For a simply supported rectangular beam under the same central load and made of the same material, the central depression varies as δ ∝ L³ / [bd³]. The beam length is changed to 3L/2, its width is changed to b/2 and its thickness is changed to 2d. If δ'/δ = N/32, find N.
Physics · Properties of solid and fluid · properties of solid stress ,strain and modulus of elasticity
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Question

For a simply supported rectangular beam under the same central load and made of the same material, the central depression varies as δ ∝ L³ / [bd³]. The beam length is changed to 3L/2, its width is changed to b/2 and its thickness is changed to 2d. If δ'/δ = N/32, find N.

Physics · Properties of solid and fluid · properties of solid stress ,strain and modulus of elasticity

G1 Physics · Accepted Answer

Using δ ∝ L³ / [bd³], we obtain δ'/δ = (3/2)³ × [b/(b/2)] × [d³/(2d)³]. Therefore, δ'/δ = 27/8 ×2 ×1/8. Hence, δ'/δ = 54/64 = 27/32. Thus, N = 27.