https://ced.
Performance Evaluation of Simple Regular Buildings using FBD and DDBD Methods with a Consistent Target Drift Pudjisuryadi.
Sumargo.
Kho.
1, and Lumantarna.
1 Faculty of Civil Engineering and Planning.
Civil Engineering Department.
Petra Christian University Jl.
Siwalankerto 121-131.
Surabaya 60236.
INDONESIA DOI: https://doi.
org/10.
9744/ced.
Article Info:
Submitted: Feb 28, 2025 Reviewed: Mar 04, 2025 Accepted: Mar 11, 2025 Keywords:
Direct Displacement Based Design.
Force Base Design, nonlinear analysis.
Reinforced Concrete Structure.
Corresponding Author:
Pudjisuryadi.
Faculty of Civil Engineering and Planning.
Civil Engineering Department.
Petra Christian University.
Jl.
Siwalankerto 121-131.
Surabaya 60236.
INDONESIA Email: pamuda@petra.
Abstract The Direct Displacement Based Design (DDBD) method, proposed by Priestley, is an alternative to the traditional Force-Based Design (FBD) method for earthquake-resistant design.
This study compares the performance of 4-story and 12-story buildings designed using both FBD and DDBD with the same target drift of 2%.
The differences in base shear used for the design of the two approaches are discussed.
evaluate the buildings' performance.
Nonlinear Dynamic Procedure (NDP) analysis, or nonlinear time history analysis, was conducted considering 500 and 2500 years return period earthquakes.
The results indicate that the actual drift of both designs deviates from the target drift.
the observed drifts remain within the maximum limits set by FEMA Moreover, plastic damages were observed in unexpected areas of the columns, suggesting that the strong-column weak-beam design concept, as stipulated by building codes, does not entirely prevent damage to This is an open access article under the CC BY license.
INTRODUCTION
Seismic design concepts can be classified into Force Based Design (FBD) and Displacement Based Design (DBD).
Although improvements are ongoing .
FBD is more widely adopted across design codes, including the Indonesian standard SNI 03-1726-2019 .
In contrast.
DBD is still under development .
, with one notable method.
Direct Displacement-Based Design (DDBD), proposed by Priestley et al.
As the name suggests.
DDBD focuses on ensuring that a structure does not exceed a predefined displacement target when subjected to a target earthquake.
After DDBD was first introduced, researchers began evaluating the performance of structures designed with DDBD, applying it to various types of structures.
Sadan et al.
and Cademartori et al.
assessed existing bridge structures using DDBD and yielded accurate results.
Dong et al.
extended the application of DDBD to glulam structures with buckling restrained braces in 3-, 6-, and 9-story buildings, finding them effective in resisting lateral earthquake forces.
However.
Chikmath et al.
observed that a 12-story reinforced concrete frame designed using DDBD exhibited a drift ratio exceeding the allowable inter-story drift limit, suggesting that DDBD may not be ideal for buildings where the fundamental mode is not dominant.
Furthermore, there has been growing interest in comparing the performance of DDBD with FBD, which is more commonly used.
Muljati et al.
conducted a comparative study of structures designed using the Indonesian code SNI 03-1726-2019 (FBD) and DDBD.
The study .
concluded that buildings designed with DDBD often result in larger dimensions than those designed with FBD.
Note : Discussion is expected before July, 1st 2025, and will be published in the AuCivil Engineering DimensionAy, volume 27, number 2.
September 2025.
ISSN
: 1410-9530 print / 1979-570X online Published by : Petra Christian University Performance Evaluation of Simple Regular Buildings This study aims to further investigate the factors that may contribute to the differences between FBD and DDBD.
aids engineers in recognizing design factors that are more sensitive to the results, enabling them to exercise greater care when determining values that rely on engineering judgment.
A comparison is made between the design concepts and assumptions underlying both methods.
Two reinforced concrete buildings, with 4 and 12 stories, were designed using both methods and serve as case studies for the analysis.
The buildings' performance was evaluated using nonlinear dynamic procedures .
onlinear time history analysi.
A brief overview of the DDBD method is presented in the followings.
Direct Displacement based Design (DDBD) Method DDBD method determines the earthquake load on a building based on a target displacement (AE.
that the structure aims to achieve during its final phase of deformation .
Initially, the structure is idealized as a single-degree-offreedom (SDOF) system, characterized by its effective height (H.
, effective mass .
, and effective stiffness (K.
Structural equivalent damping (Ae.
which is a combination of elastic damping .
%) and hysteretic damping, is determined depending on the type of structure.
A reduction factor (RA) is then calculated based on the target displacement and damping characteristics.
This reduction factor is applied to derive the displacement response spectrum corresponding to the structural damping.
From the spectrum, the effective period (T.
of the structure is Subsequently, the effective stiffness and total base shear (Vbas.
can be calculated.
Figure 1 summarizes the conceptual framework of the DDBD method.
Figure 1.
Direct Displacement based Design Concept .
For multi-degree-of-freedom (MDOF) structures, such as frames, the step-by-step DDBD procedure for calculating the total base shear (Vbas.
is as follows:
Step 1.
Develop an Equivalent SDOF system An equivalent SDOF system is derived from the MDOF system, as illustrated in Figure 2.
In the figure, di represents the inelastic mode shape, defined by Equations 1 and 2, where n is the number of floors.
Hn is the height of the structure, and Hi is the elevation of the ith floor.
The displacement of the ith floor (D.
is given by Equation 3, where Dc and dc are the design displacement and value of the mode shape at the critical mass c, respectively.
The target displacement can then be calculated using Equation 4, where mi is the mass of the ith floor.
The effective mass .
and effective height (H.
of the SDOF system can be determined using Equations 5 and 6.
yaya ycuycu O 4 O yuyuycnycn = yaya ycnycn ycuycu Vol.
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4 yaya 3 yayaycuycu ycuycu > 4 O yuyuycnycn = ( ycnycn ).
OIycnycn = yuyuycnycn .
uyuycayca ) yayaycnycn ycayca yuuyuuyccycc = Ocycuycuycnycn=1.
coycoycoyco yuuyuu2ycnycn ) / Ocycuycuycnycn=1.
coycoycoyco yuuyuuycnycn ) .
ycoycoyceyce = Ocycuycuycnycn=1.
coycoycoyco yuuyuuycnycn ) /yuuyuuyccycc .
yayayceyce = Ocycuycuycnycn=1.
coycoycoyco yuuyuuycnycn yayaycnycn ) / Ocycuycuycnycn=1.
coycoycoyco yuuyuuycnycn ) .
Figure 2.
Equivalent SDOF System .
Step 2.
Estimate the Equivalent Viscous Damping .
For a frame, the equivalent viscous damping .
is calculated using Equations 7 and 8, where m and Dy represent the ductility and yield displacement, respectively.
The yield displacement is estimated from the effective height (H.
, yield moment (M), and yield rotation .
of the beams, as calculated from Equation 9, where b is the number of bays in the frame.
The beam yield rotation depends on the beam's length (LB), section height (HB), and its reinforcement yield strain .
, as given by Equation 10.
yuNyuNOe1 yuOyuOyceyceyceyce = 0.
565( )
yuuyuuycyc = yuNyuN = yuNyuNyuNyuN Ocycayca ycnycn=1 ycAycAycnycn yuEyuEycycycyc Ocycayca ycnycn=1 ycAycAycnycn yuEyuEycyc = 0.
5yuAyuAycyc yayayaAyaA yaAyaA Step 3.
Determine the Effective Period (T.
From the acceleration design spectrum, a displacement design spectrum is developed for the SDOF system with damping equal to the equivalent viscous damping .
Given the target displacement (D.
, the effective period (T.
can be determined .
ee Figure 1.
Step 4.
Calculate the Effective Stiffness (K.
and the Total Base Shear (Vbas.
The effective stiffness (K.
and total base shear (Vbas.
are calculated using Equations 11 and 12.
2yuUyuU ycNycNycNycN yayayceyce = ( )2 ycoycoyceyce The Case Studies ycOycOycaycaycaycaycaycaycayca = yayayceyce yuuyuuyccycc The key variable used for comparison between the two design methods is the target displacement.
The dimensions of the structural elements are determined such that the nonlinear displacement of the building designed using the Vol.
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Performance Evaluation of Simple Regular Buildings FBD method .
stimated by multiplying the elastic displacement by Cd, the deflection amplification facto.
is the same as the target displacement set in the DDBD method.
In this study, an inter-story drift ratio of 2% was selected to determine the target displacement.
As mentioned previously, two buildings .
- and 12-stor.
of a typical floor plan, as shown in Figure 3.
, were designed for a site in Surabaya with a site class E.
The typical story height is 4 meter, resulting in overall building heights of 16 meters for the 4-story building and 48 meters for the 12-story building.
The corresponding basic elastic design response spectrum is presented in Figure 3.
In the FBD method, a special moment-resisting frame is selected as the seismic resisting system, with concrete and steel strengths of 25 MPa and 420 MPa, respectively.
The gravity loads considered in this study consist of self-weight of the structure, superimposed dead load, and live load.
A live load of 2.
4 kN/m2 .
was applied to all floors because the building is assumed as an office.
A superimposed dead load of 1.
5 kN/m2 was applied to all stories.
Using the equivalent static force procedure .
, the resulting element dimensions required to achieve the 2% story drift ratio are presented in Table 1.
These dimensions were subsequently used for buildings designed using the DDBD approach.
Figure 3.
Building Plan, .
Basic Elastic Design Response Spectrum Table 1.
Beam and Column Dimensions used for FBD and DDBD approaches Story Main Beam .
4-Story Secondary Beam .
Column .
Main Beam .
12-Story Secondary Beam .
Column .
Variables and Assumptions for Each Method Both FBD and DDBD methods involve several variables (Table .
that must be determined.
It is important to note that the assumed values for these variables can significantly influence the resulting earthquake loads.
Thus, a direct comparison between the two methods can be challenging.
Table 3 provides the values of these variables as utilized in this study.
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Sumargo.
Kho.
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Table 2.
Determination of Key Variables of FBD and DDBD Methods Variable FBD
DDBD
Importance Factor Depending on the building risk category Not a design variable given in Table 3 of SNI 1726:2019 .
Mode Shape Not a design variable An inelastic mode shape is assumed (Priestley et al.
) to determine the design displacement .
Effective mass .
Effective height Not a design variables Calculated from equations by (H.
Target Displacement .
Priestley et al.
Yield Displacement .
Structural Ductility () The maximum response modification Design ductility is determined from coefficient (R), which is a function of id/iy ductility, is given in Table 12 of SNI 1726:2019 .
Structural Damping An elastic damping of 5% is assumed Using a combination of 5% elastic damping and additional hysteresis damping based on the type of structure .
Story Shear Distribution Determined by empirical equations based Determined by empirical equations on the seismic weight and elevation of based on the story mass .
and each floor .
story target displacement (AE.
Structural Analysis Standard finite element analysis Simplified approach .
Table 3.
Values of the Key Variables Used/Calculated in this Study FBD
DDBD
Variable 4-story 12-story 4-story Importance factor (I.
Effective mass .
Effective height (H.
Design displacement .
Yield displacement .
Structural ductility () Structural damping (Ae.
12-story Total Base Shear and Story Shear of the Buildings With different values of the previously mentioned variables, it is expected that the resulting total base shear and distributed story shear, will differ between the two methods, as shown in Table 4.
In this study, the resulting base shear forces differ by approximately a factor of two.
Story Base Shear Table 4.
Total Base Shear and Story Shear of the Buildings Story Shear.
Fi .
N) FBD-4
DDBD-4
FBD-12
DDBD-12
Longitudinal Reinforcement for Beams and Columns Tables 5 and 6 illustrate the longitudinal reinforcement for the beams and columns of the 4-story building, respectively, while Tables 7 and 8 provide the corresponding details for the 12-story building.
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Performance Evaluation of Simple Regular Buildings Table 5.
Beam Reinforcement for 4-Story Building Story Location Dimension .
Rebar Position 400 x 650 Longitudinal Rebar .
einforcement rati.
FBD
DDBD
5D22 .
3D22 .
3D22 .
3D22 .
7D16 .
3D22 .
4D16 .
3D22 .
7D22 .
4D22 .
4D22 .
4D22 .
5D22 .
4D22 .
3D22 .
4D22 .
7D22 .
5D22 .
4D22 .
5D22 .
5D22 .
5D22 .
3D22 .
5D22 .
7D22 .
6D22 .
4D22 .
6D22 .
5D22 .
6D22 .
3D22 .
6D22 .
Table 6.
Columns Reinforcement for 4-Story Building Story Location Dimension .
Interior Exterior Corner Interior Exterior Corner Interior Exterior Corner Interior Exterior Corner 650 x 650 Longitudinal Rebar .
einforcement rati.
FBD
DDBD
12D22 .
20D22 .
8D25 .
16D22 .
8D25 .
8D22 .
12D19 .
20D22 .
8D22 .
20D22 .
8D19 .
12D22 .
12D19 .
24D22 .
8D25 .
20D22 .
8D25 .
12D22 .
12D25 .
28D22 .
12D25 .
20D22 .
12D25 .
12D22 .
Table 7.
Beam Reinforcement for 12-Story Building Story Location Dimension .
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Longitudinal Rebar .
einforcement rati.
FBD
DDBD
4D22 .
5D16 .
2D22 .
5D16 .
8D13 .
5D16 .
4D13 .
5D16 .
5D22 .
3D22 .
3D22 .
3D22 .
4D22 .
3D22 .
2D22 .
3D22 .
6D22 .
4D22 .
3D22 .
4D22 .
5D22 .
4D22 .
3D22 .
4D22 .
7D22 .
5D22 .
4D22 .
5D22 .
6D22 .
5D22 .
4D22 .
5D22 .
7D22 .
6D22 .
4D22 .
6D22 .
6D22 .
6D22 .
4D22 .
6D22 .
Pudjisuryadi.
Sumargo.
Kho.
, and Lumantarna.
Story Location Dimension .
Rebar Position 400 x 900 Longitudinal Rebar .
einforcement rati.
FBD
DDBD
8D22 .
7D22 .
4D22 .
7D22 .
7D22 .
7D22 .
5D22 .
7D22 .
8D22 .
7D22 .
5D22 .
7D22 .
7D22 .
7D22 .
5D22 .
7D22 .
8D22 .
8D22 .
5D22 .
8D22 .
7D22 .
8D22 .
5D22 .
8D22 .
8D22 .
8D22 .
5D22 .
8D22 .
7D22 .
8D22 .
5D22 .
8D22 .
7D22 .
9D22 .
4D22 .
9D22 .
6D22 .
9D22 .
5D22 .
9D22 .
6D22 .
9D22 .
3D22 .
9D22 .
5D22 .
9D22 .
4D22 .
9D22 .
5D22 .
9D22 .
3D22 .
9D22 .
4D22 .
9D22 .
2D22 .
9D22 .
Table 8.
Columns Reinforcement for 12-Story Building Story Location Interior Exterior Corner Interior Exterior Corner Interior Exterior Corner Interior Exterior Corner Interior Exterior Corner Interior Exterior Corner Interior Exterior Corner Interior Exterior Corner Interior Exterior Corner Dimension .
1000 x 1000 1200 x 1200 Longitudinal Rebar .
einforcement rati.
FBD
DDBD
8D25 .
16D25 .
8D22 .
12D25 .
8D22 .
8D22 .
8D25 .
16D25 .
8D25 .
12D25 .
8D19 .
8D25 .
8D25 .
20D25 .
12D22 .
16D25 .
8D22 .
8D25 .
8D22 .
24D25 .
12D22 .
20D25 .
8D22 .
12D25 .
8D13 .
20D25 .
12D19 .
16D25 .
8D22 .
8D25 .
8D13 .
24D25 .
8D22 .
16D25 .
8D22 .
12D22 .
8D13 .
24D25 .
8D22 .
20D25 .
8D22 .
12D22 .
8D13 .
24D25 .
8D22 .
20D25 .
8D22 .
12D22 .
12D13 .
20D25 .
12D13 .
16D25 .
12D19 .
12D22 .
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Performance Evaluation of Simple Regular Buildings Story Location Dimension .
Interior Exterior Corner Interior Exterior Corner Interior Exterior Corner 1200 x 1200 Longitudinal Rebar .
einforcement rati.
FBD
DDBD
12D13 .
20D25 .
12D16 .
16D25 .
12D25 .
12D22 .
12D13 .
20D25 .
12D22 .
16D25 .
16D25 .
12D22 .
12D16 .
20D25 .
20D22 .
16D25 .
20D29 .
12D19 .
Performances of the Buildings The performances of the designed buildings were evaluated using nonlinear time history analysis.
Ground acceleration records from the 1940 El-Centro and the 1995 Kobe - Chihaya Station earthquakes (Figure .
are used as input for the analysis.
These original ground motions were modified to match the response spectrum of Surabaya City.
The buildings were subjected to two levels of seismic loading: the Basic Design Earthquake (BDE) and the Maximum Considered Earthquake (MCER).
Ground motions were applied along two orthogonal directions, with intensities set at 100% in the N-S direction and 30% in the E-W direction.
The parameters considered in evaluating structural performance were story drift ratio, damage level, and structural failure mechanism.
Figure 4.
Ground Motion Record of: .
El-Centro 1940 N-S, .
El-Centro 1940 E-W, .
Kobe 1995 Chihaya Station N-S, .
Kobe 1995 Chihaya Station E-W .
Drift Ratio .
Figure 5.
Inter Story Drift Ratio of 4-Story Building: .
BDE, .
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The inter-story drift ratios for the 4-story and 12-story buildings are presented in Figures 5 and 6.
According to FEMA 356 .
, for earthquakes with 10% and 2% probability of exceedance in 50 years .
he BDE and MCER, respectivel.
, the inter-story drift ratios are limited to 2% and 4%.
The results indicate that all inter-story drift ratios remain within their respective limits.
The maximum inter-story drift ratio values are summarized in Table 9.
Figure 6.
Inter Story Drift Ratio of 12-Story Building: .
BDE, .
MCER Table 9.
Maximum Inter Story Drift Ratio of Each Building Building 4-FBD
4-DDBD
12-FBD
12-DDBD
El Centro
BDE
Kobe
El Centro
MCER
Kobe Damage Level and Failure Mechanism All buildings are expected to have a safe beam side sway mechanism, where controlled plastic damage might occur at the beam ends and the bottom of the first-floor columns.
However, the results indicate that plastic damage also occurs in columns at other locations.
In this study, the level of plastic damage is adopted from FEMA 356 .
and presented in Figure 7 and Table 10.
In Figure 8, it can be seen that for 4-story buildings designed with both approaches and subjected to the El Centro earthquake at the BDE level, plastic damages have already occurred in some columns.
These damages are in the very early stage, indicated by pink color (Stage B, see Table .
With a higher level earthquake (Figure .
, the MCER, the damages become more severe, with buildings designed using the FBD approach experiencing column damage up to the Life Safety stage .
yan colo.
Similar results are observed for 4-story buildings subjected to the Kobe earthquake (Figures 10 and .
Again, the damages are more severe in buildings designed using the FBD approach .
maller base shea.
, with column damage reaching the Immediate Occupancy stage .
ark blue colo.
at the MCER As for the beams, as expected, plastic damages were observed, with a maximum of Life Safety stage for buildings designed using the FBD approach and Immediate Occupancy stage for those designed using the DDBD In Figure 12, the 12-story buildings designed with both approaches and subjected to the El Centro earthquake at the BDE level show plastic damages in some columns up to the Collapse Prevention stage .
reen colo.
With a higher level earthquake (Figure .
, the MCER, more plastic damages entered the Collapse Prevention stage, but none went beyond .
Figures 14 and 15 show similar results for 12-story buildings subjected to the Kobe earthquake.
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Performance Evaluation of Simple Regular Buildings Damages to the beams and columns of buildings designed with the FBD approach entered the Life Safety and Collapse Prevention stages, respectively.
The beams of buildings designed with the DDBD approach showed slightly less damage, experiencing only the Immediate Occupancy stage.
Strong Column Weak Beam (SCWB) concept is applied during the design stage.
However, the SCWB approach from Priestley is different from the SNI SCWB standard.
Priestley's SCWB concept uses simplified formulas to determine the column design moment, but the results indicate that this approach is less effective, as many columns fail before the beams.
Tables 11 and 12 summarize the analysis results.
In these tables, the "Mechanism" is marked with "OK" if the plastic damage occurs as expected, the "Damage Level" is marked with "OK" if the maximum plastic damage conditions are within the "Life Safety" and "Collapse Prevention" for BDE and MCER, respectively, and the AuDrift RatioAy is marked with AuOKAy if its value does not exceed the specified limit.
Table 10.
Plastic Hinge Color and State by FEMA 356 .
Plastic Hinge State Immediate Occupancy Life Safety Collapse Prevention Figure 7.
ForceAeDisplacement Relationship of Plastic Hinge (FEMA 356 .
) .
Figure 8.
Plastic Damages in 4-Story Buildings subjected to El CentroAeBDE: .
FBD, .
DDBD .
Figure 9.
Plastic Damages in 4-Story Buildings subjected to El CentroAeMCER: .
FBD, .
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Figure 10.
Plastic Damages in 4-Story Buildings subjected to KobeAeBDE: .
FBD, .
DDBD .
Figure 11.
Plastic Damages in 4-Story Buildings subjected to KobeAeMCER: .
FBD, .
DDBD .
Figure 12.
Plastic Damages in 12-Story Buildings subjected to El CentroAeBDE: .
FBD, .
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Figure 13.
Plastic Damages in 12-Story Buildings subjected to El CentroAeMCER: .
FBD, .
DDBD .
Figure 14.
Plastic Damages in 12-Story Buildings subjected to KobeAeBDE: .
FBD, .
DDBD .
Figure 15.
Plastic Damages in 12-Story Buildings subjected to KobeAeMCER: .
FBD, .
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Table 11.
BuildingsAo Performance (El Centro Earthquak.
Building 4-FBD
4-DDBD
12-FBD
12-DDBD
Mechanism BDE
Damage Level El Centro
Drift Ratio
Mechanism MCER
Damage Level Drift Ratio
MCER
Damage Level Drift Ratio Table 12.
BuildingsAo Performance (Kobe Earthquak.
Building 4-FBD
4-DDBD
12-FBD
12-DDBD
Mechanism BDE Damage Level Kobe Drift Ratio Mechanism CONCLUSIONS Based on this study case of regular 4-story and 12-story buildings designed using the FBD and DDBD approaches, it can be concluded that:
Buildings designed using both methods have actual drifts that differ from the target of 2%.
In the FBD method, it was expected that the actual drift would be close to the target drift of 2% at the MCER earthquake level.
However, the actual drift values for both buildings at the MCER earthquake level exceeded the target drift.
Nevertheless, all drift values remained within the maximum allowable limits at both the BDE and MCER earthquake levels.
It should also be noted that in the FBD method, buildings are designed based on BDE, which is 2/3 of the MCER.
In the DDBD method, it was expected that the actual drift value is close to the target drift of 2% at the BDE earthquake level.
However, the actual drift values for the 4-story and 12-story buildings were significantly lower than the target drift of 2%.
Even at the MCER earthquake level, the actual drift values remained below the 2% target.
This means that in terms of drift ratio, the DDBD approach is quite conservative.
All buildings, both 4-story and 12-story, designed using the FBD and DDBD approaches, did not experience collapse due to the El Centro or Kobe earthquakes at the MCER level.
Plastic damages were generally more severe in buildings designed using the FBD approach, with beams and columns experiencing the Collapse Prevention and Life Safety stages.
For buildings designed using the DDBD approach, columns also reached the Collapse Prevention stage, although in fewer numbers, while beams only reached the Immediate Occupancy stage.
The performance differences observed in points 1 and 2 can be attributed to the distinct design processes inherent to the two approaches, as outlined in Table 2.
Despite the intended design for a safe beam-side sway mechanism, all buildings in this study experienced plastic damage at locations beyond the expected beam ends and first-floor columns.
This highlights the limitation of the strong column-weak beam concept in the code, that it is not sufficient to provide 100% assurance that the columns are free from plastic damage as expected .
REFERENCES