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If the member is subjected to a tensile stress of PX compressive stress of PVC and tensile stress of pz along the X Y and Z direction respectively then the resultant strain X along the X direction would be?
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If the member is subjected to a tensile stress of PX compressive stres...
Calculation of Resultant Strain in X Direction
Given:
Tensile stress along X direction (PX) = P
Compressive stress along Y direction (PVC) = -P
Tensile stress along Z direction (PZ) = P
Formula:
The resultant strain in the X direction can be calculated using the equation:
εX = (1/E) [PX - ν(PVC + PZ)]
Where,
E = Young's modulus of elasticity
ν = Poisson's ratio
Explanation:
The given problem has provided the stress values acting along X, Y, and Z directions. We need to calculate the resultant strain in the X direction using the formula mentioned above.
The formula for calculating the resultant strain in the X direction is derived based on the assumption that the material behaves linearly, i.e., the strain is proportional to the stress applied to it. The Poisson's ratio is the ratio of the lateral strain to the longitudinal strain, and it helps to determine the deformation of a material in response to an applied stress.
Calculation:
Given that PX = P, PVC = -P, and PZ = P
Let us assume that the value of E = 2.1 x 105 N/mm2 and ν = 0.3
Substituting the values in the formula, we get:
εX = (1/2.1 x 105) [P - 0.3(-P + P)]
On simplifying the above equation, we get:
εX = (1/2.1 x 105) [2P]
εX = P/1.05 x 105 mm/mm
Therefore, the resultant strain in the X direction is P/1.05 x 105 mm/mm.
Conclusion:
Hence, the resultant strain in the X direction can be calculated using the given formula, which involves the Young's modulus of elasticity and the Poisson's ratio, based on the stress values acting along X, Y, and Z directions.
Given:
Tensile stress along X direction (PX) = P
Compressive stress along Y direction (PVC) = -P
Tensile stress along Z direction (PZ) = P
Formula:
The resultant strain in the X direction can be calculated using the equation:
εX = (1/E) [PX - ν(PVC + PZ)]
Where,
E = Young's modulus of elasticity
ν = Poisson's ratio
Explanation:
The given problem has provided the stress values acting along X, Y, and Z directions. We need to calculate the resultant strain in the X direction using the formula mentioned above.
The formula for calculating the resultant strain in the X direction is derived based on the assumption that the material behaves linearly, i.e., the strain is proportional to the stress applied to it. The Poisson's ratio is the ratio of the lateral strain to the longitudinal strain, and it helps to determine the deformation of a material in response to an applied stress.
Calculation:
Given that PX = P, PVC = -P, and PZ = P
Let us assume that the value of E = 2.1 x 105 N/mm2 and ν = 0.3
Substituting the values in the formula, we get:
εX = (1/2.1 x 105) [P - 0.3(-P + P)]
On simplifying the above equation, we get:
εX = (1/2.1 x 105) [2P]
εX = P/1.05 x 105 mm/mm
Therefore, the resultant strain in the X direction is P/1.05 x 105 mm/mm.
Conclusion:
Hence, the resultant strain in the X direction can be calculated using the given formula, which involves the Young's modulus of elasticity and the Poisson's ratio, based on the stress values acting along X, Y, and Z directions.
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If the member is subjected to a tensile stress of PX compressive stress of PVC and tensile stress of pz along the X Y and Z direction respectively then the resultant strain X along the X direction would be?
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If the member is subjected to a tensile stress of PX compressive stress of PVC and tensile stress of pz along the X Y and Z direction respectively then the resultant strain X along the X direction would be? 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 If the member is subjected to a tensile stress of PX compressive stress of PVC and tensile stress of pz along the X Y and Z direction respectively then the resultant strain X along the X direction would be? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the member is subjected to a tensile stress of PX compressive stress of PVC and tensile stress of pz along the X Y and Z direction respectively then the resultant strain X along the X direction would be?.
If the member is subjected to a tensile stress of PX compressive stress of PVC and tensile stress of pz along the X Y and Z direction respectively then the resultant strain X along the X direction would be? 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 If the member is subjected to a tensile stress of PX compressive stress of PVC and tensile stress of pz along the X Y and Z direction respectively then the resultant strain X along the X direction would be? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the member is subjected to a tensile stress of PX compressive stress of PVC and tensile stress of pz along the X Y and Z direction respectively then the resultant strain X along the X direction would be?.
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