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 Total Downloads : 553
 Authors : Arvind. S. Khedkar, Rajkuwar. A. Dubal, Sandeep. A. Vasanwala
 Paper ID : IJERTV3IS21114
 Volume & Issue : Volume 03, Issue 02 (February 2014)
 Published (First Online): 09042014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Performance Based Seismic Design Of Reinforced Concrete Moment Resistant Frame With Vertical Setback
Arvind. S. Khedkar1, Rajkuwar. A. Dubal 2, Sandeep. A. Vasanwala3
1 P. G. student, Rajarshi Shahu College of Engineering, Tathawade, Pune
2 Professor, Department of Civil Engineering, Rajarshi Shahu College of Engineering, Tathawade, Pune, MH, India
3 Professor, Applied Mechanics Dept, SVNIT Surat, Gujrat,India
Abstract A performancebased seismic design (PBSD) method is aimed at controlling the structural damage based on precise estimations of proper response parameters. PBSD method evaluates the performance of a building frame for any seismic hazard, the building may experience. This paper gives a comparison between Performance based Seismic design and conventional design method (using I.S 1893; 2002) for irregular RC building frames (10 storeys) and evaluates performance using pushover and Time History analysis.

INTRODUCTION
Earthquakes have the potential for causing the greatest damages, among all the natural hazards. Since earthquake forces are random in nature & unpredictable, need of some sophisticated methods to analyze our structures for these forces. Performance based design can relate to a new dimension in the seismic design philosophy. We need to carefully understand and model the earthquake forces to study the actual behavior of structure so that structure faces a controlled damage. India has witnessed more than 690 earthquakes of Richter magnitude (M) greater than 5 during 1828 to 2010. Damage survey reports show that life and property losses occur in urban and semiurban areas. It is uneconomical to design a building so as not to suffer any damage during strong earthquake. An engineering approach aims for achieving balance in cost and performance through controlled damage. The goal of performancebased seismic design is to ensure that performance objectives are satisfied. A successful conceptual design could hopefully reduce the impact of uncertainties on the real structural behaviour.

PERFORMANCE BASED SEISMIC DESIGN OF REINFORCED CONCRETE MOMENT RESISTANT FRAME:
Reinforced Concrete Building stock in India is mainly classified from low to medium rise buildings. Approach of I.S 1893 is in tune with typical code practice followed by many other countries. In spite of knowing drawbacks of force based seismic design procedures, the practice is in vogue due to its simplicity and nonavailability of the alternative. We can use guidelines given by FEMA and ATC documents by modifying them for Indian condition. The objective of this study is to develop and validate a seismic
design methodology for Reinforced Concrete Moment Frame which enables us to produce structures of seismic performance which is predictable and intended. Based on performance limit states of target drift and desired yield mechanism, this design methodology accounts for inelastic structural behaviour directly, and practically eliminates the need for assessment or iteration by nonlinear static or timehistory analysis after initial design. The methodology for steel frames has been developed by Goel et al., in recent years (1999~2008). It is called PerformanceBased Plastic Design (PBPD) method.An outline of the stepbystep PerformanceBased Seismic Design (PBSD) procedure is given in the following.

Design Procedure

Select a desired yield mechanism and target drift for the structure for the design earthquake hazard.

Estimate the yielding drift, y, the fundamental period, T, of the structure and determine an appropriate vertical distribution of design lateral forces.

Determine the elastic design spectral acceleration value, Sa (Fig 1), by multiplying seismic response
coefficient, C s, with R
I

Calculate the design base shear, V. In order to estimate the ductility reduction factor and the structural ductility factor, an inelastic seismic response of EPSDOF is needed, such as idealized inelastic response spectra by NewmarkHall (1985) used in this study.

Modify V for Reinforced Concrete MF as needed since the forcedeformation behavior is different from the assumed EP behavior and PDelta effect is not considered in the calculation of V in Step 4.

Use plastic method to design the designated yielding members (DYM), such as beams in Reinforced Concrete Moment Frames. Members that are required to remain elastic (nonDYM), such as columns, are designed by a capacity design approach.


Determination of Fundamental Period
The fundamental period, T, in seconds, for Reinforced Concrete MF can be determined from the following equation, as given in ASCE 705 (2006)
n
T = Cu . Ta = Cu. Ct. hx
Table No 2 Ductility reduction factor and its corresponding structural period range
Period range
Ductility Reduction factor
0 T < T1
10
R=1
T1 T < T1 10 4
R
= (2s
1
T1 2.513.log ( )
1) (2.s 1)
4T
T1 T
T < 1
4 4
R = (2s 1)
T T < T1
1
R = Ts
T1
T1 T
R = s
T > C . C . hx (1)
actual /model u t n
where Ta is the approximate fundamental period per ASCE 705 (2006) section 12.8.2.1; 'Cu represents the coefficient for upper limit on calculated period, and for SD1
0.3g , Cu is 1.4 (Table 12.81 in ASCE 705); hn is the height in feet above the base to the highest level of the structure and the coefficient Ct and x for concrete moment resistant frames are 0.016 and 0.9
(Table 12.82 in ASCE 705), respectively.

Design Base Shear
Assuming an idealized EP forcedeformation behavior of the system as shown in figure, the workenergy
1
1
Note:1 = 0.57 ; = . (((2 1))/ ) sec.
equation can be written as:
(Ee + Ep ) = . 1 M. S2 =


C2 METHOD FOR MODIFICATION OF TARGET DRIFT
After studying the hysteretic (degradation of strength
2 v
a
1 . M. T S g 2 (2) where Ee
2 2
and Ep are, respectively, the elastic and plastic components of
the energy (work) needed to push the structure up to the target drift. Sv is the design pseudospectral velocity; Sa is the pseudo spectral acceleration, which can be obtained from the seismic design response spectrum in ASCE 705 (2006) With the assumed yield drift y for different structural systems (Table 1), the energy modification factor, , depends on the structural ductility factor (s) and the ductility reduction factor ( R) and can be obtained from the following relationship.
Table No .1 Assumed design yield drift ratios as given in ASCE7
and stiffness) it is revealed that the Peak displacements for nondegrading frames are large for
short periods but are equal for longer periods as that of degrading frames. The coefficient C2 is a modification factor to represent the effect of pinched shape of hysteretic loops, stiffness degradation, and strength deterioration on the maximum displacement response according to FEMA 356. The equations of simplified linear regression trend line of
C2for different force reduction factor, R, are summarized in Table below.
0.2 <= T < 0.4
0.4 T < 0.8
0.8 T
R=
3.0 ~ 6.0
3.0 7.5 (T
0.2
1.5 1.0 (T
0.4)
1.1 0.045
(T 0.8)
R=
2.0
2.5 6.5 (T
0.2)
1.1 0.077 (T 0.4)
Table No 3 C2 factor
R2
= 2s 1
(3)
After determining the value of C2 , the modified target design drift u , ductility s
Frame Type
Reinforced Concrete
Steel
SMF
MF
EBF
STMF
CBF
Yield Drift ratio
y (%)
0.5
1
0.5
0.75
0.3
Ductility reduction factor Rand energy modification factor
can be calculated as follows:
Plots of energy modification factor as obtained from Equation 3 are also shown in Figure 3.3(b) (Lee and Goel, 2001).. Other inelastic spectra for EPSDOF systems can also
u = t
C 2
s
= u y
(4)
(5)
be used as preferred, such as those by Miranda and Bertero (1994).
= 2s 1
R2

Design lateral forces
(6)
Shear distribution factor for the respective story factor for the respective story is calculated by using following equation;
V n
wj hj
0.2
i = i = ( j =1 )0.75T
(7)
Vn wn hn
Vi = shear force at ith level
i = Shear distribution factor at ith level wj = Seismic weight atlevel j
shear force and bending moment at the desired beam plastic hinge locations at all levels are assumed to reach the expected strengths, Hence they are calculated as following equations;
hj = height of level j from the base
wn = Seismic weight at top level
Mpcpc
= Vp
4
(13)
hn = height of roof level from the base
Then, the lateral force at level i, Fi , can be obtained
as,
V = M PR POSITIVE +M PR NEGATIVE
i
L
(14)
V = M PR POSI TIVE +M PR NEGATIVE
+ W i tributary L 2
W i tributary L
Fi = i i+1 . Vn =
Lateral force at ith level
(15)
i L 2
Vn = Story shear at roof level
Vy= Design base shear
Substituting the values of Vn we get following
equation
h 1= height of first story


PERFORMANCE BASED SEISMIC DESIGN OF REINFORCED CONCRETE MOMENT RESISTANT IRREGULAR FRAME:
In our study we have considered one regular 10
F =
( w n hn )0.75T0.2 . V
(8)
storey frameand compared our seismic design with
i i i+1
n
j =1
wj hj y
Performance based Seismic design Methodology.Also to study the effect of vertical Geometric Irregularity we have compared two 10 storey frames with one step and two step setbacks with

Design of Designated Yielding Members (DYM)
i=1
When using the target yield mechanism for moment frames as shown in fig 5 beams become the primary designated yielding members (DYM). The required beam moment capacity at each level can be determined by plastic design approach (external work equals internal work).For Reinforced Concrete moment frames, in general, because of strength contribution from slabs and nonrectangular beam shapes (ie, T shape beam), as well as the use of different amounts of top and bottom reinforcement, plastic moments in positive and negative direction of DYM may be different.
conventional and Performance based Seismic design method.We have shown a detail design calculation procedure for frame with one step setback.And compiled the results of all the three frames (10 storey regular & 10 storey irregular with two step setback designed in similar manner .Following are the three frame models considered for the study. Basic Dimensions for the frames and general design parameters were taken coomonly as follows.
Type of frame:Moment Resistant frame Size of Column = 450 x 450mm Size of Beam = 350 x 500 mm
n i=1
Fihi p = 2. Mpc p + n
i . (Mpb positive +
Thickness of Slab = 125mm thick
Mpb negative )i (9)
Wall thickness = 150mm
Floor Finish = 1 KN/m2
n i=1
Fihi p = 2. n
Fihi p + n
(1 +
Live load at all floor levels = 2 kN/m2
i=1
i=1
x )i . (Mpb positive )i (10)
Zone III, Medium type of soil.
i Mpb positive = i
n
i=1
Fi hi 2Mpc
L
(11)
i=1
(1+x) n
i L i
Where x is the ratio of the absolute value of negative Bending moment to positive Bending moment.

Design of Non Designated Yielding Members (NONDYM)
Members that are not designated to yield (Non DYM), such as columns in, must be designed to resist the combination of factored gravity loads and maximum expected strength of the DYM by accounting for reasonable strain hardening and material over strength.. According to the concept of column tree is used to design the columns. The columns must be designed for maximum expected forces by including gravity loads on beams and columns and by considering a reasonable extent of strainhardening and material over strength in the beam plastic hinges.
Mpr= Mpb = 1.25Mpb. (12)
The overstrength factor ( ) was taken as 1.25 which was established recognizing all these effects in ACI 318 (Moehle et al, 2008).when the frame reaches its target drift the
Figure 1Plan &Elevation of 10 storied regular and irregular frames considered for study
Table 4 Seismic parameters considered for design


COMPARATIVE PERFORMANCE EVALUATION OF REINFORCED CONCRETE MOMENT RESISTANT FRAME
Seismic zone factor Z
0.16
Soil Profile Type
Type 2 Medium
Importance factor, I
1
Sa Inelastic
0.1875 g
T
0.8s
Yield drift ratio y
0.5%
Target drift ratio u
2%
Inelastic drift ratio (u – y)
1.5%
Ductility factor
4
Reduction Factor due to
Ductility R
4
Energy Modification Factor
0.43
Design Base shear
816.832
Capacity spectrum curve is actual plot representing the performance point i.e intersection point of spectral displacement and spectral acceleration. It is clear that in PBSD method performance point (intersection of demand and capacity curves) shifts due to extra confined steel which is normally incorporated in design. Hence provision for extra ductility is avoided since this care is already taken while designing.
Table No 7 Performance point comparison for Irregular frame with one set back
Performance point parameters
I.S 1893 method
PBSD
method
Base shear vs Displacement
2575
3535
Spectral acceleration vs
Spectral displacement
0.278
0.421
Effective Time
1.122
0.951
Table No.5 Steel area calculation for beams
4000
2000
0
for
For
Series1
Story
B
d
Mpr
+ve
Ast (mm2)
Mpr – ve
Ast (mm2
10
350
500
867
6015
975
6131
09
350
500
865
6003
977
6143
08
350
500
891
5859
1001
6287
07
350
500
855
5943
986
6197
06
350
500
848
5901
994
6245
05
350
500
838
5841
1004
6305
04
350
500
819
5728
1022
6413
03
350
500
791
5560
1051
6586
02
350
500
739
5249
1102
6891
01
350
500
760
5375
1082
6771
1893 PBSD
Performance point (V ,D)
Table No6 Steel for columns
0.6
0.4
0.2
0
for 1893
For PBSD
Series1
Widt h
Dept h
Ac(mm 2)
Fck(N/mm 2)
fy N/mm
2)
Axial force
Ast(mm 2)
450
450
202500
20
415
624.797
1
1620
450
450
202500
20
415
1260.86
1
1620
450
450
202500
20
415
1896.92
5
1620
450
450
202500
20
415
2532.98
8
3402
450
450
202500
20
415
3169.05
2
5811
450
450
202500
20
415
3805.11
6
8344
450
450
202500
20
415
4441.17
9
10602
450
450
202500
20
415
5077.24
3
12966
450
450
202500
20
415
5713.30
7
15208
450
450
202500
20
415
6349.37
17621
Performance point (Sa, Sd)
1.2
1.1
1
0.9
0.8
for 1893
For PBSD
Series1
Performance point (Teff)
Fig 2 Push over curve comparison for I.S 1893 method and PBSD method for irregular frame with one step back.
Table No 8 Performance point comparison for Irregular frame with two step setback
Performance point parameters
I.S 1893 method
PBSD
method
Base shear vs Displacemet
2770
3990
Spectral acceleration vs
Spectral displacement
0.32
0.514
Effective Time
1.13
0.78
0.6
0.4
0.2
0
Series1
for 1893 For
PBSD
Performance point (V, D
1.5
1
0.5
Series1
0
for 1893 For PBSD
Performance point (Sa, Sd)
1.2
1
0.8
0.6
0.4
0.2
0
Series1
for 1893For PBSD
Performance point (Teff)
Fig3Push over curve comparison for I.S 1893 method ad PBSD method for irregular frame with two steps back

TIME HISTORY ANALYSIS
In order to get a validation of performance with nonlinear static analysis this study includes nonlinear time history analysis and comparison of all the three frames designed by both methods ie (By I.S 1893;2002 method and Performance
based Seismic design method). We have considered 4 standard ground motions(Superstition Hills1987 (Brawley), Imperial Valley, 1940(El Centro), 1989 Loma Prieta (Corralitos Station), 1994 Northridge (Santa Monica City Hall), Imperial Valley, 1940 (El Centro) Intensity factor=2.0). These ground motions are taken considering their maximum intensity and peak ground acceleration. After performing the time history analysis the major aspect considered is displacement. Hence this aspect is studied with reference to height of the structure. Since the building is 10 story, we had considered 6 intervals as shown. Time history results for regular, and two irregular frames designed by I.S 1893; 2002 and PBSD method are shown below.
0.01
Regular
M1 M2
2.00E02
1.50E02
1.00E02
5.00E03
0.00E+00
s
1 2 3 4 5 6
0.015
Regular
Regular 1st step
2nd step
1.5
1
0.5
1 2 3 4 5 6
0
M2
0.005
M1
Fig4 Comparative summarization of the three frames designed by 1893; 2002 and PBSD method
3
2
7
12
No of mode shapes
0
Figure 5 Time period and mode shape variation Curve for frames designed by PBSD method
observed from the table and graph it is For irregular frame with two step setback at top it is seen that the time period decreases initially up to 4th mode and then follows same trend as that of other irregular frame and regular frame. This indicates that for irregular frame, if designed by PBSD method it is more efficient than conventional I.S.1893; 2002 method.

CONCLUSION
Following points are observed during whole design process; The Performance Based Seismic Design method is based on the strong column weak beam concept in which the beams
are designed as per plastic moments calculated .And columns
are designed which ensures larger life safety of the structure. Performance objective was first decided and lateral forces are determined using inelastic design spectra which incorporate to actual behavior of the structure. These lateral forces are distributed according to new distribution factor which is defined on basis of real ground motion. Basic difference between regular and irregular frame design is for upper storey the calculations for base shear decreases due to asymmetry. This method requires little or no evaluation after the initial design because the nonlinear behavior and key performance criteria are built into the design process from the start. Performance point of the frames designed by PBSD method is enhanced than for all frames designed by conventional method. For the irregular frame with two step setback when designed by conventional method (I.S 1893;2002) method displacement is maximum than other two frames after performing time history analysis. For the irregular frame with two step setback when designed by PBSD method the displacement is lowes after time history analysis compared to the irregular frame with one step setback and regular frame. This proves the degree of reliability of Performance based seismic design method. Time period is one of the effective means to check the reliability of PBSD method. Time period for the irregular frame with two step setback is lowest than other two frames. The Performance Based Seismic Design method can be successfully applied to the design of Reinforced Concrete Moment Resistant Frames
REFERENCES:

ASCE, 2000, Prestandard and Commentary for the Seismic Rehabilitation of Buildings, FEMA 356 Report, prepared by the American Society of Civil Engineers for the Federal Emergency Management Agency, Washington, D.C.

ASCE, 2006, Standard Methodology for Seismic Evaluation of Buildings. Standard No. ASCE31. American Society of Civil Engineers, Reston, Virginia.

ATC, 1997, NEHRP Commentary on the Guidelines for the Seismic Rehabilitation of Buildings, FEMA 274 Report, prepared by the Applied Technology Council, for the Building Seismic Safety Council, published by the Federal Emergency Management Agency, Washington, D.C

Athanassiadou C.J., Seismic performance of R/C plane frames irregular in elevation, Engineering Structures (2008), Vol 30 , pp.12501261.

Barros.R.C, Almedia .R., Pushover Analysis of Asymmetric 3 Dimensionless building frames., Journal of Civil Engg and management (2005) ,Vol 11, 1pp,312

Barbara B, Pinho.R, Crowley.H., Simplified pushoverbased vulnerability analysis for largescale assessment of Reinforced Concrete buildings, Engineering Structures Vol 30 (2008) pp804820

Goel, S. C., Liao, W. C., Mohammad R. B., and Leelataviwat S., An Energy Spectrum Method for Seismic Evaluation of Structures, Conference on improving the seismic performance of existing buildings and other structures, ATC & SEI Conference, San Francisco, CA., 2009.