The Effective Length of Columns in Unbraced Frames

Paper presented by JOSEPH A. YURA (April 1971 issue)

Discussion by Anand B. Gogate

The writer would like to thank Professor Yura for writing a useful paper from the structural designer's standpoint. The paper focuses attention on oneof the areas of the AISC Specification that has not been adequately articulated even in the Commentary on the Specification. The inelastic " G " concept and the equivalent axial load concept are indeed ingenious and extremely simple to apply. The author has also brought to attention two very important features of column instability in a structural system, viz.,

1. Sidesway mode of buckling has to be associated with all the story columns collectively. If all the columns are loaded to their full capacity; and if the effective slenderness ratio falls in the elastic range; then and only then, the basic assumptions of the AISC alignment chart are fulfilled.

2. If the effective slenderness ratio of a compression member is less than Cc, the alignment chart gives con­servative values for K. For columns with slenderness ratios under 100, the K values from the AISC chart are ultra-conservative. The alignment chart is invalid for compression members having a slenderness ratio smaller than Cc since the chart is evolved for elastic buckling, whereas the actual column instability would fall in the inelastic range.

The author's paper makes one aware of the great importance of basic assumptions in code provisions; and the benefits that a designer can derive by obtaining familiarity with them.

Papers, like the present one and the one authored by Dr. Higgins (Reference No. 7 in the original paper) do a great service to the average structural designer who does

Anand B. Gogate is Chief Structural Engineer, Alden E. Stilson & Associates, Columbus, Ohio.

not enjoy the personal participation in and the associate familiarity with research and, particularly, the basis f< the AISC code provisions.

Activating the unused capacity of adjoining colum to augment the deficiency in capacity of a particul column can result in optimum use of all the colun sections. I t must, however, be borne in mind that tl structural system tying the column extremities m i possess the requisite shear-diaphragm action to brii about this load sharing.

One practical example where the author's meth< can really pay rich dividends is in the design of era] columns.

The author has already made reference to the va] able contribution of Dr. Adel H. Salem (Reference > 6). The writer would like to add a few more signifies excerpts from the same paper. Figures 1 and 2 drama cally show the insensitivity of the sum of the criti< column loads to their ratio for fixed base and hing base frames. The effect of the relative stiffness of t girder to the column on the total column capacities c also be noted. For most practical cases (excluding fte pole type structures), the ratio of K2 to K± will be i ward of 1.5.

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1.9842 .8422

.7386

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Fig. 7. Elastic critical sum of loading versus axial load ratio f fixed base portal frame. PE — Euler-Load

110

A I S C E N G I N E E R I N G J O U R N A L

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Fig. 2. Elastic critical sum of loading versus axial load ratio for a hinged base portal frame

In the same paper Dr. Salem has elaborated on the "Theory of Multiples" for the elastic buckling of multi-bay frames, which can be stated as follows:

The sway buckling load of a multi-bay frame is equal to that of a single bay frame when the following two conditions are satisfied:

1. When it is possible to split a multi-bay frame into a number of identical single bay frames, each of which has the same column stiffness and the same column loads.

2. When each of the two components of pure-shear sway, and no-shear sway at the "split" columns are the same.

Figures 3 and 4 explain the theory of multiples and its domain of validity quite well.

2P|

I I

2PI 2PI

^ 21 I

2PI 2P

(a) 1 I 1 1

*

IP |2P [ f

I I

2P PI t

I I

IP f

I

PI

I

IP

I

r

PI

1 2

ip f

1 2

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1 (b)

Fig. 4. Examples of frames where the theory of multiples can be applied

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IP PI t t

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IP PI

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H ^ . 3. Examples of frames where the theory of multiples can be ap

111

J U L Y / 1971