Maximum shear stress in an assymetric cross-section

[FEAnalyst]

TL;DR

Is it possible to calculate maximum shear stress due to bending of a beam with assymetric cross-section analytically ?

Hi,

the formula for average shear stress in cross-section due to bending is simple: $$\tau=\frac{V}{A}$$
There’s also a formula for maximum shear stress in cross-section: $$\tau_{max}=\frac{VQ}{Ib}$$
But, from what I know, this equation is limited to symmetric cross-sections (rectangular, I section, T section and so on). What about the asymmetric sections such as the L section ? Is it possible to calculate maximum shear stress analytically in such case ?

 

[Dr.D]

If we talk about an L section (an angle), how will it be loaded? Parallel to one of the sides (in which case you have non-principal axis bending), or will it be loaded along a principal axis?

 

[FEAnalyst]

To be honest, I didn't think about it. I just wonder if it's possible to calculate maximum shear stress in asymmetric cross-sections because all examples I've seen are symmetric in at least one axis. I've checked various books but none of them confirms nor denies that.

 

[Dr.D]

To be honest, I didn't think about it. I just wonder if it's possible to calculate maximum shear stress in asymmetric cross-sections because all examples I've seen are symmetric in at least one axis. I've checked various books but none of them confirms nor denies that.

Then this is a prime opportunity to work it out for yourself. No telling what you may learn in the process!

 

[jrmichler]

Yes, it is possible. My copy of Aircraft Structures by Peery has a chapter titled Beams With Unsymmetrical Cross Sections that discusses how to calculate shear in detail.