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PERFORMANCE BASED DESIGN BANGUNAN BETON BERTULANG TIDAK BERATURAN TIGA DIMENSI MENGGUNAKAN ANALISIS INELASTIK

PERFORMANCE BASED DESIGN OF THREE DIMENSIONAL REINFORCED CONCRETE IRREGULAR BUILDINGS USING INELASTIC ANALYSIS

Sri Susanty Satya A.Dukalang1, Herman Parung2, Jonie Tanijaya3

1Mahasiswa Program Pasca Sarjana Jurusan Tekni Sipil Universitas Hasanuddin 2Dosen Tetap Jurusan Teknik Sipil Universitas Hasanuddin 3Dosen Jurusan Teknik Sipil Universitas Kristen Indonesia

Alamat Korespondensi: Sri Susanty Satya A Dukalang Fakultas Teknik Jurusan Sipil Universitas Hasanuddin Makassar, 90245 HP: 085242672732 Email: meine_satya@yahoo.com

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Abstrak Performance Based Design dapat digunakan sebagai pendekatan untuk mengatasi kerugian bangunan yang ditimbulkan oleh gempa bumi. Secara konsep, bangunan diberikan beban gempa berupa beban lateral yang mengakibatkan bangunan mengalami respon non linier. espons struktur bangunan berupa batas peralihan atap dan nilai dari performance level yang terdiri dari Operational (O), Immediate Occupancy (IO), Life Safety (LS) and Collapse Prevention (CP). Tujuan dari penelitian ini adalah untuk mencapai performance objektif pada Level Operational dan menentukan performance point. Bangunan yang di disain adalah bangunan beton bertulang tidak beraturan 5 tingkat dengan menggunakan sistem rangka pemikul momen, di atas tanah keras yang terletak di wilayah 6 dari peta gempa Indonesia. Hasil penelitian menunjukkan Base Shear bangunan berada pada 2321,5KN, Periode 1,038detik dan Performance Point berada pada 0,120m. Dapat disimpulkan bahwa bangunan berada pada ditinjau berada pada level Operasional dimana bangunan pada saat gempa tetap beroperasi dengan tingkat kerusakan yang kecil. Kata kunci: Performance Based Design, Performance Objective, Capacity Spectrum, Performance Point.

Abstract Performance Based Design can be useful approach for mitigating the potential losses due to hazards of earthquake. Conceptualized the problem is a building is loaded by earthquake-induced lateral forces that produce nonlinear response (damage) in structural components. Relations were established between structural response indices (drift limitations, inelastis member deformations), and performance level such as Operational (O), Immediate Occupancy (IO), Life Safety (LS) and Collapse Prevention (CP).The aim of this study are to find the performance objective of the building and to determine the performance point by doing inelastic analysis with pushover of 5 stories of irregular reinforced concrete building and determine the capacity of building structure. The target of Performance Objective is in Operational Level. Building was designed use moment resisting frame,located in hard soil and zone 6 of Indonesian seismic zone. Research shows that the base shear of the building model at 2321,5KN come on in the event of period at 1,038seconds and the Performanve Point is 0,120m. This can be concluded that the building model in this research at the Operational Level which means that the damage tobuilding during earthquake is small and continous in operation. Keywords: Performance Based Design, Performance Objective, Capacity Spectrum, Performance Point.

INTRODUCTION

Every structural system is designed to have a seismic capacity that exceeds the anticipated

seismic demand. Capacity is a complex function of strength, stiffness and deformability

conjectured by the system configuration and material properties of the structure.(Naem, 2007).

The development and use of performance-based design of buildings has been in progress for

several years, primarily within the seismic and blast communities. Within the engineering

community as a whole, the use of Performance based Design is being considered for applications to

specific design issues such as progressive collapse, as well as full-scale infrastructure projects such

as bridge designs (Tang, 2008).

Seismic Performance based Design was introduced in FEMA 273/274, published in October

1997, which was then issued in November 2000 as FEMA 356 –Prestandard and Commentary for

the Seismic Rehabilitation of Buildings. It is generally accepted that these efforts constituted the

first generation of seismic Performance based Design. ASCE 41-06 – Seismic Rehabilitation of

Existing Buildings has since superseded both versions of the FEMA standard.(FEMA 440, 2005)

Following the Northridge earthquake, the Applied Technology Council conducted a survey

of 530 buildings in which were located within 300 meters of strong motion recording sites. From

the total of 530 buildings which were located in the areas of strong shaking (San Fernando Valley,

Santa Monica, and West Los Angeles) with peak ground acceleration in their vicinity ranging from

0.15g to 1.78g, only 10 (less than two percent) showed heavy damage, a total of 78 buildings

(about 15-percent) showed moderate damage and 340 (64-percent) were marked by insignificant

damage. If response of these buildings were predicted by standard design analysis techniques, a far

worse picture would have been predicted (ATC,1996).

One of the main advances that the seismic Performance based Design paradigm offers is

that it acknowledges the uncertainty present in seismic design of buildings, or any other

infrastructure. The uncertainties in defining the seismic hazard, performing the design process, and

estimating consequences are all included within the paradigm. This is in sharp contrast with

prescriptive designs. Yet Performance based Design allows for far more freedom in prescribing

desired degrees of exceedance levels and probabilistic levels for the building. The ability to

determine an appropriate uncertainty level can be one of the major advantages of Performance

based Design. (Tang, 2008).

The aim of the study are to determine performance objective and performance point of the

building structure model. Performance objective is Performance Level that describes a limiting

damage condition. Performance point represents the point of the global behavior of the structure

that can able to handle the seismic ground motion.

METHODOLOGY

The type of this research is quantitative and the tool is computer softwere. The methodology

emphasizes the use of nonlinear analysis procedures in general and focuses on the capacity

spectrum method through pushover analysis. It provides a particularly rigorous treatment of the

reduction of seismic demand for increasing displacement.

The first step in Performance Based Design is to establish performance objectives described

as the combination of an expected performance level is an expression of the maximum desired

extent of damage to a building. The target of performance level of this research is in the level of

operational with the frequent of ground motion is 43 years, probability of axceedance 50% in 30

years on the basic Objective (Figure 1). It’s means that limit damage control not less 0,0001(Table

1).

Simplified nonlinear analysis procedures using pushover methods, such as the of capacity

spectrum method and displacement coefficient method, require determination of three primary

elements: capacity, demand (displacement) and performance. Each of these elements is briefly

discussed below.

Capacity : The overall capacity of a structure depends on the strength and deformation

capacities of the individual components of the structure. A lateral force distribution is again applied

until additional components yield. This process is continued until the structure becomes unstable or

until a predetermined limit is reached.

Demand (displacement) : Ground motions during an earthquake produce complex

horizontal displacement patterns in structures that may vary with time. Tracking this motion at

every time-step to determine structural design requirements is judged impractical. For nonlinear

methods it is more direct to use a set of lateral displecement as a design condition. For a given

structure and ground motion, the displacement demand is an estimate of the maximum expected

response of the building during the ground motion.

Performance : Once a capacity curve and demand displacement are defined, a performance

check can be done. A performance check verifies that structural and nonstructural components are

not damaged beyond the acceptable limit of the performance objective for the forces and

displacements implied by the displacement demand.

To find the point where demand and capacity are equal, the engineer selects a point on the

capacity spectrum as an initial estimate. Using the spectral acceleration and displacement defined

by this point, the engineer then can calculate reduction factors to apply to the 5% effective damping,

associated with the specific point. If the reduced demand spectrum intersects the capacity spectrum

at or near the initial assumed point, then it is the solution for the unique point where capacity equals

demand. In the other words, the building structure have the capacity to resist the demands of the

earthquake ground motion such that the perfomance of the structure is compatible with the

objectives of design.

To convert a spectrum from the standard 푆푎(Spectral Acceleration) vs T (Period) format

found in the building codes to ADRS format, it is necessary to determine the value of 푆푑 (Spectral

Displacement) for each point on the curve, 푆푎 ,Ti . This can be done with the equation:

푆푑 = 푆푎 푔 ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... (1)

The capacity spectrum can be developed from the pushover curve by a point by point

conversion to the first mode spectral coordinates. Any point Vi (Base Shear), δi(Roof Displacement)

on the capacity (pushover) curve is converted to the corresponding point Sai, Sdi on the capacity

spectrum using the equations:

푆푎 = ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... (2)

푆푑 = ,

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... (3)

Where 훼1 and PF1 are the modal mass coefficient and participation factors for the first

natural mode of the structure respectively. ϕ1,roof is the roof level amplitude of the first mode. The

modal participation factors and modal coefficient are calculated as:

PF1=∑ ( )/∑ ( )/

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... (4)

훼 = [∑ ( )/ ][∑ ( )/ ][∑ ( )/ ]

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

Where wi is the weight at any level i.

Design of Building Model

The building frame system is moment resisting frames. Building location in seismic zone 6

on the map of earthquake seismic zone in Indonesia (SNI 1726). The model of building structure is

irregular building with five stories (Figure 2). The beam and column size show in Table 2. The

height at each story is 3,5m. The modulus of elasticity, E = 23677,926N, poisson ratio, U=0,2, fc’ =

25Mpa. Fy=390Mpa. The building structure will be analysis through pushover analysis and

evaluate the plastic hinge mechanism.

The Equivalent Static Lateral Force Analysis

The UBC-97 is very specific about when the static method can be used. In general, any

structure may be designed using the dynamic method at the option of the structural engineer, and

some structures must use the inelastic analysis method. The static method may be used for

buildings with the following characteristics are (1) Regular structures under 240ft (73 m) in heigtht

using one of the lateral force-resisting systems except regular structures located on soil profile SF

which hto fiveave natural periods greater than 0.7 sec, (2) Irregular structures less than or equalto

five stories or 65 ft (19.80m) in height, (3) Structures with flexible upper portions (e.g., towers)

supported on a rigid tower portion if three conditions are met: (1) both portions, when considered

individually, are regular, (2) the average story stiffness of the lower portion is at least ten times the

average story stiffness of the upper portion, and (3) the period of the entire structure is no more

than 1.1 times the period of the upper portion considered as a separate structure fixed at the base.

All structures not meeting these requirements, including irregular building, must be designed using

the inelastic analysis method.

Step by Step Input Data in Computer Softwere

Structure capacity is represented by a pushover curve. The most convenient way to plot the

force-displacement curve is by tracking the base shear and the roof displacement. When a softwere

computer program is used, the following procedure can be used to construct pushover curve are

(1)Create a computer model of the structure following the modeling rules in ACECOMS, AIT,

(2)Apply lateral story forces to the structure, should also include gravity loads,(3)Calculate member

forces for the required combinations of vertical and lateral load,(4)Adjust the lateral force level so

that some element is stressed,(5)Record the base shear and the roof displacement,(6)Revise the

model,(7)Apply a new increment of lateral load to the revised structure such that another element

yield,(8)Add the increment of lateral load and the corresponding increment of roof displacement to

the previous totals to give the accumulated values of base shear and roof displacement,(9)Repeat

steps 6,7,and 8 until the structure reaches an ultimate limit,(10)If the incremental loading was

stopped in step 9 as a result of reaching a lateral deformation level at which all or a significant

portion of an element’s load can no longer be resisted, that is, its strength has significantly

degraded, then the stiffness of the elements is reduced. A new capacity curve is then created,

starting with step 6. Create as many additional pushover curves as necessary to adequately define

the overall loss of strength. Figure 3 illustrates the process, for an example where three different

capacity curves are required.(11)The Perfomance Point is intersection of capacity curve and

demand spectrum.

RESULTS

From the table of Pushover Curve (Table 3) shows that the Ultimate Force of the building is

2446.644 KN in step 11, there are 13 frames in Immediate Occupancy, 22 frames in Life Safety, 13

frames in Collapse. Yield Force is 2325.118 KN in step 6, there are 171 frames in Immediate

Occupancy.

From computer softwere, the capacity spectrum (Figure 5) shows that performance point is

in 0.12m. The Performance Point for is defined by the intersection of the pushover curve versus

displacement (green) and the single demand curve (grey).

The building’s roof displacement is 0,12m. Height building is 21m. The roof drit ratio is

0,005m. Hence, the performance objective of this building reach the target in Operational level

which maximum total drift limit not less 0,0001m.

DISCUSSION

This research found that the building level at in Operational Level in Performance Based

Design which means that building continous operation during earthquake ground motion with

frequent 43 years with the probably in 50% in 30 years and the damage is negligible.

Structure capacity is represented by a pushover curve (Figure 4). Pushover curve can estimate

of the maximum expected response of the building during the seismic ground motion. After create a

computer model of the structure following the modeling rules in ACECOMS, AIT (step by step

procedure), the pushover curve can be result. From Pushover Curve table can be found the number

of frame in each Performance Level such as Operational Level (that means no damage in beams),

Immediate Occupancy (that means minor damage to building), Life Safety (that means damage to

building is moderate), Collapse Prevention(that means damage to the building is severe).

Structure Performance can achieve if structure have a good capacity. On the other words,

structure must have a ductile pushover curve. Performance objective can found through capacity

spectrum. To check if building can reach Operational Level like the target of this research before,

the pushover curve must intersection with demand spectrum. The intersection of pushover curve

and demand spectrum is called Performance Point.

CONCLUSIONS

The conclusions from the analysis are the performance objective of this building is in

Operational level which means the building continues in operation with negligible damage after

frequent event of seismic ground motion and the performance point of this building occur at

0,120m and the base shear at 2321,5KN come on in the event of period at 1,038seconds.

REFERENCES ATC-40. (1996). Applied Technology Council. Volume 1 and 2, Report No. SSC 96-01, Seismic

Safety Commission, Redwood City, CA. ACECOMS, AIT. (2007). SAP 2000 Practical Example. FEMA 440. (2005). Improvement of nonlinear static seismic analysis procedures, Washington, D.C Naeim, F. (2007). The Seismic Design Handbook, Second Edition. Paz, Mario and Leigh, William. (2004). Structural Dynamics, by Kluwer Academic Publishers. Powell, Graham. (2009). Performance Based Design Using Nonlinear Analysis. Seminar Notes. SNI. (2002). SNI-1726-2002, Standar Perencanaan Ketahanan Gempa Untuk Struktur Bangunan

Gedung, Standar Nasional Indonesia . Tang, Margaret. (2008). Performance Based Design with Application to Seismic Hazard. Structure

Magazine UBC.(1997). Earthquake Design Volume 2 Division IV, , ICBO.

Appendix

Figure 1. Performance Objective

(a) The 3D perspective of Building (b) The Plan of Building

Figure 2, The 3D perspective and Plan of Building

Seism

ic

Haz

ard

Earthquake Performance Level

Life Safety Operational Collapse Prevention

Immediate Occupancy

Figure 3, Multiple Capacity Curves Required To Model Strength Degradation

Figure 4, Pushover Curve of the bulding model

Capacity curve #3

Base

She

ar

Roof Displacement

First point of significant strength degradation in capacity curve #2. Stop capacity curve at this point, revise model to reflect newly degraded element and start new capacity curve, capacity curve #3

First point of significant strength degradation. Stop capacity curve #1 at this point, revise model to reflect degraded element and start new capacity curve, capacity curve #2

Point at which structure as modeled for capacity curve #3 reaches an ultimate limit, such as, instability; excessive distortions, or an element (or group of elements) reaching a lateral deformation level at which loss of gravity load carr ying capacity occurs.

Capacity curve #1

Capacity curve #2

Figure 5, Performance Point of the bulding model

Tabel 1, Deformation Limit.

Perfomance Limit Interstrory Drift Limits

Immediate Occupancy

Damage Control

Life Safety

Maximum Total Drift 0.01 0.01- 0.02 0.02 Maximum Inelastic Drift

0.005 0.005- 0.015 No Limit

Table 2, Size of beam and column _________________________________ Element 5 stories ------------------------------------------------------------- Beam (mm) 300 x 500 Column (mm) 600 x 600 ------------------------------------------------------------- f’c = 25 MPa;

fy = 390 MPa;

Total Heigth = 21 m

Performance Point

Table 3, Pushover Curve Table

Step Displacement BaseForce

A to

B

B to

IO

IO

to

LS

LS

to

CP

CP

to

C

C

to

D

D

to

E

Beyond

E

m KN

0 5.38E-06 0 516 0 0 0 0 0 0 0

1 0.039676 1933.897 510 6 0 0 0 0 0 0

2 0.043263 2085.619 450 66 0 0 0 0 0 0

3 0.045237 2126.896 411 105 0 0 0 0 0 0

4 0.046469 2142.347 391 125 0 0 0 0 0 0

5 0.05131 2169.997 365 151 0 0 0 0 0 0

6 0.122007 2325.118 345 171 0 0 0 0 0 0

7 0.129239 2333.51 342 174 0 0 0 0 0 0

8 0.229239 2345.647 342 114 60 0 0 0 0 0

9 0.33185 2383.496 339 3 174 0 0 0 0 0

10 0.473487 2428.729 334 8 45 129 0 0 0 0

11 0.521074 2446.644 329 13 22 139 0 13 0 0

12 0.525724 2445.962 329 13 18 121 0 35 0 0

13 0.530463 2440.878 329 13 14 105 0 55 0 0

14 0.537525 2424.231 329 13 13 73 0 88 0 0