Theoretical Research On Combined Torsion And Flexural-torsional Buckling Of The I-shaped Beams With Concrete-filled Steel Tubular Flange Based On The Plate-beam Theory

For the modern society,the building structure is gradually developing towards the direction of the large-span and large-height,and the concrete-filled steel tube composite structure is a kind of structure components which is widely used and has good development prospects.The I-shaped beam with concrete-filled steel tubular flange is a new type of composite component with high bending rigidity and torsional rigidity of the section,which can improve the strength and out-plane stability of the component.In addition,the existence of the concrete-filled steel tubular flange can reduce the height of the web,the ratio of height and thickness of the web is relatively small which is also beneficial to the shearing.The I-shaped beam with concrete-filled steel tubular flange is consists of steel and concrete,which can also be seen as a combination of open-closed-solid parts in form,all these make the related theoretical researches more complicated and can not be applied to the existing theoretical formulas.At present,the theoretical researches on the combined torsion and flexural-torsional buckling of the I-shaped beam with concrete-filled steel tubular flange are seen seldom,meanwhile,solving the torsion problem is the necessary precondition to solve the problem of flexural-torsional buckling.In this paper,according to the plate-beam theory proposed by Professor Zhang Wenfu,theoretical research on combined torsion and flexural-torsional buckling of the I-shaped beams with concrete-filled steel tubular flange are conducted starting with the uniform torsion of the concrete-filled steel tube,and the finite element method is used to verify the correctness of the theoretical derivation.The main research contents of this paper are as follows:(1)Based on the plate-beam theory,the theoretical analysis of the uniform torsion problem of the concrete-filled steel tube beam is conducted,and the expressions of the total potential energy and uniform torsion rigidity of concrete-filled steel tube with square or rectangular section are given,12 finite element models of concrete-filled steel tube with square or rectangular section are established by ANSYS respectively,extracting the torsional angle of the free end and comparing with the theoretical to verify the correctness of theoretical derivation and the uniform torsional rigidity.(2)Based on the plate-beam theory,the theoretical analysis of the combined torsion problem of the I-shaped beams with concrete-filled steel tubular flange is conducted,and the expressions of the total potential energy,uniform torsion rigidity and non-uniform torsion rigidity of the biaxial-symmetric and mono-symmetric I-shaped beams with concrete-filled steel tubular flange are given,the energy variational model and differential equation model are established,and the analytical solution of the torisonal angle are also given,12 finite element models of the biaxial-symmetric and mono-symmetric I-shaped beams with concrete-filled steel tubular flange are established by ANSYS respectively,extracting the torsional angle of the free end and comparing with the theoretical to verify the correctness of theoretical derivation,the uniform torsional rigidity and non-uniform torsional rigidity.(3)Based on the plate-beam theory,the theoretical analysis of the flexural-torsional buckling of the I-shaped beams with concrete-filled steel tubular flange is conducted,and the expressions of the total strain energy,total initial stress potential energy and total potential energy of biaxial-symmetric and mono-symmetric I-shaped beams with concrete-filled steel tubular flange are given,and the calculation method of the asymmetric coefficient of mono-symmetric section is shown,meanwhile,the energy variational model and differential equation model are established.(4)Based on the expression of the total potential energy for flexural-torsional buckling of the I-shaped beams with concrete-filled steel tubular flange,the calculation formulas of the critical moment of elastic flexural-torsional buckling under pure bending,uniform load and concentrated load at mid-span for simply supported beam is given,the eigenvalue buckling analysis is proceeded for 12 finite element models of biaxial-symmetric and mono-symmetric I-shaped beams with concrete-filled steel tubular flange by ANSYS respectively to verify the correctness of the calculation formula of the critical moment.