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Analytic solution of second-order effect for frame structure

QIU Hongxing,HU Tao,SUN Jian (Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University,Nanjing 210096,China)  
A theoretical basis for the practical method was provided to analyze the behavior and influencing factors of second-order effect of multi-story frame structures.Through the establishment of equilibrium equation of the deformed structure,an analytic model of three-story frame was presented based on solving the differential equation of the deflection curve of members.This model considers both the gravity second-order effect(P-Δ effect) and the deflection curve effect of compression members(P-δ effect),and is an exact solution.Analysis shows that there are different mechanisms of second-order effect for the shear mode deformation and the flexural mode deformation.For the shear mode deformation,the additional moments of each story depend only on the story drift and axial force of column in this story.For the flexural mode deformation,the additional moments of each story are interconnected.The practical formula for the second-order effect provided by the GB 50010 specification is applicable to the shear mode frame.The accuracy decreases with the increase of the axial force and increases with the increase of the rotational stiffness.When the coefficient of the rotational stiffness is larger than 18,the proportion of the shear mode deformation is over 50% and the error less than 5%.
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