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A flat plate 30mm wide and “t”mm wide is subjected to a tensile force of 5kN. The plate has a circular hole of diameter 15mm with the centre coinciding with the diagonal intersection point of the rectangle. If stress concentration factor=2.16, find the thickness of the plate if maximum allowable tensile stress is 80N/mm².
- a)9 mm
- b)10 mm
- c)11 mm
- d)12 mm
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A flat plate 30mm wide and “t”mm wide is subjected to a te...
σ=P/ (w-d) x t
σ=5000/(30-15)xt ;
σ(max)=K x σ
σ(max)=2.16 x σ
σ(max)=720/t;
Also, σ(max)=80.
so 80 = 720/t
t = 9 mm
Most Upvoted Answer
A flat plate 30mm wide and “t”mm wide is subjected to a te...
Given data:
- Width of the plate (b) = 30 mm
- Diameter of the hole (d) = 15 mm
- Tensile force (P) = 5 kN = 5000 N
- Stress concentration factor (Kt) = 2.16
- Maximum allowable tensile stress (σallow) = 80 N/mm²
Calculations:
- Total width of the plate with the hole = b + d = 30 mm + 15 mm = 45 mm
- Area of the plate without the hole = b * t
- Area of the hole = π*(d/2)² = π*(15/2)² = 88.36 mm²
- Area of the plate with the hole = Area of the plate without the hole - Area of the hole = 30t - 88.36
- Maximum stress without the hole = P / (b * t) = 5000 / (30t) = 166.67 / t N/mm²
- Maximum stress with the hole = Maximum stress without the hole * Stress concentration factor = 166.67 / t * 2.16 = 360 / t N/mm²
Solving for thickness:
- Maximum stress with the hole = σallow
- 360 / t = 80
- t = 360 / 80 = 4.5 mm
Final answer:
The thickness of the plate should be 9 mm (option A) to ensure that the maximum stress does not exceed the allowable stress limit.
- Width of the plate (b) = 30 mm
- Diameter of the hole (d) = 15 mm
- Tensile force (P) = 5 kN = 5000 N
- Stress concentration factor (Kt) = 2.16
- Maximum allowable tensile stress (σallow) = 80 N/mm²
Calculations:
- Total width of the plate with the hole = b + d = 30 mm + 15 mm = 45 mm
- Area of the plate without the hole = b * t
- Area of the hole = π*(d/2)² = π*(15/2)² = 88.36 mm²
- Area of the plate with the hole = Area of the plate without the hole - Area of the hole = 30t - 88.36
- Maximum stress without the hole = P / (b * t) = 5000 / (30t) = 166.67 / t N/mm²
- Maximum stress with the hole = Maximum stress without the hole * Stress concentration factor = 166.67 / t * 2.16 = 360 / t N/mm²
Solving for thickness:
- Maximum stress with the hole = σallow
- 360 / t = 80
- t = 360 / 80 = 4.5 mm
Final answer:
The thickness of the plate should be 9 mm (option A) to ensure that the maximum stress does not exceed the allowable stress limit.
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A flat plate 30mm wide and “t”mm wide is subjected to a tensile force of 5kN. The plate has a circular hole of diameter 15mm with the centre coinciding with the diagonal intersection point of the rectangle. If stress concentration factor=2.16, find the thickness of the plate if maximum allowable tensile stress is 80N/mm².a)9 mmb)10 mmc)11 mmd)12 mmCorrect answer is option 'A'. Can you explain this answer?
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A flat plate 30mm wide and “t”mm wide is subjected to a tensile force of 5kN. The plate has a circular hole of diameter 15mm with the centre coinciding with the diagonal intersection point of the rectangle. If stress concentration factor=2.16, find the thickness of the plate if maximum allowable tensile stress is 80N/mm².a)9 mmb)10 mmc)11 mmd)12 mmCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A flat plate 30mm wide and “t”mm wide is subjected to a tensile force of 5kN. The plate has a circular hole of diameter 15mm with the centre coinciding with the diagonal intersection point of the rectangle. If stress concentration factor=2.16, find the thickness of the plate if maximum allowable tensile stress is 80N/mm².a)9 mmb)10 mmc)11 mmd)12 mmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A flat plate 30mm wide and “t”mm wide is subjected to a tensile force of 5kN. The plate has a circular hole of diameter 15mm with the centre coinciding with the diagonal intersection point of the rectangle. If stress concentration factor=2.16, find the thickness of the plate if maximum allowable tensile stress is 80N/mm².a)9 mmb)10 mmc)11 mmd)12 mmCorrect answer is option 'A'. Can you explain this answer?.
A flat plate 30mm wide and “t”mm wide is subjected to a tensile force of 5kN. The plate has a circular hole of diameter 15mm with the centre coinciding with the diagonal intersection point of the rectangle. If stress concentration factor=2.16, find the thickness of the plate if maximum allowable tensile stress is 80N/mm².a)9 mmb)10 mmc)11 mmd)12 mmCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A flat plate 30mm wide and “t”mm wide is subjected to a tensile force of 5kN. The plate has a circular hole of diameter 15mm with the centre coinciding with the diagonal intersection point of the rectangle. If stress concentration factor=2.16, find the thickness of the plate if maximum allowable tensile stress is 80N/mm².a)9 mmb)10 mmc)11 mmd)12 mmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A flat plate 30mm wide and “t”mm wide is subjected to a tensile force of 5kN. The plate has a circular hole of diameter 15mm with the centre coinciding with the diagonal intersection point of the rectangle. If stress concentration factor=2.16, find the thickness of the plate if maximum allowable tensile stress is 80N/mm².a)9 mmb)10 mmc)11 mmd)12 mmCorrect answer is option 'A'. Can you explain this answer?.
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