Hand calculations for a slender beam-column structure?
Hand calculations for a slender beam-column structure?
(OP)
Hi there,
I am currently carrying out a buckling finite element analysis of a simple, slender beam-column structure. I am after the force-deflection curve for the structure when it is loaded at each one of 3 different locations (A, B and C).
The structure is pin jointed at the supports and a quick sketch of the structure is provided below:
ht tp://i165. photobucke t.com/albu ms/u57/god isadj_2007 /frame.gif
I'm wondering if anyone can suggest some typical hand calculations or theory which would help verify my FE results. The results are partially verified by a (very) simple implementation of the Euler buckling equation for the column member when the structure is loaded at point B, but obviously this does not take into consideration the effect of the conjoined beam, or indeed the load eccentricities when loaded at points A or C.
Any help or insight would be much appreciated.
Thanks.
I am currently carrying out a buckling finite element analysis of a simple, slender beam-column structure. I am after the force-deflection curve for the structure when it is loaded at each one of 3 different locations (A, B and C).
The structure is pin jointed at the supports and a quick sketch of the structure is provided below:
ht
I'm wondering if anyone can suggest some typical hand calculations or theory which would help verify my FE results. The results are partially verified by a (very) simple implementation of the Euler buckling equation for the column member when the structure is loaded at point B, but obviously this does not take into consideration the effect of the conjoined beam, or indeed the load eccentricities when loaded at points A or C.
Any help or insight would be much appreciated.
Thanks.






RE: Hand calculations for a slender beam-column structure?
Just wondering if you could analyse your beam /column
using Castigliano's Theorem.
regards
desertfox
RE: Hand calculations for a slender beam-column structure?
RE: Hand calculations for a slender beam-column structure?
2.Find out your end moment by moment distribution.
3.Find out deflections of beam as pin supported. Reduce this by the restraint moment obtained in 2. Use design charts in steel designers manual or code.
Why us FEM for something so simple?
RE: Hand calculations for a slender beam-column structure?
I am using FEM as I am not familiar with the above methods.
Please forgive my ignorance, but as I understand, since the structure is statically indeterminate, i.e the degree of indeterminancy is 1 (4 unknown reaction forces minus 3 equations of equilibrium), in order to formulate the primary system for use with the moment distribution method I must release one reaction force, and replace it with a redundant force. This leads me to believe I must replace either the upper or lower pin support with a roller support, but wouldnt replacing either one result in a structure that is unstable?
csd72, you mention that the frame is "braced". Does this mean that my frame is braced against sway and I do not need to take joint translation into account? But surely the joint at B will indeed translate when a force is applied to either A, B, or C.
Im new to this method, so thanks for staying with me this far!
Cheers.
RE: Hand calculations for a slender beam-column structure?
RE: Hand calculations for a slender beam-column structure?
If you "heard" it on the internet, it's guilty until proven innocent.
RE: Hand calculations for a slender beam-column structure?
My reference to braced frame is a steel code reference referring to the sway behaviour of the frame.
The frame will have minimal translation of joint B. Not zero as there will be axial force in the horizontal member that will change its length, but this is usually ignored.
This is a very fundamental problem, and you really should get a structures text to understand the theory (there may be one in your local public library).
RE: Hand calculations for a slender beam-column structure?
a singly redundant structure is easily solved by deflection methods; i prefer "unit load" method myself.
the vertical member would be a beam column if you're applying a moment at the intersection of the two beams ... the horizontal member is the stiffer loadpath for horizontal loads (stiffer than bending of the vertical member), and the vertical member would similarly react vertical loads ... this also indicates the end reactions of the beams (the horizontal member reacts horizontal loads, so its vertical reaction at the supported end should be very small (unless you're applying moments).
I'd use Bruhn "analysis of Flight Vehicle Structures" for both these methods.
RE: Hand calculations for a slender beam-column structure?
RE: Hand calculations for a slender beam-column structure?