Considering the difference of the maximum amplitude and phase of the shearing angle of top and bottom flanges as well as the equilibrium of the internal force of the section

the two-parameter shear lag warpage displacement function of the stress balance was proposed. On this basis

the differential equations and boundary conditions of simply supported box girder were established based on the principle of minimum potential energy. Then

the self-equilibrating stress of the simply supported box girders at nonlinear temperature was calculated and compared with the finite element results. Numerical analysis show that results of the two-parameter method were consistent with those of the finite element analysis

and the calculation accuracy of the two-parameter function satisfying the axial force self-balance of section was higher than that of the direct method. The self-equilibrating stress of the simply supported box girder in the nonlinear temperature gradient led to the shear lag effect at the end. The influence range of the temperature shear lag effect was about 1.5 times of the width of the box girder

and the stress result was greater than the stress based on the plane cross-section assumption. For the cantilever box girder with symmetry section

the calculation results of the stress in the span considering the shear lag effect were the same with the results obtained based on the plane cross-section assumption. For the cantilever flanged box girder with asymmetric section

the plane section method neglected the modification of section curvature which was caused by shear force due to nonlinear temperature

so the calculation error of the mid-span stress by plane section method was still smaller than the exact solution. While the two-parameter method modified the influence of shear force on section curvature and improved the calculation precision.