Research On P -Δ Effect Design Method Of Dropped Stories Frame Structure

The influence of second-order effect is an important link in the design of reinforced concrete structures.In recent years,many breakthroughs have been made in the study of the second-order effect of structure in the academic circles at home and abroad.However,in the mountainous area,the mountainous buildings often adopt the dropped stories frame structure or the suspension structure combined with the mountainous topography and hydrogeology.but research on the second-order effect of the dropped stories structure is seldom touched.On the basis of continuing team’s research on the influence of second-order effect on regular structure,this paper extends it to dropped stories structure,and demonstrates the applicability of the design scheme of second-order effect of current “Code for Design of Concrete Structures”(GB50010-2010)to dropped stories structure.It provides a reference for the design method of second-order effect in the "Design Standard for Mountain Architectural Structures" which is being compiled.To solve the engineering practice needs under mountainous conditions,and to supplement and improve the vacancy of the second-order effect system.Based on the analysis and study of the second-order effects of the frame structures with and without tied beams,the following results are obtained in this paper:(1)In the current “Code for Design of Concrete Structures”(GB50010-2010),the application scope of considering the P-(35)effect by the method of the story augmenting factor method is generally recognized as a frame structure with shear deformation as the dominant factor on the same horizontal plane only for the restrained parts of the bottom lateral resistance members.But,the validity of story-falling frame structures with two or more fixed ends not on the same horizontal plane in the same structural unit needs to be verified.Based on the deformation characteristics of the layered structure between the upper grounding end and the lower grounding end,the applicability of considering the second-order effect of the layered structure by the layer-increasing coefficient method is analyzed.(2)For the layers above the upper grounding end of the dropped stories frame structure with pull beam.In addition to the bottom layer,the law of the deformation of this layer is affected by the constraint of the upper grounding end.The other layers are dominated by shear deformation,and the "layer effect" is very obvious.Considering the effect of internal force and displacement caused by the P-(35)effect,the story augmenting factor method has good engineering accuracy.For the dropped stories part below the upper grounding end,due to the influence of the overall bending moment deformation of the superstructure,the shear deformation of the dropped stories part above the grounding end under the action of horizontal force no longer plays a major role.It is no longer appropriate to consider the internal force and displacement of the dropped stories part after the structure has been deformed by using the story augmenting factor method.(3)For the dropped stories frame structure with no pull beam,the method of "the story augmenting factor method " can still be used in all layers above the ground end,except the bottom layer.For the dropped stories part below the upper grounding end,without the stiffness contribution of the pull beam,the influence of the whole bending moment deformation of the upper structure on the dropped stories part will be further increased,and the story augmenting factor method can’t objectively reflect the P-(35)effect law of the dropped stories structure.(4)By adjusting the stiffness ratio of the grounding column in the upper grounding layer,the conclusion that The story augmenting factor method can not be used to consider the P-(35)effect of the dropped stories part is still valid.(5)For the dropped stories structures,the elastic second-order analysis can accurately calculate the real internal forces and deformations including the P-(35)effect under the elastic state.The stiffness of each structural member is further reduced to reflect the non-linear characteristics of reinforced concrete structures,such as concrete cracking,bond and slip between reinforcement and concrete.The elastic second-order analysis method considering stiffness reduction is a practical engineering method of considering both geometric and material nonlinearity of the delaminated structure.Its accuracy depends to a great extent on the value of stiffness reduction coefficient.The results of Pushover’s nonlinear analysis and elastic second-order analysis considering stiffness reduction are compared with those of the equivalent second-order effect of the whole structure to verify the applicability of the stiffness reduction factor of the regular frame in the drop-out structure in the current “Code for Design of Concrete Structures”(GB50010-2010)(6)Combining the deformation law and the second-order effect law of the floor-drop structure,the non-linear analysis results are compared.Then,putting forward an envelope design method for different stiffness reduction coefficients of dropped stories part of dropped stories structure,which is different from traditional regular frames...