Research On Torsion And Torsional Torsion And Buckling Theory Of Triangular Cross-section Beam Based On Plate-beam Theory

In the closed section,most researchers focus on the box section,and the research direction mainly focuses on the experimental research and finite element analysis of the stress state of axial compression and eccentric compression.There is little theoretical research on torsion and moment buckling,and there is less research on triangular section.In order to facilitate the calculation and use of triangular section members in practical engineering,based on Professor Zhang Wenfu’s “plate-beam theory”,this paper makes a theoretical study on the torsional and flexural buckling of general closed triangular section,open and closed mixed triangular section with plate and triangular concrete-filled steel tubular（CFST）section beams of different materials.The corresponding model is established by finite element software for verification.The section characteristics of general closed triangle are compared with those derived from classical thin-wall theory.The main contents of this paper are as follows:（1）Based on the "plate-beam theory",the theoretical analysis and research of three kinds of three triangular-section cantilever beams under torsion.The free torsional stiffness and constrained torsional stiffness of the triangular section are solved,and compared with the free torsional stiffness and constrained torsional stiffness of the classical thin-wall theory,and the total strain energy of the cantilever beam torsion is obtained.Then,according to the energy variation model and differential equation model The formula for the angle of rotation of the cantilever beam subjected to torsion at the free end is obtained.The corresponding finite element model is established and solved,and the correctness of the "plate-beam theory" is verified by comparing the rotation angle formula with the finite element solution.（2）Based on the “plate-beam theory”,the theoretical analysis and research of three kinds of simply supported beams under bending are carried out.The free torsional stiffness,bending resistance stiffness and constrained torsional stiffness of the triangle section are derived,and the bending torsional buckling critical bending moment formula of the simple supporting beam under the pure bend is obtained according to the energy variation model and the differential equation model.The corresponding finite element model is established and the finite element solution is solved,and the critical bending moment formula is compared to verify the correctness of the "plate-beam theory".