Deflection comparison: point load at midspan vs UDL (same total load) Beam A: simply supported, span L, central point load W. Beam B: simply supported, uniformly distributed load with total load W. Find δA/δB, the ratio of their maximum midspan deflections. Choose the correct value.
Mechanical Engineering
Strength of Materials
Difficulty: Medium
Choose an option
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A5/8
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B8/5
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C5/4
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D4/5
Answer
Correct Answer: 8/5
Explanation
FormulasPoint load at midspan: δmax = W L³ / (48 E I)UDL of intensity w = W/L: δmax = 5 w L⁴ / (384 E I) = 5 (W/L) L⁴ /(384 E I) = 5 W L³ /(384 E I)
Compute ratioδA/δB = [W L³ /(48 E I)] / [5 W L³ /(384 E I)] = (1/48) ÷ (5/384) = 384/240 = 8/5.
Final Answer8/5