Eleventh East Asia-Pacific Conference on Structural
Engineering & Construction (EASEC-11)
“Building a Sustainable Environment”
November 19-21, 2008, Taipei, TAIWAN
PERFORMANCE OF PARTIAL CAPACITY DESIGN ON FULLY DUCTILE
MOMENT RESISTING FRAME IN HIGHLY SEISMIC AREA IN INDONESIA
I. MULJATI1, B. LUMANTARNA2
ABSTRACT : The Partial Capacity Design offers a more effective design procedure than the
conventional Capacity Design method since columns can be designed independently to the beam
capacity. Partial Side-Sway Mechanism is allowed to occur as collapse mechanism during severe
earthquake. In this mechanism, the exterior columns are kept to be elastic while all interior columns
are allowed to be plastic. To model this concept, exterior columns are designed to sustain the
excessive loading during severe earthquake represented by a Magnification Factor (MP). The
determination of MP is based on the natural period of the structure in plastic condition predicted by
the correlation between the elastic and the plastic natural period of several structures previously
observed. Four symmetrical, six-, eight-, ten- and twelve-story fully ductile concrete moment resisting
frame are designed in accordance with the latest Indonesian Seismic Code (SNI 1726-2002) using the
proposed method. For comparison, the buildings are also designed using Capacity Design method
based on the latest Indonesian Concrete Building Code (SNI 03-2847-2002). The seismic
performances of these buildings are evaluated using three-dimensional static nonlinear pushover
analysis and dynamic nonlinear time history. The results show that both methods do not meet the
expected collapse mechanism. It is concluded that the formulation of MP needs further observation
and the column overstrength factor applied in the Indonesian Concrete Building Code is not
conservative to meet the “strong column weak beam” requirement.
KEYWORDS: Partial capacity design, Partial side sway mechanism, Fully ductile moment resisting
frame, Indonesian seismic code, Indonesian concrete building code.
1.
INTRODUCTION
In general, the seismic design for moment resisting system
applies the concept of “strong column weak beam” due to
its safe collapse mechanism called beam side sway
mechanism as shown in Fig.1. To ensure the concept, the
capacity of columns is designed larger than the capacity of
beams. Therefore, the design of columns can be performed
after completing the design of beams. This procedure
known as Capacity Design (CD) is not practical in design
practice in Indonesian due to the limited design period.
Figure 1. Beam Side Sway Mechanism
Previous study [1,2] explored and suggested alternative
design methods which allowed partial side sway mechanism, as shown in Fig. 2. In the proposed
method, for a certain seismic load level (target seismic load) plastic hinges were allowed to develop in
the interior columns, while the exterior columns were designed to remain elastic. The method is called
Partial Capacity Design (PCD). It offers some convenience compared to the CD method because
1
2
Lecturer, Department of Civil Engineering, Petra Christian University, Surabaya, Indonesia 60236.
Professor, Department of Civil Engineering, Petra Christian University, Surabaya, Indonesia 60236.
EASEC-11
1
Eleventh East Asia-Pacific Conference on Structural Engineering & Construction (EASEC-11), Taipei, TAIWAN
columns can be designed before the design of beams is completed. The design procedure of PCD is
shown in Fig. 3.
Based on the maximum drift, plastic hinges location
and damage indices, the previous observed structures
[2] performed well under the target seismic load for
low seismic area (zone 2 of the Indonesian seismic
map). Therefore, it is recommended to conduct
further investigation on the application of PCD
especially for highly seismic area.
2.
MAGNIFICATION FACTOR
In PCD, the load distribution among
the interior and exterior columns
(marked white and black color in
Fig. 4) are defined based on
assumption
that
during
the
application of the target seismic load,
the interior columns can only take
the shear force due to the nominal
seismic load multiplied by the
overstrength factor, f1 (=1.6). Then
the excess of shear force due to the
target seismic load is sustained
entirely by the exterior columns
according to:
T
nex  Sex
 Vt 
T
Figure 2. Partial Side Sway Mechanism
Start
Calculate internal forces due to
factored gravity and seismic load
Beam
design
Interior column
design
Calculate MagnificationFactor, MF, using Eq. (2)
Exterior column design
Finish
Figure 3. Flowchart Diagram for PCD
f1  nin  SinN
(1)
where nex and nin are the total number of exterior and interior
columns; STex is the shear force in the exterior column due to
the target seismic load; SNin is the shear force in the interior
column due to the nominal seismic load; f1 is the
overstrength factor; and VTt is the total base shear due to the
target seismic load.
In order to keep the exterior columns (black color in Fig. 4)
to remain elastic during the target seismic load, they should
be designed larger than the ordinary design seismic load as
specified in the code. The magnification factor of the
external columns’ shear force is derived from [2]:
 CT 
 500     1.6  nin  RinN
C 

MF  
nex  RexN




(2)
Figure 4. Layout of Structures
where CT is the spectral acceleration of the target seismic load; C500 is the spectral acceleration of a
five hundred years return period earthquake; μ is the structural ductility; nin and nex are the total
EASEC-11
2
Eleventh East Asia-Pacific Conference on Structural Engineering & Construction (EASEC-11), Taipei, TAIWAN
number of interior and exterior column; RNin and RNex are the ratio of interior and exterior columns’
base shear to the total base shear due to the nominal seismic load.
However, during the application of the target seismic load the structure already in the non-linear stage,
the spectral acceleration due to the five hundred years return period earthquake, C500 should be
obtained from the non-linear response spectrum [3]. Unfortunately, the non-linear response spectrum
is not provided in the code. Therefore, it is proposed to obtain the spectral acceleration in the plastic
stage, CT, using the natural period of the structure in plastic condition predicted by the correlation
between the elastic and the plastic natural period (Telastic and Tplastic) of several structures previously
observed [4,5] according to:
Tplastic  2.969Telastic  0.313
(3)
The procedure to obtain the CT using elastic spectral
acceleration is explained graphically in Fig. 5.
3.
DESIGN AND ANALYSIS
Four buildings, four-, six-, eight-, and ten-story with
symmetrical layout (as shown in Fig. 4) and equal
story height of 3.5 m are used in this study. These
buildings are assumed to be built on soft soil in zone
Figure 5. Spectral Acceleration in
6 of the Indonesian seismic map [6]. These buildings
Plastic Range, CT
are designed using the proposed method with 500
years period ground acceleration as the target seismic
load. The properties of the buildings are shown in Table 1.
On the other side, these structures are also
designed using the capacity design method
based on the latest Indonesian Concrete
Building Code [7]. The detailed reinforcement
resulted from both method are available in
[4,5].
Table 1. Structural Properties and Dimension
Compression strength of concrete, f’c = 30 MPa
Yield stress of longitudinal reinforcement, fy = 400 MPa
Yield stress of transverse reinforcement, fy = 240 MPa
Floor thickness = 120 mm
Typical floor height = 3.50 m
Number
Column
Beam
Buildings
of Floor
Dimension
Dimension
PCD4
4
CD4
550 x 550
PCD6
6
CD6
350 x 700
PCD8
8
600 x 600
CD8
PCD10
10
650 x 650
CD10
Note:
PCD = Partial Capacity Design ; CD = Capacity Design
The performance of the observed structures are
determined by nonlinear static pushover
analysis [8] using SAP2000-nonlinear [9] and
nonlinear time history analysis using
RUAUMOKO 3D [10]. The hinge properties
of the beams and columns are obtained using
ESDAP [11] a program for developing
moment-curvature relation of sections. This
program is developed at Petra Christian
University, Surabaya based on the algorithm
proposed by D.J. King [12]. The ground acceleration used for the time history analysis is spectrum
consistent ground acceleration modified from N-S component of El-Centro 1940. The modification is
achieved using RESMAT [13], a program developed at Petra Christian University, Surabaya.
EASEC-11
3
Eleventh East Asia-Pacific Conference on Structural Engineering & Construction (EASEC-11), Taipei, TAIWAN
4.
STRUCTURAL PERFORMANCE
The plastic period of the
structures determined using Eq.
(3) are shown in Table 2. It can
be seen that the period during
plastic stage, Tplastic is close to
the predicted value, Tpredicted.
Table 2. Structural Periods and Magnification Factor
Buildings
Telastic
4-story
6-story
8-story
10-story
0.77
1.16
1.46
1.75
For Partial Capacity Design
Tplastic
Magnification
Tplastic
(predictied)
Factor, MP
2.61
2.68
2.422
3.76
3.30
1.670
4.64
4.32
1.725
5.52
5.40
1.763
PCD results in larger number
of reinforcement compared to
CD method, especially for shear and bending reinforcements of the exterior columns [4,5]. It is
predictable, because in PCD all exterior columns are designed to sustain larger shear force due to
magnification factor. On the other hand, the shear and bending reinforcement of interior columns in
PCD are smaller than those in CD. Beams in both methods use the same amount of reinforcement.
Overall, structures designed using PCD need larger columns reinforcement than those designed using
CD, ranging from 70% for 4-story structure to 18% for 10-story structure.
Floor displacement and inter-story drift resulted from pushover and time history analyses, both for
PCD and CD, are shown in Fig. 6. Based on floor displacement and drift consideration, all structures
show same tendency. Pushover analysis resulting larger value of floor displacement and drift
compared to time history analysis. At the same time, both PCD and CD result more or less the same
value of floor displacement and drift.
Indonesian Seismic Code [6] specifies maximum relative floor displacement as much as 0.7R times
the floor displacement, where R is the seismic reduction factor (taken 8.5 for fully ductile moment
resisting frame). And the maximum inter-story drift up to 0.02 (floor height = 3.5 m). Fig. 6 shows
that the inter-story drifts of all structures are less than the specified value.
The study also checked the location of plastic hinge as predicted by pushover and time history analysis,
both for PCD and CD. Plastic hinge location will define the collapse mechanism of each structure,
which is expected to be the partial side-sway mechanism (for PCD) or the beam side sway mechanism
(for CD). The result of plastic hinges location of all structures are shown in Fig. 7.
Although the plastic hinges location are not similar, pushover and time history analysis detect
inappropriate mechanism either for structure designed using PCD or CD. As expected, in structures
designed using PCD, some interior columns experience nonlinearity due to the development of plastic
hinge. Unfortunately, some plastic hinges also develop at their exterior columns as shown in Fig. 7
(see PCD4, PCD6, PCD8, and PCD10). Thus, the targeted collapse mechanism (partial side-sway
mechanism) is not achieved. This condition is caused by the use of magnification factor which is too
small in designing the exterior columns.
Surprisingly, structures designed using CD (se CD4, CD6, CD8, and CD10) also develop some plastic
hinges at inappropriate locations (at columns other than the base of column at the first floor). It
indicates that columns are not as strong as expected to meet the “strong column weak beam” needed
by the side-sway mechanism. This result has been reported in some other study [14] which proposed
further investigation on the value of column overstrength factor used in the Indonesian Building
Concrete Code.
EASEC-11
4
Eleventh East Asia-Pacific Conference on Structural Engineering & Construction (EASEC-11), Taipei, TAIWAN
5.
CONCLUSIONS
Based on the observation of 4-, 6-, 8-, and 10-story concrete structure designed as moment resisting
frame using Partial Capacity Design (PCD) and Capacity Design (CD), it is concluded that:
1. For highly seismic risk area in Indonesia, the formulation of Modification Factor applied in
PCD needs further observation in order to meet the intended collapse mechanism, i.e. partial
side sway mechanism.
2. In its application in highly seismic area, PCD tends to be not too effective because it needs
larger amount of column reinforcement compared to CD.
3. The use of column overstrength factor in Indonesian Building Concrete Code, to assure
“strong column weak beam” should be applied carefully.
Figure 6. Displacement and Drift of 4-, 6-, 8- and 10-story Structures
EASEC-11
5
Eleventh East Asia-Pacific Conference on Structural Engineering & Construction (EASEC-11), Taipei, TAIWAN
Time History Analysis
Exterior Frame
Interior Frame
CD10
PCD10
CD8
PCD8
CD6
PCD6
CD4
PCD4
Pushover Analysis
Exterior Frame
Interior Frame
Figure 7. Plastic Hinge Location
EASEC-11
6
Eleventh East Asia-Pacific Conference on Structural Engineering & Construction (EASEC-11), Taipei, TAIWAN
ACKNOWLEDGEMENTS
This paper is a summary of a series of studies on partial capacity design, conducted in the Civil
Engineering Department of Petra Christian University. Thanks are extended to our students Amelia
Kusuma, Zico Yanuar Wibowo, Stefani Reni, Irwan Tirtalasana, and our reaserch partner, Pamuda
Pudjisuryadi, for contributing the work and collaboration.
REFERENCES
1. Lumantarna, B., et.al. “Alternatives to the capacity design method, a preliminary proposal”,
Proceedings of the 18th Australasian Conference on the Mechanics of Structures and
Materials, 2004, pp. 485-491.
2. Muljati, I., and Lumantarna, B., “Partial capacity design, an alternative to the capacity design
method”, Proceedings of the 19th Australasian Conference on the Mechanics of Structures and
Materials, 2007, pp. 409-414.
3. Saputra, R.H. and Soegiarto, A., Penentuan Faktor Pengali untuk Perencanaan Pseudo
Elastis pada Struktur Rangka Penahan Momen Khusus. Undergraduate Thesis, Petra Christian
University, Surabaya, 2005.
4. Kusuma, A., and Wibowo, Z.Y., Evaluasi Kinerja Struktur 4 dan 10 Lantai yang Didesain
Sesuai Pseudo Elastis dan SNI 03-2847-2002 di Wilayah 6 Peta Gempa Indonesia.
Undergraduate Thesis, Petra Christian University, Surabaya, 2008.
5. Reni, S., and Tirtalaksana, I., Evaluasi Kinerja Struktur 6 dan 8 Lantai yang Didesain Sesuai
Pseudo Elastis dan SNI 03-2847-2002 di Wilayah 6 Peta Gempa Indonesia. Undergraduate
Thesis, Petra Christian University, Surabaya, 2008
6. SNI 03-1726-2002. Standar Perencanaan Ketahanan Gempa untuk Struktur Gedung.
Departemen Pemukiman dan Prasarana Wilayah, Bandung, 2002.
7. SNI 03-2847-2002. Tata Cara Perencanaan Struktur Beton untuk Bangunan Gedung.
Departemen Pemukiman dan Prasarana Wilayah, Bandung, 2002.
8. Applied Technology Council – ATC 40. Seismic Evaluation and Retrofit of Concrete
Buildings, Volume I. California, 1996.
9. CSi Berkeley, Integrated Building Design Software SAP Version 10.0.7, Computers and
Structures. Inc., California, 2001.
10. Carr, A., Ruaumoko Computer Program Library. University of Canterbury – New Zealand,
Department of Civil Engineering, 2002.
11. Lidyawati and Pono, G.B.W., Penyempurnaan Program Komputer untuk Desain Beban
Lentur dan Aksial serta Analisa Momen Kurvatur Penampang Beton Bertulang.
Undergraduate Thesis, Petra Christian University, Surabaya, 2003.
12. King, D.J., Computer Program for Concrete Column Design. University of Canterbury – New
Zealand, 1986.
13. Lumantarna, B., and Lukito, M. “RESMAT, Sebuah Program Interaktif untuk Menghasilkan
Riwayat Waktu Gempa dengan Spektrum Tertentu”, Proceedings of HAKI Conference, 1997,
pp. 128-135.
14. Pudjisuryadi, P., “Evaluation of Column’s Flexural Strength of Special Moment Resisting
Frame in Accordance to the Indonesian Concrete and Earthquake Codes”, Proceedings of the
International Conference on Earthquake Engineering and Disaster Mitigation”, 2008, pp. 9098.
EASEC-11
7