Column problem
Column problem
(OP)
Hi there,
I have a column with 2 rigid ends (L/4) attached to pinned connections (the upper on being on rollers) then an elastic section in the middle for the other L/2 length of the beam. This is subjected to a load P. I don't even know where to start as other column buckling problems have just been dealing with fully elastic beams.
Any help towards this would be appreciated.
The solution is numerical as stated in the question
I have a column with 2 rigid ends (L/4) attached to pinned connections (the upper on being on rollers) then an elastic section in the middle for the other L/2 length of the beam. This is subjected to a load P. I don't even know where to start as other column buckling problems have just been dealing with fully elastic beams.
Any help towards this would be appreciated.
The solution is numerical as stated in the question






RE: Column problem
By inspection, the answer is going to be between π2EI/L2 and 4π2EI/L2. You can assume a deflected shape, say a sin curve for the central portion and a straight line extension at each end for the two rigid portions, then use the techniques you have been taught to find the critical load.
If the end rotation is θ at the onset of buckling, the moment at L/4 is PθL/4, so you might consider treating the problem as a straight column of length L/2 with an axial load P and an applied moment of PθL/4 at each end.
BA
RE: Column problem
a bit more information, it says to also prove that (alpha).L/2 = 1.72 numerically, as well as the critical buckling load.
a question, why is the moment at L/4 pθL/4. I got PsinθL/4?
would you then treat this as an eccentrically loaded column?
thanks for the help this is really racking my brain.
RE: Column problem
By the way, I don't think you're supposed to be asking homework questions on here.
RE: Column problem
I agree with CANEIT. "Theory of Elastic Stability" is an excellent reference which covers buckling of columns with variable cross section and specifically treats buckling of bars with changes in cross section using Newmark's Numerical Procedures.
BA
RE: Column problem
Analysis and Design of arbitrary cross sections
Reinforcement design to all major codes
Moment Curvature analysis
http://www.engissol.com/cross-section-analysis-des...