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For a beam and a circular rod having the same cross-sectional area and subjected to the same load, what is the ratio of their depressions if the beam has a square cross-section?

1. 3: π
2. π: 3
3. 1: π
4. π: 1

Correct answer: 3: π

Solution

For equal area A: I_square = a^4/12 = A^2/12, I_circle = pi*r^4/4 = A^2/(4*pi). Since delta ~ 1/I, delta_beam:delta_rod = I_circle:I_square = (1/(4*pi)):(1/12) = 3:pi.

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