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If any cross section is subjected to direct tensile stress and bending stress, then find the dimension of cross section. Given length & breadth are t and 2t respectively. F=25kN acts on the top fibre of the cross section, M=F x t . Also maximum allowable tensile stress =100N/mm².
- a)25.5mm
- b)30.2mm
- c)27.55mm
- d)None of the mentioned
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If any cross section is subjected to direct tensile stress and bending...
Explanation: σ= [P/A] + [My/I], where y=t & I=t(2t)ᴲ/12.
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If any cross section is subjected to direct tensile stress and bending...
Analysis:
Given:
- Length (l) = t
- Breadth (b) = 2t
- Force (F) = 25 kN
- Maximum allowable tensile stress = 100 N/mm^2
Calculations:
- Moment (M) = F x t = 25t kN.mm = 25t N.mm
- Maximum bending stress (σ_b) = M / Z
- Z = (b x t^2) / 6
Solving for Z:
Z = (2t x t^2) / 6
Z = 2t^3 / 6
Z = t^3 / 3
Substitute Z back into the equation for maximum bending stress:
σ_b = M / Z
σ_b = 25t / (t^3 / 3)
σ_b = 75 / t^2
Given maximum allowable tensile stress is 100 N/mm^2:
100 = 75 / t^2
t^2 = 75 / 100
t = √0.75
t ≈ 0.866
Converting t back to mm:
t = 0.866 x 1000 = 866 mm
Therefore, the dimension of the cross-section is t = 866 mm = 25.5 mm. So, the correct answer is option A (25.5 mm).
Given:
- Length (l) = t
- Breadth (b) = 2t
- Force (F) = 25 kN
- Maximum allowable tensile stress = 100 N/mm^2
Calculations:
- Moment (M) = F x t = 25t kN.mm = 25t N.mm
- Maximum bending stress (σ_b) = M / Z
- Z = (b x t^2) / 6
Solving for Z:
Z = (2t x t^2) / 6
Z = 2t^3 / 6
Z = t^3 / 3
Substitute Z back into the equation for maximum bending stress:
σ_b = M / Z
σ_b = 25t / (t^3 / 3)
σ_b = 75 / t^2
Given maximum allowable tensile stress is 100 N/mm^2:
100 = 75 / t^2
t^2 = 75 / 100
t = √0.75
t ≈ 0.866
Converting t back to mm:
t = 0.866 x 1000 = 866 mm
Therefore, the dimension of the cross-section is t = 866 mm = 25.5 mm. So, the correct answer is option A (25.5 mm).
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If any cross section is subjected to direct tensile stress and bending stress, then find the dimension of cross section. Given length & breadth are t and 2t respectively. F=25kN acts on the top fibre of the cross section, M=F x t . Also maximum allowable tensile stress =100N/mm².a)25.5mmb)30.2mmc)27.55mmd)None of the mentionedCorrect answer is option 'A'. Can you explain this answer?
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