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For a rectangular section, the ratio of the maximum and average shear stresses is
- a)1.5
- b)2
- c)2.5
- d)3
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
For a rectangular section, the ratio of the maximum and average shear ...
τmax = 1.5 τavg
Most Upvoted Answer
For a rectangular section, the ratio of the maximum and average shear ...
Explanation:
Maximum Shear Stress:
- The maximum shear stress in a rectangular section occurs at the neutral axis, which is at the center of the section.
- The formula for calculating the maximum shear stress is: τ_max = VQ / It, where V is the shear force, Q is the first moment of area about the neutral axis, I is the moment of inertia of the entire section, and t is the thickness of the section.
Average Shear Stress:
- The average shear stress in a rectangular section is calculated by dividing the shear force by the cross-sectional area of the section.
- The formula for average shear stress is: τ_avg = V / A, where V is the shear force and A is the cross-sectional area of the section.
Ratio of Maximum and Average Shear Stresses:
- To find the ratio of the maximum and average shear stresses, we need to compare the formulas for maximum and average shear stresses.
- Divide the formula for maximum shear stress by the formula for average shear stress: τ_max / τ_avg = (VQ / It) / (V / A) = AQ / It.
- For a rectangular section, Q / t = h / 2, where h is the height of the rectangle.
- Therefore, the ratio of maximum and average shear stresses is: τ_max / τ_avg = Ah / 2It = h / 2t.
Conclusion:
- For a rectangular section, the ratio of the maximum and average shear stresses is h / 2t.
- Since the height of a rectangle is twice the thickness (h = 2t), the ratio simplifies to 2 / 2 = 1.5.
- Hence, the correct answer is option 'A' (1.5).
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