Theoretical Study On Out-of-plane Buckling Of Transversely Laid Dumbbell-shaped Solid-web Beams (archs) Based On Plate-beam Theory

The CFST structure can give full play to the advantages of steel and concrete.For example,the core concrete can prevent the local buckling of the steel pipe,and the restraint effect of the steel pipe on the concrete makes the bearing capacity of the CFST structure higher than the sum of the compressive bearing capacity of the steel and concrete alone.And has better plasticity and toughness.Because the arch ribs are mainly under compression,CFST arch bridges are widely used in China.In order to facilitate the calculation and use of transverse dumbbell-shaped components in practical engineering,this paper,on the basis of Prof.Zhang Wenfu’s plate-beam theory,analyzes the solid-web arch of a single-material transversely-placed dumbbell-shaped section and a composite material transversely-placed dumbbell-shaped section.The flexural-torsional beam/buckling was theoretically analyzed and studied.The corresponding finite element model is established by the finite element software ANSYS,which is compared with the theoretical solution.The main research contents of this paper are as follows:⑴Based on the plate-beam theory,the total strain energy and total initial stress potential energy of flexural torsional buckling of single material transverse dumbbell shaped section(single web + empty steel pipe flange,double web + empty steel pipe flange)are derived,and the flexural stiffness,free torsional stiffness and restrained torsional stiffness of single material transverse dumbbell shaped section(single web +empty steel pipe flange,double web + empty steel pipe flange)are calculated.Based on the energy variation model and the differential equation model,the critical load formula of the simply supported beam under pure bending is given,and the correctness of the formula is verified by the finite element method.⑵Based on the plate-beam theory,the total bending torsional buckling potential energy and initial stress potential energy of composite material transverse dumbbell shaped sections(single web + CFST flange,double web + CFST flange and double steel plate concrete filled web + CFST flange)are deduced,and the flexural stiffness,restrained torsional stiffness and free torsional stiffness of composite material transverse dumbbell shaped sections(single web + CFST flange,double web + CFST flange and double steel plate concrete filled web + CFST flange)can be obtained.Based on the energy variation model and the differential equation model,the critical load formula of the simply supported beam under pure bending is given,and the correctness of the formula is verified by the finite element method.⑶According to the thin-wall theory,the free torsional moment of inertia of single material transverse dumbbell shaped section(single web + empty steel pipe flange,double web + empty steel pipe flange),composite material transverse dumbbell shaped section(single web + CFST flange,double web + CFST flange and double steel plate filled concrete web + CFST flange)is deduced,The corresponding model is built through the finite element software ANSYS,and compared with the free torsional moment of inertia and thin-wall theory of various sections deduced based on the plate beam theory,so as to verify the correctness of the characteristics of transverse dumbbell shaped sections in this paper.⑷ According to the total potential energy of flexural-torsional buckling of the solid-web circular arc arch with transverse dumbbell-shaped section,and assuming the flexural-torsional buckling displacement function of the hinged ends at both ends,the equilibrium of flexural-torsional buckling of the circular-arc arch with transverse dumbbell-shaped section under pure bending is obtained.equation,and then the critical load formula for bending-torsional buckling of the horizontally placed dumbbell-shaped cross-section solid-web circular arc arch is obtained.The finite element models of different section shapes were established by the finite element software ANSYS,and the eigenvalues of flexural-torsional buckling obtained by the finite element were used to verify the correctness of the critical load formula for the transversely laid dumbbell-shaped solid-web circular arc arch under pure bending.