Thermal behavior of elastic columns with second-mode imperfections

• The buckling equilibrium equations are obtained by using the energy method.
• The formulae for the axial compression and transversal displacement are presented.
• The relationship between the imperfection and the axial compression is studied.
• The effect of elevated temperature is also discussed.
• The response of the column to the modified slenderness ratio is investigated.

Pin-ended columns having an initial imperfection in a second buckling mode and subjected to thermal loading have been studied in this paper. Based on a nonlinear relationship between strains and displacements, the buckling equilibrium equations are given with the energy method. Then the formulae for the axial compression and transversal displacement are presented. The relationship between the anti-symmetric imperfection and the axial compression has been studied along with the effect of elevated temperature on the initial imperfection. The response of the column in fire to the modified slenderness ratio is investigated. The proposed method has the potential to provide more detailed information for column designs and thus be deployed in future research to minimize the need for expensive laboratory testing.

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