Simplified Vulnerabiltiy Analysis ( SVA ) Preliminary Design of The Frame Structure In The Architectural Design Process

There is a need of a good cooperation between the architects and structural experts for the creation of earthquake architecture. Through some ways in the design process, the architects can identify and evaluate the vulnerability of the building towards earthquakes. Unfortunately, there is no evaluation method available, so that the alternative is by adopting SVA (Simplified Vulnerability Analysis) method which is the limited engineering analysis based on the information from the architecture and structure drawings on the existing buildings. The Japan Building Disaster Prevention Association (JBDPA) and Matsutaro Seki developed the SVA. Seki adopted the SVA of JBDPA and adjusted it with the international earthquake regulation. In principle, the JBDPA and Seki SVA is a safe structure if the seismic structure index ≥ the seismic demand index. The modification of the JBDPA dan Seki SVA in this research is that the seismic structure index is the column dimension index, column rigidity index, strong column/weak beam index, redundancy index , and structure ductility index. Meanwhile, the seismic demand index is the multiplication between seismic response index and the priority factors of building functions. It is a quantitative research with experimental research method. The modified SVA formulation was experimented through the pushover analysis from other researchers. The results were then tabulated and compared. In general, it is concluded that the modification on SVA formulation from JBDPA and Seki shows a relatively good result in evaluating the vulnerability of preliminary design of the structure in the architectural design process.


INTRODUCTION
Indonesia is an earthquake-prone area, so that the buildings should be constructed resistant to earthquakes.In oder to create an earthquake architecture [1] which is aesthetically appealing and structurally resistant to earthquake, it needs a good cooperation between architects and structural experts.The first step in creating the earthquake architecture, in the design process, the architects can identify and evaluate the vulnerability of the building towards the earthquakes [2].Unfortunately, there is still no evaluation method available, so that the alternative is by adopting the SVA (Simplified Vulnerability Analysis) method [3] which is a limited engineering analysis based on the information from architectural drawings and structures in the existing buildings.Some of the developers of SVA are The Japan Building Disaster Prevention Association (JBDPA) [4] and Matsutaro Seki [5].Seki adopted the SVA of JBDPA and adapted it to international earthquake regulation.The purpose of the SVA they develop is the structural verification for retrofitting so that there is a need of modification in the architectural design process when using it to identify and evaluate the vulnerability of buildings.The proposed purpose of SVA in this research is to build the procedures or methods which can be used by architects in evaluating the vulnerability of buildings to earthquakes in the architectural design process in accordance with the conditions in Indonesia.In the architectural design process, the focuses are on the dimensions of structure and geometric shapes.The research is limited to the dimension and type of structure commonly used in Indonesia which is moment-resisting frame with 1 or 2-way floor system.The middle rise maximum height (± 10 floors) and regular-category building's geometric shape.
In principle, the SVA of JBDPA and Seki is a safe structure if the seismic structure index (I S ) ≥ the seismic demand index (I SO ).The lateral force retaining system is at least influenced by redundancy, column dimensions, column rigidity, strong column / weak beam and structural ductility [6].The seismic structure index consists of the lateral force of the column defined as the ratio of the minimum column area and the design column area (I Ac-i ), redundancy is defined as the period of structural vibration (I T ), column rigidity is defined as the ratio of the height and width of the column (I C-i ), index strong column/weak beam is defined as the ratio of the number of columns fulfill the strong column/weak beam and the total number of the columns (I SCWB-i ), and structural ductility adopts the Matsutaro Seki's procedures by including the ratio of response modification factor (R) and the overstrength factor (Ω 0 ) (R/Ω 0 ).The modification of SVA of JBDPA and Seki in this research is based on the explanation that the seismic structure index (I S ) is the multiplication between column dimension index (I Ac-i ), column rigidity index (I C-i ), strong column/weak beam index (I SCWB-i ), redundancy index (I T ), structure ductility index (R/Ω 0 ) , irregularity index (S D ) and time index (T).The limited geometric shapes are regular and considered as new buildings, so that it is assumed that S D =1 and T=1.The seismic demand index (I SO ) is the multiplication between seismic response index (I CS ) and the primary factors of building function (I e ).The problem in the proposed procedures is to what extent the accuracy in evaluating and assessing the vulnerability of buildings in the design process.In order to find out the reliability of building vulnerability assessment procedure in this design process, it will be compared with the more detailed vulnerability assessment procedure, that is the pushover analysis from other researchers.

Seismic Structure Index (I S )
In general, JBDPA and Seki define the formulation of the seismic structure index as follow: I S = E 0 .S D .T (1) Where, I S = Seismic structure index; E 0 = Basic seismic structure index; S D = Irregularity Index (regular building S D =1); T = time index (new building T=1).The modification of the Basic seismic structure index (E 0 ) is based on the concept that the resistance of the column in resisting the lateral load of the earthquake is defined into column dimension, influenced by column rigidity, forms strong column/weak beam, good structure ductility and the unity of the whole structural elements (redundancy).The formulation is as follow: Where n = the number of levels of the building; i = The evaluated level(s).Where the first level is given number  The concept of column lateral force (IAc-i) is assumed as the ratio of design column area (∑A C ) and minimum column area (∑A C min ) as follow: Where, ∑A C = total design column area (m2); ∑A C min = total minimum column area (m2) 0.15% of the cumulative area of column load [9], in which the minimum column area is 0.09 m2 or 0.3x0.3 m.
The concept of column rigidity (I C-i ) is assumed as the ratio of the average of column types (N C x0.7-1.0) and total columns (∑N C ) as follow: Where, N C-a = total of column types -a (Table 1); N C-b = total of column types-b (Table 1); N C-c = total of column types-c (Table 1); 0.7, 0.8, 1.0= index of column types of a, b & c (Table 1); ∑N C = Total columns.Table 1.Index of combined shear stress average and ductility index of structure elements (Source: processed from [4,5]) The concept of strong column/weak beam (I SCWB-i ) is assumed as the ratio of the number of columns fulfill the strong column-weak beam (N SCWB ) and total columns (∑N C ) as follow: Where, ∑N C = total columns, N SCWB = number of columns fulfill the Wp column ≥ 1.2xWp beam, Wp=plastic modulus, Wp=0.25xbxh 2 , b&h= dimension of width and height of beam or column [10].

Seismic Demand Index (I SO )
The concept of column lateral capacity (I Ac-i ) which is the ratio of the design column area and minimum column area is also applied to the lateral seismic load (I SO ) concept, which is the ratio of the design and minimum lateral seismic loads.For the design lateral seismic loads is based on the spectral responses of S S and S 1 for those using SNI 1726:2012 or coefficients of Ca and Cv for those using SNI 1726:2002 in each building site, while the minimum lateral seismic loads is based on seismic zone division FEMA 155 [11] which is a low seismic zone with S S =0.25 g and S 1 =0.1 g or zone 2A according to UBC 1997 [12].The concept of seismic demand index or lateral seismic load index (I SO ) is the multiplication of seismic response coefficient index (I CS ) and the primary factor of building function (Ie).Meanwhile, the seismic response index (I CS ) is the ratio of design seismic coefficient (C S ) and the minimum seismic coefficient (C Smin ).

Seismic Structure Index (I S ) Vs Seismic Demand Index (I SO )
The concept of ratio of seismic structure index (I S ) and seismic demand index (ISO).Structure is said to be safe if: I S ≥ I SO (8) Where, I S = seismic structure index; I SO = seismic demand index.For other ratios, in evaluating the vulnerability of building structures, by comparing the seismic structure index towards the seismic demand index, and each level can be identified for its possible level of damage (table 2).

Table 2.
Recommendation for the evaluation of potential seismic vulnerability based on the seismic performance (source : modification of procedure [5])

RESEARCH METHOD
It is an experimental research.In order to verify the proposed procedure, it will be compared with the result of pushover analysis conducted by other researchers, so that the result will be more objective.Although the proposed SVA procedure is to analyze the vulnerability of building with a middle rise maximum height (± 10 floors) but the validity limit of the observed model was determined up to 14 floors.The data of earthquake zones and structures were collected from the research [14][15][16][17][18][19] in table 3 and 4. The calculation steps are as follows: -Calculate the modification factor of level shear capacity of each floor, based on the data -data from table 3 and 4 are to calculate the column dimension index -I Ac-i (formulation 3), calculate the column type index -I C-i (formulation 4) and calculate the strong column/weak beam index-I SCWB-i (formulation 5).Obtain a T C and compare it to T max specify the index of the structural vibration period (I T ) and obtain R and Ω 0 values from table 9 of SNI 1726:2012 or table 3 of SNI 1726:2002 calculate the structure ductility R/Ω 0 .Multiply all values (formulation 1) so that the basic seismic index of structure (E 0 ) can be obtained.Multiply the basic seismic index of structure (E 0 ) with the irregularity index (S D ) for regular building S D =1 so that the seismic capacity index of structure (I S ) can be obtained.
-Calculate the modification factor of level seismic demand of each floor, based on the data from table

Model a [14]
Table 5. Seismic structure index (I S ) model a.
Table 6.Seismic demand index (I SO ) of location model a.
Table 7.Comparison between seismic structure index (I S ) and seismic demand index (I SO ) as well as comparison between SVA and pushover analysis model a.
Fig. 1.Comparison between between SVA and pushover analysis model a.
In table 5, I S value is the multiplication between E 0 and S D .E 0 is the basic seismic structure index of the special moment-resisting frame which is the result of multiplication between the modification factor of level shear capacity ( 1, column type index (I C-i )=0.8 normal column (2<h0/D<6), strong column/weak beam index (I SCWB- i )=1, structural vibration period index (I T ) = 1, structural system ductility index (R/Ω 0 )=8/3 and S D is the irregularity of building geometry because model a has a regular geometric shape so that the value = 1.Table 6, I SO is the seismic demand index which is the multiplication of the modification factor of level seismic demand ( 18 and the primary factor of the building function (I e )=1 (office).Table 7 shows that from the 1st floor to the roof floor, the comparison is I S > I SO , means that the column and beam dimensions are well designed so that ensuring the adequate rigidity, strength and ductility when a strong earthquake occurs, so that will only result in light damage or IO (Immediate Occupancy).Table 7 and Fig. 1, the research conducted by Siti Aisyah et.al. on model a with pushover analysis resulted in the target displacement= 0.132 m with drift ratio= 0.61%.Based on FEMA 273, model a, which is located in the Earthquake Zone 6 with Moderate Soil, is in inelastic condition which is able to resist the earthquake load up to the level of Immediate Occupancy (IO).At the IO level, there is only little potential for structural damage that can be repaired.The prediction on the proposed SVA procedure is relatively similar to the result of the research conducted by Siti Aisyah et.al.

Model b [15]
Table 8.Seismic structure index (I S ) model b.

Table 9. Seismic demand index (I SO ) of location model b.
Table 10.Comparison between seismic structure index (I S ) and seismic demand index (I SO ) as well as comparison between SVA and pushover analysis model b.

Fig. 2. Comparison between between SVA and pushover analysis model b.
In table 8, I S value is the multiplication between E 0 and S D .E 0 is the basic seismic structure index of the special moment-resisting frame which is the result of multiplication between the modification factor of level shear capacity ( 1, column type index (I C-i )=0.8 normal column (2<h0/D<6), strong column/weak beam index (I SCWB-i )=1 except for the roof floor=0.29,structural vibration period index (I T )=1, structural system ductility index (R/ Ω 0 )=8/3 and S D is the irregularity of building geometry because model b has a regular geometric shape so that the value = 1.Table 9, I SO is the seismic demand index which is the multiplication of the modification factor of level seismic demand ( 18 and the primary factor of the building function (I e )=1 (office).Table 10 shows that from the 1st floor to the 13th floor, except for the roof floor, the comparison is I S > I SO , means that the column and beam dimensions have been quite-well designed so that ensuring the adequate rigidity, strength and ductility when a strong earthquake occurs, so that will only result in light damage or IO (Immediate Occupancy).Table 10 and Fig. 2, the research conducted by Puput R et. al. on model b with pushover analysis resulted in the target displacement=0.474m with drift ratio=0.85%.Based on FEMA 273, model b, which is located in the Earthquake Zone 6 with Soft Soil, is in inelastic condition which is able to resist the earthquake load up to the level of Immediate Occupancy (IO).At the IO level, there is only little potential for structural damage that can be repaired.The prediction on the proposed SVA procedure is relatively similar to the result of the research conducted by Puput R et. al.   seconds, structural system ductility index (R/Ω 0 )=8/3 and S D is the irregularity of building geometry because model c has a regular geometric shape so that the value = 1.Table 12, I SO is the seismic demand index which is the multiplication of the modification factor of level seismic demand (

Model c [16]
), seismic response index (C S /C Smin )=1.81 and the primary factor of the building function (I e )=1 (office).Table 13 shows that from the 1st floor to the roof floor, I S < I SO .Actually, the column and beam dimensions had been well designed but there is a need of combination with the shear wall structure, so that it does not only guarantee the strength and ductility but also the adequate rigidity so that the building will not be too flexible (T C >T max ) and the requirements on the security of the architectural elements and structure and the comfort of the habitants will be met.
Table 13 and Fig. 3, the research conducted by Yosafat et.al. on model c with pushover analysis resulted in the target displacement=0.648m with drift ratio=1.78%.Based on FEMA 273, model c, which is located in the Earthquake Zone 6 with Hard Soil, is in inelastic condition which is able to resist the earthquake load up to the level of Life Safety (LS) -Collapse Prevention (CP), means that there is a potential moderate structural until severe damage.The prediction on the proposed SVA procedure has relatively approached the result of the research conducted by Yosafat et.al.

Model d [17]
Table 14.Seismic structure index (I S ) model d.16 shows that from the 1st floor to the 4th floor, except for the roof floor, the comparison is I S > I SO , means that the column and beam dimensions have been quite-well designed so that ensuring the adequate rigidity, strength and ductility when a strong earthquake occurs, so that will only result in light damage or IO (Immediate Occupancy).
Table 16 and Fig. 4, the research conducted by Yanuar H et. al.on model d with pushover analysis resulted in the target displacement=0.060m with drift ratio=0.31%.Based on FEMA 273, model d, which is located in the Earthquake Zone of Banyumas with Hard Soil with S S =0.7 g and S 1 =0.25 g in inelastic condition which is able to resist the earthquake load up to the level of Immediate Occupancy (IO).At the IO level, there is only little potential for structural damage that can be repaired.The prediction on the proposed SVA procedure is relatively similar to the result of the research conducted by Yanuar H. et.al..

Model e [18]
Table 17.Seismic structure index (I S ) model e.In table 17, I S value is the multiplication between E 0 and S D .E 0 is the basic seismic structure index of the moderate moment-resisting frame which is the result of multiplication between the modification factor of level shear capacity ( i n n   1 ), column dimension index (I Ac-i ) > 1, column type index (I C-i )=0.6 slender column (6≤h0/D), strong column weak/beam index (I SCWB-i )=1 except for the roof floor=0.30,structural vibration period index (I T ) = 1, structural system ductility index (R/Ω 0 )=8/3 and S D is the irregularity of building geometry because model e has a regular geometric shape so that the value = 1.Table 18, I SO is the seismic demand index which is the multiplication of the modification factor of level seismic demand ( ), seismic response index (C S /C Smin )=0.26 and the primary factor of the building function (I e )=1 (office).Table 19 shows that from the 1st floor to the 3th floor, except for the roof floor, the comparison is I S > I SO , means that the column and beam dimensions have been quite-well designed so that ensuring the adequate rigidity, strength and ductility when a strong earthquake occurs, so that will only result in light damage or IO (Immediate Occupancy).22 shows that from the 1st floor to the 11th floor has 0.5I SO ≤ I S ≤ I SO (LS) while for the roof floor I S < 0.5I SO (CP), means that the column and beam dimensions have not been well designed although the rigidity and ductility have been adequate but the structure is less adequate so that there is a potential for moderate damage or LS (Life Safety) when an earthquake occurs.
Table 22 and Fig. 6, the research conducted by Sudarman et.al. on model f with pushover analysis resulted in the target displacement=0.65m with drift ratio=0.36%.Based on FEMA 273, model f, which is located in Bobong City, North Maluku, with Moderate Soil with S S =1.355 g and S 1 =0.537 g is in inelastic condition which is able to resist the earthquake load up to the level of Immediate Occupancy (IO) -Life Safety (LS), but according to drift ratio, it has already approached the LS, means that there is a potential moderate structural damage which is still possible to repair.The prediction on the proposed SVA procedure has relatively approached the result of the research conducted by Sudarman et.al.

CONCLUSIONS
Based on the results of the research, there are some conclusions as follows: -The prediction on the proposed SVA procedure for model a (6 floors), d (5 floors), and e (4 floors) has a relatively similar result to which have been conducted by other researchers on the building models.-The prediction on the proposed SVA procedure for model b (14 floors), c (10 floors), and e (12 floors) has a relatively approaching result to which have been conducted by other researchers on the building models.-For the buildings with moment-resisting frame < 10 floors, the building performance is dominated by the dimensions of beam, column, and the ratio of height and width of the building, while for the buildings ≥ 10 floors, the building performance is dominated by the dimensions of beam, column and the height of building.
The purpose of the prediction on SVA procedure here does not look for exactly similar results to the more accurate results of the procedure analysis such as pushover analysis, but the result of SVA prediction is one level higher or lower than the accurate calculation is considered adequate because according to [3],the result of the SVA procedure can be used to underlie the potential status of the selected buildings and subsequently there are a list of the lower buildings which needs more detailed vulnerability assessment conducted by the structural experts.
1 and the followings are given n; = the modification factor of level shear capacity.It follows the distribution of ; I Ac-i = column dimension index of the evaluated level; I C-i = column type index of the evaluated level; I SCWB-i = strong column/weak beam index of the evaluated level; I T = structural vibration period index, T c ≤T max I T = 1 dan Tc>TmaxI T = 0; T c = structural vibration period based on the software calculation (seconds); T max = The maximally allowed structural vibration period (seconds) article 7.8.2 of SNI 1726:2012 or formulation 25 of SNI 1726:2002; R/Ω0= structure ductility, R = The modification factor of moment-resisting frame SO = seismic demand index; n = number of building levels; i = evaluated level(s), where the first level is given number 1 and the followings are given n; of seismic demand of the levels, following the distribution of ; C S = Seismic response coefficient of the design based on formulations 21-25 of SNI 1726:2012 or formulation 26 of SNI 1726:2002; C Smin = minimum seismic response coefficient S S =0.25g and S 1 =0.1g based on FEMA 155 or zone 2A of UBC 1997; I CS = seismic response coefficient index; I e = primary factor of building functiontable 1 & 2 of SNI 1726:2012 or table 1 of SNI 1726:2002.

Fig. 3 .
Fig. 3. Comparison between between SVA and pushover analysis model c.In table 11, I S value is the multiplication between E 0 and S D .E 0 is the basic seismic structure index of the special moment-resisting frame which is the result of multiplication between the modification factor of level shear capacity (

Fig. 4 .
Fig. 4. Comparison between between SVA and pushover analysis model d.In table14, I S value is the multiplication between E 0 and S D .E 0 is the basic seismic structure index of the moderate moment-resisting frame which is the result of multiplication between the modification factor of level shear capacity (

Fig. 5 .
Fig. 5. Comparison between between SVA and pushover analysis model e.

Fig. 6 .
Fig. 6.Comparison between between SVA and pushover analysis model f.In table 20, I S value is the multiplication between E 0 and S D .E 0 is the basic seismic structure index of the moderate moment-resisting frame which is the result of multiplication between the modification factor of level shear capacity (

Requirements Jenis Kolom Tinggi bersih/dimensi kolom dari aksis yang ditinjau : h0/D Rata-rata tegangan geser : τ (N/mm2) Indeks daktilitas : F Definisi dari h0/D
5, calculate the C S and C Smin values, and then input them to formulation 7 to obtain I CS value.Obtain I e value from table 1 and 2 of SNI 1726:2012 or table 1 of SNI 1726:2002 for the office function of I e =1.

Table 11 .
Seismic structure index (I S ) model c.

Table 12 .
Seismic demand index (I SO ) of location model b.

Table 13 .
Comparison between seismic structure index (I S ) and seismic demand index (I SO ) as well as comparison between SVA and pushover analysis model c.

Table 15 .
Seismic demand index (I SO ) of location model d.

Table 16 .
Comparison between seismic structure index (I S ) and seismic demand index (I SO ) as well as comparison between SVA and pushover analysis model d.

Table 18 .
Seismic demand index (I SO ) of location model e.

Table 19 .
Comparison between seismic structure index (I S ) and seismic demand index (I SO ) as well as comparison between SVA and pushover analysis model e.

Table 19 and
Fig.5, the research conducted by Mufti A et. al. on model e with pushover analysis resulted in the target displacement=0.872m with drift ratio=0.60%.Based on FEMA 273, model e, which is located in Ternate in the Earthquake Zone 4 with Moderate Soil in inelastic condition which is able to resist the earthquake load up to the level of Immediate Occupancy (IO).At the IO level, there is only little potential for structural damage that can be repaired.The prediction on the proposed SVA procedure is relatively similar to the result of the research conducted by Mufti A et. al..

Table 21 .
Seismic demand index (I SO ) of location model f.

Table 22 .
Comparison between seismic structure index (I S ) and seismic demand index (I SO ) as well as comparison between SVA and pushover analysis model f.