Response Analysis for Steel Reinforced Concrete Frame Structures under Earthquake Load

In order to understand the whole process of the steel reinforced concrete frame structure from elastic to elasto-plastic cracking gradually, damage until the collapse, the elasto-plastic finite element analysis theory and ETABS structural analysis software were used, then the spatial three-dimensional truss system model of frame structures was established. Based on the analysis of the elasto-plastic response for the frame structure under onedimensional and two-dimensional earthquake load, the interbedded displacement angle-time curve and horizontal displacement-time curve were obtained. Through the analysis of the model, the sequence of appearance of plastic hinges in the frame structure under earthquake load was cleared and the weak location of the frame structure was detected.


INTRODUCTION
Commonly used structural seismic analysis methods are equivalent to base shear method, model analysis response method and time-history analysis method (Chung et al., 2007).The first two belong to the static elastic analysis methods.In order to understand the whole process of the structure from elastic to plastic cracking gradually, damage until the collapse, analysis of elastic-plastic response of structures is done for looking for measures to prevent structural collapse.The study of elastic-plastic time history method experienced from the layer-truss model, plane truss model to the three-dimensional truss system model.Many simplifications are done for the layer-truss model and the plane truss model, so the calculation becomes relatively convenient.However, the ground motion is a multi-dimensional movement when earthquake happens; the action of earthquake on structures is spatial (Geng et al., 2012).The structure will bear forces from two directions; in this case, its seismic performance is largely different from that of uniaxial force state (Tao et al., 2007).It is very difficult to obtain accurate result of the seismic performance through the plane response (Lu and Jing, 2002;Wu, 2002).Therefore, ETABS software is used to establish the framework of three-dimensional structure of the space truss model, the frame structure is under the elastic-plastic response analysis on the one-way seismic wave and two-way seismic waves, the two sets of data were compared (Lu and Yang, 2012;Xu et al., 2011).

Characteristics of resilience:
Restoring force is the capacity of restore the deformation; restoring-force characteristic shows the relationship between restoringforce and deformation.Restoring force model is a base of elastic-plastic time history analysis of the structure, generally obtained by test.In accordance with the material properties, component types and loading methods, restoring force model is idealized and then based on the crack, yield and ultimate displacement of structural feature points, hysteretic bone curve is defined.Commonly used restoring force model of concrete structures includes curve type and broken line type.Curve-type restoring force model is a continuous curve, the stiffness changes continuous, closer to the actual project, but more complicated method of calculating stiffness (Li, 1980).Broken line-type restoring force model posed by a number of line segments, the stiffness change is not continuous because of inflection point or mutation, but the stiffness calculation is relatively simple, so it is widely used in practice.For steel reinforced concrete structures, due to the material properties and different types of components, the restoring-force characteristic under major earthquake is very complex.In this study, the calculation of the analysis selected the bilinear restoring force model, as shown in Fig. 1.
The plastic hinges of structure are shown in Fig. 10.At about 2.5 sec, plastic hinge firstly happened at the bottom of frame column and then more plastic hinges appeared in order of floor at the end of beams and columns.At last a plastic hinge area is formed and structure is in the state of elasticplastic deformation.
Analysis of layer-truss model: Figure 11 is the layer-truss model only by the north-south El-Centro seismic waves.The contrast of two types of models is shown in Table 1.
The maximum displacement of vertex in Y direction of the three-dimension truss model is larger than that in the layer-truss model under both of the frequent and occasional earthquakes.The following reasons are included: • Three-dimension truss model is affected by the two direction seismic waves, but layer-truss model is only affected by single direction seismic wave.• Under the action of multi-force, its seismic performance will be reduced.• As a result of uneven weight distribution, the structure will have a reverse effect, thus the displacement increased.

DISCUSSION AND CONCLUSION
In this study, elasto-plastic response of steel reinforced concrete frame structures under earthquake was analyzed with ETABS.Threedimension truss model and layer-truss model were used.Based on the analysis of the elastic-plastic response under two-directions and one-direction El-Centro seismic waves, the story drift and horizontal time-displacement curve were compared.The response under two-directions El-Centro seismic waves has a coupling effect and causes larger response than that under one-direction.In the design for ultimate limit states of components, the method of calculating the bearing capacity of the two orthogonal directions respectively and stacking is unsafe and it should be considered by the multi-dimensional combined effect of cross-section internal forces.Through the analysis of the model, the sequence of appearance of plastic hinges in the frame structure under earthquake load was cleared and the weak location of the frame structure was detected.It is basically agreement with that of previous study by SAP2000 and ANSYS software.

Fig. 1 :
Fig. 1: Restoring force model Fig. 7: The largest layer disp. of Y direction (mm) selected.The peak south and 210.1 gal in way seismic waves are used to dimensional truss system model, norths used to analyze layer-truss

Table 1 :
The contrast of seismic response Maximum