Partial capacity design, an alternative to the capacity design method
I. Muljati, B. Lumantarna, R.H. Saputra, A. Soegiarto
Civil Engineering Department, Petra Christian University, Surabaya, Indonesia
ABSTRACT: In the capacity design procedure of ductile open frames, the columns could not be designed before the beams are designed. This is not practical in the real world of design practice. In the previous study,
several alternatives allowing partial side sway mechanism were proposed. In the proposed method, the perimeter columns of the reinforced concrete frames were designed to remain elastic for a certain seismic load level.
In this study a refined method is proposed. Three symmetrical of six, eight and ten story fully ductile open
frame buildings are designed in accordance to the new Indonesian Earthquake Code (SNI-03-1726-2002) using the proposed method. The seismic performances of these buildings are evaluated using three dimensional
static pushover analysis. The results are then compared with the outputs of three dimensional non-linear time
history analysis.
1 INTRODUCTION
Capacity design method is commonly used in the
structural seismic design of reinforced concrete open
frames. In this method, columns are designed
stronger than the capacity of the beams to assure
the beam side sway mechanism (Fig. 1). Thus
the columns can only be designed after the beams
design is completed, which is not practical in real
design practice in Indonesia, where the design period is very short.
columns were designed to remain elastic for a certain seismic load level (target seismic load). In this
study a refined method called Partial Capacity Design is proposed.
Figure 2. Partial side sway mechanism
2 THEORETICAL BACKGROUND
Figure 1. Beam side sway mechanism
Lumantarna et.al. (1994, 1997, 1998, 2005) explored and suggested alternative design methods
which allowed partial side sway mechanism (Fig. 2).
In the proposed method, plastic hinges were allowed
to develop in the interior columns, while the exterior
The seismic load in the exterior column due to the
target seismic load can be derived as follows (Fig.
3):
nex  SexT  VtT  f1  nin  SinN
(1)
where nex is the total number of exterior column; nin
the total number of interior column; STex the shear
force in the exterior column due to the target seismic
load; SNin the shear force in the interior column due
to the nominal seismic load; f1 the overstrength factor, and VTt the total base shear due to the target
seismic load. Equation (1) is derived based on the
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.
Since 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. 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 using the
elastic response spectrum at the predicted period of
the structure in the plastic stage, Tplastic (Fig. 4). Saputra & Soegiarto (2005) proposed to use 12 % of I
gross for the beams and interior columns, and 30 %
at the base of the exterior columns to obtain the plastic period, Tplastic. This proposed effective second
moment of area is solely used to obtain CT in Equation (3) used in designing the exterior columns. Using the proposed effective second moment of area, it
is shown in Figure 4 that the non-linear spectral acceleration could be predicted.
Figure 3. Load distribution in partial capacity design
The total base shear due to the nominal seismic
load VNt (SNI 1726, 2002) is:
Vt N 
C 500  I  Wt
f1  
(2)
where C500 is the spectral acceleration due to a five
hundred years return period earthquake; I the importance factor of the structure; Wt the total weight
of the structure; f1 the overstrength factor which is
taken as 1.6; and μ the structural ductility. The total
base shear due to the target seismic load, VTt is:
C T  I  Wt
Vt 
f1
T
(3)
where CT is the spectral acceleration due to the target
seismic load. Note that since the exterior columns
are expected to remain elastic, the ductility factor, μ
is taken as 1.
Substitution of Equations (2) and (3) into Equation (1) and modification, resulting in the magnification factor of the external columns shear force as follows:
 CT 
 500     1.6  nin  RinN
C 
f 
nex  RexN



Figure 4. The determination of T plastic (Saputra & Soegiarto
2005)
The design procedure of the Partial Capacity Design is shown in Figure 5.

(4)
where f = STex / SNex is the magnification factor of the
seismic shear force that should be used in the design
of the 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.
Figure 5. Flowchart diagram for Partial Capacity Design
3 STRUCTURES OBSERVED
Three buildings, six-, eight-, and ten-story with
symmetrical layout as shown in Figure 6 are used in
this study. The properties of the buildings are shown
in Table 1. These buildings are assumed to be built
on soft soil in zone 2 of the Indonesian Seismic
Code (SNI 03-1726-2002). These buildings are designed using the proposed method with 500 years
period ground acceleration as the target seismic
load.
gram developed at Petra Christian University, Surabaya. The modified ground acceleration and the response spectrum are shown in Figure 7 and 8 respectively.
Figure 7. Modified seismic record
Figure 6. Layout of structure
Table
1. Properties and member dimension of the structures
________________________________________________
Compression strength of concrete, f’c = 25 MPa
Yield stress of the longitudinal reinforcement, fy = 400 MPa
Yield
stress of transverse reinforcement, fy = 240 MPa
________________________________________________
Building
Story* Member
dimension (mm)
______________________________
Column
____________________ Beam
Exterior
Interior
______________________________
10KES**
10
650 × 650 650 × 650
450 × 700
10KEB***
10
700 × 700 650 × 650
450 × 700
8KES
8
650 × 650 650 × 650
450 × 700
8KEB
8
850 × 850 650 × 650
450 × 700
6KEB
6
750
×
750
500
×
500
450 × 700
________________________________________________
*
Story height is 3.5 m
**
Exterior columns same dimension with interior columns
***
Exterior columns different dimension with interior columns
4 ANALYSIS
The performance of the structures are tested to static
non-linear pushover analysis (ATC 1996) using
ETABS-nonlinear (Habibullah 1998) and nonlinear
time history analysis using RUAUMOKO 3D (Carr
2002). The hinge properties of the beams and columns are obtained using ESDAP (Lidyawati & Pono
2003) a program developed at Petra Christian University, Surabaya based on the algorithm proposed
by D.J. King (1986). 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 (Lumantarna & Lukito 1997), a pro-
Figure 8. Response spectrum of modified El Centro 1940
5 RESULTS
Typical results of the ten-story building, 10KES, are
shown in Figures 9-14. Detailed results can be found
in Saputra & Soegiarto (2005).
5.1 Lateral displacement and drift
The lateral displacements of 10KES are shown in
Figure 9, while the drift are shown in Figure 10. It is
shown that the displacement and drift of the structures design using the proposed method are less than
the maximum allowed in the Indonesian Seismic
Code (SNI-03-1726-2002).
Figure 11. Plastic hinges of 10KES, 500-yrs, pushover
Figure 12. Plastic hinges of 10KES, 1000-yrs, pushover
Figure 9. Displacement of 10KES structure
Figure 13. Plastic hinges of 10KES, 500-yrs, time history
Figure 14. Plastic hinges of 10KES, 1000-yrs, time history
Figure 10. Drift of the 10KES structure
5.2 Plastic hinges location
Plastic hinges locations obtained from the pushover
analysis of 10KES due to 500- and 1000-years return period earthquake are shown in Figure 11-12
respectively, while the plastic hinges obtained from
nonlinear time history analysis are shown in Figure
13-14.
The plastic hinges locations show a safe mechanism. The other structures show the same tendency
except for 10KEB which develops plastic hinges in
the external column due to 1000-years return period
earthquake (Fig. 15-16).
Figure 15. Plastic hinges of 10KEB, 1000-yrs, pushover
Figure 16. Plastic hinges of 10KEB, 1000-yrs, time history
5.3 Damage indices
Damage index is a parameter to measure the level of
damage of structural member. It is defined as the
ductility demand divided by the available ductility
which can be obtained from RUAUMOKO-3D
(Carr, 2002). Figure 17-20 show the damage indices
of structure due to 500- and 1000-years return period
earthquake respectively.
5.4 Performance level
Based on the maximum drift and the average of
damage indices in each structure, the performance of
all structure are presented in the matrix form as
shown in Figure 21-22. Notice that the damage indices of structures are calculated for the ten-story
structures only.
Figure 19. Damage indices, exterior frame of 10KES, 1000-yrs
Figure 17. Damage indices, exterior frame of 10KES, 500-yrs
Figure 20. Damage indices, interior frame of 10KES, 1000-yrs
Figure 18. Damage indices, interior frame of 10KES, 500-yrs
Figure 21. Performance level of structures based on maximum
drift
Figure 22. Performance level of structures based on average
damage index
6 CONCLUSIONS
The partial capacity design offers some convenience
compared to the capacity design because columns
can be designed before the design of beams is completed. Based on the maximum drift, plastic hinges
location and damage indices shown in Fig. 11-20, all
observed structures performed well under the target
seismic load. Therefore, it is recommended to conduct further investigation on the application of the
partial capacity design in design practice.
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