Given that drawing, with no dimensions, no cross section of the channel, no alloy nor what force "F" is, no with and location of the force nor the cut-out notches in the channel legs, nor without any positions of the forces nor the channel nor the notches, nor the length nor restraints of the channel, and with no additional information that sketch from you, I have no idea.
Guessing that you are interested in post yield behaviour, and that the material is mild steel, you could get an approximate answer by considering a mechanism of hinge lines that would allow the beam to deform, and then do a work calculation on that mechanism, assuming a fully plastic moment for the section across the hinge. This is an upper bound solution as the assumed mechanism may not be the most effective. Working out the angle that each hinge line rotates by is the tricky bit. The 'obvious' mechanism has 7 hinge lines, if the beam is simply supported,
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376
How can we help you without some dimensions of the beam or forces, a 4mmm deflection is quite a large but depending on the beam length and section at this stage we can't tell whether it's in a plastic or elastic region of stress.
Hi All,
thanks for feed back. I am after a formula to find what force (F) the beam can withstand before plastic deformation and what force (F) caused it to bend by 4 mm.
It's a fully FIXRED beam fixed both ends, the difficulty for me is that its not a normal square beam it's a channel section.
Are you saying that you would know the answer to your question if the beam were rectangular? To me that means that you know all the dimensions, and you know the formula for deflection of a rectangular beam. If so, then just apply the cross section moment of inertia of a channel rather than that of a rectangular tube.
like above if you can solve a rectangular section, and you know the general equations at work then you should be able to adapt them for a channel.
your beam does have a couple of interesting features, like ...
1) the stress concentration of the cut-out (the U-shaped notch) and in compression at that, and
2) the compression allowable of the standing legs (their allowable is probably not fcy).
i think the critical failure mode will be the legs splaying out, deflecting out of plane.
show us you know something that can be found in a strength of material text, and we'll probably help with the rest.
we like to help; we (well, i at least) don't like to spoon-feed.
another day in paradise, or is paradise one day closer ?
