الفهرس 
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Abstract
The design of over-hanging C-beams is not sufficiently covered in the current standards and specifications. The buckling length specified in the current standards and specifications was firstly defined by Nethercot, 1973 and covered only doubly symmetric I-sections. In this research program, both experimental and theoretical programs were performed to study the elastic and inelastic lateral torsional buckling behavior of C-sections bent about the major axis. In the experimental program, six full-scale over-hanging beams were tested. The back-span length was 3150 mm and the over-hanging lengths were variable and had the lengths of 2700, 3600 and 4500 mm. The tip of the cantilever was laterally restrained at top and bottom flanges. The cross section considered in the test program was UPN160 and UPN260. The root (intermediate) support was laterally restrained at the bottom flange only while the end support was laterally restrained at top and bottom flanges. The specimens were subjected to a concentrated load applied at the top flange at the tip of the cantilever.
Standard tension tests were performed on coupons cut from the web to determine the actual mechanical properties of the steel used.
A finite element model was developed to simulate the behavior of such specimens. To include the effect of large displacement on the behavior, a nonlinear geometric analysis was performed. A multi-linear elasto-plastic response of the material was considered. The modified Newton-Raphson iterative method was used to perform the nonlinear analysis and the load was applied in increments.
The results from the developed finite element model showed a good agreement with the experimental results. Once the validity of this model was verified, the model was used to conduct parametric studies with the over-hanging length to back span length ratio ranging from 0.166 to 6. Four types of lateral supports at the tip of the over-hanging beams were studied. In the first case, the tip was laterally-restrained. In the second case, the tip was free, while in the third case, the top flange only was laterally-restrained. In the last case, the bottom flange was laterally-restrained, which was not considered in any of the standards or specifications. Three types of lateral supports at the root (intermediate support) of the over-hanging beams were studied. In the first case, the root was laterally-restrained. In the second case, the top flange only was laterally-restrained, while in the last case, the bottom flange was laterally-restrained. Three different loading positions were considered at the tip. The three loading positions are at the Y-axis, passing through the centroid of the section. The first one was applied at the upper flange and the second one was applied at the section mid height (centroid location), while the third one was applied at the lower flange.
Two proposed design models, based on the results developed from the parametric study and the results obtained experimentally were proposed. The ultimate moment capacities of such beams computed according to many standards and specifications as well as those computed using the proposed design model were compared to those obtained experimentally from the tests performed in this study.
The comparison showed that the proposed design models results had a good agreement with the experimental results. The ultimate moment capacities obtained using the developed models were within ± 10% of those obtained experimentally. The comparison showed that the ultimate moment capacities computed according to the AISC Specifications, (2005), BS5950, (1990), Eurocode 3, (2005) and ECP, (2001), varied from conservative up to 85% to unconservative up to 15%, depending on the over-hanging length, and the load location along the beam depth.