An Evaluation Of Pushover Analysis For Various Load Distributions

Besinci Ulusal Deprem Muhendisligi Konferansi, 26-30 Mayis 2003, Istanbul Fifth National Conference on Earthquake Engineering, 26-30 May 2003, Istanbul, Turkey Paper No: AE-017

AN EVALUATION OF PUSHOVER ANALYSIS FOR VARIOUS LOAD DISTRIBUTIONS Armagan KORKMAZ1, Ali SARI1, Bulent AKBAS2

1

Department of Civil Engineering, University of Texas at Austin, Austin, TX 78712, USA. 2 Department of Earthquake and Structural Science, GYTE, Gebze, Kocaeli, Turkey.

ABSTRACT The main purpose of this study is to evaluate the performance of the frame structures for various load distributions (patterns) and variety of natural periods by performing pushover and nonlinear dynamic time history analyses. The load distributions for pushover analyses are chosen as triangular, IBC (k=2) and rectangular. The four frame structures used in this study are typical reinforced concrete (R\C) frame systems and have four different natural periods. To evaluate the results from the pushover analyses for three load distributions and also four natural periods, nonlinear dynamic time history analyses are performed. Earthquake ground motions recorded at 10 stations during various earthquakes overall the world are used in the analyses. Pushover and nonlinear time history analyses results are compared to choose the best load distribution for specific natural period for this type of frame structure. Keywords: Pushover analysis, nonlinear time history, load distribution, moment-resisting frame

INTRODUCTION Earthquake-resistant design is based on evaluating the seismic performance of structures. It is required to consider inelastic behavior while evaluating the seismic demands at low performance levels. FEMA 273 and ATC 40 use pushover analysis as nonlinear static analysis but nonlinear time history analysis has more accurate results on computing seismic demands (ATC-40, 1996, FEMA 273, 1997). The purposes in earthquake-resistance design are: (a) to prevent non-structural damage in minor earthquakes, which may occur frequently in life time, (b) to prevent structural damage and minimize non-structural damage in moderate earthquakes which may occur occasionally, (c) to prevent collapsing or serious damage in major earthquakes which may occur rarely. Designs are explicitly done only under the third condition. The objective of this study is to evaluate the performance of the frame structures for various load distributions (pattern) and variety of natural periods by performing pushover and nonlinear dynamic time history analyses. 3, 5, 8 and 15-story R\C frame structures are used in the analyses and the load distributions for pushover analyses are chosen as triangular (IBC, k=1), IBC (k=2) and rectangular, where k is the an exponent related to the structure period to define vertical distribution factor (IBC, 2000). The four frame structures have been analyzed using nonlinear program DRAIN-2D (Prakash, V., Powell, G., Campbell, S., 1993) and the results have been compared by recorded response data. Both nonlinear static pushover analysis and nonlinear dynamic time history analysis are performed. The correlations between these nonlinear analyses are studied. The performance of the buildings subjected to various representative earthquake ground motions is examined. Finally, pushover and nonlinear time history analyses results are compared to choose the best load distribution (pattern) for specific natural period for these types of reinforced concrete frame structures.

GROUND MOTION DATA Ground motion data used in the nonlinear dynamic time history analyses are given in the Table 1. All the data are for site class A&B. These site classes are defined in Table 2. The ground motion data are chosen from different destructive earthquakes around the world earthquake name, date of earthquake, data source, record name, peak ground

accelerations (pga) for the components, effective durations and fault types for each data are presented in the Table 1., respectively. The peak ground accelerations are in the range 0.0633 to 1.4973g, where g is acceleration due to gravity. Acceleration time histories for ten ground motion data are presented in Figure1. During the nonlinear time history analyses, scaling of some of the original seismic acceleration records has been carried out. The ground accelerations of the G06090 data are scaled half; G06230, ORR090 and CLS000 are scaled 1/4th; and finally KJM000, TCU084-W and CPM000 are scaled 1/8th of their original accelerations. All ground motion data except ORR090 are recorded in near-field region. Their closest distances to the epicenter of the sources are between 0 and 20 km.

DESCRIPTION OF THE FRAME STRUCTURES Diagram of analyzed 3, 5, 8 and 15-story R\C frame structures with typical cross sections and steel reinforcements are shown in Figure 2. The reinforced concrete frame structures have been designed according to the rules of the Turkish Code. The structures have been considered as an important class 1 with subsoil type of Z1 and in seismic region 1. The dead, live and seismic loads have been taken account during design. All reinforced concrete frame structures consist three-bay frame, spaced at 800 cm. The story height is 300 cm. The columns are assumed to be fixed to the ground. Yield strength of the steel reinforcements is 22 kN/cm2 and compressive strength of concrete is 1.6 kN/cm2. The first natural period of the 3-story frame structure is computed 0.54 s. The cross section of all beams in this frame is rectangular-shapes with 25 cm width and 50 cm height. The cross section of all columns is 30cmx30cm. The first natural period of 3-story frame structure is 0.72 s and the cross section of beams is 25 cm width and 50 cm height similar to 3-story frame. Cross section of columns at the first three stories is 40cmx40cm and at the last two stories, it is 30cmx30cm. The eight-story and 15-story frame structures have natural period of 0.90 s and 1.60 s. The cross section of beams for these frame structures are 25cmx55 cm and 30cmx60cm respectively. The 8-story frame structure has 50cmx50cm columns for the first five stories and 40cmx40cm for the last three stories. The cross section of columns for first 8 stories in the 15-story frame structures is 80cmx80cm and at the last seven stories, it is 60cmx60cm.

NONLINEAR STATIC PUSHOVER AND NONLINEAR DYNAMIC TIME HISTORY ANALYSES OF FRAME STRUCTURES The pushover analysis can be described as applying lateral loads in patterns that represent approximately the relative inertial forces generated at each floor level and pushing the structure under lateral loads to displacements that are larger than the maximum displacements expected in design earthquakes (Li, Y.R., 1996). The pushover analysis provides a shear vs. displacement relationship and indicates the inelastic limit as well as lateral load capacity of the structure. The changes in slope of this curve give an indication of yielding of various structural elements. The main aim of the pushover analysis is to determine member forces and global and local deformation capacity of a structure. The information can be used to assess the integrity of the structure. After designing and detailing the reinforced concrete frame structures, a nonlinear pushover analysis is carried out for evaluating the structural seismic response. For this purpose the computer program Drain 2D has been used. Three simplified loading patterns; triangular (IBC, k=1), IBC (k=2) and rectangular, where k is an exponent related to the structure period to define vertical distribution factor, are used in the nonlinear static pushover analysis of 3, 5, 8 and 15story R\C frame structures. Vertical distribution factor for triangular, where k is 1, and IBC load distribution, where k is 2, is given in Equation 1.

Cvx =

wx hxk n

∑ wi hik

(1)

i =1

where; Cvx is vertical distribution factor, V is total design lateral force or shear at the base of structure, wi and wx is the portion of the total gravity load of the structure, hi and hx are the height from the base and finally k is an exponent related to the structure period. In addition these lateral loadings, frames are subjected live loads and dead weights. P-∆ effects have been taken into the account during the pushover analyses. The lateral force is increased for 3, 5 and 8-story frame structures until the roof displacement reached 50 cm and 100 cm for 15-story frame structure. Beam and column elements are used to analyze the frames. The beams are assumed to be rigid in the horizontal plane. Inelastic effects are assigned to plastic hinges at member ends. Strain-hardening is neglected in all elements. Bilinear moment-rotation relationship is assumed for both beam and column members. Axial load-Moment, P-M, interaction relation, suggested by ACI 318-89, is used as yielding surface of column elements. Inertial moment of cracked section, Icr, is used for both column and beam members during analyses. Icr is computed as half of the gross moment of inertia, Ig.

The results of the pushover analyses are presented in Figures 3 to 6. The pushover curves are shown for three distributions, and for each frame structures. The curves represent base shear-weight ratio versus story level displacements for uniform, triangular and IBC load distribution. Shear V was calculated by summing all applied lateral loads above the ground level, and the weight of the building W is the summation of the weights of all floors. Beside these, these curves represent the lost of lateral load resisting capacity and shear failures of a column at the displacement level. The changes in slope of these curves give an indication of yielding of various structural elements, first yielding of beam, first yielding of column and shear failure in the members. By the increase in the height of the frame structures, first yielding and shear failure of the columns is experienced at a larger roof displacements (Figures 3-6.) and rectangular distribution always give the higher base shear-weight ratio comparing to other load distributions for the corresponding story displacement (horizontal displacement). After performing pushover analyses, nonlinear dynamic time history analyses have been employed to the four different story frame structures. Drain 2D has been used for nonlinear time history analysis and modeling. The model described for pushover analyses has been used for the time history analyses. Mass is assumed to be lumped at the joints. The frames are subjected to 10 earthquake ground motions, which are recorded during Parkfield (1996), Morgan Hill (1984), Kocaeli (1999), Coyota Lake (1979), Northridge (1994), Loma Prieta (1989), Kobe (1995), Chi-Chi (1995), and Cape Mendocino (1992) earthquakes, for the nonlinear dynamic time history analyses. The selected earthquake ground motions have different strong motion durations (effective durations are presented in Table 1.), frequency contents and peak ground accelerations. The ground motion data are chosen from near-field region (except ORR090) to evaluate the response of the frame structures in this region and comparison of them with pushover analyses results. During the nonlinear time history analyses, the seismic acceleration records with large peak accelerations are scaled. The results of nonlinear time history analysis for 3, 5, 8 and 15-story frame structure are presented in Figure 7. Pushover and nonlinear time history analyses results are compared to for specific natural period for four different frame structure and for each load distributions; rectangular, triangular and IBC (k=2).

CONCLUSIONS After designing and detailing the reinforced concrete frame structures, a nonlinear pushover analysis and nonlinear dynamic time history analysis are carried out for evaluating the structural seismic response for the acceptance of load distribution for inelastic behavior. It is assumed for pushover analysis that seismic demands at the target displacement are approximately maximum seismic demands during the earthquake. According to Figures 3, 4, 5 and 6, for heigher story frame structures, first yielding and shear failure of the columns is experienced at the larger story displacements and rectangular distribution always give the higher base shear-weight ratio comparing to other load distributions for the corresponding story displacement. As it is presented in Figure 7, nonlinear static pushover analyses for IBC (k=2), rectangular, and triangular load distribution and nonlinear time history analyses results for the chosen ground motion data (most of them are near-field data) are compared. Pushover curves do not match with nonlinear dynamic time history analysis results for any frame structures. The pushover analyses results for rectangular load distribution estimate maximum seismic demands during the given earthquakes more reasonable than the other load distributions, IBC (k=2), and triangular.

REFERENCES ATC-40 (1996), “Seismic evaluation and Retrofit of Concrete Buildings”, Vol.1, Applied Technology Council, Redwood City, CA. Prakash, V., Powell, G., Campbell, S. (1993), DRAIN 2D User Guide V 1.10, University of California at Berkeley, CA. FEMA 273 (1997). “NEHRP Guidelines for the Seismic Rehabilitation of Buildings, federal Emergency Management Agency”, Washington D.C. Li, Y.R. (1996), “Non-Linear Time History And Pushover Analyses for Seismic Design and Evaluation” PhD Thesis, University of Texas, Austin, TX. IBC (2000) “International Building Code” Vision 2000 Committee (1995). Structural Engineering Association of California, CA.

Table 1: Ground motion data used in the analyses Earthquake Parkfield Morgan Hill Kocaeli Morgan Hill Coyota Lake Northridge

Date 06/28/1966 04/24/1984 08/17/1999 04/24/1984 08/06/1979 01/17/1994

Data Source CDMG CDMG KOERI CDMG CDMG CDMG

Record/Component C12320 GIL067 ARC000 G06090 G06230 ORR090

Pga (g) 0.0633 0.1144 0.2188 0.2920 0.4339 0.5683

Loma Prieta

10/18/1989

CDMG

CLS000

0.6437

B

6.88

Kobe Chi-Chi

01/16/1995 09/20/1999

N/A CWB

KJM000 TCU084-W

0.8213 1.1566

B (1) Hard Site*

8.38 14.59

Cape Mendocino * Taiwan CWB

04/25/1992

CDMG

CPM000

1.4973

A

3.10

Table 2. Definition of site classes

Site Class A B

Vs30 > 750 m/s 360 m/s to 750 m/s

Site Class B B B B B B

Duration (s) 26.84 8.57 11.02 6.47 3.24 9.10

Fault Type Strike-Slip Strike-Slip Strike-Slip Strike-Slip Strike-Slip Reverse Normal Reverse Oblique Strike-Slip Reverse Normal Reverse Normal

30/60

60/60

fc= 1.6 kN/cm2 fy= 22 kN/cm2

60/60

60 cm

55 cm 50cm 30 cm

25 cm

As = 10.30 cm2

As= cm2

As = 13.26 cm2 (Cross Sections for Beams)

60/60 60/60 80 cm

50 cm

40 cm

30 cm 30 cm

50 cm

40cm 2

As= 25.12 cm

As= 30.40 cm2

As= 45.20 cm

80 cm

As= 63.72 cm2

25/55

40/40

3m

25/55

As= cm2

3m

40/40 25/55

3m

40/40 25/50

•

30/30

3m

30/30 3m

3m

40/40

3m 25/50

3m

3m

40/40

25/50

30/30

3m

8m

8m

8m

30/60

3m

50/50

3m

8m

8m

3-story

5-story

(a)

(b)

8m

3m

80/80

30/60

3m

80/80

30/60

3m

30/60

80/80

3m

25/55

3m

50/50

30/60

50/50

3m

8m

8-story (c)

3m

30/60

3m

30/60 3025

80/80

8m

3m

30/60

80/80

25/55

8m

3m

80/80

25/55

50/50

3m

30/60

3m

25/50

40/40

30/60

80/80

25/55

50/50

60/60

3m

25/50

25/50 30/30

3m

3m

80/80

25/55

25/50

30/30

30/60

60/60

(Cross Sections for Columns)

25/50

3m

60 cm

60 cm 2

3m

30/60

60/60

25 cm

3m

30/60

3m

30/60

80/80

8m

8m

3m

8m

15-Story (d)

Figure 1. Diagram of analyzed 3, 5, 8 and 15-story R\C frames with typical cross sections and steel reinforcements

Figure 2. Acceleration Time Histories for 10 Ground Motion Data

R C F ram e, P ushover C urve, IB C (k= 2) Load

R C F ram e, P ushover C urve, T riangular Load

0 .1 4

0.12

0.12

0 .1 2

0.10

0.10

0 .1 0

0.08

0.08

0 .0 8

0.06 0.04

0.06

2.00

4.00

6.00

8.00

2nd F loor 3rd F loor R o of

0.02 0.00 0.00

10.00

0 .0 6 0 .0 4

0.04 2nd F loor 3rd F loor R oof

0.02 0.00 0.00

V /W

0.14

V /W

V /W

R C F ram e , P u sho ve r C urve , R e ctan g ula r L oa d

0.14

2.00

displacem ent (cm )

4.00

6.00

8.00

2nd F loor 3rd F loor R oof

0 .0 2 0 .0 0 0 .0 0

10.00

2 .0 0

4 .0 0

6 .0 0

8 .0 0

1 0 .0 0

displacem ent (cm )

displacem ent (cm )

Figure 3. Push-over Curves of 3-story R\C Frame for three different Load Patterns R C F ram e, P ushove r C urve, T riang ula r Lo ad

R C F ram e, P ushove r C urve, IB C (k= 2) Load

0.09

0.08

0.08

0.08

0.07

0.07

0.07

0.06

0.06

0.06

0.05

0.05

0.05

0.04 0.03

2nd floor 3rd floor 4th floor 5th floor R oof

0.02 0.01 0.00 0.00

3.00

6.00

9.00

displacem ent (cm )

12.0 0

V /W

0.09

V /W

V /W

R C F ram e, P ushove r C urve, R ectan gular L oad

0.09

0.04 0.03

2nd floor 3rd floor 4th floor 5th floor R oof

0.02 0.01 0.00 0.00

3.00

6.00

9.00

12.0 0

0.04 0.03

2nd floor 3rd floor 4th floor 5th floor R oof

0.02 0.01 0.00 0.00

3.00

displacem ent (cm )

Figure 4. Push-over Curves of 5-story R\C Frame for three different Load Patterns

6.00

displacem ent (cm )

9.00

12.0 0

R C F ram e, P ushove r C urve, T riang ula r Lo ad

R C F ram e, P ushove r C urve, IB C (k= 2) Load

0.08

0.07

0.07

0.07

0.06

0.06

0.06

0.05

0.05

0.05

0.04

2nd floor 3rd floor 4th F loor 5th floor 6th floor 7th floor 8th floor R oof

0.03 0.02 0.01 0.00 0.00

5.00

10.0 0

15.0 0

0.04

2nd floor 3rd floor 4th floor 5th floor 6th floor 7th floor 8th floor R oof

0.03 0.02 0.01 0.00 0.00

20.0 0

5.00

displacem ent (cm )

10.0 0

15.0 0

V /W

0.08

V /W

V /W

R C F ram e, P ushove r C urve, R ectan gular L oad

0.08

0.04

2nd floor 3rd floor 4th floor 5th floor 6th floor 7th floor 8th floor R oof

0.03 0.02 0.01 0.00 0.00

20.0 0

5.00

displacem ent (cm )

10.0 0

15.0 0

20.0 0

displacem ent (cm )

Figure 5. Push-over Curves of 8-story R\C Frame for three different Load Patterns R C F ram e, P ushove r C urve, R ectan gular L oad

R C F ram e, P ushove r C urve, T riang ula r Lo ad

0.08 0.07

V /W

0.06 0.05 0.04 0.03 0.02 0.01 20.0 0

40.0 0

60.0 0

displacem ent (cm )

80.0 0

0.10 2nd floor 3rd floor 4th floor 5th floor 6th floor 7th floor 8th floor 9th floor 10th floor 11th floor 12th floor 13th floor 14th floor 15th floor 16th floor

0.09 0.08 0.07 0.06

V /W

2nd floor 3rd floor 4th floor 5th floor 6th floor 7th floor 8th floor 9th floor 10th floor 11th floor 12th floor 13th floor 14th floor 15th floor R oof

0.09

0.00 0.00

R C F ram e, P ushove r C urve, IB C (k= 2) Load

0.10

0.05 0.04 0.03 0.02 0.01 0.00 0.00

20.0 0

40.0 0

60.0 0

80.0 0

2nd floor 3rd floor 4th floor 5th floor 6th floor 7th floor 8th floor 9th floor 10th floor 11th floor 12th floor 13th floor 14th floor 15th floor R oof

0.09 0.08 0.07 0.06

V /W

0.10

0.05 0.04 0.03 0.02 0.01 0.00 0.00

20.0 0

displacem ent (cm )

Figure 6. Push-over Curves of 15-story R\C Frame for three different Load Patterns

40.0 0

displacem ent (cm )

60.0 0

80.0 0

re cta n g u la r A R C 000 G 06230 C LS 000 O R R 090

tria n g u la r C 12320 G IL 0 6 7 C P M 000

IB C (k= 2 ) G 06090 K JM 0 0 0 T C U 0 8 4 -W

re cta n g u la r A R C 000 G 06230 C LS 000 O R R 090

0 .1 4

0 .0 9

0 .1 2

0 .0 8

tria n g u la r C 12320 G IL 0 6 7 C P M 000

IB C (k= 2 ) G 06090 K JM 0 0 0 T C U 0 8 4 -W

0 .0 7 0 .1 0

0 .0 6

V /W

V /W

0 .0 8 0 .0 6

0 .0 5 0 .0 4 0 .0 3

0 .0 4

0 .0 2 0 .0 2

0 .0 1 0 .0 0 0 .0 0

2 .0 0

4 .0 0

6 .0 0

8 .0 0

0 .0 0 0 .0 0

1 0 .0 0

2 .0 0

d isp la ce m e n t (cm )

a) 3-Story Frame tria n g u la r C 12320 G IL 0 6 7 C P M 000

re cta n g u la r A R C 000 G 06230 C LS 000 O R R 090

0 .0 9

0 .0 9

0 .0 8

0 .0 8

0 .0 7

0 .0 7

0 .0 6

0 .0 6

0 .0 5

0 .0 5

0 .0 4

0 .0 3

0 .0 2

0 .0 2

0 .0 1

0 .0 1 2 .0 0

4 .0 0

8 .0 0

1 0 .0 0

6 .0 0

d isp la ce m e n t (cm )

8 .0 0

1 0 .0 0

tria n g u la r C 12320 G IL 0 6 7 C P M 000

8 .0 0

1 0 .0 0

IB C (k= 2 ) G 06090 K JM 0 0 0 T C U 0 8 4 -W

0 .0 4

0 .0 3

0 .0 0 0 .0 0

6 .0 0

b) 5-Story Frame IB C (k= 2 ) G 06090 K JM 0 0 0 T C U 0 8 4 -W

V /W

V /W

re cta n g u la r A R C 000 G 06230 C LS 000 O R R 090

4 .0 0

d isp la ce m e n t (cm )

0 .0 0 0 .0 0

2 .0 0

4 .0 0

6 .0 0

d isp la ce m e n t (cm )

c) 8-Story Frame d) 15-Story Frame Figure 7. Pushover and Nonlinear Time History Results of 3, 5, 8 and 15-story Frames