Last Updated on September 19, 2026 by Maged kamel
Local Buckling for stiffened and unstiffened elements.
Local Buckling for stiffened and unstiffened elements.
This section covers local Buckling of stiffened and unstiffened elements. Sections are classified as non-slender elements or slender elements. We need to check some chapters, especially Chapters B and E.
For non-slender elements, we have two factors, one for the Flange and the other for the Web. If b Flange / t Flange < a certain ratio λr, the section is non-slender.The ratio, which we have already discussed via tables, is also important.
Chapter B covers design requirements, and Part B4 provides information on classifying elements for local Buckling—here, a snapshot of Chapter B’s summary.
The next slide shows the classification of sections for local Buckling in moBuckling Table B4.1a, which specifies the sections based on whether they are stiffened or non-stiffened.
h Web/ t Web < λr for a certain factor; then the section is non-slender if > λr. As shown in the Table, the section is slender, then a coefficient reduction.
This is part E7, concerned with members of slender elements—slide image for the summary of Chapter E for the design of members for compression.
There are two coefficients: Qs and Qa. Qs is for the Flange; if λ is bigger than the ratio given. Meanwhile, the QA is for the effective area/A gross—Non-slender not exceeding λr, from Table B4.1a.
Pn, the nominal compressive Strength, will be the lowest Value based on the applicable limit states of flexure and Buckling: Pn = fcr*Ag.
First, check whether the column is Long or short using the formula KL/r < 4.71*sqrt(E/FY).
Q=Qs*Qa or Q*FY/Fe< or=2.25 then the Fcr can be Fcr=Q(0.658^Q*Fy/FE)fy =Q*(0.658^Q*Fy/FE)Fy, but if Kl/r>4.71*sqrt(E/Q*Fy), the Fcr=0.877 Fe.
Let us look at Kl/r = 4.71*sqrt (E/Qfy); how was the equation derived?
Consider QFy/Fy when Q=1, and when Fy/Fe=2.25,again when shifting( Kl/r)^2=2.25*(pi^2*E/fy).
Take the SQRT (Kl/r)^2, gives ( Kl/r)= SQRT(2.25*pi^2*E/fy)=SQRt of (50), this 50 = pi^2*2.25, which is = 7.41.
So we arrive at the 4.71*sqrt(E/Fy) equation, which determines whether the column is short or long. K The graph shows K*l/ras a vertical line.
If the column is long, fcr = 0.877 * Fe, and the Table lists different values of Fy. For instance, for Fy =36, then the limiting Kl/r=134, while for Fy=50 ksi.
Limiting Kl/r based on the different Fy values.
If the column is long, then fcr=(0.877 *Fe). The Table lists different Fy values. For instance, if Fy = 36, then the limiting Kl/r = 134; for Fy = 50 ksi, the limiting Kl/r = 113; and for Fy = 60 ksi, the limiting Kl/r = 104. The controlling factor is 4.71*sqrt(E/Fy), and the corresponding 0.44 Fy values are listed. The 2016 specification replaced the ratio (K*L/r) with Lc/r.
If the column is long, then the graph is the black-shifted curve from the dotted Euler graph. 0.877Fe: let us look at the Euler graph. The ordinate is at when is = fy/2.25.
Draw a horizontal line from that point that intersects the Euler curve at 7.41 sqrt(E/fy). The ordinate at the intersection with the shifted curve will be fy/2.25(0.877)=0.39 Fy.
If Kl/r < 7.41 * sqrt(E/Fy), then use equation E 7.2 as fcr = 0.658^ Fy; for Q, when the equation is modified, Q will appear with fy.
If the column is long, then the graph is the black-shifted curve from the dotted Euler graph. 0.877Fe:: look at the Euler graph;; the ordinate is fcr when is = fy/2.25.
Draw a horizontal line from that point that intersects the Euler curve at 7.41 * sqrt(E/fy). The coordinate at the intersection with the shifted curve will be fy/2.25*(0.877)=0.39 Fy.
If Kl/r < 7.41 *sqrt(E/fy), then use Equation E7.2 as fcr = 0.658^ (Fy/Fe)*Fy. For Q, when the equation is modified, Q will appear with fy.
Parameters for local Buckling for unstiffened elements.
For local Buckling of stiffened aBucklingffened elements, especially unstiffened elements, the elements are free on one side and fixed on the other, similar to flanges; for instance, the ratio bf/2tf applies to the C channel and the outer portion.
A- For flanges of I-shaped members and tees, the width b is (1/2)of the full-flange width, bf/2tf. For legs of angles and flanges of channels and zees, the width b is the full nominal dimension, b/tf.
B—C-channel has only one part, so there is no division by two compared with I-shaped sections. The Qs factor for b/t indicates slenderness if it exceeds certain criteria; otherwise, it can be considered non-slender.
For hot rolled when b/t<= 0.56 *sqrt (E/Fy), then the Qs is =1, but if b/t > = 0.56*sqrt (E/Fy) and < 1.03 *sqrt (E/Fy) and < 1.03 *sqrt (E/Fy.
You can calculate Qs per Equation E7.5, but if b/t >= 1.03*sqrt (E/fy), then evaluate Qs per Equation E7.6.That was for the Flange.
Table B4.1a for the unstiffened elements part.
This is part of the unstiffened Web in an I-shaped section; the Web is stiffened by the upper and lower flanges, as shown.
For estimating the ratio, use the full height of the section; use ks, where ks is the fillet or corner radius at each Flange. From Table λr = 1.49*sqrt (Fy/E).
Table B4.1a for stiffened elements part.
The stiffened elements are listed from no. 5 to no. 9.
Refer to the Table from case no. 5 for I-beam sections for stiffened elements.
Qa is given by E7-16 & E7-17; Qa is the factor relating to the Web. A stiffened part: Qa = Ae/Ag (effective Area/gross Area) after checking the b/t Value.
For the Web of an I-section, if 1.49 sqrt(E/fy) or greater, the be was b-2ks will be modified; the be will be determined from equation E 7-17, which is based on Qa =1.
First, we start with the Flange to evaluate the relevant Qs, assuming Q = 1.
From the graph, we will estimate the F Value as Fcr. As we will see later, we take f as Fcr, with Fcr calculated based on Q=1.
The PDF for this Post is available for viewing and download in the document below.
This is a Link to solved problem 5.2 from Prof. McCormac’s handbook, which will be our next Post.
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.