar b has diameter 2d.if both are subjected to same axial load ratio of strain energy of bar b to bar a?.
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