Test Verification of the Effect of Stress Gradient on Webs of Cee and Zee Sections FINAL REPORT March 2002 submitted to the American Iron and Steel Institute and the Metal Building Manufacturers Association by Ben Schafer, and Cheng YuExecutive Summary 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 (www.ce.jhu.edu/bschafer) 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. (a) local buckling, λ =5 in., Mcr/My=0.98 (b) distortional buckling, λ = 27 in., Mcr/My=0.74 Elastic buckling of 8.5 in. deep t=0.073 in. ZeeTable of Contents Progress Report 1 – February 2001 1 Introduction ......................................................................................................................1-1 2 Design Methods ..................................................................................................................... 1 2.1 Existing methods for C’s and Z’s in flexure ...................................................................1 2.1.1 Expressions for the web (AISI, S136 (Cohen), Schafer).................................................................. 1 2.1.2 Expressions for the flange ................................................................................................................ 1 2.1.3 Direct Strength Design ..................................................................................................................... 1 2.2 Analytical evaluation of existing methods ...................................................................... 2 2.2.1 web expressions................................................................................................................................ 2 2.2.2 flange expressions ............................................................................................................................ 3 2.2.3 flange/web interaction ...................................................................................................................... 3 2.3 Local flange/web interaction........................................................................................... 3 2.3.1 Expressions for flange/web local buckling....................................................................................... 3 2.3.2 Impact of local flange/web interaction ............................................................................................. 3 2.3.3 Fixed bc is optimistic for web equation............................................................................................ 5 3 Evaluation via Existing Experiment.................................................................................... 5 3.1 Member geometry ........................................................................................................... 5 3.1.1 MBMA Z members .......................................................................................................................... 6 3.1.2 Elhouar and Murray study ................................................................................................................ 6 3.1.3 Compilation of C’s with known experimental results ...................................................................... 6 3.1.4 Geometric range of SSMA members................................................................................................ 6 3.1.5 Geometric