AISI Cold-Formed Steel Design Using Custom Section in RFEM 6

Custom sections are often required in cold-formed steel design. In RFEM 6, the custom section can be created using one of the “Thin-Walled” sections available in the library. For other sections that do not meet any of the 14 available cold-formed shapes, the sections can be created and imported from the standalone program, RSECTION. For general information on AISI steel design in RFEM 6, refer to the Knowledge Base article provided at the end of the page.

Example

Example III-14 of the AISI manual [1]?is used to compare the results obtained from the RFEM model. Since the?cross-section?does not match any of the Thin-Walled?sections, RSECTION is utilized to create the custom sigma?section.

The example presents two cases where the?member?is fully braced along its length (case 1) and braced at 66 inches (case 2). Only case 2 using LRFD method is examined in this article. The Finite Strip Method (FSM) is selected to calculate the available compressive?strength, Pa. Two (2) 66-inch long simply supported members are modeled in RFEM using rounded corner and angled corner (Image 03). The reason for using a?straight?line?section?(angled corner) is explained subsequently.

Compressive Strength

The critical elastic buckling loads (Pcrl, Pcrd, Pcre) required to determine the available compressive?strength, Pa?are presented below.

Pcrl?(Local)

The critical elastic local column buckling load, Pcrl?equals 34.4 kips is shown under the global buckling design check EE2701 and agrees with what is shown in the AISI example. The total curve shows a?distinct first minimum where Pcrl?equals 33.8 kips is obtained for both rounded corner and angled corner?sections?(Image 04). The small discrepancy between the values listed in the design check and the plot is negligible.

Pcrd?(Distortional)

The critical elastic distortional column buckling load, Pcrd?is shown under design check EE2801. For the?section?with rounded corners (rounded?section), Pcrd?equals 14.9 kips. It can be seen from the signature (total) curve that the second minimum is not distinct. In such case, the distortional curve is used to identify the appropriate length along the horizontal axis. From there, the location is projected to the total curve to obtain the critical load factor. The individual curves (local, distortional, global) can be displayed separately from the drop-down menu (Image 05). For custom?sections, it could take some time to load the individual graph.

The 14.9 kips at 89-inch length is the last relevant minimum on the distortional graph. Buckling shapes beyond this length are categorized as global buckling. RFEM applies a?“geometrical factor” to characterize the?buckling shapes?as global or distortional.

The AISI manual states, “Examination of the?mode shape?for the?member?at a?length of 66 inches shows both lateral translations associated with flexural (global) buckling and distortional buckling; consequently, the elastic buckling load at this length is used for the distortional buckling limit state check”[1]?. At 66-inch length, Pcrd?equals 19.4 kips on the total curve.

Due to difference in the approach, RFEM value of 14.9 kips at the 89-inch length is lower than the 19.4 kips at the 66-inch length listed in the AISI example.

Straight-Line Section (Angled Corner)

When using a?rounded?section?(rounded corner), the FSM solver divides the rounded corners into many small segments. In doing so, the calculation can be conservative. An option to verify the result is to model the?section?using straight?lines?(angled corners). For the straight?line?section, Pcrd?equals 17.7 kips. This value is closer to the 19.4 kips listed in the AISI example (Image 06).

Pcre?(Global)

Th elastic global (flexural, torsional, flexural-torsional) buckling load, Pcre?is shown under design check EE2701. Pcre?equals 19.4 kips for the rounded?section?and 19.2 kips for the straight?line?section. These values are taken from the total curve at the 66-inch length. As can be seen in Image 07, the?buckling shape?at this length contains both flexural (global) buckling and distortional buckling.

The AISI manual states, “The dashed?line?superimposed on the right half of the graph represents the global?buckling mode?isolated from other limit states. The elastic buckling load at this length from this?line?is used for the global buckling limit state check”?[1]. Consequently, Pcre?equals 38.9 kips listed in the AISI example is taken from the individual global curve (Image 08).

RFEM takes the conservative approach of obtaining Pcre?from the total curve instead of the global curve. Engineers can make their own judgement to use the higher value shown on the global curve after examining the?buckling shapes?at the 66-inch length. In RFEM, the alternative Pcre?value equals 44.3 kips on the global curve (in a?proximity of the 38.9 kips value listed in the AISI example).

Nominal Compressive Strength

The nominal compressive?strength?is taken as the smallest of the values according to the following AISI?sections:

• Section E2 - Yielding and Global Buckling
• Section E3 - Local Buckling Interacting with Yielding and Global Buckling
• Section E4 – Distortional Buckling

In RFEM, section E3 is the governing case with Pnl?equals 16.7 kips (Image 09). In AISI manual, distortional buckling (section E4) is the governing case with Pnl?equals 21.0 kips.

AISI Table B4.1-1 Applicability Limits

The safety factor, Ω or resistance factor, Φ used in chapter E through H are only appropriate for?sections?that comply with the limitations in Table B4.1-1. For all other?sections?that exceed any of the limits, higher safety factors or lower resistance factors are applied according to?section?A1.2(C). In RFEM, this limitation is checked by default. The user has the option to deactivate this check in the?Strength Configuration?(Image 10).

Shapes that can be checked in RFEM include C, Z, L, I (double back-to-back C), hat, rectangular and round HSS. For all other general/complex?sections?such as the sigma?section?used in this example, the more conservative factors are automatically applied. As a?result, Φc?equals 0.80 is shown in RFEM design checks (Image 09).

Calculation in the AISI manual?[1]?shows that the sigma?section?actually meets the applicability limits and Φc?equals 0.85 can be used.

Stiffened elements in compression:

w/t = [8.00 - 2(0.0451 + 0.0712)] / 0.0451 = 172 ≤ 500 OK

Edge-stiffened element in compression:

b/t = [0.875 - 2(0.0451 + 0.0712)] / 0.0451 = 14.2 ≤ 160 OK

Unstiffened element in compression:

d/t = [0.500 - (0.0451 + 0.0712)] / 0.0451 = 8.51 ≤ 60 OK

Inside bend radius:

R/t = 0.0712/ 0.0451 = 1.58 ≤ 20 OK

Single edge?stiffener?length/width ratio:

do/bo?= 0.500 / 0.875 = 0.571 ≤ 0.7 OK

Edge?stiffener?type: Simple or complex OK

Maximum number of intermediate stiffeners in w: nf = 1 ≤ 4 OK

Nominal yield?stress: Fy?= 50 ksi ≤ 95 ksi OK

Conclusion

Custom?cross-sections?can be created in RSECTION and imported into RFEM 6 for design according to AISI S100 or CSA S136. When analyzing a?complex?section, it is important to examine the?buckling shapes?and the signature (total) curve to determine if additional evaluation (i.e., using straight?line?section) should be performed. Straight?line?section?without rounded corners can at times provide a?better signature curve and result.

In a?case where the mode shows both flexural (global) buckling and distortional buckling, RFEM applies a?“geometrical factor” to characterize the?buckling shape?as global or distortional buckling.

By default, RFEM checks the applicability limits of Table B4.1-1 and applies the more conservative factors for general/complex?sections?without applicable limits.

Try out in the comfort of your office and test our Free Full Trial Version!

Keywords

#AISI?#Coldformed?#Steeldesign?#AISIS100?#Bucklingshapes?#Localbuckling?#Distortionalbuckling?#Globalbuckling?#Finitestripmethod?#FSM?#Parametricsection

Reference

[1]??AISI D100-17, Cold-Formed Steel Design Manual (2017)