Eleventh East Asia-Pacific Conference on Structural Engineering & Construction (EASEC-11), Taipei, TAIWAN

PERFORMANCE OF PARTIAL CAPACITY DESIGN ON FULLY DUCTILE MOMENT RESISTING FRAME in highly seismic area in Indonesia

I. MULJATI[1], B. LUMANTARNA[2]

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.

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 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:

(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]:

(2)

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 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:

(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 6 of the Indonesian seismic map [6]. These buildings 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.

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
Buildings / Number of Floor / Column Dimension / Beam Dimension
PCD4 / 4 / 550 x 550 / 350 x 700
CD4
PCD6 / 6
CD6
PCD8 / 8 / 600 x 600
CD8
PCD10 / 10 / 650 x 650
CD10
Note:
PCD = Partial Capacity Design ; CD = Capacity Design

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].

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.

4.  STRUCTURAL PERFORMANCE

The plastic period of the structures determined using Eq.

Buildings / Telastic / For Partial Capacity Design
Tplastic (predictied) / Tplastic / Magnification Factor, MP
4-story / 0.77 / 2.61 / 2.68 / 2.422
6-story / 1.16 / 3.76 / 3.30 / 1.670
8-story / 1.46 / 4.64 / 4.32 / 1.725
10-story / 1.75 / 5.52 / 5.40 / 1.763

(3) are shown in Table 2. It can be seen that the period during plastic stage, Tplastic is close to the predicted value, Tpredicted.

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.

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

Pushover Analysis / Time History Analysis
Exterior Frame / Interior Frame / Exterior Frame / Interior Frame
PCD4 / / / /
CD4 / / / /
PCD6 / / / /
CD6 / / / /
PCD8 / / / /
CD8 / / / /
PCD10 / / / /
CD10 / / / /

Figure 7. Plastic Hinge Location

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.

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EASEC-11 7