A simply supported beam is obtained by balancing the beam on a pivot at each 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) = w''(L) = 0The 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.
Index
Explore: Simply supported beam experiment
Next: Doubly Supported Beams
Up: Introduction
Previous: Cantilevered Beams