SEISMIC RESISTANT DESIGN STANDARD FOR BUILDING STRUCTURES SNI–1726–2002 By : Wiratman Wangsadinata Emeritus Professor, Tarumanagara University President Director, Wiratman & Associates Chairman SNI-1726-2002 Committee
ABSTRACT In this summary paper, the main principles of the Indonesian Seismic Resistant Design Standard for Building Structures SNI-1726-2002 are explained. The summary covers seismic design provisions on basic requirements for building design and material strengths. The Design Earthquake considered has a return period of 500 years (10 % probability of exceedance in 50 years) and the resulting peak base rock acceleration forms the basis for establishing the Indonesian Seismic Zoning Map. The peak ground acceleration depends on the soil category (site-class) present on top of the base rock. With this acceleration the response spectra of the Design Earthquake are defined for determining the effect of the Design Earthquake upon building structures. Under the effect of the Design Earthquake the building structure is at its state of near collapse with a maximum deflection, assumed to be the same for any ductility level of the structure. With this assumption and known overstrength in the structure, for a certain level of ductility, a simple formulation is established regarding the effect of the Design Earthquake upon a building structure, such as elastic load, maximum load on the structure at its state of near collapse, first yield load and nominal load for design. Against the effect of the Design Earthquake, a building structure is in general analysed dynamically using response spectrum modal analysis method. However, regular building structures, having their first and second mode motion dominantly in translation, may be analysed statically using equivalent static seismic loads. The substructure (basement and foundation) may be analysed as a separate structure subjected to the effect of the Design Earthquake originating from the superstructure, from own inertial forces and from the surrounding soil. Finally the strength design of the substructure based on the Load and Resistance Factor Design method is discussed.
Key words: Standard, earthquake, dynamic response, structure, building, ductility. ductil ity. 1.
INTRODUCTION
This standard has taken into account as far as possible the latest development of earthquake engineering in the world, particularly what has been reported by the National Earthquake Hazards Reduction Program (NEHRP), USA, in its report titled “NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures” (February 1998), but on the other hand maintains as close as possible the format of the previous Indonesian standard “Rules for Earthquake Resistant Design of Houses and Buildings” (SNI 03-1726-1989). In general this standard is sufficient to be used as the basis for the modern design of seismic resistant building structures, particularly highrise buildings. In order that the building engineering community understands what the basic principles are of this standard, in this paper their background are explained. More detailed explanations can be found in the commentary of the respective clauses, which is an integral part of the standard. 2. DESIGN EARTHQUAKE AND SEISMIC ZONING MAP OF
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INDONESIA
An earthquake is a natural phenomena in the form of local ground motion generated by tectonic movements of the earth’s crust, its occurrence being probabilistic. This means that if a certain period of time is considered, the probability of occurrence of mild earthquakes is higher than of large earthquakes during that period. In other words, mild earthquakes have a relatively short return period, while strong earthquakes a relatively long one. For the seismic resistant design of building structures, according to this standard a Design Earthquake causing local ground motion with a return period of 500 years must be considered. According to the probability theorem, approximately such an earthquake has a probability of exceedance of 10% in a period of 50 years. This period of 50 years is assumed to be the life time of normal buildings with no particular importance. The local ground motion as the basis for the seismic resistant design of building structures, is generally expressed in the peak ground acceleration. This motion is the result of seismic waves propagating from the base rock located below the surface. While propagating, the waves undergo amplifications. The softer the soil layers are on top of the base rock, the greater the amplification. Conversely, the harder the soil layers are on top of the base rock, the smaller the amplification. To determine the local ground motion with a return period of 500 years caused by the Design Earthquake, Earthquake, a probabilistic seismic hazard analysis must be conducted. conducted. From the result of such an analysis peak base accelerations with a return period of 500 years at numerous locations throughout Indonesia have been obtained. Thus, on the map of Indonesia contour lines, showing points with equal peak base acceleration with a return period of 500 years, have been drawn. Based on such a contour line map, the Seismic Zoning Map of Indonesia has been established as shown in Figure 1. The seismotectonic input data for the probabilistic seismic hazard analysis consist of: earthquake source areas; magnitude frequency distribution at the earthquake source areas; attenuation function, relating local peak base acceleration, earthquake magnitude at the focus and distance from the focus to the site; minimum and maximum magnitude at the source areas; annual frequency of occurrence of earthquakes of any magnitude at the source areas; and the mathematical model of the earthquake occurrence itself. For the earthquake source areas, all foci recorded in the seismic history of Indonesia have been considered, including foci at subduction zones, shallow crustal foci within tectonic plates and foci on active faults so far identified. The magnitude-frequency distribution at the earthquake source areas has been computed based on the available statistical seismic data. This distribution is better known as the Gutenberg-Richter and exponential magnitudefrequency recurrence function. For the attenuation functions, several ones have been considered, namely the ones proposed by Fukushima & Tanaka (1990), Youngs (1997), Joyner & Boore (1997) and Crouse (1991). Earthquake occurrence has been mathematically modelled following Poisson’s function. In this probabilistic seismic hazard analysis, peak base accelerations and their return periods have been obtained through successive computations of the following items: (1) total probability by considering all possible earthquake magnitudes and distances to the foci (the double integral after
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0
5
O
0
80
200
400
Kilometer
O
10 N
N
O
I
N D I
O
5 S
A N O C E A N
O
10 S
1
0.03 g
2
0.10 g
3
0.15 g
4
0.20 g
5
0.25 g
6
0.30 g
O
15 S O
O
5 9 0
0 0 1
Figure 1.
O
5 0 1
O
0 1 1
O
5 1 1
O
0 2 1
O
5 2 1
O
0 3 1
O
5 3 1
O
0 4 1
The Seismic Zoning Map of Indonesia with peak base acceleration with a return period of 500 years.
Cornell, 1968), (2) the annual total probability, (3) the annual event probability (Poisson’s function), (4) the return period (which is the inverse of the annual probability), and (5) the peak base accelerations with a mean return period of 500 years, obtained through interpolation (logarithmic). On the Seismic Zoning Map of Indonesia (Figure 1) it can be seen, that Indonesia is divided into 6 seismic zones, Seismic Zone 1 being the least and Seismic Zone 6 the most severe seismic zone. The mean peak base acceleration for each zone starting from Seismic Zone 1 to 6 are respectively as follows : 0.03 g, 0.10 g, 0.15 g, 0.20 g, 0.25 g and 0.30 g (see Figure 1 and Table 2). It should be noted, that the peak base acceleration for Seismic Zone 1 is the minimum value to be considered in the design of building structures, to provide a minimum robustness to the structure. Therefore, this peak base acceleration has a rather longer return period than 500 years (conservative). 3.
LOCAL SOIL CATEGORY AND PEAK GROUND ACCELERATION
From the previous discussion it follows, that the peak ground acceleration may be obtained from the result of a seismic wave propagation analysis, whereby the waves are propagating from the base rock to the ground surface. However, this standard provides conveniently the value of the peak ground acceleration for every seismic zone for 3 categories of soil present on top of the base rock, namely Hard Soil, Medium Soil and Soft Soil. According to this standard, the differentiation of the soil category is defined by the following 3 parameters : shear wave velocity v s, Standard Penetration Test (SPT) or N-value and undrained shear strength (S u). The base rock for example is defined as the soil layer below the ground surface having shear wave velocities reaching 750
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m/sec, with no other deeper layers having lower shear wave velocity values. According to another definition, the base rock is the soil layer below the ground surface having Standard Penetration Test values of at least 60, with no other deeper layers having lower N-values. The soil on top of the base rock generally consists of several layers, each with different values of the soil parameters. Therefore, to determine the category of the soil, the weighted average of the soil parameter must be computed using the thickness of each soil layer as the weighing factor. The weighted average shear wave velocity ν , Standard Penetration Test value N and undrained shear strength S u , can be computed from the following equations : s
m
∑ vs =
ti
i =1
……………………….. (1)
m
∑
t i / v si
i =1
m
∑ N =
ti
i =1
………………………….. (2)
m
∑
t i / N i
i =1
m
∑ Su =
ti
i =1
...……………………….. (3)
m
∑
t i / S ui
i =1
where ti is the thickness of layer i, v si the shear wave velocity of layer i, Ni the Standard Penetration Test value of layer i, S ui the undrained shear strength of layer i and m is the number of soil layers present in the considered soil. Due to the fact that the amplification of waves propagating from the base rock to the gound surface is determined only by the soil parameters up to a certain depth from the ground surface, in using eqs.(1), (2) and (3) the total depth of the considered soil must not be taken more than 30 m. To consider soil depths of more than this is not allowed, as the weighted average of the soil strength tends to increase with depth, whereas soil layers below 30 m do not contribute in amplifying the waves. So, using the weighted average of soil parameters according to eqs.(1), (2) and (3) for a total depth of not more than 30 m, the definition of Hard Soil, Medium Soil and Soft Soil is shown in Table 1. In Table 1, PI is the plasticity index and w n the natural water content. Furthermore, what is meant by Special Soils are soils having high liquefaction potentials, very sensitive clays, soft clays with a total thickness of 3 m or more, loosely cemented sands, peat, soils containing organic materials with a thickness of more than 3 m, and very soft clays with a plasticity index of more than 75 and a thickness of more than 30 m. For these Special Soils the peak ground acceleration must be obtained from the result of a seismic wave propagation analysis. For the soil categories defined in Table 1, the peak ground acceleration A o for each seismic zone is shown in Table 2.
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Table 1. Soil Categories
Soil Category
Average shear wave velocity
Average Standard Penetration
Average undrained shear strength
νs (m/sec)
N
S u (kPa)
Hard Soil Medium Soil
νs > 350
N > 50
175 < ν s < 350
15 < N < 50
νs < 175
N < 15
S u > 100 50 < S u < 100
S u < 50
Soft Soil
Or, any soil profile with more than 3m of soft clays with PI > 20, w n > 40% and S u < 25 kPa.
Special Soil
Site specific evaluation required.
Table 2.
Peak Base Acceleration and Peak Ground Acceleration Ao
Seismic Zone
Peak Base Acceleration (‘g)
Hard Soil
Medium Soil
Soft Soil
1
0.03
0.04
0.05
0.08
2
0.10
0.12
0.15
0.20
3
0.15
0.18
0.23
0.30
4
0.20
0.24
0.28
0.34
5
0.25
0.28
0.32
0.36
6
0.30
0.33
0.36
0.38
4.
Peak Ground Acceleration Ao (‘g’) Special Soil Site specific evaluation required.
RESPONSE SPECTRA OF THE DESIGN EARTHQUAKE AND MODAL ANALYSIS
In general a response spectrum is a diagram representing the maximum response acceleration of a Single Degree of Freedom (SDOF) system to the input earthquake ground motion, as a function of the damping factor (fraction of critical damping) h and the natural vibration period T of the SDOF system. Thus, a response spectrum may be computed analytically and its diagram plotted for any input earthquake ground motion with given accelerogram. For T=0 the SDOF system is very stiff, so that it follows almost completely the ground motion. Therefore, for T=0 the maximum response acceleration becomes identical with the peak ground acceleration Ao. For a certain damping factor h, the maximum response acceleration follows a random function. Taking the T-axis in horizontal direction and the maximum response acceleration axis in vertical direction, that random function starts with an initial value Ao at T=0, then goes upwards until it reaches a certain maximum value, after which it goes downwards again approaching the T-axis asymptotically. In this standard the maximum response acceleration of the SDOF system due
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to the Design Earthquake is expressed in the gravity acceleration (g) and is called the Seismic Response Factor C (non-dimensional). Furthermore, the C-T function is simplified into a smooth curve, consisting of 3 branches, namely : for 0 < T < 0.2 sec the C value increases linearly from A o till Am; for 0.2 sec < T < T c the C value is constant and equal to A m; for T > Tc the C value decreases following a hyperbolic function C = Ar /T. In this case, Tc is called the natural corner period, while the SDOF system considered has a damping factor of h = 5 %. For the short range of natural period 0 < T < 0.2 sec, the C value contains various uncertainties in relation to the ground motion as well as to the ductility of the SDOF system considered. Therefore, in this range the C value should be taken equal to A m. It can then be stated that for T < T c the response spectrum is associated with a constant maximum response acceleration, while for T > Tc it is associated with a constant maximum response velocity, as a consequence of the hyperbolic function in this range. Table 3. Response Spectra of the Design Earthquake Hard Soil Tc = 0.5 sec.
Seismic Zone 1 2 3 4 5 6
Medium Soil Tc = 0.6 sec.
Soft Soil Tc = 1.0 sec.
Ao
Am
Ar
Ao
Am
Ar
Ao
Am
Ar
0.04 0.12 0.18 0.24 0.28 0.33
0.10 0.30 0.45 0.60 0.70 0.83
0.05 0.15 0.23 0.30 0.35 0.42
0.05 0.15 0.23 0.28 0.32 0.36
0.13 0.38 0.55 0.70 0.83 0.90
0.08 0.23 0.33 0.42 0.50 0.54
0.08 0.20 0.30 0.34 0.36 0.38
0.20 0.50 0.75 0.85 0.90 0.95
0.20 0.50 0.75 0.85 0.90 0.95
According to this standard A m is defined as 2.5 A o, which is an average condition found in response spectra in general. It is also defined that T c = 0.5 sec for Hard Soil, Tc = 0.6 sec for Medium Soil and T c = 1.0 sec for Soft Soil, all of which being approximate values. Based on these conditions for each seismic zone, the values of Ao, Am and Ar of the response spectra of the Design Earthquake are as listed in Table 3. For easy application, the response spectra of the Design Earthquake for Hard Soil, Medium Soil and Soft Soil for each seismic zone of Indonesia are shown on Figure 2. The response spectra C-T of the Design Earthquake are used as input data for the dynamic response analysis of building structures in the elastic range, using the response spectrum modal analysis method. In this method the building structure is modelled as a Multi Degree of Freedom (MDOF) system, being excited at its foundation by the Design Earthquake. Applying the modal analysis method, whereby a coordinate transformation is performed, the equations of motion of the MDOF system, which in the original coordinates constitute of coupled second order differential equations, become uncoupled in the new coordinates. Each free equation has the form of the equation of motion of an SDOF system. The transformation Seismic Zone 1
Seismic Zone 2
0.50
C= 0.38
C=
C
0.20 (Soft soil) T
C=
0.08 (Medium soil) T
0.20
0.05
0.30
C
25-8
0.20
0.50 (Soft soil) T C=
0.23 (Medium soil) T
C=
0.15 (Hard soil) T
Figure 2.
Response Spectra of the Design Earthquake.
matrix involved is the eigenvector matrix, which contains orthogonality properties among its modes, causing the uncoupling of the equations. Furthermore, the expression of the total dynamic response of the MDOF system takes the form of a superposition of the dynamic response of each single mode, whereby the higher the mode is the smaller its participation in producing the total response. This fact creates the possibility of using the response spectra of the Design Earthquake as a basis for determining the maximum dynamic responses of those single modes. It should be recognized however, that the dynamic responses of the single mode, determined from the response spectra of the Design Earthquake, are maximum responses, whereas in general each mode reaches its maximum response at different times. Therefore, the
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superposition of the maximum dynamic responses must be modified. According to this standard, which is based on various studies, if the MDOF system possesses sparsely spaced natural periods, the superposition of the maximum dynamic responses may be performed using the method known as Square Root of the Sum of Squares (SRSS), while if those natural periods are closely spaced, the superposition must be performed using the method known as Complete Quadratic Combination (CQC). Natural periods must be considered closely spaced, if their difference is less than 15%. The number of modes considered in the superposition may be limited, as long as the total mass participation in producing the total response is at least 90%. The vertical effect of earthquakes shall be considered in balconies, canopies, long cantilevers, transfer beams, long-span prestressed beams, simultaneously with their horizontal effect. The vertical acceleration induced by the Design Earthquake to the building is expressed as ψ Ao I, where Ao is the peak ground acceleration, I is the importance factor (see section 6.1) and ψ is a coefficient depending on the seismic zone as listed in Table 4. It is obvious that the value of ψ is increasing with increasing seismicity of the seismic zone, as the epicenters become closer. Table 4. Coefficient to compute the vertical acceleration of the Design Earthquake
5.
Seismic Zone
Coefficient ψ
1
0.5
2
0.5
3
0.5
4
0.6
5
0.7
6
0.8
DUCTILITY, OVERSTRENGTH AND THE EFFECT OF THE DESIGN EARTHQUAKE ON THE BUILDING STRUCTURE
According to this standard, against the effect of the Design Earthquake any building structure must be designed to remain standing, although it may have reached a state of near collapse. The load-deflection history of a building structure until reaching its state of near collapse, depends on the level of ductility of the structure. However, whatever the level of ductility, the maximum deflection reached by the building structure at its state of near collapse, is assumed to be the same according to this standard. This is known as the constant maximum displacement concept, a phenomena shown by many elasto-plastic systems (Veletsos, Newmark, 1960). The load-deflection diagram of a building structure designed to remain elastic and designed to possess a certain level of ductility, based on the constant maximum displacement concept may be visualized as shown in Figure 3, whereby δm =
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constant. In this figure the load is represented by the base shear load V resisted by the structure, and the deflection is represented by the top floor deflection δ of the building structure. Furthermore, the level of ductility according to this standard is expressed by a factor called ductility factor μ, which is the ratio between the maximum deflection δm and the deflection at first yield δy (at which the first plastic hinge develops), so that : 1≤ μ =
δm δy
≤ μm
..........…...………………… (4)
where μ = 1 is the ductility factor of a building structure designed to remain elastic up to its state of near collapse (δm = δy), while μm is the maximum ductility factor which can be mobilized by the structure. For various structural systems this standard provides the values of μm. The largest μm value is of a full ductile structure, namely μm = 5.3. The higher the value of μ possessed by a structure (the more ductile the structure) the lower the value of the first yield load Vy and also the lower the value of the maximum seismic load V m absorbed by the structure at its state of near collapse. In the process of load increase from V y to Vm the V-δ diagram follows a parabolic curve, during which more and more plastic hinges are developed in the highly redundant structure, accompanied by continuous redistribution of moments, until a condition is reached at which the structure is at its state of near collapse. The higher the value of μ, the longer the V- δ curve will be. V R Vn
Ve elastic
Vm
μ R
ductile f
Vy Vn
δ
f Vn
f 2 f 1
Fi zi
0
δn δy
δm
V
Figure 3. Load deflection diagram (V-δ diagram) of a building structure. If the elastic load Ve of a building structure in its elastic condition is known, for example from the result of a response spectrum modal analysis as described in section 4, and the building structure is to be designed to have a certain ductility factor μ, which according to this standard may be chosen by the designer or the building owner, then from Figure 3 it can be seen, that the seismic load producing first yield is: Vy =
Ve
...…………………….…… (5)
μ
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At the seismic load level Vy, the first plastic hinge begins to develop at the most critical section of the structure. To design the strength of that critical section based on the Load and Resistance Factor Design method as required by this standard, the seismic load to be considered, called the nominal seismic load V n, must be taken lower that Vy, to accommodate the strength margin required to cope with overload on the structure and understrength of the material. The nominal seismic load V n is obtained by reducing Vy by a certain overstrength factor f 1, so that the following expression applies : Vn =
Vy f 1
=
Ve R
..…………………….…… (6)
in which R = μ f 1
...…………………….…… (7)
where R is called the seismic reduction factor (see Figure 3). Theoretically the minimum value of f 1 is the product of the load factor and the material factor used in the Load and Resistance Factor Design, namely f 1 = 1.05 x 1.15 = 1.2. The material factor is the inverse of the capacity reduction factor (= 1/ φ). In reality there will always be oversized steel sections or excessive concrete reinforcements in structural members, so that in general f 1 > 1,2. According to this standard the overstrength factor is assumed to be constant namely f 1 = 1.6. Therefore, eqs. (6) and (7) becomes : Vn =
Vy 1.6
=
Ve R
.......…………………….…… (8)
in which 1. 6 ≤ R = 1.6 μ ≤ R m
…………………….…… (9)
where R m is the maximum seismic reduction factor that can be mobilized by the building structure, its value being given in the standard together with its related μm value for various structural systems. The largest R m value is therefore that of a full ductile structure, namely R m = 1.6 x 5.3 = 8.5. The ratio between Vm and Vy is another factor called overstrength factor f 2, which is mobilized because of the redundancy of the structure. Hence, the following relationship can be written (see figure 3) : Vm = f 2 Vy
................................................. (10)
The higher the redundancy of the building structure, the higher the value of f 2 that can be mobilized by the building structure. The largest value of f 2 is of a full ductile structure (μ = 5.3), namely f 2 = 1.75. The smallest value of f 2 is of a full elastic building structure μ( = 1.0), where no plastic hinges have developed nor redistribution of moments has occurred, namely f 2 = 1.00. Applying the equal initial slope principle of a parabola, based on the above boundary conditions, the relationship between μ and f 2 may be expressed as follows :
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= 0.83 + 0.17 μ
f 2
...................................... (11)
The relationship between Vm and Vn can now be expressed as follows : Vm = f Vn
...………………….……(12)
f = f 1 f 2 = 1.6 f 2
...………………….……(13)
where
For the whole spectrum of ductility of building structures, from the full elastic (μ = 1) up to the full ductile ( μ = 5.3), in Table 5 the values of the parameters R, f 2 and f are listed. All ductility levels between full elastic and full ductile is referred to as partially ductile. Table 5. Ductility parameters of building structures Performance level Full elastic
Partially ductile
Full ductile
μ
R eq.(7)
f 2 eq.(11)
f eq.(13)
1.0
1.6
1.00
1.6
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
2.4 3.2 4.0 4.8 5.6 6.4 7.2 8.0
1.09 1.17 1.26 1.35 1.44 1.51 1.61 1.70
1.7 1.9 2.0 2.2 2.3 2.4 2.6 2.7
5.3
8.5
1.75
2.8
In the implementation of the seismic resistant design of building structures in practice, the process starts with an analysis of the building structure under the effect of the nominal seismic load V n, for example by performing a response spectrum modal analysis as described in section 4, using the response spectra of the Design Earthquake. The ordinates are firstly multiplied by the importance factor I (see section 6.1) and then divided by the seismic reduction factor R for the selected μ value. The whole result can thus be used for the strength design of the structure based on the Load and Resistance Factor Design method. The deflection of the building structure δn due to the nominal seismic load V n, can also be used to calculate deflections of the building structure at various conditions under the effect of the Design Earthquake, such as the deflection at first yielding :
δy = f 1 δn = 1.6 δn and the deflection at its state of near collapse :
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...………………….…… (14)
δm = R δn
...………………….…… (15)
The deflection at first yielding δy is used as a measure of its serviceability limit state performance, in preventing excessive yielding of the steel or excessive cracking of the concrete, excessive non-structural damage and inconvenience to the occupants. This deflection is oftenly said to have been caused by a small to moderate earthquake, which occurs only once in the life time of the building, thus with a probability of occurrence of about 60% in the life time of the building according to the probability theorem. The deflection of the building structure at its state of near collapse δm is used as a measure of its ultimate limit state performance, in limiting the possibility of structural collapse that may cause loss of human lives and limiting the possibility of dangerous pounding between buildings or between structural components separated by separation joints. The detailed provisions can be found in the respective clauses in the standard.
6.
THE ANALISIS OF 3D STRUCTURES
6.1. GENERAL
If soil-structure interaction is not considered, for the analysis of the upper part of a building structure (the superstructure), it may be assumed that it has its lateral restraint (fixity) at the level of the ground floor, if there is a basement, and at the level of the top of the pile cap of a pile foundation or at the level of the bearing plane of a footing or a raft foundation, if there is no basement. Based on the structural layout of the building, the most critical direction of the earthquake action must be determined, which is parallel to the most dominant direction of the structural subsystems (open frames, shear walls). Usually this direction is also the most suitable one to be use as the direction of one of the coordinate axis (x-axis or y-axis) of the global coordinate system for the structural analysis. For highly irregular structural layouts, the critical direction of the earthquake action must be determined through a trial and error procedure. In reality the earthquake action will have an arbitrary direction, so that in general there will always be 2 components of earthquake action on the structure, each parallel to the orthogonal coordinate axes. Biaxial earthquake loading may have a more detrimental effect on the structure than the full uniaxial one. This condition is simulated by the requirement in this standard to always consider 100% earthquake action in one direction, in combination with 30% earthquake action in its perpendicular direction. Stiffness reduction due to concrete cracking must be taken into account, by assigning proper flexural and torsional stiffness modifiers in the analysis of the structure. If in the direction of a coordinate axis the R value is not known yet, its value must be computed as the weighted average of the R value of all structural subsystems present in that direction, using the seismic base shear V s resisted by each subsystem as the weighing factor. In this case the R value of each subsystem in that direction must be known, for example R = 8.5 for an open frame and R = 5.3 for a shear wall,
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which are their maximum values according to this standard. For the x-axis direction, the weighted average R value may be computed as follows : R x =
Σ Vxs
=
Σ Vxs /R xs
Vxo Σ Vxs /R xs
...………………….……(16)
and for the y-axis direction : R y =
Σ Vys Σ Vys / R ys
=
Vyo
Σ Vys / R ys
...………………….……(17)
To be able to apply eqs. (16) and (17), a common way is to carry out a response spectrum modal analysis as described in section 4 due to the elastic Design Earthquake (R = 1 and I = 1) for each of the direction of the coordinate axis, to determine Vs of each structural subsystem. The representative value of the overall seismic reduction factor R of the 3D building structure, is then computed as the weighted average of R x and R y, using Vxo and Vyo as the weighing factors :
R =
Vxo + Vyo Vxo / R x + Vyo / R y
...………………….……(18)
The R value according to eq.(18) is a maximum value that can be used, so that a lower value may be considered if desired in accordance with the chosen μ value. In the analyses of the 3D building structure, the P-Delta Effect must be considered, if the building height is more than 10 stories or 40 m. The P-Delta Effect is a phenomena occurring in flexible building structures, where due to the large lateral displacements of the floors, additional lateral loads are generated as the result of the overturning moments produced by the laterally displaced gravity loads. The 3D character of the building structure is reflected by the requirement in the standard to consider a design eccentricity e d between the Center of Mass and the Center of Rotation of each floor, each floor being considered as horizontally rigid diaphragms. This is to cope with the effect of the rotational component of the ground motion, the possible change of the position of the Center of Mass due to change in gravity loads and the possible change of the Center of Rotation due to post-elastic plastification. The detailed provisions can be found in the respective clauses in the standard. Before proceeding with the seismic response analysis of the structure, the fundamental vibration period T 1 of the building structure must be examined. For irregular building structures, T1 is obtained directly from the result of a 3D free vibration analysis (with due consideration of the P-Delta Effect and the design eccentricity ed), while for regular building structures behaving almost as 2 D structures in each principle direction (see section 6.3) T 1 can be obtained from the static deflections of the structure as the result of a static load 3D analysis (again with due consideration of the P-Delta Effect and the design eccentricity e d), by substituting those deflections into the well-known Rayleigh’s formula (see further section 6.3). The fundamental vibration period must satisfy the following
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requirement : T1 < ζ n
...………………….…… (19)
where n is the number of stories of the building and ζ is a coefficient depending on the seismic zone where the building is located according to Table 6. Table 6. The ζ coefficient for the limitation of T1 Seismic Zone
ζ
1
0.20
2
0.19
3
0.18
4
0.17
5
0.16
6
0.15
Before proceeding with the seismic response analysis of the structure, also the category of the building must be determined, by assigning the value of its importance factor I. This factor is intended to adjust the return period of the Design Earthquake, whether it is longer or shorter than the return period of 500 years. A return period longer then 500 years (I > 1) must be considered, if the 2 following cases are encountered : (1) the probability of occurrence of the Design Earthquake in the 50 years life time of the building must be taken lower than 10% (for example for hospitals), or (2) the life time of the building is much longer than 50 years (for example for monuments and very tall buildings), while the 10% probability of occurrencre of the Design Earthquake in the longer life time is maintained. For both cases the return period of the Design Earthquake is longer than 500 years. A return period shorter than 500 years (I < 1) may be considered, if the life time of the building is shorter than 50 years (for example for low-rise buildings), so that with a 10% probability that in the shorter life time of the building the Design Earthquake will occur, the return period of that earthquake is shorter than 500 years. For various categories of buildings, the importance factor I according to this standard is formulated as follows : I = I1 I2 ...………………….…… (20) where I1 is the importance factor to adjust the return period of the Design Earthquake related to the adjustment of its occurrence probability and I 2 is the importance factor to adjust the return period of the Design Earthquake related to the adjustment of the life time of the building. The factors I 1 and I2 are given in Table 7. Table 7. Importance Factor for several building categories Building Category
I1
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Importance Factor I2 I
General buildings such as for residential, 1.0 1.0 1.0 commercial and office use Monuments and monumental buildings 1.0 1.6 1.6 Post earthquake important buildings such as hospital, clean water installation, power plant, 1.4 1.0 1.4 emergency and rescue center, radio and television facilities Buildings for storing dangerous goods such as 1.6 1.0 1.6 gas, oil products, acid, toxic materials Chimneys, elevated tanks 1.5 1.0 1.5 Note: For all building structures, which usage permit is issued prior to the enforcement date of this standard, the importance factor I may be multiplied by 0.8.
6.2. THE IRREGULAR BUILDING STRUCTURE
After the fundamental period T1 satisfies eq.(19), its modal motions must further be examined. According to this standard, the fundamental mode motion must be dominant in translation, in order that the building structure doesn’t respond dominantly in torsion to the seismic loading, which is disturbing the convenience of the occupants. If this requirement is not satisfied, the structural system must be rearranged by placing more rigid structural elements at the periphery of the building to increase its overall torsional stiffness. Based on the fundamental period T 1, the nominal static equivalent base shear due to the Design Earthquake is computed as follows : V1 =
C1 I R
Wt
...………………….…… (21)
where C1 is the Seismic Response Factor obtained from the response spectra of the Design Earthquake shown on Figure 2 for the first natural period T 1, I the importance factor of the building, R the representative seismic reduction factor of the building structure (Table 5) and Wt the total weight of the building, including an appropriate portion of the live load (see section 6.3). The base shear V1 is a reference quantity for the total nominal base shear V t obtained from the result of a response spectrum modal analysis as described in section 4, whereby the response spectrum used is that of the Design Earthquake shown on Figure 2, its ordinates being multiplied by I/R. The following requirement must be satisfied : Vt > 0.8 V1
...………………….…… (22)
to ensure that a certain minimum effect of the Design Earthquake is guaranteed in cases where the total response is smaller than the static equivalent base shear. To satisfy the requirement expressed by eq.(22), the nominal story shears obtained from the result of the response spectrum modal analysis, must be multiplied by a scaling factor as follows :
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Scaling Factor =
0,8 V1 Vt
≥1
...………………….…… (23)
Visually the result of the above described scaling, is shown on Figure 4, where the CQC curve is the nominal story shear distribution obtained from the result of the response spectrum modal analysis.
CQC (total response) 0.8V1 Vt
CQC (design curve) First mode resp onse
y r o t S
Modified de sign curve
0
Vt 0.8V1 V1
Nominal Story S hear
Figure 4.
The nominal story shear diagrams along the height of the building structure.
The example shown on Figure 4 represents a case, where the nominal story shear curve is showing an inward turn. For such a case, if desired the curve may be modified conservatively as shown by the broken line. From the final nominal story shear curve, the nominal static equivalent seismic load at each floor level can be obtained by subtracting story shears of two adjoining stories. With these nominal static equivalent seismic loads, a 3D static analysis is carried out to obtain the internal forces in the building structure. For the commonly used structural system, consisting of a combination of open frames and shear walls, it is required by this standard, that the story shears resisted by the open frames are not less than 25% of the total story shears. If this requirement is not met, additional lateral loads must be applied in such a way, that the above requirement is fulfilled, keeping the story shears resisted by the shear walls unchanged. The objective of this requirement is to give the open frames extra strength, to cope with a possible redistribution of lateral loads if cracking occurs in the shear walls. If desired, the dynamic response analysis of the irregular building structure may be performed using 3D time history dynamic response analysis, using a digitized accelerogram as the input earthquake motion. The detailed provisions can be found in the respective clauses in the standard.
6.3. THE REGULAR BUILDING STRUCTURE
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A building structure is catagorized as regular, if it meets the following criteria: - The height of the building structure, measured from its ground floor, is not more than 10 stories or 40 m. - The building structure in plan has a rectangular layout without any protrusions; where this is not met, the length of the protrusion is not more than 25% of the largest plan dimension of the structural layout plan in that direction. - The building structure in plan has no re-entrant angles at the corners; where this is not met, the length of the wings is not more than 15% of the largest plan dimension of the structural layout plan in that direction. - The structural system of the building is composed of orthogonally arranged lateral load resisting subsystems, each parallel to the orthogonal principle axes of the building structure as a whole. - The building structure has no setbacks; where this is not met, the plan dimension of the upper portion in each direction is at least 75% of the largest corresponding plan dimension of the lower portion of the building structure. In this case, a penthouse structure of not more than 2 stories in height need not be considered as a setback. - The structural system has a uniform stiffness distribution along its height, without having any soft story. A soft story is one having lateral stiffness less than 70% of that of the story above it, or less than 80% of the average stiffness of 3 stories above it. In this case, stiffness of a story is defined as the shear applied at that particular story, causing unit interstory drift of that story. - The structural system has a uniform floor weight distribution along its height, meaning that the weight of any floor does not exceed 150% of the weight of the floor above it. The weight of a penthouse need not be considered to comply with this requirement. - The structural system has continuous vertical structural elements of its lateral load resisting subsystems without any offset of their vertical axis; where this is not met, these offsets must not be more than half of the dimension of that element in the offset direction. - The structural system has continuous floor slabs without any opening larger than 50% of the area of the whole floor slab. If floor slabs with openings meeting this requirement are present, their number must not exceed 20% of the total number of floors of the building. Regular building structures meeting the above criteria, has a typical dynamic characteristic. If a 3D free vibration analysis is conducted on a regular building structure, its first mode motion will be dominant in translation in the direction of one of its principle axes, while its second mode motion will be dominant in translation in the direction of the other principle axis. Therefore, the regular 3D building structure behaves almost like a 2D structure in the direction of its principle axes. With the above dynamic characteristic, the response spectrum modal analysis described in section 4 may be modified, because the following 2 assumptions can be made : - the total dynamic response of the structure is dominantly determined by that of the first mode, so that the contribution of the response of the other modes may be neglected (as in the case of a 2D structure); - the shape of the first mode may be simplified into a straight line (instead of a curve), as the structure is not very high (less than 10 stories or 40 m).
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With the above assumptions the effect of the Design Earthquake in the direction of the principle axis of a regular building structure, will appear as an equivalent static seismic loading according to the 2 following provisions : - The nominal static equivalent base shear V at the base of the building structure induced by the effect of the Design Earthquake is V =
C1 I R
Wt
...………………….…… (24)
- The nominal base shear according to eq.(24) may be distributed along the height of the building structure into nominal static equivalent seismic loads F i acting at the center of mass of floor i according to the following expression : F1 =
Wi z i
V
n
∑
...………………….……(25)
Wi z i
i =1
where Wi is the weight of floor i, including an appropriate portion of the live load; zi is the height of floor i measured from the level of its lateral restraint at the base; while n is the top floor number. Hence, for regular building structures dynamic analyses are not at all necessary. Even to compute its fundamentral period T 1 no free vibration analysis is necessary, because as mentioned in section 6.1, to determine its value the well-known Rayleigh’s formula of a 2D structure may be used : n
∑W
d i2
i
T1 = 2 π
i =1
...………………….……(26)
n
g
∑F
i
di
i =1
where Wi and Fi have the same meaning as described previously, while d i is the horizontal static deflection of floor i from the result of a static analysis and g is the gravity acceleration. This static analysis may be performed using static equivalent seismic loads Fi based on an arbitrary base shear V. 7.
SUBSTRUCTURE
7.1. SEISMIC LOADING ON THE SUBSTRUCTURE
What is meant by substructure is that portion of the building structure, which is below the ground surface, consisting of the basement, if any, and the foundation. To simplify the analysis, this standard allows the substructure to be considered as a separate underground structure, isolated from the superstructure. The substructure is then considered to be exerted by seismic loading originated from the superstructure, from inertial forces at the basement floor levels and from the surrounding soil. During any strong seismic event, it is not possible for the superstructure to
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perform well, if the substructure has failed earlier. Therefore, this standard requires the substructure to be designed to remain full elastic at any time, including under the effect of the Design Earthquake, at which the superstructure is in its state of near collapse. This means that the nominal maximum seismic load exerted by the superstructure on the substructure is: V
mn
=
Vm f 1 f 2 Vn = = f 2 Vn R f 1
...………………….……(27)
In line with eq.(27), the support reactions of all vertical elements (columns and shear walls) at the ground floor level due to the nominal seismic loading on the superstructure, multiplied by the overstrength factor f 2, become the nominal seismic loading on the substructure. Inertial forces acting at the basement floors are generated by the interaction of soil and structure under the effect of the Design Earthquake, so that masses on the basement floors undergo accelerations. If it is not determined through other more rational methods, the effect of the Design Earthquake on the basement floor masses may be assumed to appear as static equivalent seismic loads. Its nominal value for the strength design of the substructure based on the Load and Resistance Factor Design method is to be computed according to the following empirical formula : F bn = 0.10 Ao I W b
...………………….……(28)
where Ao is the peak ground acceleration due to the effect of the Design Earthquake (Table 2), I the importance factor of the building and W b the weight of the basement floor, including an appropriate portion of the live load. The last effect of the Design Earthquake upon the substructure, is the lateral soil pressure from the front soil, the value of which may be assumed to have reached its maximum possible value, that is equal to its yield stress (identical with the passive soil pressure) along the height of the substructure and other components of the substructure. As the substructure must be fully elastic under any circumstances, for its strength design based on the Load and Resistance Factor Design method, the said soil yield stress must be transformed into its nominal value by reducing it by the required seismic reduction factor R = f 1 = 1.6 (full elastic). In the analysis of the 3D substructure, the existence of the back soil must be considered by modelling it as compression springs, while the side and bottom soil may be modelled as shear springs. The properties of the compression and shear springs must be derived rationally from the existing soil data. 7.2. THE LOAD AND RESISTANCE FACTOR DESIGN FOR THE SUBSTRUCTURE
The strength of the basement structure, similar to that of the superstructure, must be designed based on the Load and Resistance Factor Design method according to this standard. Therefore, it is but logical that the strength of the foundation is designed based on the same principles, like it is recommended by this standard. By so doing a consistency is reached in the strength design of the building structure as a
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whole. The Load and Resistance Factor Design method for the foundation is in principle the same as that for the superstructure and the basement structure, namely that at the ultimate condition, the ultimate bearing capacity of the foundation R u is at least equal to the ultimate loading Qu on it, according to the following expression: R u > Qu
...………………….……(29)
where R u, being the ultimate bearing capacity of the foundation, is the multiplication of the nominal bearing capacity R n and the capacity reduction factor φ, as follows : R u = φ R n
...………………….……(30)
and Qu, being the ultimate loading on the foundation, is the multiplication of the nominal loading Qn and the load factor γ, summed up for all loadings, as follows : Qu = Σ γ Qn
...………………….……(31)
On the load-settlement curve, the nominal bearing capacity R n is at a point, where the foundation’s behaviour is still elastic, with an ample margin to the point where any increase in load will produce continuing larger settlements. Therefore, the nominal bearing capacity of a foundation is most accurate, if it is obtained from the result of a loading test until failure. However, this standard allows its value to be determined analytically using rational methods, based on the available soil data. As an approximation, the nominal bearing capacity of a foundation is twice the allowable bearing capacity computed in a conventional way. The capacity reduction factor φ for a foundation is given in Table 8 for footings and rafts, and in Table 9 for driven piles and bored piles. Table 8. Capacity reduction factor φ for footings and rafts Soil category
φ
Sand Clay Rock
0.35 – 0.55 0.50 – 0.60 0.60
Table 9. Capacity reduction factor φ for driven piles and bored piles. Foundation type
Source of resistance
φ
Driven piles
Friction + end bearing
0.55 – 0.75
Axial compression
pure friction
0.55 – 0.70
Axial compression/tension
pure end bearing
0.55 – 0.70
Axial compression
friction + end bearing
0.50 – 0.70
Axial compression
pure friction
0.55 – 0.75
Axial compression/tension
Bored piles
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Type of loading
pure end bearing
0.45 – 0.55
Axial compression
In Table 8 and 9, the lowest value of φ in its range is used, if the nominal bearing capacity of the foundation R n is computed analytically using soil data derived from Standard Penetration Test result (N-SPT). The average value of φ in its range is used, if the nominal bearing capacity of the foundation R n is computed analytically using soil data derived from Cone Penetration Test result (CPT). The highest value of φ in its range is used, if the nominal bearing capacity of the foundation R n is determined from the result of a loading test until failure.
8. REFERENCE
SNI-1726-2002, Indonesian Seismic Resistant Design Standard for Building Structures.
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