A particleboard shelf plank

PHYSICS · Multi-part · 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 particleboard shelf plank,

0.90\,\mathrm{m}

long,

0.20\,\mathrm{m}

wide and

18\,\mathrm{mm}

thick, rests on two brackets at its ends, one at each end, each acting as a pinned support that exerts no bending moment. Books of total mass

20\,\mathrm{kg}

are spread evenly along its length. The particleboard has

E = 4.0\,\mathrm{GPa}

. Take

g = 9.8\,\mathrm{m\,s^{-2}}

and neglect the plank's own weight. ((a)) Write down the boundary conditions at each end in terms of

w

and its derivatives. ((b)) Solve

EIw'''' = q

with those boundary conditions and find the deflection at the centre of the plank.

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