| With the trend of modern bridges towards large spans,light weight,fast construction,and cost-effectiveness,the composite box girder with corrugated steel web(CBG-CSWs)has become a new type of bridge structure with wide application prospects.The restrained torsion and distortion effects under eccentric loads can no longer be calculated using elementary mechanics methods.In the design of the CBG-CSWs,the restrained torsion secondary shear stress and distortion effects on stress magnification were often ignored,making it difficult to achieve a refined design of the CBG-CSWs.An accurate theory that can reflect the spatial mechanical characteristics of the CBG-CSWs needs to be sought.In addition,there is limited research on the effects of restrained torsion and distortion of single-box multi-cell and variable-section CBG-CSWs.Combining the deficiencies in current research and relying on the National Natural Science Foundation of China(51968040),this study investigates the torsion and distortion theory of the CBG-CSWs,and the main contents and results are as follows:(1)The governing differential equation for the restrained torsion of the CBG-CSWs was established using the Umanskii’s second theory and the Reissner’s principle,and the initial parameter solution of the governing differential equation was given.Since effect of all secondary shear stresses on shear deformation were considered when establishing the governing differential equation for the restrained torsion based on the Reissner’s principle,the calculation results were in better agreement with the finite element solution.The fundamental difference between the Reissner’s principle and Umanskii’s second theory is the different formula of the warping coefficient that reflects the torsional characteristics.The influence of geometric parameter variation on the restrained torsion effect was further studied with a numerical example,and it was clarified that the secondary shear stress can not be ignored in the design of the CBG-CSWs.Based on the expression form of the initial parameter solution and the distribution characteristics of generalized internal forces,a simplified calculation method for generalized internal forces was proposed,and the reliability of the simplified calculation method was verified by the three warping bi-moment solution and the initial parameters solution.(2)In-depth study was conducted on the influence of shear deformation and diaphragm on the distortion effect of the CBG-CSWs.The governing differential equation for the distortion was established using the plate element method,principle of stationary potential energy,Reissner’s principle and energy method without shear deformation,respectively.The analytical solution of the governing differential equation considering the inner-span diaphragm was also provided.The influence of shear deformation is not taken into account by both the plate element method and the energy method without shear deformation,the distortional warping normal stress,shear stress and transverse bending moment of calculated by the two methods are almost identical.When no inner-span diaphragm is set,the differences between the generalized force and distortion angle calculated by various theories based on energy method are small.However,when inner-span diaphragms are set,there are significant differences in the calculated the distortional angle and transverse bending moment according to various theories due to the influence of shear deformation.Numerical examples verified that the calculation results of the Reissner’s principle are in better agreement with the finite element solution,and the influence of geometric parameter changes and inner-span diaphragm settings on distortion effects was further studied.The research results show that the inner-span diaphragms with appropriate number can reduce distortion deformation,but the influence of shear deformation on distortion effects can not be ignored.(3)A resolution calculation method for the restrained torsion and distortion effect of the single-box multi-cell CBG-CSWs was proposed.The eccentric vertical load acting on the CBG-CSWs was decomposed into rigid torsional load,main distortion load,and secondary distortion load.When analyzing the restrained torsion and main distortion effects,a calculation method for the resolution of shear flow was proposed.The calculation formulas for warping normal stress,shear stress,and sectional geometric properties were established based on the shear flow transfer law.The proposed calculation method is simple and its physical meaning is clear.The results of numerical examples show that the distortional warping normal stress under the eccentric vertical load is significantly larger than the torsional warping normal stress,while the torsional shear stress is approximately equal to the distortion warping shear stress.The distortion effects under the secondary distortion load also can not be neglected.(4)Considering the influence of shear deformation,the spatial stress state of the CBGCSWs including shear lag,shear flexure,restrained torsion and distortion under eccentric vertical load was studied.When solving the effects of restrained torsion and distortion,each plate was divided into multiple micro-element layers along the wall thickness.The calculation formulas for warping normal stress,shear stress,and corresponding geometric characteristics on each micro-element layer were established,and the governing differential equations for the restrained torsion and distortion considering the influence of wall thickness were established using the Reissner’s principle.According to the distribution of cross-sectional stresses,the normal stress magnification factor and the influence degree of stress under various deformation modes on the normal stress magnification factor under the eccentric vertical load were studied.The numerical examples show that the influence of shear-flexural and distortion effect on the normal stress magnification factor is the most prominent.(5)The finite beam element equations for the torsion and distortion analysis of the CBGCSWs were established,and the finite beam element program systems YSNZ and JBFX were developed.According to the initial parametric solutions of the governing differential equations for the restrained torsion and distortion and the physical meaning of the element stiffness matrix,the torsion angle and the torsional generalized warp displacement were selected as the node displacement of torsion analysis,and the distortion angle and the distortional warp displacement were selected as the node displacement for distortion analysis.The stiffness matrices of restrained torsion and distortion elements were derived separately,and the relationship equations between the free torque,the secondary torque,and the nodal displacement under restrained torsion were established.The reliability of the developed finite beam element program was verified by comparing the generalized internal forces calculated by the self-developed program with analytical solutions.Taking a three-span variable crosssection continuous CBG-CSWs as a numerical example,the generalized internal forces and displacements under restrained torsion and distortion were analyzed using the self-developed program,respectively,the sectional stresses were calculated,and the stress magnification factor was studied accordingly. |
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