Basically I have little. I've tried a simple beam and a fixed beam but am not sure if either is correct. So far I haven't found anything in Machinery's Handbook or any textbook to help.
A couple of things to check. What kind of connection from plate to C-channel and how stiff are the C-channels. How are C-channels mounted. Depending on the "stiffness" of all these - things could a bit dicey.
the load will be reacted by the webs of the channels, no?
so you could say the reactions are ...
1) point loads in-line with the channel webs,
2) point loads at the fasteners (so there's a little flange bending happening),
3) distributed loads on the channel flanges.
i would expect to see some prying action ... the plate wants to react the load in-line with the channel webs, and the fasteners are preventing the plate from deflecting the way it's want to (which will amount to a fixed end).
For the direction of the force as shown, the plate will act more fixed due to the prying action on the bolts. Moment will be generated between the bearing point on the channel and the centerline of the bolt, with the lever arm somewhere between 1" and 1.75"
If the force is reversed, then the plate will act more like a simple beam, still with some moment, but not as much. The lever arm for any moment development will be from the centerline of the bolt to the outside edge of the channel - far less than an inch.
Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask
again you can estimate the twisting problem of the channels by asusming the highest possible moment (ie torque on the channel) being the fully fixed end support. if the channels don't like this then you can back off to a partially fixed end, the twist of the channels would create the same slope in the plate ... clear as mud ?
then how are the channels connected to the rest of the world ?
The channels are frame members of an endtruck for an underhung crane. See the attachment. Note: the attachment shows a sample only. The endtruck in question has MC's and straight-cut ends.
Your first step should be to get a Strength of Materials reference book.
See the attached file.
Case #1. As a first approximation, you could consider the plate as a simply supported beam with a concentrated load of 20K at the center. That's figure 7 on my attachment.
Case #2. A more rigorous approach might be to consider the plate as "fixed at both ends", with a concentrated load at the center. The bolted connection of the plate to the channels could be considered a "fixed" connection. The maximum moment in this case would be PL/8, where P = 20 Kips, and L = beam length. Note - the the maximum moment for "fixed" is 1/2 the max moment for the simply supported case
I had consulted AISC, strength of materials books, PE Reference books, Roark's, etc., and am familiar with beam calculations. This problem, on the surface, was not quite as cut-and-dried as a simple beam or a fixed beam, due to several reaction points.
Anyway, I ultimately analyzed it as a fixed beam with supports at 14" (between the channel edge and the bolts).
