The Pushover Analysis of R.C frames Based on SAP2000

Jing Li1, a, Xinghua Yu2,b 1 No.1 Zhongshan North Road, Longhu Town, Xinzheng City, Henan Province, China

2 No.1 Zhongshan North Road, Longhu Town, Xinzheng City, Henan Province, China

azz_lijing@126.com,

b yuxinghua9810@yahoo.com.cn

Keywords: R.C frames; Pushover analysis; Pushover

Abstract: The pushover analysis had been done for a R.C frame model, vertex displacement,base

shear , appear order and development situation of plastic hinges of the model had been get in different

steps of pushover analysis, The pictures of basal shear-vertex displacement and response spectrum

displacement-accelerated speed had been studied. The analysis results show that ,the R.C frame

model correspond with the seismic design principle of stronger column weaker beam ’,and meet the

seismic requirements of the first stage and the calculating resistance to collapse of the second stage.

1. The analysis method of Static elastic-plastic Pushover

Pushover methods are widely applied to assess the performance, based on the existing structure and

design of the structure at home and abroad in recent years. Static nonlinear he analysis of the structural

analysis model distribution patterns along the structural height required for a gradual increase in the

lateral force or lateral displacement under the action until the structural model of the control point of

the process until the target displacement or structural overturning[1].

1.1 The basic principles of Pushover analysis

Pushover method is the one used to predict earthquakes caused by the force and deformation demand.

The basic principle is:

Impose some kind of distribution pattern (such as uniform loads, inverted triangular load) analog

seismic level of the lateral force of the inertial force, and gradually monotonic increase in the

structural analysis model, until the structure to achieve the desired state (as institutions, excessive

displacement of the limit or to reach the target displacement), and then assess the performance of the

structure. The deductive method can be used for seismic evaluation and strengthening of buildings,

and seismic design and performance evaluation of the new structure.

In essence, Pushover method is a static analysis method, which uses two-dimensional or

three-dimensional model to replace the original structure, the lateral edge of the level of analog

seismic inertia force imposed on the model in some way, and increase gradually and monotonously, if

the component is to coming into being cracking or Yield, then modify its stiffness, until the structure

to achieve the desired state (as a plastic bodies or reach the target displacement).In this analysis, to get

the structure base shear and the entire process curve of with the top floor displacement. Although the

lateral distribution of power is a kind of static load, but can be approximated to reflect the structure

under the earthquake effect the dynamic response of a moment in the whole process of analysis.

Relatively active for designers to grasp the structure of the lateral load, the plastic hinge location, the

plastic hinge reaches its ultimate rotation capacity corresponding feature point displacement and base

of the total shear, which can control the extent of structural damage.

1.2 The implementation steps of Pushover analysis[2]

(1) Prepare to structure data including establishing structure model, the physical constants of

component and restoring force model and so on.

Advanced Materials Research Vols. 594-597 (2012) pp 812-815 Online: 2012-11-29© (2012) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/AMR.594-597.812

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(2) Computing architecture of the internal forces in the vertical loads(superimposed with the internal

forces in the horizontal force components under the force of a certain level of internal forces, to

determine whether the component cracking or yield);

(3) The centroid of each layer in the structure, the load is applied along a certain level of height

distribution. The size of the horizontal force is applied according to the following principles: After the

superposition of the horizontal forces generated by internal forces and step (2) the calculation of

internal forces, so that one or a number of component cracking or yield;

(4) Cracking or yield components, and modify its stiffness, and then apply a load to another or group

of component cracking or yield;

(5) Repeated (3)(4)step, until the structure of vertex displacement is large enough or the plastic hinge

is more than enough to achieve the desired destruction of limit state.

(6)Draw basis shear-top displacement curve, that is, to derive curves.

2. Reinforced concrete frame structure nonlinear static analysis

2.1 Reinforced concrete frame structure KJ-1

In this paper, the reinforced concrete frame prototype for one or two industrial plants, the size of the

frame column grid is 6m×6m storey is 5.1m, design framework for the cross section and

reinforcement, according to 9 degree earthquake intensity PKPM Software. And then using 1:3 scale

model, designed, produced a framework of test specimen, No. KJ- 1, the test model and the

reinforcement shown in Figure 1.

2.2 KJ-1 Pushover analysis of the implementation steps

Sap2000 software Pushover Analysis of Frame Structure KJ-1.First Grave vertical load (load +0.5

live load) analysis, and then based on the result of this analysis, the derivation of horizontal load.

During the derivation of horizontal load analysis, the second lateral load pattern is adopted by the

Structure loading, that is, Inverted triangular load pattern. Also, according to the specifications that

default PM3 hinge and PMM hinge are adopted respectively when defining the plastic hinges of

beams and columns.

2.3 The nonlinear static analysis results for KJ-1 structure model

(1)The structure of the base shear – top displacement for KJ-1

Table 1list the KJ-1 structural model in different Pushover analysis steps corresponding vertex

displacement, base shear and plastic hinge order and development. Figure2, Figure3 are the base shear

by the pushover analysis-vertex lateral map and the response spectrum of displacement-Acceleration

diagram of KJ-1.

Fig.1 Details of the KJ-1

Advanced Materials Research Vols. 594-597 813

Tab.1 The analysis results of Pushover for KJ-1

steps Topdisplacement(mm) Base shear(kN) The formation and development of plastic hinge

1 2.3 18.28 Beam appear plastic hinge on both ends

2 2.6 19.29 The below of left column appears the plastic hinge

3 2.9 19.77 The below of right column appears the plastic hinge ,

being form of agency

4 10.9 20.51 All plastic hinge into immediate use phase

5 18.9 21.25 The bottom hinge of the two columns to enter the

“safety life” stage

6 19.6 21.32 The below of left column reaching the ultimate

bearing capacity

7 19.6 14.25 The below of left column failure

It can be seen from Table 1, when the Pushover carried out to the first step, Beam appear first

plastic hinge on both ends, indicating to the elastic limit state, at this time corresponding to the base

shear 18.28KN greater than the maximum lever of more than 9 degrees earthquake seismic force

10.7KN, and 7 degrees rare earthquake class Ⅱ site, two-group calculation of horizontal seismic

forces 16.73KN description of the structure of the framework to fully meet the preliminary seismic

design requirements.

Table 1 and Figure 2 shows the Maximum base shear of the structure comes to 21.32KN, close to

horizontal seismic force 24.1KN of 7 degrees (0.3g) severe earthquake calculated by two group of

class III site, corresponding to the vertices of the maximum horizontal displacement increased to

19.6mm, less than the maximum plasticity displacement between floors limits[3]

:

[θp]h=1700/50=34mm, base shear —— lateral curve shows obvious turning point. When to achieve

the maximum base shear, the response spectrum acceleration corresponded by figure 3 is 11.84m/ s2,

far more than the maximum acceleration 1.4 m/s2

of 9 degrees frequent earthquake and design basic

acceleration 4.0 m/s2 of 9 degrees seismic fortification intensity.

To sum up, the frame structure KJ-1 designed by the current seismic code meets frequent

earthquake seismic requirements in the first stage and second stage anti-collapse of the checking and

less than maximum plasticity displacement between floor limits.

(2) The formation and development of plasticity of the KJ-1 model

The plastic hinge formation and development in a different class Pushover analysis for KJ-1 model

is as shown in Figure 4. Figure 4(a) is the plastic hinge state under the first level horizontal loading

(Horizontal loading to right), it can be seen that Frame beams form plastic hinge first on both ends

under the first level horizontal loading, according with the seismic design principles of the “strong

column weak bean”; corresponding to the horizontal displacement of 2.3mm. The first inconspicuous

turning point is in KJ-1 Basel shear-vertex lateral figure of the figure 2. Add to the second load, the

bottom of the left column appears plastic hinge (figure4 (b)). Add to the third load, the bottom of the

right column appearing plastic hinge at the bottom of the right column (figure4 (c)), but the agency of

Fig.2 The picture of basal

shear-vertex displacement

Fig.3 The picture of response spectrum

displacement-accelerated speed

814 Advances in Industrial and Civil Engineering

framework does not reach the ultimate bearing capacity, and a significant turning point appears in

KJ-1 Basel shear -vertex lateral figure in figure 2. When add to the fourth load, all plastic hinges from

the beams and columns get into “immediate use” session (figure 4 (d) the color of plastic hinge is

blue). Add to the fifth load, the bottom hinges of the two columns (plastic hinge color is green) get

into the “life safety” session firstly. Napping to the fifth step from the third step, basal shear increases

less, and the vertex displacement increases greatly. When napping to the fifth step, the plastic hinge of

the bottom of left column gets into the limit working state, plastic hinge color of yellow, framework to

achieve maximum capacity(figure4(e)).

The above analysis results show that for the framework structure KJ-1, the order of appearance of

plastic hinge under the effects of earthquake is: beam and the bottom of column. Complying with the

seismic design principles of “strong column weak bean”, but in the last the destruction of KJ-1 is in

the plastic hinge in the bottom of left column. Of course, historical damage indicates that the

reinforced concrete frame structure can not design to make the entire structure to form the desired

beam hinge failure mechanism. However, the energy dissipation mechanism of the framework

structure tends to reasonable and ideal by adjusting the design.

3. The conclusion

(1) The results of The Pushover calculation show that the order of appearance of plastic hinge of KJ-1

under the effects of earthquake is: beam and the bottom of column. Complying with the seismic

design principles of “strong column weak bean”.

(2)The results of The Pushover calculation show that the frame structure KJ-1 designed by the current

seismic code meets frequent earthquake seismic requirements in the first stage and second stage

anti-collapse of the checking.

(3)The results of The Pushover calculation show that the destruction of the frame structure KJ-1 is in

the plastic hinge in the bottom of left column. The reinforced concrete frame structure does not form

the desired beam hinge failure mechanism.

References

[1]Civil King Software Technology Ltd., China Institute of Building Standard Design and Research.

The Chinese Version User Manual of SAP2000 [M]. 2006，China Communications Press, In

Chinese.

[2] Xinling Wang. Theoretical and Experimental Studies on New Chevron Bracing Compound

Structures [D]. Doctoral Dissertation of Southeast University.2006, In Chinese.

[3] GB50011-2001 Code for seismic design of buildings [S], In Chinese.

Fig.4 The development of plastic hinge during the Pushover analysis of different levels

Advanced Materials Research Vols. 594-597 815

Advances in Industrial and Civil Engineering 10.4028/www.scientific.net/AMR.594-597 The Pushover Analysis of R.C Frames Based on SAP2000 10.4028/www.scientific.net/AMR.594-597.812