A short rectangular shelf bracket is modelled as a cantilever with span and depth

PHYSICS · Subjective · Fermi University Physics · Fluids & Continuum Physics · Solid continuum mechanics and complex fluids · Solid continuum mechanics and complex fluids

Bending, Ringing, Breaking and Flowing, Ch Torsion and bending of rods and beams

Problem

A short rectangular shelf bracket is modelled as a cantilever with span L=150 mmL = 150\,\mathrm{mm} and depth h=50 mmh = 50\,\mathrm{mm}, made of a material with Poisson's ratio ν=0.3\nu = 0.3. Using the quoted estimate that the shear deflection of a rectangular cantilever is a fraction δshearδbending≈0.8(hL)2\frac{\delta_{\text{shear}}}{\delta_{\text{bending}}} \approx 0.8\left(\frac{h}{L}\right)^2 of the bending deflection, estimate how large this fraction is for the bracket, and comment on whether treating it as a slender Euler-Bernoulli beam is reasonable.

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