Slender steel column: Linear FEA vs Moment Magnification
Slender steel column: Linear FEA vs Moment Magnification
(OP)
Apologies if this seems like an elementary question, but I haven't been able to confirm the answer searching here or elsewhere. Given: a slender steel column with a downward vertical force P at the top and a sideways force P, also at the top. Assume the material is in the elastic region and deflections are not large.
If statics equations are used to find the moment at the base, then AISC code says apply moment magnification equations to adjust the result to account for the P-Delta effect. Those equations are basically a fudge to make first-order analysis a good approximation of what a second-order analysis would achieve. That's fine, no problem there.
Now assume the column is modeled in a _linear_ FEA program, with the column refined into many segments. The result shows the expected deflection curve. Does this result include the P-Delta effect because the FEA calculation automatically considered the P-Delta moment when it solved for the equilibrium solution that balances nodal deflections and strain? Therefore one would not apply moment magnification equations to this linear FEA result? (I understand the best answer would be to use non-linear FEA. What I'm asking is the linear FEA result "good enough" to be used in lieu of the moment magnification approximation).
If statics equations are used to find the moment at the base, then AISC code says apply moment magnification equations to adjust the result to account for the P-Delta effect. Those equations are basically a fudge to make first-order analysis a good approximation of what a second-order analysis would achieve. That's fine, no problem there.
Now assume the column is modeled in a _linear_ FEA program, with the column refined into many segments. The result shows the expected deflection curve. Does this result include the P-Delta effect because the FEA calculation automatically considered the P-Delta moment when it solved for the equilibrium solution that balances nodal deflections and strain? Therefore one would not apply moment magnification equations to this linear FEA result? (I understand the best answer would be to use non-linear FEA. What I'm asking is the linear FEA result "good enough" to be used in lieu of the moment magnification approximation).






RE: Slender steel column: Linear FEA vs Moment Magnification
That being said, some programs will use a hand-calc type of moment magnfication method. Others will include an option for P-Delta analysis (though this would make them something more than a pure linear FEA program).
RE: Slender steel column: Linear FEA vs Moment Magnification
RE: Slender steel column: Linear FEA vs Moment Magnification
RE: Slender steel column: Linear FEA vs Moment Magnification
So, your best bet is to test it out yourself to be sure. From your description, it is not likely. But, the only way to know for sure is to test it out.
RE: Slender steel column: Linear FEA vs Moment Magnification
RE: Slender steel column: Linear FEA vs Moment Magnification
It follows that a linear analysis does not include the effect of deflections on the structure geometry, and moment magnification factors must be included.
If the program can do non-linear analysis it is possible to specify linear elastic material properties, but the analysis still needs to iterate to find the deflected shape, taking account of the deflections.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Slender steel column: Linear FEA vs Moment Magnification
Of course, thank you for the suggestion. Set up a simple model of a 20-foot tall HSS 2.50x0.125 A36 steel tube. 100 lbs of lateral force at the top and 3.1 slugs mass (100 lbs weight) also perched on the top. Results:
The only thing that changed was the plot of the tube, it went from straight to a nice curve. Okay, I'm convinced, the P-delta effect is not reflected in the results. Thanks to all for your replies.