## Tuesday, November 1, 2011

### Re: Standard Portal Frame Analysis

Syed,

I'm sure you'd remember the fundamental principals pretty quickly, particularly if you had an instructor who understood the fundamental principals himself and not just how to do the calculations.

The principals are very simple: just the behaviour of single span beams with applied end moments plus linear superposition.  Only the accounting can get to be a nightmare.

Fortunately for me, my instructor is one of the best engineers in the world.  That's now; back then (50 years ago) he was just a young kid, hardly any older than me, with the ink on his Ph.D. still wet.  You've probably heard of him, maybe even used his textbook.  His name is James G. MacGregor; and it was several years before I fully realized just how fortunate I'd been to have him.

Regards,

H. Daryl Richardson
----- Original Message -----
Sent: Tuesday, November 01, 2011 12:44 AM
Subject: RE: Standard Portal Frame Analysis

Wow

We did this stuff at school. But the way it is reiterated here (no pun intended) I wonder if I could get through school if I had to do it again.

Syed A Masroor
Karachi, Pakistan

From: h.d.richardson@shaw.ca
To: seaint@seaint.org
Subject: Re: Standard Portal Frame Analysis
Date: Mon, 31 Oct 2011 23:48:22 -0600

Thor,

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.

Regards,

H. Daryl Richardson

----- Original Message -----
From: Thor Tandy
To: SEAInt
Sent: Monday, October 31, 2011 12:28 PM
Subject: 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?"

Thanks

Thor A. Tandy P.Eng, C.Eng, Struct.Eng, MIStructE
Victoria, BC, V8T 1Z1
Email:
vicpeng@telus.net

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