الفهرس 
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Abstract
Continuous composite girders are extensively employed in the construction of buildings due to their efficient usage of structural materials. Concerning Eurocode 4, When the extreme-fiber tensile stress in concrete reaches twice the mean value of the axial tensile strength specified by EN 1992-1-1, concrete cracking decreases flexural stiffness in hogging moment zones but not in sagging regions. Moreover, the variation in relative stiffness of the composite girder must be taken into consideration in the effective length factor calculation. Since the alignment charts were developed for members with constant cross-section, the direct use of the original parameter, G, for the restraining composite girders in the current alignment charts may lead to unreasonable results. Therefore, depending on the slope deflection equation, a proposed buckling factor formula was developed for these framed columns restrained by composite girders with different far end conditions. In addition,the proposed buckling factor formula was programmed to facilitate the analysis of the results. In different codes, the relative stiffness of the composite girder is taken into account by using the equivalent flexural stiffness equation with different weight factors to figure out the moment of inertia of the composite girder. Consequently, a program was prepared to make the comparison between (EC3, AISC, and ECP codes) easier and more effective. Research scope: Develop the proposed buckling formula of columns in braced and unbraced frames with composite girders.Research objective: The main objective of this study is to develop the proposed buckling formula of columns in braced and unbraced frames with composite girders and also to compare between different codes (ECP, AISC, and EC3) in the effective length factor calculation, to determine which code is more economical for calculating the buckling factor. Some results will be analyzed by computer programs. Study steps: In the present study, the closed-form and approximate solutions of the stiffness modification factor (α) for composite girders are derived. Furthermore, the proposed buckling formula of columns in braced and unbraced frames with composite girders is programed. This program figures out the effective length factor according to different codes (American, Egyptian, and European). Moreover, the program is based on the C#.NET language and Excel spreadsheets are used to generate what designers need fromthe codes in a clear, simple method. The thesis includes a comparison between the Egyptian code, American code, and European code.Conclusions: This study illustrates the calculation method of the effective length factor for columns in braced and unbraced frames with composite girders. The far ends of the girders are depicted as fixed, rigid, and hinged. Furthermore, the equations for the proposed buckling factor have been proven using methodology based on the parameter (α). Moreover, the parameter (α) has been deduced in its closed form. In addition, approximate solutions for the parameter (α) are derived. The proposed formula for calculating the buckling.factor is programed. This program also computes the effective length factor according to different codes (American, Egyptian, and European).Subject Titles.Stability functions, unbraced frames, The alignment charts, composite frames, braced frames, composite girders, 15% cracked analysis, stiffness coefficients, and sagging.moment.