an economic comparison of direct displacement …...economic comparison between a simpler form of...

INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING

Volume 2, No 1, 2011

© Copyright 2010 All rights reserved Integrated Publishing services

Research article ISSN 0976 – 4399

Received on October, 2011 Published on November 2011 338

An economic comparison of Direct displacement based Design with IS-1893

Response Spectrum method for R.C. Frame Buildings Sunil S. Mayengbam

1, Choudhury.S

2

1- Research Scholar, Department of Civil Engineering, NIT Silchar, India

2- Professor, Dept. of Civil Engineering, NIT Silchar, India

[email protected]

ABSTRACT

Displacement based design deals with the level of damage of structure by designing a

structure with a specified target displacement. Traditional codal Force-based method of

design cannot design structures for target design objectives under a specified hazard level. An

economic comparison between a simpler form of Direct Displacement-based Design and IS-

1893 Response Spectrum method for reinforced concrete frame buildings is reported here.

Buildings of two different plans, three different heights are designed with the method for the

performance levels achieved from those designed by the codal method and their respective

costs of structural frame members are compared. It has been found that the frame buildings

designed with the method is more economical than those designed with the codal method for

the performance levels achieved by the said codal under similar conditions of modeling and

performance levels.

Keywords: Direct displacement based design; IS-1893 response spectrum method;

differences in procedure; performance levels; similar condition; structural costs.

1. Introduction

Seismic design of buildings has traditionally been force-based. In the force-based codal

method of design, the base shear is computed based on perceived seismic hazard level,

importance of the building and probable reduction in demand due to nonlinear hysteresis

effects. The computed base shear is distributed at floor levels with some prescribed or

estimated distribution pattern. It is widely understood now that it is not the force but

displacement, which can be directly related to damage. The constancy of stiffness in force-

based design is also not tenable (Priestley 1993, 2003). Through force-based method of

design an engineer cannot deliberately design structure for an intended performance level.

The alternative approaches are displacement-based design and performance-based design

which are gradually becoming popular in recent times. In these methods the design is done

for an intended displacement or, an intended performance under a perceived hazard level.

Displacement-based design procedures have been reported in the literatures (Aschheim 2002,

Paulay 2002, Qi and Moehle 1991, etc). An offshoot of the displacement-based design is

Direct Displacement-based Design (DDBD) which has been reported by several authors

(Pettinga and Priestley 2005; Xue 2001 etc.). The DDBD method for hollow-tube R.C. frame

buildings by Pettinga and Priestley (2005) appears to be appealing where the building is

designed for some specified interstorey drift limit (2%) by considering an Equivalent Single

Degree of Freedom (ESDOF) system of the building. Under the specific modeling and target

drift condition, dynamic amplification of storey shear, column moment and storey drift are

considered and modified to achieve the target inter storey drift.

An economic comparison of Direct displacement based Design with IS-1893 Response Spectrum method for

R.C. Frame Buildings

Sunil S. Mayengbam, Choudhury.S

International Journal of Civil and Structural Engineering

Volume 2 Issue 1 2011

339

The Performance-Based Design (PBD) apparently started with the Freeman’s Capacity

Spectrum Method (Freeman 1975), developed fast with the contribution from vast research

community and with the publication of various documents by Applied Technology Council

and Federal Emergency Management Agency. The performance levels of the buildings are

described in terms damage level reflected by inelastic rotation in members differentiated as

Immediate Occupancy (IO) level, where damage level is least; Life Safety (LS) level, where

damage level is intermediate and life is not threatened under strong ground motion; and,

Collapse Prevention (CP) level where damage is substantial and the structure is on the verge

of collapse.

2. DDBD design procedure

The design is done by a simpler DDBD method similar to Pettinga and Priestley (2005). The

target design drift and performance level of the building are decided. The beam depth has

been derived from UPBD (S. Choudhury et al, communicated to Earthquake Spectra in

2011). The beam width varies from one-third to half of beam depth as per general design

practice. The column sizes are so adjusted that the column steel is restricted 4% of column

sectional area.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 1 2 3 4 5 6

Displacemen

t (m

)

Period (seconds)

IS-Displacement Spectra5%

10%

15%

20%

25%

Figure 1: IS-Displacement spectra for 0.36g, medium type soil.

However, for ready reference the design steps are elaborated below, with mention of

difference with DDBD method of Pettinga and Priestley (2005), wherever applicable.

The equivalent single degree of freedom system properties are determined as follows

∑∑

∆

∆=∆

ii

ii

m

m 2

d

(1)

d

e ∆

∆=∑ iim

m

(2)






340

∑∑

∆

∆=

ii

iii

m

hmH e

(3)

Here, mi, hi and ∆i are respectively the mass, height from base and displacement for ith

storey.

∆d is target (spectral) displacement, me is equivalent mass, He is the effective height of the

ESDOF system.

The displacement spectra corresponding to design acceleration spectra are generated for

various damping shown in figure 1.

The deflection profile suggested by Pettinga and Priestley (2005), as shown in Eq. (4a) and

(4b), has been used. Here, Øi is the mode shape coefficient of building at ith

floor and n is

total number of storey.

n<=4,H

hii =φ

(4a)

n>4,H

hii

3

4=φ

−H

hi

4

11

(4b)

Storey displacement, ∆i in step 3 and 8 is given by

∆=∆

c

cii φφ

(5)

Where, ∆c and ϕc are the critical storey displacement and the corresponding mode shape

at the critical storey level.

The damping in the system is computed from ductility as given below: The yield

displacement (∆y) of ESDOF system is given by Eq. (6) and frame ductility (µ) is given by

Eq. (7). Now equivalent effective damping (ξ) in the system is obtained from Eq. (8).

eyFy Hθ=∆

(6)

yd ∆∆= /µ

(7)

−+=

−

πµ

ξ5.01

1205 % (8)

The design base shear is computed as follows. The effective time period (Te) is obtained from

displacement spectra corresponding to the curve for damping ξ and the value of target

displacement ∆d. Effective stiffness for ESDOF system is given by Eq. (9) and base shear is

given by Eq. (11).






341

2

e

e2

e 4T

mK π=

(9)

∆−P effect is considered as per Pettinga and Priestley, (2007) where stability ratio (ӨP∆),

post yield stability ratio unaffected (ro=0.01,assumed) and affected (rp) by ∆−P effect and

overall moment (MB) are given by Eq. (10a), (10b) and (10c) respectively.

eB

PHV

P∆=∆θ

(10a)

∆

∆

−

−=

P

Pop

rr

θθ

1

(10b)

D

p

peDeB Pr

rHKM ∆

−−−

+∆=∆

∆

)1(1

)1(2

µµ

(10c)

The overall moment has directly been converted to Design base shear for easy application

e

B

H

MV =b

(11)

The base shear is then distributed at floor levels as per Eq. (12a). If the building is more than

10-storey high, then to take into account the effect of higher modes, Eq. (12b) is used, in

which Ft is typically 10% of base shear applied at roof level.

∑∆∆

=ii

iii

m

mVF b

(12a)

∑∆∆

+=ii

iii

m

mVFF bt 9.0

(12b)

The design is done with expected material strengths. The load combinations are as below:

LD + (13a)

xFLD ±+

(13b)

yFLD ±+

(13c)

Where, D and L stand for dead load and live load respectively. Fx and Fy stand for seismic

load in two mutually perpendicular directions of the building for the floor concerned obtained

from Eq. (12).In the design stage effective member stiffness as specified in FEMA-356 are

considered. Unlike the general DDBD, the typical effective stiffness factors for beams and

columns are 0.5 and 0.6 respectively.

Capacity design is carried out to ensure weak-beam strong-column. Columns are ensured to

behave as elastic member. In the general DDBD, bottom ground storey columns are designed

to behave as elastic members. Shear failure of beams are also avoided. The column sizes are






342

restricted in way that the maximum steel in columns is 4%. Nominal reinforcement of beam

was taken as 0.32% at each face for ductile behavior.

Here, in contrast to the general DDBD method, dynamic amplification is not considered in

the design. The target drift has been achieved by assuming trial reduced design drift until it is

achieved. Moreover, the purpose of this report is just to compare the structural cost under

similar modeling condition and performance level.

3. Differences between the two procedures

The difference between DDBD and IS response spectrum method are stated as follows. The

first is a displacement based design which uses expected material strength in the design stage.

It also uses constant beam section for a particular frame; load combination as per Eq. (13);

inelastic 1st mode displacement profile (Eq. (4a) and (4b)); lateral load distribution accounts

for higher mode effect for buildings above 10-storey as in Eq. (12b); P-∆ effect as in Eq.

(10a), (10b) and (10c).

The latter is a force based design where characteristic material strength is used. Here, it uses

variable beam sections according to the demand and range of percentage reinforcement; load

combination: (1) 1.5(DL+IL), (2) 1.2(DL+IL±EL), (3) 1.5(DL±EL), (4) 0.9DL±1.5EL, where

DL stands for dead load, IL for imposed load and EL for seismic load along the frame; the

number of modes depends on the sum total of their modal mass to make up at least 90% of

the total seismic mass; lateral load distribution does not accounts for higher mode effect;

missing mass correction beyond 33% for higher mode effect.

Force-based design methods for other codes are more or less similar regarding the basic

assumptions mentioned above. However, some assumptions like factor of safety for loading

apart from the basic limit state design may vary. So, they are expected to behave similarly

specially in inelastic time history analysis for similar conditions and also their structural cost.

4. Performance evaluation and cost comparison

For structural cost comparison between the two design methods, two plans designated as plan

I and Plan II as shown in figure 2a and figure 2b have been considered. The heights of

buildings considered are 4-storey, 8-storey and 12-storey for both plans. The nomenclature of

the buildings and target performance objectives has been listed in Table 1. Symbols IS and

DDBD represents buildings designed by I.S. response spectrum method and DDBD

respectively. The second numerical figure indicates the type of plan and the last numerical figure in building name reflects the total number of storey in the building.

Table 1: Nomenclature and target performance objectives of buildings considered.

Building

Category

No.

Plan

No.

used

Building nomenclature Design method

1 I IS1-4, IS1-8, IS1-12 IS-1893

2 II IS2-4, IS2-8, IS2-12 IS-1893

3 I DDBD1-4, DDBD1-8, DDBD1-12 DDBD

4 II DDBD2-4, DDBD2-8, DDBD2-12 DDBD






343

Figure 2: (a) Plan No. I of buildings and (b) Plan No. II of buildings.

Design spectrum considered is as per IS-1893 at acceleration level 0.36g for medium type

soil. A corner period extension of 5 seconds has been applied to tackle larger displacement

demand (also to incorporate the significance of magnitude on the corner period as per

Facciolli et al., 2004) for higher storey buildings designed by DDBD.

The spectrum compatible ground motions (SCGM) have been constructed by using the

software developed by Kumar (2004) where the phase angle, frequency content and duration

of the background earthquake are incorporated in the SCGM highlighted in Table 2. The

match between the IS design spectrum and SCGM response spectrums at 5% damping are

shown in figure 3a.The Final member sizes of various buildings have been furnished in Table

3. Concrete of cube strength 30 MPa and reinforcing steel with yield strength 415 MPa have

been used. Expected material strengths as per FEMA-356 have been used in design and non

linear time history analysis.

Table 2: Details of artificial ground motions

Sl.

No.

Name Background

Earthquake

Record No. Duration

(sec)

1 GM1 Duzce 1999 Duzce, 270 (ERD) 25.9

2 GM2 El Centro 1940 N-S Component 31.8

3 GM3 Gazli 1976 Karakyr, 090 16.3

4 GM4 Kocaeli 1999 Sakarya, 090 (ERD) 30.0

5 GM5 N. Palm Spring 1986 0920, USGS station 5070 20.0

However, characteristic material strengths have been used in design stage for the I.S. code

method. The post-elastic force-deformation behavior has been taken as per FEMA-356 shown

in figure 3b. Buildings have been modeled using SAP2000 v.12.

Effective section properties of beams and columns have been used for all considered

buildings for non linear analysis. The yield moments are obtained from design steel. The

effective beam flexural rigidity is given by Eq. (14a), in which E is modulus of elasticity of

concrete, Ieff, beam is effective moment of inertia of beam, Myb is beam yield moment and Øyb is

beam yield curvature given by Eq. (14b)






344

0

0.5

1

1.5

2

2.5

3

0 1 2 3 4 5

Sa/g

Period (sec)

GM-1GM-2GM-3GM-4GM-5IS

Norm

alized force

Deformation or deformation ratio

(a) (b)

Figure 3: (a) Design IS spectrum Vs. SCGM response spectrum and (b) Force-deformation

behaviour (FEMA-356).

Table 3: Member size of the buildings considered.

Beam Size (mm)

Depth × width

Building

Names

Column Size (mm)

Long-direction Short-direction

IS1-4 410×410 to 350×350 400×300 to 350×300 400×300 to 350×300

IS1-8 600×600 to 350×350 450×300 to 350×300 500×300 to 400×300

IS1-12 800×800 to 350×350 450×300 to 350×300 500×300 to 400×300

IS2-4 350×480 to 320×420 400×300 to 350×300 450×300 to 400×300

IS2-8 480×620 to 350×450 450×300 to 350×300 500×300 to 400×300

IS2-12 660×860 to 320×420 450×300 to 350×300 500×300 to 400×300

DDBD1-4 360×360 to 350×350 450×300 540×300

DDBD1-8 440×440 to 350×350 500×350 600×350

DDBD1-12 480×480 to 350×350 550×300 660×350

DDBD2-4 320×420 to 300×370 550×300 660×350

DDBD2-8 370×470 to 350×400 550×300 660×350

DDBD2-12 450×580 to 350×420 550×300 660×350

Effective flexural rigidity of column is given by Eq. (14c), in which Ieff, column is effective

moment of inertia of column, Mc is column moment corresponding to axial load in column

under gravity load and is obtained from interaction diagram of column at expected strength

level of materials. Øyc is yield curvature of column given by Eq. (14d), in which bc is column

depth under direction of earthquake under consideration. Eq. (14a) through (14d) is after

Priestley (2003).

yb

yb

beam eff, φ

MEI =

(14a)

b

y

yb 7.1h

εφ = (14b)

yc

ccolumn eff, φ

MEI = (14c)

IO LS

CP

Plastic range






345

cyyc /1.2 bεφ = (14d)

The buildings are subjected to Nonlinear Time history analysis (NLTHA) under spectrum

compatible ground motions (SCGM). As the design is done for design spectrum, the energy

level of the ground motions are set to level of design spectrum, which is assured through

SCGM.

The buildings designed by the IS method are first checked for their performance through

NLTHA where some of the buildings performance level has been found to beyond CP which

is not an ideal level for comparison. Irrespective of their real performance level, just to make

an ideal ground for comparison, columns were arbitrarily modeled as elastic members so that

hinges were made to form only in beams through capacity design (strong column weak beam)

which is also done in case of DDBD.

Figure 5: IDR diagram in the mentioned direction for IS-1893 designed buildings.

Capacity design has been performed as per EC-8,

∑MRc = 1.3∑MRb. (15)

Where, ∑MRc represents the sum of the design moments of resistance of the columns framing

into the joint and ∑MRb is the corresponding sum of the design moments of resistance of the

beams.

0

1

2

3

4

0 0.5 1 1.5 2 2.5

Storey level

IDR %

IS2-4 short

0

1

2

3

4

5

6

7

8

0 0.5 1 1.5 2 2.5

Storey level

IDR %

IS2-8 short

01

234

56

789

101112

0 0.5 1 1.5 2 2.5

Storey level

IDR %

IS2-12 short

0

1

2

3

4

0 0.5 1 1.5 2 2.5

Storey level

IDR %

IS1-4 long

GM-1

GM-2

GM-3

GM-4

GM-5

0

1

2

3

4

5

6

7

8

0 0.5 1 1.5 2 2.5

Storey level

IDR %

IS1-8 long

0

1

2

3

4

5

6

7

8

9

10

11

12

0 0.5 1 1.5 2 2.5Storey level

IDR %

IS1-12 long






346

Figure 6: Hinges in typical IS code designed frames with the mentioned directional SCGMs.

Table 4: Structural cost with performance level for IS code designed buildings.

Performance level Building names Structural Costs

(Rs.) Long direction Short direction

IS1-4 16,30,165 2.3% LS 2.2% LS

IS1-8 36,30,531 2.2% LS 2.3% LS

IS1-12 68,66,970 2.0% LS 2.1% LS

IS2-4 24,14,469 2.2% LS 2.3% LS

IS2-8 52,29,694 2.1% LS 2.1% LS

IS2-12 99,73,989 1.9% LS 2.1% LS

Table 5: Structural cost with performance level for DDBD designed buildings.

Target

Performance

Level

Achieved Performance level Building

names

Structural

Costs (Rs.)

Long

direction

Short

direction

Cost with

respect to

IS code

buildings

DDBD1-4 13,52,450 2.3% LS 2.1% LS 2.1% LS -17.0%

DDBD1-8 31,41,469 2.0% LS 2.2% LS 2.2% LS -13.5%

DDBD1-12 56,94,397 2.0% LS 2.2% LS 2.2% LS -17.1%

DDBD2-4 21,98,512 2.0% LS 2.2% LS 1.8% LS -9.0%

DDBD2-8 45,60,174 1.8% LS 2.0% LS 2.0% LS -12.8%

DDBD2-12 87,03,575 1.8% LS 2.0% LS 2.0% LS -12.7%

The performance levels of resulting buildings have been found ideal shown in Table 4, the

inter storey drift diagrams (%IDR) been shown in figure 5 where the %IDR comes around

1.9% to 2.3%. The member hinge formation at last step in time history analysis for typical

cases of IS code designed buildings has been highlighted in figure 6.

The pink and the blue hinges on the frame members of figure 6 and figure 8 indicate IO and

LS level respectively. Here, the maximum member performance is LS. Any target






347

performance level, especially % IDR for DDBD is not expected to be achieved through

NLTHA without slight deviations because of dynamic amplifications (not considered), design

irregularities and other minor factors like empirical consideration of higher mode effect in the

design procedure, etc. Buildings of trial target performance level by DDBD have been tested

through NLTHA for those achieved by the IS method (Table 4 and Table 5). until a close,

preferably lesser performance level is achieved. The interstorey drift diagrams for DDBD

design buildings have been shown in figure 7 and hinges formation at last step in time history

analysis are also found to be LS, typical cases has been highlighted in figure 8.

The structural costs i.e. the costs of the total volume of concrete and steel used only for

beams and columns has been evaluated for both the categories of buildings (Table 4 and

Table 5) according to Delhi Schedule of Rates 2007. The ratio of volume of concrete and

steel provided against building heights is shown in figure 9a. The ratio is lesser by a

significant amount in case of the IS code designed buildings than the other showing that the

volume of steel is dominant for the codal buildings.

Figure 7: IDR diagram in the mentioned direction for DDBD designed buildings.

0

1

2

3

4

0 0.5 1 1.5 2 2.5

Storey level

IDR %

DDBD1-4 long

0123456789

101112

0 0.5 1 1.5 2 2.5

Storey level

IDR %

DDBD2-12long

0

1

2

3

4

5

6

7

8

0 0.5 1 1.5 2 2.5

Storey level

IDR %

DDBD2-8long

0

1

2

3

4

0 0.5 1 1.5 2 2.5

Storey level

IDR %

DDBD2-4long

0

1

2

3

4

5

6

7

8

9

10

11

12

0 0.5 1 1.5 2 2.5

Storey level

IDR %

DDBD1-12 long

0

1

2

3

4

5

6

7

8

0 0.5 1 1.5 2 2.5

Stor

ey level

IDR %

DDBD1-8 long






348

Since, the cost of reinforcing steel is usually higher than that of concrete, the volume of steel

is one of the implied factors (resulting from the differences in the two design methods)

responsible for the higher cost (figure 9b). For similar performance levels, buildings designed

with DDBD has found to be more economical averaging to about -13.68% of the buildings

designed with IS response spectrum method for the considered buildings under similar

conditions of modeling.

The same study can also be performed for forced-based design codes of other countries to

monitor their differences with DDBD, the most important being their economic aspects.

(a) (b)

Figure 9: (a) Ratio of volume of concrete and steel Vs. height and (b) Structural costs Vs.

height.

5. Conclusion

The costs of R.C frame buildings designed with direct displacement based design has been

compared with those designed with I.S. response spectrum method at the performance level

given by the latter. Frame buildings of two plans and different heights have been designed with I.S. response spectrum method. The performance of the buildings has been evaluated

0

4

8

12

20 40 60 80

Height

Vc/Vs

IS1

IS2

DDBD1

DDBD2

0

4

8

12

0 40 80 120

Height

Cost (Rs.)x100000

IS1

IS2

DDBD1

DDBD2






349

through nonlinear time history analysis using five spectrum compatible ground motions. The

same category of buildings has been designed with direct displacement based design for the

performance levels given by those designed with I.S. response spectrum method. The

performance of the buildings has been evaluated and checked through nonlinear time history

analysis using five spectrum compatible ground motions. Results have been presented for

various response quantities. The structural costs of both the categories of buildings have been

evaluated. It has been found that buildings designed with direct displacement based design

are more economical than those designed with the IS response spectrum method.

6. References

1. Aschheim, M (2002), “Seismic design based on the yield displacement”, Earthquake

Spectra, 18(4), pp 581-600.

2. Ezio Faccioli et al. (2004), “Displacement spectra for long periods”. Earthquake

Spectra, 20(2), pp 347–376.

3. Freeman, S.A., Nicoletti, J.P. and Tyrell, J.V (1975), “Evaluation of existing

buildings for seismic risk: A case study of Puget Sound naval shipyard, Bremerton,

Washington”, Proceedings of the US National Conference on Earthquake Engineers,

EERI, Berkeley, California.

4. Kumar, A (2004), “Software for generation of spectrum compatible time history”,

Proceedings of 13th World Conference on Earthquake Engineering, Aug. 1-6, Canada,

Paper No. 2096.

5. Paulay, T (2002), “An estimation of displacement limits for ductile systems”,

Earthquake Engineering and Structural Dynamics, 31, pp 583-599.

6. Pettinga, J.D. and Priestley, M.J.N (2005), “Dynamic behavior of reinforced concrete

frames designed with direct displacement-based design”, Journal of Earthquake

Engineering, 9(2), pp 309-330.

7. Pettinga, J.D. and Priestley, M.J.N (2007), “Accounting for p-delta effects in

structures when using direct displacement-based design”, Research Report ROSE

(European School for Advanced Studies in Reduction of Seismic Risk), IUSS Press,

Pavia.

8. Priestley, M.J.N (2003), “Myths and fallacies in earthquake engineering, Revisited”,

European School for Advanced Studies in Reduction of Seismic Risk, 9th

Mallet-Milne

Lecture.

9. Qi, X. and Moehle, J.P (1991), “Displacement design approach for reinforced

Concrete Structures Subjected to Earthquakes”, Report No. UCB/EERC-91/02.

10. Xue, Q (2001), “A direct displacement-based seismic design procedure of inelastic

structures”, Engineering Structures, 23, pp 1453-1460.

11. ___SAP2000 V. 10.12 (2006), Nonlinear, Educational version. “Structural analysis

program”, Computer and Structures Inc., Berkley, CA.






350

12. ___Delhi Schedule of Rates (2007), Central Public Works Department, New Delhi.

13. ___FEMA-356 (2000), “Prestandard and commentary for the seismic rehabilitation of

buildings”, US Federal Emergency Management Agency, 2000.

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