Maximum beam stress calculation 1

[tnteng]

I was wondering if anyone could tell me what is the standard for calculation the maximum stress on the outer fiber of a beam that is loaded laterally such that it has a beanding stress and a shear stress. My current understanding is that if the beam is short then the bending and shear stresses would need to be combined. I have been told that when these are combined, the aveage shear stress is combined with the maximum bending stress using Von Mises formula. If it is a wide flange section then only the web of the beam is considered when calculating the shear stress. When the web of the beam is considered, would the average shear stress (as opposes to the tranverse shear) on the web be combined with the max bending stress on the flange outer fiber?

How would the shear formula VQ/IT fit into the above analyses. Is it used in these calculations or only the average shear stress?

Thanks in advance,

 

[ishvaaag]

Well, for ductile materials such steel one may choose to elect a Von Mises criterium as the onset of failure. There is much more to be said, but what precedes can also be.

So in this setup you effectively need to make a Von Mises check for every point in the beam, if you want to be as complete in the check. This of course involves first getting the relevant stresses, for a typical steel beam, longitudinal stresses coming from flexure at the point, and shear stresses at the point. Longitudinal stresses you may determine by

sigma=M/(I/y) where y is at the point, and the formula you refer to provides you with the shear. Then you combine it by Von Mises and you get the stress of comparison (or so we call it here) to be compared with the yield stress of the steel, Fy.

That is, you calculate stresses elastically, combine by Von Mises and check against Fy.

This said, experience proves that for ordinary rolled beams if and where suitably braced you can separately check the beam against moment and shear and get a satisfactory design. To ensure one does things well, one follows some standard, for others mainly to attest compliance of technical standards and for oneself to not forget something that is important.