A timber shelf

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 timber shelf,

b = 45\,\mathrm{mm}

wide and

h = 95\,\mathrm{mm}

deep (

E = 11\,\mathrm{GPa}

), is built rigidly into a wall at

x=0

and rests on a bracket at its far end

x = L = 1.8\,\mathrm{m}

that prevents deflection but exerts no moment (a propped cantilever). It carries books modelled as a uniform load

q = 150\,\mathrm{N\,m^{-1}}

along its whole length. The shelf's own weight is ignored, and slopes are small enough for

\kappa = w''

. ((a)) Using the Euler-Bernoulli beam equation

EIw''''=q

with

w(0)=w'(0)=0

at the wall and

w(L)=w''(L)=0

at the bracket, find the bending moment at the wall and the force taken by the bracket. ((b)) Find the deflection at midspan,

x=L/2

Browse the problem library