professor ben schafer's thin-walled structures research group - johns hopkins university


Local Buckling of C's & Z's in Bending


The research reported on this page is based on sponsored research conducted with the American Iron and Steel Institute which completed in March 2002. 


Abstract (go to Executive Summary)

    C- and Z-Sections are one of the most common cold-formed steel shapes in use today. Accurate prediction of the bending performance of these sections is important for reliable and efficient cold-formed steel structures. Recent analytical work has highlighted discontinuities and inconsistencies in the current AISI design provisions for stiffened elements under a stress gradient (i.e., the web of C- or Z-Sections). New methods have been proposed for design. Existing tests on C- and Z-Sections do not provide definitive evaluations of the design expressions for the web due to: incomplete restriction of the distortional mode, arrangement of the specimens (back-to-back vs. toe- to-toe), and lack of information on bracing details. A series of new flexural tests focused on the role of web slenderness in local buckling failures of C- and Z-Sections is proposed. Through careful bracing and an understanding of the inherent interaction between the flange and the web the results may be used for evaluation of existing and proposed methods for strength prediction of webs.


Project Documentation

    American Iron and Steel Institute's RFP (RFP ) - June 2000

    Response to RFP (Proposal) - July 2000

    Organization and initiation of work (selection of specimens) ( testing plan) - October 2000

    Progress report 1 (report) (presentation) - February 2001

    Progress report 2 (report) (presentation) - July 2001

    Progress report 3 (report) (presentation) - February 2002

    Final report (report) - March 2002


Related papers and presentations

Yu, C., Schafer, B.W. (2003). “Local Buckling Tests on Cold-Formed Steel Beams.” ASCE, Journal of Structural Engineering. 129 (12) 1596-1606. (doi:10.1061/(ASCE)0733-9445(2003)129:12(1596))

Schafer, B.W., Trestain, T. (2002). “Interim Design Rules for Flexure in Cold-Formed Steel Webs.” 16th International Specialty Conference on Cold-Formed Steel Structures October, Orlando, FL

Yu, C., Schafer, B.W.. (2002). “Local Buckling Tests on Cold-Formed Steel Beams.” 16th International Specialty Conference on Cold-Formed Steel Structures October, Orlando, FL (paper)

Schafer, B.W. (2001). “Experiments on Braced Thin-Walled Cold-Formed Steel C and Z Beams in Flexure.” Recent Advances in Stability of Structural Components and Systems combined ASCE-EMD and ASME Summer Conference. San Diego, California. (Presentation)


Executive Summary (from final report)

This report details the work performed under a research grant funded by the American Iron and Steel Institute (AISI) and the Metal Building Manufacturers Association (MBMA) entitled "Test Verification of the Effect of Stress Gradient on Webs of Cee and Zee Sections." The project evolved in response to the inconclusive nature of existing test data on Cees and Zees in bending and the need for a set of simple repeatable tests on industry standard sections that account for typical details in current practice and provide the actual bending capacity in local buckling. Findings and recommendations from the research follow.


Existing design procedures for the effective width (strength) of webs (AISI 1996) are theoretically inconsistent, discontinuous, and ignore the influence of the flange. Modifications adopted in the new North American Specification (AISI 2002) partially remove the web/flange interaction issue but introduce a strength discontinuity at web width to flange width ratios (h/b) of 4.


Existing test data on Cees and Zees in bending has inordinate scatter compared with the test-to-predicted ratio for the AISI Specification. Previous research did not distinguish between local and distortional buckling failures, so it is difficult to resolve the data meaningfully. However, capacity of members with panels through-fastened to the compression flange, and h/b ratios less than 4, generally agree well with existing (AISI 1996) standards. Academic testing on Cees and Zees without attached panels consistently produce lower strength predictions than AISI (1996).


Developing a new test procedure requires that specific attention be paid to the restriction of the compression flange. In typical unrestrained industry standard Cees and Zees, distortional buckling occurs before local buckling. In the testing performed here, a pair of panel-to-purlin fasteners (as opposed to a single fastener through mid-flange of the purlin) was required to fully restrict distortional bucking and initiate local buckling failures. The strength and failure mode is sensitive to the fastener detail.


Evaluation of the test results suggests that existing design provisions are adequate as long as distortional buckling is restricted. In several tests, even inelastic reserve capacity (tested moment capacity greater than moment at first yield) was observed. Assuming the flange expressions are accurate, the observed web effective width generally falls between that assumed by AISI (1996) and the Canadian (S136 1994) standard. The newly proposed Direct Strength method ( provides the best prediction of member capacity, and also suggests quite different optimum dimensions than existing methods, particularly with regard to lip length.


Future research is needed to evaluate and develop design expressions for distortional buckling. Cees and Zees with unrestrained compression flanges have systematically lower strength than the local buckling tests performed here. These lower strengths are potentially relevant for purlins and girts under suction, continuous beams over supports, or any other purlin, girt, stud or joist in which no restriction of the compression flange is provided and distortional buckling can form.



Project Timeline

9-2000 Project commenced

10-2000 Detailed examination of existing test data

10-2000 Analytical work on web/flange interaction issues in current AISI Specification

10-2000 Finite strip and further hand analysis to determine dimensions of specimens for testing

10-2000 Detailed testing plan and approval of AISI task group

11-2000 Physical overhaul of JHU structures lab facility in preparation of project

11-2000 C and Z specimens delivered to JHU 

12-2000 Specimens organized and labeled, damaged specimens re-ordered as needed

12-2000 Additional structural steel for reaction frame and loading mechanisms acquired

1-2001 Detailed dimensional measurements of 8.5" Z's and 8" C's completed

1-2001 Controller, DAQ system acquired

1-2001 Finalization of testing apparatus for tests on 8.5" Z's (first set of tests)

3-2001 Completion of first full specimen and testing - see gallery for 19 March 2001

4-2001 Analysis of first test and re-design for future testing - see gallery and analysis of 22 March 2001 test

4-2001 Continued testing on 8.5" zeds, tension testing of specimens - test results on 8.5" zeds with t=0.073in.

5-2001 Testing on 8.5" zeds, thinnest specimen tested and failure mechanism assessed.

6-2001 Testing on 8.5" zeds completed (summary). Most tension testing on 8.5" zeds completed

7-2001 Testing on 8" deep C's underway

8-2001 Testing on 8" deep C's completed

9-2001 Testing on 3.6" to 12" deep Cees underway

10-2001 Continued testing and modifications to accommodate various member sizes

11-2001 Completion of cees testing, initiation of 11.5" deep zed testing

12-2001 Continued testing on 11.5" zeds and modifications to deal with high strength of zeds

1-2002 Write-up of results and completion of 11.5" zeds

4-2002 Completion of project


last updated 07/19/05