Beam welded to plate. Plate stress?

Engineer_Phil

I have a design where a beam gets welded to a plate. The plate is not against a wall or foundation, but for simplicity I can say that the edges of the plate are fixed. I am concerned about the stress in the plate, and the deflection in the beam. I have access to solidworks simulation, but I want to know if anyone knows of an analytical solution or experimental solution that I can compare to. I don't like to just blindly trust a simulation.
I have attached an image of my setup. In the future I want to vary the beam cross section size and style.

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Windadct

The process and quality of the weld is critical - welding is MUCH more organic than people recognize.

Engineer_Phil

We have qualified welding procedures and a good quality control program the welding should be fine. I am more concerned about how to determine the required thickness of the plate. The stress cannot exceed 20 kpsi.

Windadct

Do you mean the stress caused by the welding - or how much stress the weldament can withstand once complete?
For stress caused by the weld - there are different ways to make the weld, different processes and different electrode types. The determination of the HAZ will have a large impact in both the stress created by the process and how much the weld can take.
Probably the best is to get the datasheet for the electrodes your best welder would like to use.
I do think Solidworks has a simulator for welds - but you will need to know the parameters of the weld process and electrodes details.

pongo38

An elastic analysis will tell you how the stress changes due to the applied load, but not take account of the residual stresses from welding, and takes no account of stress redistribution after the first yield of the steel. Plastic theory or yield line theory will give a good indication of the collapse load, but give no information on the working load behaviour.

Vadar2012

If I was doing this, I'd trust the simulation more than any theoretical hand calculations. I've done something similar to this for work, but with something bolted to a corrugated steel sheet. To simplify the simlation, you can use simple statics to calculate the forces at the wall. Then just model only the plate in the simulation. What you're after is the stress on the plate around the beam and plate contact. An easy way to do this is make the contact surface a different element than the rest of the plate and turn it off when analysisng the results. This just gives you the stress on the plate.

In other words, simulation is the best way.

Engineer_Phil

Thanks for the help guys.

I guess I have no choice but to accept the Simulation results as Vadar2012 suggests.
I am going to look at getting some strain gauges to verify the Simulation results.

I hope the simulation is wrong though... otherwise the plate is going to have to be very very thick.

Vadar2012

Yeah, I found it was larger than I thought. Will be interesting to hear about the strain gauge results.

Engineer_Phil

Did you run an FEA? I'd like to compare results if you did.

Vadar2012

Can't run one on yours, don't have any info.

Engineer_Phil

I made a simple drawing to give you the data.

A picture is worth a thousand words.

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0xDEADBEEF

Just out of interest: How would you use strain gauges with this. Do you glue them on beforehand and then measure the resistance before and after? Do they survive welding temperatures?

RFreund

What is the plate attached to? AISC give some guidance on welding plates to walls of HSS (hollow structural steel). Also Blodget's Design of Welded Structures also covers this.

Engineer_Phil

I am not really concerned with residual stresses from welding at this point. I would weld the beam to the plate, then put the strain gauge on the back side of the plate directly behind the bottom of the beam. Then load the beam. And take the strain gauge measurement.

Jupiter6

Accepting a simulations answer (especially Solidworks) without an approximate paper answer to corroborate it is never the way to do something correctly.

Check out Timoshenko's Theory of Plates and Shells. I don't think you'll find this to be as difficult as you think it is.

PhanthomJay

I would think that Roarke's "Stress and Strain" would give a solution, but i don't have a copy right now. But being very conservative by assuming simple supports along the short edges and free along the long side, I get a 5/8" thick plate required using a hand calc on the back of a matchbook. Looks like a 1/2 inch plate will do, as you have drawn. But someone needs to quality review my work
M_max in beam at beam/plate interface = 3(12) = 36 in-k
Load to short edge = M/L = 36/18 = 2 kips
M_max in plate at plate/beam interface = 2(6) = 12 in-k
S_req'd = M/allowable stress = 12/20 = 0.6 in^3
t_required = sq rt( 6S/b) = sq rt(6(.6)/10) = 0.6 in

Is a 5/8" plate too thick for you? i wouldn't cut it back too much...why fool with it.

nvn

PhanthomJay: Roark does not seem to contain the given problem. Nice approach. Using your approach, I get the same answer you got, except a different allowable stress (and therefore a different wall plate thickness). I currently do not know how you got your allowable stress. My allowable bending stress is currently, Sta = 197 MPa. Therefore, I currently obtain the following wall plate thickness (t1), using your above approach.

t1 = sqrt[3(1 - h2/h1)*L*V/(b1*Sta)] = 12.75 mm,

where b1 = wall plate width, h1 = wall plate height, h2 = cantilever beam plate height, L = cantilever beam length, and V = cantilever transverse tip load.