Eccentric column buckling FEA and hand calculation 1

[damyan66]

Hello everyone,

I am currently carrying out a university project in which I am trying to model a ski pole shaft being eccentrically loaded. The shaft is a hollow cylinder of dimensions:
inner radius = 8mm
outer radius = 9mm
length = 100cm

I am using MSC Marc Mentat software to load the cylinder eccentrically, at a distance of 50mm from the centre axis. However, the deflection I get from my FEA is 6.8mm, compared to 1.65mm when using the formula for eccentrically loaded columns, below:
deflection = e[sec((L/2)*(P/EI)^0.5)-1]
where e = eccentricity, L = length, P = force applied, E = Young's mod, I = second moment of area.
In my case, e = 0.05m, L = 1m, P = 100N, E = 200GPa, I = 1.94E-9m^4.

I have applied the eccentricity by connecting infinitely stiff beam elements from a node, 50mm away from the centre axis, to each top node on the left half of the cylinder. The bottom of the cylinder is fixed in all directions.

Screenshots of setup and results:
Link

Any help appreciated!

 

[rb1957]

I wonder if your built-in base is correct. The ideal problem shows a column with an offset load and an offset reaction.

I think you need to consider if your ski pole model is the complete problem … or 1/2 the problem ? Is L effective 1m or 2m ?

another day in paradise, or is paradise one day closer ?

 

[damyan66]

rb1957, thank you for that suggestion. I think this is what must be the issue, since using L = 2m in the hand calculation gives 7.2m, which is much closer to the result given in the FEA. Thanks!

 

[rb1957]

sure. You need to visualise your model (offset load with fixed support) against the analysis model (offset load and reaction) to see that you're modelling only 1/2 of the analytical problem.

another day in paradise, or is paradise one day closer ?