Short Shaft Buckling Calc for Side Load and Compression
Short Shaft Buckling Calc for Side Load and Compression
(OP)
I'm working on a problem dealing with buckling on a short shaft with combined compression and side loading. The slenderness ratio is only 10. The side loading can be significant (as much as 1:1), but as the compressive load goes up the side load decreases. I haven't been able to find a formula that directly address this issue.
I've been studying up in Roark's and have been playing around with a version of the secant formula (12.4-2, 7th edition) for an eccentrically loaded column. I have been taking the moment generated by the side load and using that to calculate the eccentric distance of the compressive force to generate the same moment. My length is 35 inches so for a particular case of 100 kips of compression and 100 kips of side load I end up with an eccentricity of 35 inches. I have a feeling this is a bit outside the original intent of the equation.
I also have tried the same formula, but using the side force to calculate the deflection in the shaft and then using that deflection as the eccentric distance. I then reduce the maximum allowable compressive stress by the stress generated by the side load. I didn't figure I would get the same answer, but they aren't even close.
Is anyone familiar with the secant method for buckling that could give me a little guidance, or tell me if I going the wrong direction. Any other methods I should look at instead?
I've been studying up in Roark's and have been playing around with a version of the secant formula (12.4-2, 7th edition) for an eccentrically loaded column. I have been taking the moment generated by the side load and using that to calculate the eccentric distance of the compressive force to generate the same moment. My length is 35 inches so for a particular case of 100 kips of compression and 100 kips of side load I end up with an eccentricity of 35 inches. I have a feeling this is a bit outside the original intent of the equation.
I also have tried the same formula, but using the side force to calculate the deflection in the shaft and then using that deflection as the eccentric distance. I then reduce the maximum allowable compressive stress by the stress generated by the side load. I didn't figure I would get the same answer, but they aren't even close.
Is anyone familiar with the secant method for buckling that could give me a little guidance, or tell me if I going the wrong direction. Any other methods I should look at instead?





RE: Short Shaft Buckling Calc for Side Load and Compression
RE: Short Shaft Buckling Calc for Side Load and Compression
RE: Short Shaft Buckling Calc for Side Load and Compression
i thought the secant equation applied to columns with an off-set (axial) load (creating a moment) ... doesn't sound like that's what you have ??
i don't think the secant equation is limited to a slenderness range.
it sounds to me that you're using slenderness ratio as the pass/fail criteria; ie for your load you calculate the critical slenderness ratio given your geometry, you then calc your actual slenderness ratio and show it good. this is the same as calculating the critical load for your column and comparing this to the applied load (which is what i'm more used to seeing). The caution i'd suggest is that it's not particularly clear to me (at least) when plasticity comes into play, and whne you need to consider Johnson-Eular (or some other similar method) dto deal with plasticity.
RE: Short Shaft Buckling Calc for Side Load and Compression
Yes, the Secant formula is for a column with an eccentric axial load. This eccentric load generates a moment. What I was trying to do was calculate the moment generated by the side load. Then use that moment to calculate the eccentric distance for the axial load that would generate the same moment in the shaft. It seems like that should work, but I was hoping to get some input from this site from people more familiar with the Secant formula and its application than I am. In essence, I am transposing the transverse load at the end of the shaft to a moment at the end of the rod and a transverse load at the base of the shaft. Then use the secant formula. This does neglect the shear stress at the base of the rod, but it is only around 700psi so it should have negligible affect.
I have the formula set up to calculate P critical with the maximum stress set equal to the material yield strength. Then I will compare the P critical to the actual compressive force.
Thoughts?
RE: Short Shaft Buckling Calc for Side Load and Compression
RE: Short Shaft Buckling Calc for Side Load and Compression
Load Case 1
Axial Load = 111 kips
Transverse Load = 108 kips
Secant Method = 20.6 ksi
Beam Method = 12.4 ksi
Load Case 2
Axial Load = 615 kips
Transverse Load = 82 kips
Secant Method = 19.3 ksi
Beam Method = 12.9 ksi
I'm inclined to use the beam method numbers, not because they are lower, but the formulas exactly match my load case and with a slenderness ratio that is 1/10 of the critical slenderness ratio I think it is a safe assumption that this shaft would fail by plastic deformation not elastically.
Thoughts?
RE: Short Shaft Buckling Calc for Side Load and Compression
Cheers
Greg Locock
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RE: Short Shaft Buckling Calc for Side Load and Compression
RE: Short Shaft Buckling Calc for Side Load and Compression
personally i'd go with the beam column, 'cause that's what you've got.