Web crippling is a form of localized buckling that occurs at points of transverse concentrated loading or supports of thin-walled structural members. The theoretical computation of web crippling strength is quite complex as it involves a large number of factors such as initial imperfections, local yielding at load application and instability of web. The existing design provision in North American specification for cold-formed steel C-sections (AISI S100, 2007) to calculate the web-crippling strength is based on the experimental investigation. The objective of this research is to extend the direct strength method to the web crippling strength of cold-formed steel C-sections. ABAQUS is used as a main tool to apply finite element analysis and is used to do the elastic buckling analysis. The work was carried out on C-sections under interior two flange (ITF) loading, end two flange (ETF) loading cases. Total of 128 (58 ITF, 70 ETF) sections were analyzed. Sections with various heights (3.5 in.to 6 in.) and various lengths (21 in. to 36 in.) were considered. Data is collected from the tests conducted in laboratory and the data from the previous researches is used, to extend the direct strength method to cold formed steel sections. Proposing a new design for both the loading cases and calculation of the resistance factors under (AISI S100, 2007) standards is done.

The 1999 AISC Specification for Structural Steel Buildings establishes two design equations for the web crippling limit state at the supports. However, investigators have suggested that the basis of these equations, which is based on an assumed collapse mechanism, is conservative especially for long bearing lengths. Most of the experimental studies conducted to validate those formulas have considered short span lengths and relatively small bearing-to-depth ratios. Therefore, a further investigation of the web crippling capacity of W-shape steel beams for larger span lengths and larger bearing-to-length ratios was undertaken. The primary objective of this study is to analytically investigate the web crippling strength of W-shape steel beams for large bearing-to-depth ratios on large span beams, and to compare the results with the 1999 AISC LRFD web crippling design equation (K1-5b). The web crippling strength of W-shape steel beams was investigated by means of the finite element technique. The commercial finite element package ANSYS 6.0 was used to model the steel beams. Material nonlinearities, large deformation effects and initial geometric imperfections were taken into account in the finite element models. The validation results shown that the finite element models closely predicted the ultimate load and web crippling failure mode shape of the tested beams. Conclusions based on the predictions of the finite element analyses and the current 1999 AISC end web crippling design equation (K1-5b) are presented in the study. / Master of Science

The main objective of this research is to extend the “Direct strength method” for determining the web crippling strength of cold-formed steel C and Z sections subjected to End one flange loading and Interior one flange loading conditions. Direct strength method is applied for designing the columns and beams earlier. The existing specifications equation for calculating the web crippling strength of cold-formed steels designed by American Institute of Iron and Steel is very old method and it is based on the extensive experimental investigations conducted at different universities. Calculating the web crippling strength of cold-formed steels using direct strength method is a new technique. In the present research the web crippling strength of cold-formed steels were calculated using Direct Strength Method. The experimental data is collected from the tests that were conducted at different universities. The critical buckling strength of the members were calculated using Abaqus. Microsoft excel is used to generate the equations. The safety and resistance factors for the designed equations were calculated using “Load and resistance factor design” and “Allowable strength design” from North American Cold-Formed Steel Specification, 2012 edition book.

The AISI (1996) Specification for the Design of Cold-Formed Steel Structural Members provisions for web-crippling are believed to be conservative for multi-web deck sections. They are based on unfastened specimens and are limited to the use of decks with certain geometric parameters. The unified web crippling equation of the North American (2002) Specification for the Design of Cold-Formed Steel Structural Members (adopted from Canadian S136-94 Specification) is also limited to certain geometric parameters. Although it has new web crippling coefficients for different load cases and different end conditions, in the End One Flange (EOF) loading case, coefficients for the unfastened configuration were used as a conservative solution for the fastened case because there was no directly applicable test data available in the literature. This thesis presents the results of an experimental study on web-crippling strength of multiple-web cold-formed steel deck sections subjected to End One Flange (EOF) loading. Seventy-eight tests were conducted at Virginia Tech. Test specimens lying inside and outside of certain geometric parameters of the specifications were tested with both unrestrained and restrained end conditions. Test specimens lying inside the specification parameters have revealed conservative results in the prediction of web crippling capacity using both AISI (1996) and North American (2002) equations. Using the unified web-crippling equation of North American Specification, a nonlinear regression analysis was performed to update the unfastened case coefficients and derive new fastened case coefficients. Also, the calibration of these coefficients is done for both Canadian S136 (1994) and AISI (1996) specifications. / Master of Science