Last Updated on September 17, 2026 by Maged kamel
How to compute critical stress- Table 4- 22 & Table 4-1?-CM#14.
On the next slide, we will find brief content for Post 4: compression. What design tables for compression members determine available strength, based on CM#14 and CM#15? We have solved the problem of estimating nominal strength using Tables 4-1 and 4-22.
How do we use Table 4-1?
The first Table used for available strength is Table 4-1, based on CM#14. But Table 4-1 requires using the larger Y (Kl) Equivalent for the x-direction and the (KL)y about the Y axis.
The Equivalent (Kl)y from the x-axis equals (Kl/rx)*ry, where rx is the radius of Gyration about the X-axis and ry is the radius of Gyration about the Y-axis. The following slide image explains the difference between (Kl)eq and (Kl)y. This Table determines available strength as factored into the Nominal Load.
However, CM#15-Aisc-360-16 changes the Table in the Lc Expression, where Lc replaces Kl. For instance, Lcy is used instead of (Kl)y, and the Table is for W sections with a yield stress of Fy = 50 ksi.
Today, we will cover how to estimate critical stress (Table 4-22). The controlling factor that distinguishes short columns from long columns is the criterion Kl/r.
Table 4-22 gives the available critical stress for yield stresses Fy from 35 ksi to 50 ksi. The Table assumes the governing (KL/r) is in the y-direction, since it is larger than (KL/r)x in the x-direction.
We evaluate the maximum kL/r Value that yields the minimum compressive strength, Fcr. Then we multiply by the Area for the factored LRFD or ASD values.
There is no Table 4-22 in CM#15; its replacement is Table 4-14.
The same problem solved in the previous Post, problem 4-2, included W14x74 of A992 steel, a height of 20 feet, and a column hinged at both ends, with the design compressive strength computed per LRFD and ASD.
The radius of Gyration about the X-direction equals 6.04 inches, while the radius of Gyration in the Y-direction is 2.48 inches. The values Kl/rx = 39.74 and Kl/ry = 96.77 indicate that buckling in the y-direction controls the design.
We need to find the KL in the y-direction.
Select the larger of the K*Ly values. We need to convert k*lcx into k*lyeq by dividing K*lcx by the rx/ry ratio, which we can find at the bottom of Table 4-1. We have two values for kl with respect to Y: 8.20 ft and 20 ft. We select the maximum Value, 20 ft, and will use it later for Part B.
How to compute critical stress-Table 4-22?-LRFD design.
We will use Table 4-22 with yield stress Fy = 50 ksi, first for LRFD. For k*L/r = 96.77, it is between 96 and 97. For LRFD, at 96, the Value is 22.9. Since 97 has a Value of 22.6, our Value will be < 22.9.
The next slide image shows how we use linear interpolation to find the Value for φ*Fcr of 22.67 ksi, we will multiply by the Area to get the Load for the LRFD there and estimated as =22.9 minus the difference between (22.9-22.6) * 0.77/ 1, which will give the Value for φ*Fcr of 22.90 ksi, we will multiply by the Area to get the Load for the LRFD =494.18 kips.
How to compute critical stress-Table 4-22?-ASD design.
This is Table 4-22; we are checking the critical stress based on the ASD design. For ASD, for K*L/r = 96, (1/ω)*Fcr = 15.30 ksi, while for K*L/r = 97, (1/ω)*Fcr = 15.0 ksi. So (1/Ω)*Fcr for 96.77 is <15.30 ksi and is estimated as (15.30 – (15.30-15.00) * (0.30/1)) = 15.07 ksi. Multiply by the gross Area A to get the ASD Load1/ωωωΩ)*Pcr = 328.50 kips.
How to compute critical stress-Table 4-1?-LRFD and ASD design.
To use Table 4-1, we need to find the Equivalent (Kl) y: Kl*ry/rx = 20*12*2.48/6.04 = 8.21 feet. We compare this with (KL), the effective length in the y-direction, which is 20 feet. Since Kl at y is greater than (KL)y, we use the larger Value for Table 4-1. Please refer to the following slide image for more information.
How to compute critical stress-Table 4-1?-LRFD and ASD design.
For Fy = 50 ksi and W14x74, φ*Pn = 495 kips, while for ASD design, (1/ω)*Pcr = 329 kips. These figures are very close to the values obtained from Table 4-22.
Thanks a lot. I hope the information is useful.
You can view or download the PDF for this Post from the following Link.
If you want to review Post 3 for compressive strength,
This is the next post, post 5, “A Solved Problem 4-9,” on available compressive strength.
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