Study On Restrained Action Among Chords Of Square Pyramid Space Grid Structure Under Localized Fires

The grid structure is one of the commonly used form of large span structures, which subjected to fire frequently. The key parameters affecting the fire resistance performance of the grid structure were systematically studied. But for the failure mechanism of the grid structure under localized fires has not been well analyzed. Under localized fires, members in the grid structure with low temperature will have restriction on the expansion of members with high temperature. And restrained members would still have bearing capacity after buckling which depends on the axial restrained stiffness value. In order to determine the value of axial restrained stiffness, we have done the following work in this paper.(1) Based on the non-classical plate theory, the upper and lower chords are equivalent to the surface and bottom of sandwich plate. The basic plane strain differential equation of upper and lower layers is respectively established, and the plane strain of upper and lower layers is obtained. Considering the simple support boundary conditions and geometric equation, the plane displacement formula under normal temperature of upper and lower layers is obtained. The deflection of grid structure under normal temperature is given in the quasi sandwich plate method.(2) Under the condition of constant load heating, the elastic modulus decreases with the increase of temperature. At the same time, the upper and lower and sandwich layers will produce thermal expansion. For the structural response under high temperature, the elastic modulus of plane displacement and deflection formula under normal temperature is corrected. With linear superposition the thermal expansion, the transient plane displacement and deflection formula of the grid structure under uniform temperature field is obtained.(3) For the grid structure under localized fires, the temperature boundary condition is non-uniform temperature field. In non-uniform temperature field, for a random infinitesimal element of the upper and lower layers, we assume that the temperature is uniform distribution. We can get the infinitesimal element’s plane displacement and deflection by corresponding formula. Taking the distance between the infinitesimal element and fire center as the integral interval, the transient plane displacement and deflection formula of the grid structure under non-uniform temperature field can be obtained.(4) Taking the members’node coordinate geometry into the plane displacement and deflection formula of the grid structure under non-uniform temperature field, we can get the node plane displacement and deflection. For the grid structure under localized fires, the change of node displacement is caused by the attenuation of the elastic modulus, the thermal expansion and the restriction of the members. The node displacement formula only considers the influence of the former two. And the numerical analysis method takes into account the effect of the three. The difference between the numerical solution and analytical solution of node displacement is the axial deformation ΔS caused by the member constraint. The additional temperature axial force ΔN is generated by numerical analysis. The axial force required for the units axial constraint deformation is obtained, which is defined as the axial restraint stiffness ks.We achieve a quantitative method of solving truss member’s axial restraint stiffness under localized fires in this paper. It is a core technology to calculate restrained member’s post-buckling load-bearing capacity. It provides a theoretical basis for further study of the failure mechanism of grid structure under fire.