Last Updated on September 17, 2026 by Maged kamel
Alignment charts for columns
Today, we are using alignment charts for columns in braced or unbraced frames.
When attached to frames, columns exist in two conditions: braced or unbraced.
If you search for this topic online, you will find alignment charts, Nomographs, and Anderson’s and Woodward’s methods. Still, this method relies on certain assumptions, such as the columns being elastic. The Beam is elastic if the conditions are met, and you use an adjusted factor if the column is inelastic. What is the alternative to this method?
The alternative method is direct analysis. First, in the figures shown on the left, a braced column is part of a frame.
Side-sway is zero due to bracing, or sometimes a small Value that can be neglected. This Expression is difficult; it is called side-sway inhibited, as shown in the figure on 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:n, 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 K is <1, KL=0.7 L and < L.
In all 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; the k-factor for the column s 50 < k < 0.70. Unlike 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 extend beyond the frame’s right edge. The Deflection curve moves upward, and the curvature returns to the hinge at the support. The k Value of the column will be > 1.
For the column on the right side, from the inflection point to the next inflection point, the k Value is 1 in the last case of an unbraced frame: kL > L but < L. Finally, for a braced frame, 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 frame 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, we derived two alignment charts for columns; 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 has two joints: the upper is GA, and the lower is GB. The G Value is the sum of EI/L for the 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, at the common joint, the G Value (the summation of EI/L for both) will be estimated. This is the numerator / the summation of 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 increase, approaching zero theoretically.
The alignment charts for columns: the second chart is for the unbraced columns.
Let us look at the other alignment chart for columns, side-sway uninhibited.
The figures for the column alignment charts have been changed from 0 to infinity for both GA and Gb. k ranges from 1 to 20, unlike the values in the other chart, since k> 1. The deformed shape is shown.
The p delta will be considered later. 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 for developing 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. Rigid joints connect them.
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. The sketch shows double curvature in the unbraced frame.
For unbraced frames, the rotations at opposite ends of each Beam are equal and opposite. 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.
You can view or download the PDF for this Post 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.