From: Thor TandyTo: SEAIntSent: Monday, October 31, 2011 12:28 PMSubject: Standard Portal Frame Analysis
I'm doing stuff I should done in school J
1) I am reviewing how to quickly arrive at sway in a rectangular (or any, for that matter) portal using simple portal frame equations.
2) I calculate the moments from the std equations and then release the top corners to arrive at a flagpole concept tied at tops by a strut/beam.
3) The resulting base moments are approx by iterative moment distribution.
4) If I use a partial, or offset, load on the beam I expect sway.
5) My question is, "Is it too simplistic to take the resulting moment difference at the bases and apply slope-deflection arithmetic to arrive at an estimate of the sway?"
Thor A. Tandy P.Eng, C.Eng, Struct.Eng, MIStructE
Victoria, BC, V8T 1Z1
Monday, October 31, 2011
Re: Standard Portal Frame Analysis
I am assuming you want to do this manually.
For a one storey multi bay plane frame structure where the axial shortening of the second storey "beams" permits only very small joint translation relative to the magnitude of joint translation permitted by bending of the "columns" I would proceed as follows:
1.) Pin a convenient upper storey joint (call it Joint "A" for future reference) to provide the location for an artificial horizontal reaction. Give Joint "A" a unit deflection keeping the beams rigid.
2.) Calculate the fixed end moments (F.E.M.) for the columns (note: the beams have zero F.E.M. because you kept them rigid in step 1).
3.) Now release the formerly rigid beams and do a moment distribution analysis to determine all of the beam forces, moments, and reactions you may need later, including the horizontal reaction at Joint "A".
4.) The horizontal reaction at Joint "A" divided by the unit deflection from step 1.) will give you a spring constant (lets call it "k" for all horizontal (sidesway) movements.
5.) Analyze the structure from 1.) including the horizontal reaction from Joint "A" for each of your actual load cases assuming no initial deflection for Joint "A" to determine all beam forces, moments, and reactions, including the horizontal reaction at Joint "A" (call it Ra).
6.) The amount of sidesway will be Ra/k.
7.) The forces on your real structure (including the effects of sidesway) will be the sum of (the forces and moments from 5.) + (Ra/k)*(the forces and moments from 3.)
I have assumed a moment distribution analysis because that is what I am most familiar with; but any method of analysis should do.
Hope this helps.
H. Daryl Richardson
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at 10:48 PM