Shear Flow Distibution in a Redundant Cross Section

[KootK]

I need to determine the shear flow distribution in a non-standard cross section. Visualize the section like this:

Start with a square tube shape section, like an HSS. Then take the top and bottom flanges and extend them to the right beyond the right side of the tube about 2/3 the width of the tube. All flanges and tube walls are of the same thickness. The resulting shape is symmetrical about thee x-axis but not the y-axis.

Using VQ/I, I can cut a horizontal section through the webs and determine the total shear flow required at that section. Unfortunately, I don't know how to determine how that force is distributed between the two web elements that cross the horizontal shear plane.

Textbooks only seem to adress these kinds of shapes when they are symmetrical about the axis of the applied shear load, in which case the distribution is obvious (symmetry). Does anybody have any ideas on how I might solve this problem, short of performing an FEM analysis?

Thanks for your help.

 

[Lion06]

I would think that as long as it is loaded through the shear center (I am just learning about the shear center) that the distribution between the webs would be equal.

 

[KootK]

That's the thing EIT, if I assume that the shear flow is equal and then follow the force distribution around the entire section, things finish up out of balance.

I kind of suspect that I can treat the flanges as beams carrying flexural compression loads out of the page and simply supported by the two webs. In that case, I could calculate how much of that load lands on each web as shear flow. This is just conjecture on my part though -- I don't know for sure.

Also, if I am correct, how does one handle a situation with more than two webs? Can the spanning flange just be treated as a continuous beam with a constant stiffness across it's length? What if the flange changes thickness along it's length? How does one modify the "stiffness" to reflect that?

Shear flow / shear center is pretty wild stuff when you really get into it...