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By application of tensile force, the crosssectional area of bar P is first reduced by 30% and then by an additional 20%. Another bar Q of the same material is reduced in crosssectional area by 50% in a single step by applying tensile force.
After deformation, the true strain in bar P and bar Q will, respectively be
 
[PI 2008]
  • a)
    0.5 and 0.5
  • b)
    0.58 and 0.69
  • c)
    0.69 and 0.69
  • d)
    0.78 and 1.00
Correct answer is option 'B'. Can you explain this answer?
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By application of tensile force, the crosssectional area of bar P is f...
Bar P:
Step 1: Reduction of cross-sectional area by 30%
Step 2: Additional reduction of cross-sectional area by 20%

Bar Q:
Single step reduction of cross-sectional area by 50%

To find the true strain in each bar, we need to compute the total reduction in cross-sectional area and then apply the formula for true strain.

Bar P:

Step 1: Reduction of cross-sectional area by 30%
- Let the initial cross-sectional area of bar P be A.
- After the first reduction, the cross-sectional area becomes 0.7A (30% reduction).

Step 2: Additional reduction of cross-sectional area by 20%
- After the second reduction, the cross-sectional area becomes 0.7A * 0.8 = 0.56A (20% reduction).

True strain in bar P:
- The true strain is given by the formula: ε = ln(Af/Ai), where Af is the final cross-sectional area and Ai is the initial cross-sectional area.
- In this case, Af = 0.56A and Ai = A.
- Therefore, the true strain is ε = ln(0.56A/A) = ln(0.56) = -0.58 (negative because the area is reducing).

Bar Q:

Single step reduction of cross-sectional area by 50%
- Let the initial cross-sectional area of bar Q be A.
- After the reduction, the cross-sectional area becomes 0.5A (50% reduction).

True strain in bar Q:
- Similar to bar P, we can apply the formula: ε = ln(Af/Ai), where Af is the final cross-sectional area and Ai is the initial cross-sectional area.
- In this case, Af = 0.5A and Ai = A.
- Therefore, the true strain is ε = ln(0.5A/A) = ln(0.5) = -0.69 (negative because the area is reducing).

Therefore, the true strain in bar P is 0.58 and the true strain in bar Q is 0.69. Hence, the correct answer is option B.
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By application of tensile force, the crosssectional area of bar P is first reduced by 30% and then by an additional 20%. Another bar Q of the same material is reduced in crosssectional area by 50% in a single step by applying tensile force.After deformation, the true strain in bar P and bar Q will, respectively be[PI 2008]a)0.5 and 0.5b)0.58 and 0.69c)0.69 and 0.69d)0.78 and 1.00Correct answer is option 'B'. Can you explain this answer?
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By application of tensile force, the crosssectional area of bar P is first reduced by 30% and then by an additional 20%. Another bar Q of the same material is reduced in crosssectional area by 50% in a single step by applying tensile force.After deformation, the true strain in bar P and bar Q will, respectively be[PI 2008]a)0.5 and 0.5b)0.58 and 0.69c)0.69 and 0.69d)0.78 and 1.00Correct answer is option 'B'. 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 By application of tensile force, the crosssectional area of bar P is first reduced by 30% and then by an additional 20%. Another bar Q of the same material is reduced in crosssectional area by 50% in a single step by applying tensile force.After deformation, the true strain in bar P and bar Q will, respectively be[PI 2008]a)0.5 and 0.5b)0.58 and 0.69c)0.69 and 0.69d)0.78 and 1.00Correct answer is option 'B'. 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 By application of tensile force, the crosssectional area of bar P is first reduced by 30% and then by an additional 20%. Another bar Q of the same material is reduced in crosssectional area by 50% in a single step by applying tensile force.After deformation, the true strain in bar P and bar Q will, respectively be[PI 2008]a)0.5 and 0.5b)0.58 and 0.69c)0.69 and 0.69d)0.78 and 1.00Correct answer is option 'B'. Can you explain this answer?.
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