Last Updated on March 1, 2026 by Maged kamel
Alignment charts for columns
Today, our subject is using alignment charts for columns for braced or unbraced frames.
When attached to frames, columns exist in two conditions: braced or unbraced columns for each case.
If you like to search for this subject on the internet, you will write the Alignment chart, Nomograph, Anderson’s, and Woodward. Still, this method relies on certain assumptions, such as the columns being elastic. The beam is elastic if the conditions are met, and an adjusted factor is used if the column is inelastic. What is the alternative to this method?
The alternative method is direct analysis. First, in the shown figures, at the left, a braced column is part of a frame.
The side-sway is zero due to bracing or sometimes a small value that can be neglected. This expression is difficult, called side-sway inhibited, for the following figure at the right.
A horizontal force acts upon the unbraced frame. There is no side-sway when a horizontal force P acts on the unbraced frame. Side-sway of large value due to non-bracing is called side-sway uninhibited, which matches the unbraced expression, and inhibited means braced.
From the book of Prof. Salmon For the first figure on the left side, the braced column, due to bracing, the k value is always <1, the joint is rigid, the angle between the girder and the column is 90 degrees, and this angle is kept unchanged, and the K is <1, KL=0.7 L and < L.
In all the cases, K<1. This is the case e of a frame with pinned support.
Let us investigate the braced column in a frame with fixed support, which is case C; what will be the k-factor for the column? K>0.50<0.70, unlike at 0.7, the inflection point distance becomes smaller.
For the unbraced frame, case b has hinged supports, while the last case has an unbraced frame with fixed base supports.
For the unbraced frame, there will be a rightward movement and a deflected shape. The beam curve will be coming out of the frame’s right edge. There will be a deflection curve moving upwards, and curvature returns to the hinge at the support. The k value of the column will be > 1.
For the column at the right side from the inflection point to the next inflection point, the k value >1, the last case of unbraced frame kL > L, but <2L. Finally, for the braced frame, the k is always < 1.
The author explains the reasons for the k values in the next slide. To understand why the minimum value of k in an unbraced is theoretically 1.0, refer to Figure no. d and go back to the shape.
The inflection point will be at the mid-height, and the buckled shape will be in fig 6-9-3, while for case b, there is a side-sway, k=2, but in case of no c, if the base is hinged with a partial restraint, the k*L
Based on these conclusions, two alignment charts for columns were derived; the first chart shows a side-sway-inhibited, or braced, column in a frame, with our k ranging from 0.5 to 1.
Our column consists of two joints: the upper one is GA, and the lower one is GB. The G value calculation is the summation of EI/L for columns. For a column, the upper part has no other column above, so EI/L applies to only one column.
The alignment charts for columns: the first chart is for the braced columns.
But for two columns above each other, for the common joint, the G value, the summation of EI/L for both, will be estimated. This is the nominator / the summation EI/L for beams at the same joint. At the right and left of the joint, for one side beam, EI/Lbeam Will be for one beam based on the same material used E for column and beam; the value is the same.
E will cancel each other. There is a comment that if the column framing is on a beam with higher inertia, a stiff beam, G will be increased, approaching zero theoretically.
The alignment charts for columns, the second chart for the unbraced columns.
Let us look at the other alignment chart for columns, side-sway uninhibited.
The figures for the alignment charts for columns have been changed from 0 to infinity for both GA and Gb. k is from 1 to 20, unlike the values in the other chart, since k is > 1. The deformed shape is shown.
The p delta will be later considered. The equation for the chart is shown here, with parameters for side-sway inhibition for different values of GA and Gb, and the corresponding k value.
If the girders at joints are very stiff, the EI/L ratio is very large; G approaches zero, and the K factor is small. The column moment cannot rotate the joint very much if G is very small.
This means the girder is rigid, and the column moments cannot rotate the joints. This joint is close to a fixed-end situation; usually, G is > zero.
The conditions of development of charts.
The conditions for developing the alignment charts for braced and unbraced columns were based on a certain set of assumptions.
First, the members are elastic, with constant cross-sections; no variable sections exist. and connected by rigid joints.
In an elastic column and beam, all columns buckle simultaneously. For braced frames, the rotations at opposite ends of each beam are equal in magnitude, and each beam bends in a single curvature, a single curvature from one end to the other in a single wave. For the unbraced frame, double curvature is shown in the sketch.
For unbraced frames, the rotations at opposite ends of each beam are equal and opposite in direction. Axial compression forces in the girders are negligible.
If these conditions are not met, the side-sway-inhibited frames and the braced frame for girder BC attached to a column are modified.
In the next post, we will discuss problem 7.1.
The PDF for this post can be viewed or downloaded from the following link.
This is the next post. A solved problem for the alignment chart for columns 7-1.
For a good A Beginner’s Guide to the Steel Construction Manual, 14th ed. Chapter 7 – Concentrically Loaded Compression Members.
For a good A Beginner’s Guide to the Steel Construction Manual, 15th ed. Chapter 7 – Concentrically Loaded Compression Members.
For a good A Beginner’s Guide to the Steel Construction Manual, 16th ed. Chapter 7 – Concentrically Loaded Compression Members.