A (hopefully) easy question to answer about cantilever beams

[ralphowilson]

Hi guys,

just wondering if you could help me out?

For a standard rectangular cross-section cantilever beam with a concentrated end load how do i work out the top surface stress at a point along the beam? do i just use sigma=My/I where y=half the depth of the beam and M=end load * distance from end load to point of interest ...?

This sounds right but I'm not certain..sorry, hope this is easy enough to answer.

thanks a lot!

Ralph

 

[Pyrrhus]

What do you mean exactly?

If you want the flexionant stresses to the extreme fiber on compression (or tension) of the beam, M will be the corresponding moment at the distance (where you want the stresses) from the diagram (which in this case is a triangle), y will be half of the depth of the beam, and I the area moment of inertia of the beam in the axis of the acting moment.

 

[AlephZero]

Sure, your standard formula will apply, unless there is something you didn't tell us about which means it does not apply.

For example if it is a short beam, or you want accurate stresses where a load or restraint is applied, or there are large deflections, or the material is anisotropic, or the loads are big enough to cause nonlinear material behavour, or ...