Cantilevered Beams

A cantilevered beam is obtained by clamping the beam at one of its ends. The static deformation of the beam can be modelled with the following fourth order differential equation:

w''''(x)=q(x)/(EI)

where q(x) is the load, E is the Young's modulus constant dependent upon the material, and I is the moment of inertia of the beam.

The following boundary conditions must also be taken into account:

w(0) = w'(0) = w''(L) = 0
w'''(L) = -mg

The solution to this differential equation is a function describing the position of the beam. It can be found by simple integration, the topic of our discussion here.

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Jennifer Powell<jpowell@geom.umn.edu>

Fati Liamidi<liamidi@geom.umn.edu>