How do I calculate stress and deflection for a simple beam?
Simply supported on both ends – rectangular cross section, either a single load at mid span, or a continuous distributed load across the whole span – how do I find the max deflection in the middle and the max stress (and the location of the max stress) on the beam? Thanks.
Tags: beam, calculate, deflection, Simple, Stress
July 20th, 2008 at 2:14 am
The maximum stress is calculated from the following relation:
sigma = Mc / I
where M is the applied moment, c is the distance from the neutral axis (generally you are interested in the maximum stress so this is the distance from the neutral axis to the outer fiber of the beam), and I is the moment of inertia.
For a simply supported beam with a concentrated load at mid-span:
max moment = W*L / 4 where W is the load & L is the beam length.
max deflection = -W*L^3/(48*E*I) where E is Young’s modulus
For a simply supported beam with a uniform load:
max moment = W*L / 8 where W is the uniform load & L is the beam length.
max deflection = -5*W*L^3/(384*E*I) where E is Young’s modulus
In both cases the max moment & max deflection occur at the center of the beam span.