Buckling analysis of pre-cracked beam-columns by Liapunov's second method |
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| Institution: | 1. Department of Mechanics and Engineering Science, School of Mathematics, Jilin University, Changchun 130012, PR China;2. College of Construction Engineering, Jilin University, Changchun 130021, PR China;3. National Key Laboratory of Science and Technology on Advanced Composites in Special Environments, Harbin Institute of Technology, Harbin 150080, PR China;1. Department of Civil and Building Engineering, and Architecture, Polytechnic University of Marche, via Brecce Bianche, 60131, Ancona, Italy;2. Department of Mechanical Engineering, State University of New York at Binghamton, Binghamton, 13902 NY, USA;3. Physical Sciences and Engineering Division, King Abdullah University of Science and Technology KAUST, Thuwal 23955-6900, Saudi Arabia;1. Mechanical Design and Production Dept., Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt, Egypt;2. Mechanical Engineering Dept., Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia;1. UFMA - Cidade Universitaria Dom Delgado, Brazil;2. UEMA - Cidade Universitaria Paulo VI, Brazil |
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| Abstract: | Interaction between reduced axial and lateral torsional buckling strengths of thin beam-columns of double symmetric sections with an edge crack at the middle is examined via Liapunov's second method. This is done in order to show how critical loads for pre-cracked thin-walled beam-columns can be obtained with out the rigour of meticulous solution of a set of differential equations. Having derived an asymptotic expression for the normalized energy release rates for the beam-column, a metric space and a Liapunov's Functional for a pre-cracked beam-column are proposed. By using Zubov's stability theorems and appropriate eigen value inequalities, expressions for reduced buckling strengths due to edge cracks are obtained. A crack reduction parameter k is proposed which is used to calculate reserve strengths for published lateral buckling strength equations. Results obtained using the proposed parameter are well in agreement with findings of earlier published works in the literature when the parameter is set to zero. The results also show that cracks cause loss of stiffness and can reduce the lateral buckling strengths of beam-columns considerably. |
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