Maximum beam stress calculation 2

[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,

 

[ccw]

Shear is normally understood as the slip boundary between planes. So, the extreme fiber of the flange of a beam cannot have shear by definition since it is a free surface.

Consider a beam of rectangular cross section. The bending stress at the extreme fiber is the classic (h/2) x M/I where I = (b x h**3)/12. The maximum transverse shear due to beam load for a rectangular cross section is not V / A {often referred to as the average shear where V is the beam vertical shear FORCE and A is Cross section Area} but (3/2) x V / A. For a solid circular cross section (solid round) beam it is (4/3) x V / A. For a circular thin wall tube, it is (2) x V / A. For most regular symmetric cross sections of beams, the maximum shear occurs at the geometric center of the beam cross section. Coincidently stress due to bending is typically zero at this point.

For stress fields located in between these two extremes, the combined shear and tensile stresses can be computed then resolved to principal stresses using appropriate techniques like the Mohr circle.

For short beams (approximating St. Venant's principle) where L<h and other special considerations such as very large deflections, extra wide beams, shear web instability, material does not obey Hooke's law, etc. then the above considerations do not apply or may yield only approximate results.