Based on the nonlinear displacement-strain relationship,the virtual work principle method was used to establish the nonlinear equilibrium equations of steel beams with semi-rigid connections under vertical uniform loads and temperature change.Considering the non-uniform temperature distribution across the thickness of beams,the formulas for stresses and vertical displacements were presented.On the basis of a flowchart for analysis of the numerical example,the effect of temperature change on the elastic behavior of steel beams was investigated.It is found that the maximal stress is mainly influenced by axial temperature change,and the maximal vertical displacement is principally affected by temperature gradients.And the effect of temperature gradients on the maximal vertical displacement decreases with the increase of rotational stiffness of joints.Both the maximal stress and vertical displacement decrease with the increase of rotational stiffness of joints.It can be concluded that the effects of temperature changes and rotational stiffness of joints on the elastic behavior of steel beams are significant.However,the influence of rotational stiffness becomes smaller when the rotational stiffness is larger.
The nonlinear behavior of fixed parabolic shallow arches subjected to a vertical uniform load is inves- tigated to evaluate the in-plane buckling load. The virtual work principle method is used to establish the non-linear equilibrium and buckling equations. Analytical solutions for the non-linear in-plane sym- metric snap-through and antisymmetric bifurcation buckling loads are obtained. Based on the least square method, an approximation for the symmetric buckling load of fixed parabolic arch is proposed to simplify the solution process. And the relation between modified slenderness and buckling modes are discussed. Comparisons with the results of finite element analysis demonstrate that the solutions are accurate. A cable-arch structure is presented to improve the in-plane stability of parabolic arches. The comparison of buckling loads between cable-arch systems and arches only show that the effect of cables becomes more evident with the increase of arch’s modified slenderness.
