Last Updated on September 13, 2026 by Maged kamel
An easy approach to Compact and noncompact sections.
What is a compact section?
A compact section can develop a plastic hinge before local Flange or web buckling, providing adequate lateral bracing. The member will fail by overall Yielding before local Flange or web buckling.
The Noncompact sections do not satisfy the limiting width-thickness ratios for compression elements.
Table B4.1B expresses the relation between lambda and MN in three zones. The graph shows that the first Zone is compact, the second Zone is noncompact, and the last zZoneis a slender Flange.
If we draw the graph representing the relation between lambda λ and Plastic Moment MP, consider λf=(bf/2tf) for the flange, while for the web λw=hw/tw. We start with the Flange case, which is more critical because the web’s λ value is nearly safe for most steel sections.
The vertical axis represents the nominal Moment Mn. The design is based on the Plastic Moment, MP. The graph starts as a straight line from λ = 0 to λ = λp.
In the case of the Flange. The Area under the straight line from λ = 0 to λp is called a compact Flange.
This can be achieved by placing concrete over the steel section’s Flange. The Flange is kept in place and braced through studs, so the buckling length is 0. In that case, the steel section is considered compact
AISC 360 Table 4.1 b defines the criteria for determining the compactness of rolled beams; please refer to the second slide.
The table shows the relationship between lambda and MN across three zones, as shown in the graph: the first is compact, the second is noncompact, and the third is a slender Flange.
What are the different zones for flanges?
The first Zone is compact; for a Flange, lateral movement is prevented by a stud, and the covering slab ranges from λf=0 to λf=λp.
The second Zone for the lambda of the Flange, λ, is called λrf. At this Time, the Flange starts to buckle laterally. The Flange section is considered noncompact.
The third Zone represents a slender Flange. The slender Flange behaves similarly to a column that has lateral buckling.
The following Expression is for the lambda value for the Flange, where Fy is the yield strength, and E is the modulus of elasticity.
While for the value of λf=λFr=1.0*sqrt(E/Fy).
The following slide shows Chapter B in the latest AISC specification, which specifies the Design requirements for columns and Beams.
The first category, laterally supported compact Beam, is quite common. For a doubly symmetric, compact I-beam, or C-shaped section bent on the major axis, AISC F2.1 gives the nominal strength as Mn=MP, where MP=Fy*ZX and Zx is the plastic section modulus.
This is part of Table B4.1b, quoted from the AISC 360 spec. For item 10, for flanges of rolled I-shape sections, C-channels, and Tees, lambda =b/t, where b is the width of the C channel, while for I-beams and sections, b is considered half the total width. Please refer to Table B4.1B, which is shown on the next slide.
The next slide shows the different values of λf, equal to (bf/2tf), when λf = λp, the plastic lambda value. The value equals 0.38*sqrt(E/Fy) and can be set to 64.7/Sqr(Fy) for any value of Fy, while E=29000ksi. When λf=λr, its value equals 1.00*sqrt (E/Fy) and can be set equal to 170.30/sqrt(Fy).
The web has three zones, each with a different value of lambda, as shown on the next slide. The approximate yield stress, Fy, is 50 ksi. For more details about the content of Table B4.1b, please refer to Post 7-7-A: A guide to Local buckling parameters for steel beams.
You can view or download the PDF for this post from the following Link.
Here is the Link to Chapter 8, “Bending Members.” A Beginner’s Guide to the Steel Construction Manual, 14th ed.
Here is the Link to Chapter 8, “Bending Members.” A Beginner’s Guide to the Steel Construction Manual, 15th ed.
Here is the Link to Chapter 8, “Bending Members.” A Beginner’s Guide to the Steel Construction Manual, 16th ed.
This is the next post: 3-Introduction to Plastic Theory.