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A bronze bar is fastened between a steel bar and an aluminum bar as shown in fig. 1.
Axial loads are applied at the positions shown. Find the total deformation of the
assembly.
Consider 𝐸𝑠 = 2 × 105 𝑀𝑃𝑎, 𝐸𝑏 = 0.83 × 105 𝑀𝑃𝑎 and 𝐸𝑎𝑙 = 0.7 × 105 𝑀𝑃𝑎?
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A bronze bar is fastened between a steel bar and an aluminum bar as sh...
Analysis of Deformation in Assembly:
- Given Data:
- Young's modulus of steel (Es) = 2 × 105 MPa
- Young's modulus of bronze (Eb) = 0.83 × 105 MPa
- Young's modulus of aluminum (Eal) = 0.7 × 105 MPa
- Calculating Total Deformation:
- Let L be the total length of the assembly
- Let P1, P2, P3 be the applied axial loads at the positions shown in the diagram
- Calculations:
- Let δs, δb, δal be the deformations in steel, bronze, and aluminum bars respectively
- Using the formula for deformation: δ = PL/AE
- δs = P1L/AsEs, δb = (P1+P2)L/AbEb, δal = (P1+P2+P3)L/AalEal
- Total deformation δtotal = δs + δb + δal
- Substitute Values:
- Substitute the given values of Es, Eb, Eal, P1, P2, P3, L, As, Ab, Aal into the above equations
- Calculate the individual deformations δs, δb, δal
- Finally, sum up the individual deformations to get the total deformation δtotal
- Final Answer:
- After substituting the values and calculating the deformations, the total deformation of the assembly can be determined as δtotal
Therefore, by following the above analysis and calculations, the total deformation of the assembly can be accurately determined considering the given data and assumptions.
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A bronze bar is fastened between a steel bar and an aluminum bar as shown in fig. 1. Axial loads are applied at the positions shown. Find the total deformation of the assembly. Consider 𝐸𝑠 = 2 × 105 𝑀𝑃𝑎, 𝐸𝑏 = 0.83 × 105 𝑀𝑃𝑎 and 𝐸𝑎𝑙 = 0.7 × 105 𝑀𝑃𝑎?
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A bronze bar is fastened between a steel bar and an aluminum bar as shown in fig. 1. Axial loads are applied at the positions shown. Find the total deformation of the assembly. Consider 𝐸𝑠 = 2 × 105 𝑀𝑃𝑎, 𝐸𝑏 = 0.83 × 105 𝑀𝑃𝑎 and 𝐸𝑎𝑙 = 0.7 × 105 𝑀𝑃𝑎? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A bronze bar is fastened between a steel bar and an aluminum bar as shown in fig. 1. Axial loads are applied at the positions shown. Find the total deformation of the assembly. Consider 𝐸𝑠 = 2 × 105 𝑀𝑃𝑎, 𝐸𝑏 = 0.83 × 105 𝑀𝑃𝑎 and 𝐸𝑎𝑙 = 0.7 × 105 𝑀𝑃𝑎? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bronze bar is fastened between a steel bar and an aluminum bar as shown in fig. 1. Axial loads are applied at the positions shown. Find the total deformation of the assembly. Consider 𝐸𝑠 = 2 × 105 𝑀𝑃𝑎, 𝐸𝑏 = 0.83 × 105 𝑀𝑃𝑎 and 𝐸𝑎𝑙 = 0.7 × 105 𝑀𝑃𝑎?.
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