push solver

ISSN 2348-5426 International Journal of Advances in Science and Technology (IJAST)

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56

Pushover Analysis of Existing 3 Stories RC Flat slab Building M. A. Ismaeil

Ph.D Candidate, Cairo University, Egypt.

ABSTRACT - A three-stories hospital existing reinforced

concrete building in the city of Khartoum-Sudan, subjected

to seismic loads ,was analysed .The Sudan is not free from

earthquakes , it has experienced many earthquakes during

the recent history, and the previous studies on this field

demonstrated this argument. This paper is focused on the

study of seismic performance of the existing hospital

buildings in the Sudan. Plastic hinge is used to represent

the failure mode in the beams and columns when the

member yields. The pushover analysis was performed on

the building using SAP2000 software (Ver.14) [1] and

equivalent static method according to UBC 97 [2]. The

principles of Performance Based Seismic Engineering are

used to govern the analysis, where inelastic structural

analysis is combined with the seismic hazard to calculate

expected seismic performance of a structure. Base shear

versus tip displacement curve of the structure, called

pushover curve, is an essential outcomes of pushover

analysis. The pushover analysis is carried out in both X and

Y directions. Default hinge properties, available in some

programs based on the FEMA -356 [3] and Applied

Technology Council (ATC-40) [4] guidelines are used for

each member. One case study has been chosen for this

purpose. The evaluation has proved that the three stories

hospital building is seismically safe.

Keywords— Pushover analysis; Reinforced concrete ;

Seismic performance ; ATC-40 ; FEMA -356.

I. INTRODUCTION

The purpose of pushover analysis is to evaluate the expected

performance of structural systems by estimating its strength and

deformation demands in design earthquakes by means of

static inelastic analysis, and comparing these demands to

available capacities at the performance levels of interest. The

equivalent static lateral loads approximately represent

earthquake induced forces. A plot of the total base shear

versus top displacement in a structure is obtained by this

analysis that would indicate any premature failure or

weakness. Many researchers have conducted studies in this

area such as: N. Jitendra BABU et al., (2012) [5] presented a

research paper on "Pushover Analysis of Unsymmetrical

Framed Structures on Sloping Ground". The paper deals with

non-linear analysis of various symmetric and asymmetric

structures constructed on plain as well as sloping grounds

(30° slope) subjected to various kinds of loads .The analysis

has been carried out using SAP2000 and ETABS software.

The paper concluded that the structure with vertical

irregularity is more critical than a structure with plan

irregularity. For the increase of seismic zoning factor over

many parts of Indian continent and based on FEMA-356 and

ATC-40 guidelines.

Kavita Golghate et.al. (2013) [6] carried out "a Pushover

Analysis of a 3 Storey's Reinforced Concrete Building" aiming

to evaluate the zone-IV selected reinforced concrete building to

conduct non-linear static analysis (pushover analysis) using

SAP 2000.The study showed that hinges have developed in the

beams and columns showing the three stages immediate

occupancy, life safety and collapse prevention.

Rahul RANA et.al. (2004) [7] performed a pushover

analysis on a 19 story, slender concrete tower building located

in San Francisco with a gross area of 430000 square feet. The

lateral system of this building consists of concrete shear walls

and it was designed conforming to 1997 Uniform Building

Code (UBC), and pushover analysis was performed to verify

code's underlying intent of Life Safety performance under

design earthquake. Utilizing the results from the analysis, some

modifications were made to the original code-based design so

that the design objective of Life Safety performance is

expected to be achieved under design earthquake .

In 2013 M. A. Ismaeil, et.al. (the Author of this paper)

presented a series of earthquake researches on "Assessment of

Seismic Performance and Strengthening of RC Existing

Residential Buildings in the Sudan" [8], "Seismic Retrofitting

of a RC Building by Adding Steel Plate Shear Walls" [9], and

"Effects of Earthquake loads on Existing School Buildings in

Sudan" [10]. These studies were conducted to investigate the

performance of samples of existing RC buildings in the city of

Khartoum, Sudan.

II. DESCRIPTION of THE STUDY CASE

This case study is a typical three stories model for hospital

building in the Sudan. The building is comprised of a

reinforced concrete structural frame with infill masonry walls.

The structure members are made of in-situ reinforced

concrete .The overall plan dimension is 21.5x13m. Height of

the building is 9.6 m .The floor is a flat slab system. Figures 1-

3 give detailed information on the architectural layout of the

hospital. The lateral force resisting system consists of moment

resisting frames without shear walls. The rectangular shape is

used for the columns. Columns and beams sizes along the

building height are listed in Tables I and II.



57

Table 1

The cross sections of columns

The cross sections of columns Story No.

300x500 Ground floor

300x500 First floor

300x500 Second floor

Table 2

The cross sections of beams

The cross sections of beams Story No.

300x500 Ground floor

300x500 First floor

300x500 Second floor

Fig 1. Foundation plan

Fig 2. Ground Floor Plan

Fig 3. South elevation

2.1 Numerical model

Numerical models for the case have been prepared using

SAP2000 version 14 (Computers and Structures) [1]. Beams

and columns are modelled as frame elements and slabs are

modelled as shell elements. In this paper the seismic

performance of the considered residential building was

evaluated using the nonlinear static analysis procedure

(Pushover Analysis).

Figure 4 and 5 show the model of 3 stories hospital building

and layout of columns.

Fig 4. Model of 3 stories hospital building

Fig 5. Label of columns



58

2.2 Load cases

For the pushover analysis, three load cases were considered:

1- PUSHGRAVITY (Applying the gravity loads).

2- PUSH+X (Appling lateral loads in the X-X direction).

3-PUSH+Y (Appling lateral loads in the Y-Y direction).

III. SEISMIC LOADS ON THE BUILDING

3.1. Base shear force

The Uniform Building Code (UBC1997) [2] requires that the

“design base shear”, V, is to be evaluated from the following

formula:

TR

WICV v .............................(1)

The total design base shear does not need to exceed

the following:

R

WICV a5.2 ………………….. (2)

The total design base shear shall not be less than the

following:

11.0 IWCV a ………………….(3)

V = total design lateral force or shear at the base.

W = total seismic dead load

The approximate fundamental period (T), in seconds, is

determined from the following equation:

T = Ct . hn3/4 ............(4)

whereas: Ca and Cv are acceleration and velocity based seismic

co-efficients respectively. Ct = 0.035 (0.0853) for steel

moment-resisting frames. Ct = 0.030 (0.0731) for reinforced

concrete moment-resisting frames and eccentrically braced

frames. Ct = 0.020 (0.0488) for all other buildings.

The base shear shall be distributed over the height of the

structure, including Level n, according to the following

formula:

............................(5)

Where as

Ft = 0 when T ≤ 0.7 sec.

Ft = 0.07 T V < 0.25 V; when T >0.7 sec.

3.2. Equivalent lateral static loads

The base shear force is distributed as a lateral force, which

affects the joint, at each level of the building.

IV. PUSHOVER ANALYSIS

The pushover analysis is a static non-linear analysis under

permanent gravity loads and gradually increasing lateral loads.

Static pushover analysis is an attempt by the structural

engineering profession to evaluate the real strength of the

structure and it promises to be a useful and effective tool for

performance based design [9].

4.1.Application of pushover analysis.

Pushover analysis may be applied to verify the structural

performance of newly designed

1. To verify the over strength ratio values.

2. To estimate the expected plastic mechanism and the

distribution of damage.

3. To assess the structural performance of existing or retrofitted

buildings.

4. As an alternative to the design based on linear analysis.

The ATC-40 [4] and FEMA-356 [3] documents have

developed modelling parameters, acceptance criteria and

procedures of pushover analysis.

4.2 STATIC NONLINEAR ANALYSIS USING FEM

SOFTWARE

SAP2000 nonlinear version offers very strong and

significant characteristics for the nonlinear static pushover

analysis. Both 2D and 3D structures can be analysed as

pushover analysis on SAP2000 nonlinear version [1].

The nonlinear behaviour of the frame members are determined

by particular hinges and the structural capacity drop occurs for

the said hinges.

After performing analysis certain points are achieved

ranging from A to E as shown in Figure 6. Point A shows the

unloaded state, Point B shows yielding state of an element,

point C represents nominal strength and co-ordinate of point C

on displacement axis shows deformation at which significant

amount of strength degradation occurs. The part from C to D in

the above figure shows the starting failure of an element and

the strength of the element to resist lateral forces is unreliable

after point C. The portion D to E on the curve shows that only

the gravity loads are sustained by the frame elements. After

point E, the structure has no more capacity to sustain gravity

loads [11]. Performance point and location of hinges in

various stages can be obtained from pushover curve as

shown in Figure 1. The range AB is elastic range, B to IO is

the range of immediate occupancy IO to LS is the range of

life safety and LS to CP is the range of collapse prevention. If



59

all the hinges are within the CP limit then the structure is

said to be safe. However, depending upon the importance

of structure the hinges after IO range may also need to be

retrofitted.

Fig 6. Force-deformation for pushover hinge [11]

4.3 Acceptance Criteria (Performance Level)

Three points labelled IO, LS and CP as referred in Figure 6

are used to define the Acceptance Criteria or performance level

for the plastic hinge formed near the joints (at the ends of

beams and columns). IO, LS and CP stand for Immediate

Occupancy, Life Safety and Collapse Prevention, respectively.

The values assigned to each of these points vary depending on

the type of member as well as many other parameters defined

in the ATC-40 and FEMA-273 documents.

4.3.1 Seismic demand and performance point

The performance point is the point where the capacity curve

crosses the demand curve according to ATC-40.Two main

approaches are used to evaluate the performance point

(maximum inelastic displacement of the structure), Capacity-

Spectrum Method of ATC-40 [4] and Coefficient Method of

FEMA 356 [3]. In the present study the Capacity-Spectrum

Method is more suitable for the evaluation task.

In the Capacity-Spectrum Method of ATC-40, the process

begins with the generation of a force-deformation relationship

for the structure. Then the results are plotted in Acceleration-

Displacement Response Spectrum (ADRS) format as shown in

Figures 7. This format is a simple conversion of the base shear

versus roof displacement relationship using the dynamic

properties of the system, and the result is termed capacity

spectrum for the structure.

(a) Base shear versus top displacement

A static nonlinear (pushover) analysis of the building was

carried out using SAP2000. A maximum roof displacement of

0.5 m was chosen to be applied .A pushover analysis was

carried out separately in the X and Y directions. The resulting

pushover curves, in terms of Base Shear-Roof Displacement

(V-U), are given in Figures 8 and 9 for X and Y directions.

Figure 7. Static approximation used in the pushover analysis [12].

1.Direction X

Figure 8. The pushover curves, in term of Base Shear-Roof Displacement

indirections X

Direction Y

Figure 9.The pushover curves, in term of Base Shear-Roof Displacement

indirections Y

(b)The performance point

The performance point is the point where the capacity curve

crosses the demand curve according to ATC-40.Figure for X



60

direction and figure 13 for Y direction show the performance

point for all push over curves. Figure 10 shows the

performance point with the red colour is the elastic spectrum,

the green curve represents the spectrum resistant and the

yellow line defines the point as defined by ATC-40.The

intersection of the yellow line (demand) and the green curve

(capacity) is the performance point.

Figure 10. Capacity and demand [13]

1. Directions X

This analysis was completed in 12 steps and performance point

was set between steps 2 and 3 of the analysis.

Table 2. Shows some of steps of the analysis for X direction

and for each step shows the details for the capacity and demand

curve. Figures 12 presents the overall yielding pattern of the

structure at the performance point for X direction.

Figure 11.Pushover capacity curve and performance point at X direction

Figure 12. Yielding pattern of the structure at the performance point in Y

direction (step 2)

Tables 3 give the coordinates of each step of the pushover

curve and su

mmarizes the number of hinges in each state (for example,

between IO, LS, CP or between D and E).

Table 3

Pushover curve demand capacity - ATC40 at X direction

Step Teff Beff SdCapacity SaCapacity SdDemand SaDemand

M m

0.00 0.13 0.05 0.00 0.00 0.00 1.00

1.00 0.13 0.05 0.00 0.95 0.00 1.00

2.00 0.13 0.06 0.00 1.09 0.00 0.95

3.00 0.17 0.18 0.01 1.49 0.00 0.59

4.00 0.18 0.21 0.01 1.53 0.00 0.54

5.00 0.18 0.21 0.01 1.53 0.00 0.54

6.00 0.33 0.33 0.04 1.49 0.01 0.44

7.00 0.43 0.34 0.07 1.55 0.02 0.44

8.00 0.56 0.77 0.07 0.92 0.03 0.40

9.00 0.56 0.76 0.07 0.92 0.03 0.40

10.00 0.60 0.89 0.07 0.81 0.03 0.37

11.00 0.60 0.88 0.07 0.81 0.03 0.37

Table 4

The computed limit states for the studied building in X direction



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Step A

toB

B

toIO

IO

toLS

LS

toCP

CP

toC

C

toD

D

toE

Bey

ondE

Total

0 1900 0 0 0 0 0 0 0 1900

1 1898 2 0 0 0 0 0 0 1900

2 1878 22 0 0 0 0 0 0 1900

3 1841 59 0 0 0 0 0 0 1900

4 1823 77 0 0 0 0 0 0 1900

5 1820 80 0 0 0 0 0 0 1900

6 1820 32 48 0 0 0 0 0 1900

7 1816 36 0 24 0 24 0 0 1900

8 1816 36 0 24 0 0 24 0 1900

9 1816 36 0 20 0 4 24 0 1900

10 1816 36 0 20 0 0 28 0 1900

11 1816 36 0 8 0 12 28 0 1900

12 1816 36 0 8 0 0 40 0 1900

Table 5

Displacement and base force at X direction

Step Displacement BaseForce

m KN

0 5E-05 0

1 0.005 3760

2 0.006 4332

3 0.013 6338

4 0.015 6576

5 0.015 6586

6 0.043 6864

7 0.074 7171

8 0.074 4238

9 0.075 4245

10 0.075 3757

11 0.077 3763

12 0.073 2230

2. Directions

This analysis was completed in 7 steps and performance point

was set between steps 2 and 3 of the analysis.

Table 6 shows the Pushover Curve Demand Capacity – ATC-

40 in direction Y and Figure 14 presents the overall yielding

pattern of the structure at the performance point for Y direction.

Figure 13.Pushover capacity curve and performance point at Y direction

Table 6

Pushover Curve Demand Capacity (ATC-40) at Y direction

Step Teff Beff Sd

Capacity

Sa

Capacity

Sd

Demand

Sa

Demand

m m

0.00 0.17 0.05 0.00 0.00 0.01 1.00

2.00 0.18 0.06 0.03 3.43 0.01 0.96

3.00 0.18 0.06 0.05 6.06 0.01 0.96

4.00 0.18 0.06 0.07 8.83 0.01 0.97

5.00 0.18 0.05 0.09 11.38 0.01 0.97

6.00 0.18 0.05 0.11 13.93 0.01 0.97

7.00 0.18 0.05 0.13 16.63 0.01 0.98

8.00 0.18 0.05 0.16 19.75 0.01 0.98

9.00 0.18 0.05 0.18 22.26 0.01 0.98

10.00 0.18 0.05 0.19 24.24 0.01 0.98

Table 7

The computed limit states for the studied building in Y direction

Step A B IO LS CP C D

Total toB ToIO toLS toCP toC toD toE

0 412 0 0 0 0 0 0 412

1 411 1 0 0 0 0 0 412

2 391 21 0 0 0 0 0 412

3 380 32 0 0 0 0 0 412

4 374 38 0 0 0 0 0 412

5 368 44 0 0 0 0 0 412

6 358 54 0 0 0 0 0 412

7 352 56 4 0 0 0 0 412



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Table 8

Displacement and base force at X direction

Step Displacement BaseForce

m KN

0 0 0

1 0.007 3626.238

2 0.032 13964.96

3 0.058 24600.137

4 0.086 35768.907

5 0.111 46062.481

6 0.137 56366.077

7 0.164 67231.236

Figure 14. Yielding pattern of the structure at the performance point in Y

direction (step 2)

V. RESULTS AND DISCUSSIONS

1- Pushover analysis was carried out separately in the X and

Y directions. The resulting pushover curves, in terms of Base

Shear – Roof Displacement (V-Δ), are given in Figures 8 & 9

for X and Y directions respectively. The slope of the pushover

curves is gradually changed with increase of the lateral

displacement of the building. This is due to the progressive

formation of plastic hinges in beams and columns throughout

the structure.

2. It is observed that the structural elements of the third floor

have not entered in the plastic zone in contrast to some

structural elements in the lower floors, as shown in Figures 12

and 14.

3. From the results obtained in X and Y directions the level of

plastic hinges are not exceed the IO Level , as shown in Tables

4 and 7.This means that the building is seismically safe .

4. It was found that the seismic performance of studied

building is adequate , because all elements were not reached

the Immediate Occupancy (IO) level ,as shown in Figures 12

and 14 for X and Y directions .

VI. CONCLUSION

The main output of a pushover analysis is in terms of

response demand versus capacity. If the demand curve

intersects the capacity envelope near the elastic range, then the

structure has a good resistance. If the demand curve intersects

the capacity curve with little reserve of strength and

deformation capacity, then it can be concluded that the

structure will behave poorly during the imposed seismic

excitation and need to be retrofitted to avoid future major

damage or collapse.

In this paper the building is investigated using pushover

analysis. These are conclusion obtained from this analysis:

1. The pushover analysis is a simple way to explore the

nonlinear behavior of building.

2. Pushover analysis can identify weak elements by

predicting the failure mechanism and account for the

redistribution of forces during progressive yielding. It

may help engineers take action for rehabilitation work.

3. Pushover analysis is an approximation method based

on static loading. It may not accurately represent

dynamic phenomena.

4. The results show that design considering only gravity

load is found inadequate. Therefore, a structural

engineer should consider earthquakes in designing

building.

5. The building that was analysed according to UBC is

satisfactory. The performance point location is at IO

(Immediate Occupancy) level. It means the design

satisfies pushover analysis according to ATC -40.

REFERENCES

[1] CSI. SAP2000 V-14. Integrated finite element analysis

and design of structures basic analysis reference manual.

Berkeley (CA, USA): Computers and Structures Inc;

2010.



63

[2] ICBO, et al.(1997) “Uniform Building Code (UBC)”, by

International Conference of Building Officials (ICBO),

Whittier, California.

[3] Federal Emergency Management Agency, FEMA-356,

(2000) “Prestandard and Commentary for Seismic

Rehabilitation of Buildings”, Washington, DC.

[4] Applied Technology Council, ATC-40 (1996): “Seismic

Evaluation and Retrofit of Concrete Buildings”, Vols. 1

and 2, California.

[5] N. Jitendra BABU, K.V.G.D. BALAJI, and S.S.S.V.

GOPALARAJU, "Pushover Analysis of Unsymmetrical

Framed Structures on Sloping Ground", International

Journal of Civil, Structural, Environmental and

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(IJCSEIERD), ISSN 2249-6866, Vol. 2, Issue 4 , pp 45-

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[6] Kavita Golghate, Vijay Baradiya and Amit

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[7] Rahul RANA,Limin JIN and Atila

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[8] M. A. Ismaeil, M. E. Sobaih, A. E.

Hassaballa.“Assessment of Seismic Performance and

Strengthening of RC Existing Residential Buildings in

the Sudan",International Journal of Engineering

Research & Technology (IJERT), ISSN: 2278-0181,

Volume 2, Issue 6, PP: 442-450, Jun. 2013.

[9] M. A. Ismaeil,A. E. Hassaballa. “Seismic Retrofitting of

a RC Building by Adding Steel Plate Shear Walls",IOSR

Journal of Mechanical and Civil Engineering (JOSR-

JMCE), e-ISSN: 2278-1684, p-ISSN: 2320-334X,

Volume 7, Issue 2, PP 49-62, May-Jun. 2013.

[10] M. A. Ismaeil,A. E. Hassaballa.“Effects of Earthquake

Loads on Existing School Buildings in Sudan",

International Journal of Computational Engineering

Research (IJCER), Volume 3, Issue 6, PP 45-56, Jun.

2013.

[11] Ashraf Habibullah, S.E.1, and Stephen Pyle, 'Practical

Three Dimensional Nonlinear Static Pushover Analysis'

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[12] Santhosh.D “Pushover analysis of RC frame structure

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ISSN: 2320-334X, Volume 11, Issue 1 Ver. V (Feb.

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[13] Sofyan. Y. Ahmed., “Seismic Evaluation of Reinforced

Concrete Frames Using Pushover Analysis”,Al-Rafidain

Engineering, Vol. 21, pp. 28-45, 2013.

http://www.iosrjournals.org/

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