Calculating Bending Moment & Force of Table with 8 Tonne Mass

[radiarich]

Hi ,

I need to find out the forces and bending moments on, put simply a table. 4 stands are welded to a flat plate to resemble a table. An 8 tonne mass is placed on the table, which is distributed equally on the 4 corner stands. The stands are 2m high and the flat top is 2m by 0.4m. Each stand is a box section 25mmx25mmx2.5mm thick

If a stand fails(something bumps into it) how do i work out the distribution of the force on the three corners/stands? and the bending moments also?

thanks

Rich

 

[nvn]

radiarich: Are the legs bolted to the floor? If not, the table could (would) become unstable. I am assuming the legs are bolted to the floor. Assuming your mass is approximately uniformly distributed over the plate, the axial load on the leg nearest the failed leg would be P = 39.23 kN. And the y-direction bending moment on the top end of that good leg would be My = 13.08 kN*m.

The leg cross section you suggested in post 1 would be severely overstressed, even with all four legs intact. If all four legs are installed and not damaged, then your square tubes must have a minimum cross section size of 70 x 70 x 5.0 mm.

But if one leg fails or is removed, then your square tubes must have a minimum cross section size of 120 x 120 x 5.0 mm.

Post the square tube cross section sizes available to you, and the material specification and tensile yield strength of the tubes, so I can check some numbers.

 

[radiarich]

Thanks for your message nvn,

yes the stands/legs will be bolted to the floor, onto rails i think. The 8 tonnes should be uniformly distributed over the table, and therefore the 4 stands in each corner.

Can i ask the formulae you used to work out the min cross sectional box size? the critical load i believe needs to be above 20,000 N or 2 tonnes (plus i will have to include a safety factor) to prevent failure.

also from using the yield stress of plain steel( i think is about 360 MPa and E=210000MPa) and the buckling formula I found that, if all 4 legs intact, the minimum box section dimensions were around the minimum 25x25x2.5 or 3mm, to prevent buckling under a critical load of 2 tonnes on each leg (8 ton/4 legs).

There are several box section dimensions i could use 30x30x2.5 all the way up to 160x160x... and the stands, the 8tonne object and the table are all to be made out of plain carbon steel.

 

[nvn]

No, I wouldn't have time to try to rewrite textbooks and all the formulas on a forum. I might only have time to compare final answers, as a reality check.

We need a material specification name and number for your steel tubes. "Plain carbon steel" could cover a rather wide range, so we need to have the material specification for your particular square tubes. Also, do your square tubes have rounded or sharp corners?

What is the thickness of your flat plate? And does the plate have stiffeners (ribs)? Also, how is the mass applied to the flat plate? Are there separate pieces of the mass very near the missing leg? Or is the entire mass all one, stiff unit, connected together, covering the entire table top? Also, can you give more details about the design or fixity of the leg connection to the floor, in both directions? Also, are there any other braces, supports, or boundary conditions, in either direction, that you have not mentioned yet? Is the table top free to sway horizontally in both directions?