Column Load on Angled Leg

[mccartbm90]

Hi All,

I have a question regarding a loading situation with involves a stand we use throughout our shop (think saw horse design). This stand is currently rated at 2500 lbs, however I'm having a bit of trouble verifying this rating with regards to the strength of the legs. This stand consists of a 1/4 x 2" x 4" cross tube 50" long, which is supported by 4 legs (11 Ga x 1 1/2" square). These legs form an A- frame shape at each end of the cross tube, and are "splayed" out at a 10 degree angle from horizontal (20 degrees inclusive from side to side). Now I've done plenty of column loading situations with members that are in a vertical orientation (90 degrees from horizontal), but I'm a little unsure how tackle a column which is on an angle. Is this even considered a column? My thought was to find the vector components of the applied load to determine what the true axial load is through each leg. Being that the leg is only angled 10 degrees I'm assuming that it would buckle before it would bend like a beam. Is this thinking correct? Thanks.

 

[drawoh]

mccartbm90,

Draw a free body diagram. Each leg is loaded at 10[°] from axial. You have a compression load that may cause buckling. You have a bending load due to the 10[°] angle, easily analyzed as a cantilever. You have a weld at the top. If this were my problem, I would assume zero friction on the ends of the legs on the floor, and solid support at the top.

I have no gut feeling of how it would fail. I would crunch the numbers.

--
JHG

 

[gruntguru]

"10 degree angle from horizontal"

I assume you mean 10 deg from vertical?

je suis charlie

 

[gruntguru]

Worst case is zero friction where the leg meets the floor, in which case drawoh's analysis is appropriate. For most friction coefficients the legs will be in pure compression - the floor acting as the third member of a triangle.

je suis charlie

 

[chicopee]

"... and are "splayed" out at a 10 degree angle from horizontal .." yeah I agree this can not be correct.

 

[Sparweb]

The stresses of column loading and bending don't just "superimpose" when they are combined this way. The bending makes the column buckling worse, and vise versa. Then, bending to failure involves plastic deformation of the metal - the flat part of the stress-strain curve which doesn't follow Young's modulus. Analysis will only get you so far. You could spend 8 hours at 100$/hour figuring it out, or buy a load cell for half that cost, and spend an hour testing a frame with a hydraulic press stand. Plus, the guys in the shop would be less likely to overload one if they see a bent example.

I forget who said it: "No one believes the analysis except the one who wrote it. Everyone believes the test except the one who ran it."


STF

 

[gruntguru]

OP. You say the legs form an "A-frame". Does that mean the feet are connected by a cross tube? If so you have a fully trangulated truss and the legs are loaded in pure compression. (If not, the cross piece (a small section member in pure tension) would make a useful addition - increasing the load rating and simplifying the analysis.

je suis charlie

 

[mccartbm90]

Yes, sorry, 10 degrees from vertical. On each end of the stand the legs form an A frame where the legs are 30 degrees from vertical, and tied together with a piece of flat stock steel at the bottom. Then this A frame shape is splayed that 10 degrees to create a wider foot print. There is not a member tying the two A frames together. So when you take a bending moment, the moment would be about the bottom of the leg where it meets the floor, or about the joint where it meets the tube? I'm assuming my goal here is to determine the reaction forces at the welded joint. And I agree that doing a real world test is ideal, but it probably won't happen in this case. In all honesty I'm very confident that our cross tube would buckle far before the legs, but really I'm just more curious on how I would solve this problem more than anything

 

[gruntguru]

Maximum bending moment at the top end, tapering linearly to zero at the foot.

je suis charlie

 

[tbuelna]

If this frame is used to support a load that people will be working near, it probably should be designed with a 4.0 or 5.0 FoS. If you apply a concentrated 2500lb load mid-span on the 50" center beam, apply a FoS of 5.0, and check the stress at the weld joints where the legs attach to the beam, you might find there are some issues. The legs are coupled laterally at their base, but they are not coupled longitudinally at the bottom.

 

[Tmoose]

I don't know about the potential for non-vertical loading on your stands.

Typical sawhorses (at least mine) get pulled and tugged in all directions from time to time. Even sometimes while supporting heavy loads.

Some saw horses apparently are made with more thought more about the affect of longitudinally angled legs that others.

I think this one might receive some added bracing after the first vigorous use.

http://www.thissortaoldlife.com/wp-content/uploads/2013/03/021218090-7_xlg.jpg

Something along the lines of the 45 degree struts anchored at mid span of the main beam on these -

http://www.safethorse.com/wp-content/uploads/2011/07/safethorse-sawhorse-hummer.jpg

This one by inspection more seriously considers loading in all directions along the horizontal plane.

http://montana-riverboats.com/Uploads/sawhorse.jpg

 

[mccartbm90]

The saw horses we use in our shop are very similar to design in the second link. The legs are angled very similarly, and are tied together with a cross brace just like those wooden ones. I did not perform a weld calculation because we have each leg welded solidly to the horse cross beam. Its roughly 10" of total weld length per leg due the angle cut on the legs. Currently, we have a SoF of 3 on the cross beam. I'm still uncertain on how I should best calculate the allowable load on the legs