How much will a steel plate bend?

[jeff davis]

Hello,
I am trying to figure out how to determine how much a simple steel plate will bend with "x" amount of weight on it. I have searched the internet looking for some good descriptive information for my studies and am having a hard time figuring it out. I understand that it is probably complicated, but if someone could please give me an equation and "dumb" it down for me i would be very appreciative. Say i had a 2x4 across 2 chairs and set a 30lb box on it. How much would it bend??
Please don't just answer the problem, i do not care what the answer is, i just am curious how to get it.

Thank you very much for your help again guys!

 

[Lok]

Hi Jeff,

I haven't done such a calculation in ages as CAE programs give a far better detail and the math looks a lot like the below formulas:
http://en.wikipedia.org/wiki/Euler-Bernoulli_beam_equation#Static_beam_equation

In engineering books you usually get simplified formulas for different Beam profiles and for really simple one this picture is what I have. Use the above link for explanations regarding E and I. "I" is usually found in metal profile tables.

An structural engineering book should suffice for more detailed things.

 

[AlephZero]

If your "plate" is only supported at the ends, it is acting like a beam, so you can use the beam formulas. From your description, the beam is simply supported at each end.

If the plate is supported along all its edges, that is a more complicated problem and there are only simple "formulas" for a few special cases of the applied loads.

 

[PhanthomJay]

The bending (deflection) of a plate or beam at a given point depends upon the loading, where it is applied, the support boundary conditions (clamped, pinned, free?), beam length, beam material (wood, steel?), beam cross section (square, rectangular, hollow tube?), beam orientation, etc. A 2x4 will deflect about 4 times more if it is placed on its side rather than its edge. There are many variables, requiring calculus (or tables!) for the solution. Plate deflection gets complex. For beams
see
http://en.wikipedia.org/wiki/Deflection_(engineering )

For a 2 x4 piece of lumber across 2 chairs say 6 feet apart, the theoretical deflection in inches at mid point for a mid point load of 30 pounds is PL^3/48EI, where P = 30 lbs., L = 72 inches, E is young modulus for wood about 1.6 million psi, and I is its area moment of inertia bh^3/12 (depending on its orientation).

 

[jeff davis]

Thanks guys for your help! I think that i grasp the basic idea now, and have been able to do a few calculations successfully!