Performance Based Seismic Design Of Reinforced Concrete Moment Resistant Frame With Vertical Setback

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 performance-based 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.

1. 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 semi-urban 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 performance-based 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.

2. 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 non-availability 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 time-history analysis after initial design. The methodology for steel frames has been developed by Goel et al., in recent years (1999~2008). It is called Performance-Based Plastic Design (PBPD) method.An outline of the step-by-step Performance-Based Seismic Design (PBSD) procedure is given in the following.

   1. Design Procedure

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

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

      3. Determine the elastic design spectral acceleration value, Sa (Fig 1), by multiplying seismic response

         coefficient, C s, with R

         I

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

      5. Modify V for Reinforced Concrete MF as needed since the force-deformation behavior is different from the assumed EP behavior and P-Delta effect is not considered in the calculation of V in Step 4.

      6. 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 (non-DYM), such as columns, are designed by a capacity design approach.

   2. 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 7-05 (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 7-05 (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 12.8-1 in ASCE 7-05); 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 12.8-2 in ASCE 7-05), respectively.

   3. Design Base Shear

   Assuming an idealized E-P force-deformation behavior of the system as shown in figure, the work-energy

   1

   1

   Note:1 = 0.57 ; = . (((2 1))/ ) sec.

   equation can be written as:

   (Ee + Ep ) = . 1 M. S2 =

3. 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 pseudo-spectral velocity; Sa is the pseudo spectral acceleration, which can be obtained from the seismic design response spectrum in ASCE 7-05 (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 non-degrading 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

   1. 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

4. 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

   1. 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 non-rectangular 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.

   2. Design of Non Designated Yielding Members (NON-DYM)

   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 strain-hardening and material over strength in the beam plastic hinges.

   Mpr= Mpb = 1.25Mpb. (12)

   The over-strength 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

5. 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

6. 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

   2.00E-02

   1.50E-02

   1.00E-02

   5.00E-03

   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.

7. 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:

1. 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.

2. ASCE, 2006, Standard Methodology for Seismic Evaluation of Buildings. Standard No. ASCE-31. American Society of Civil Engineers, Reston, Virginia.

3. 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

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

5. Barros.R.C, Almedia .R., Pushover Analysis of Asymmetric 3 Dimensionless building frames., Journal of Civil Engg and management (2005) ,Vol 11, 1pp,3-12

6. Barbara B, Pinho.R, Crowley.H., Simplified pushover-based vulnerability analysis for large-scale assessment of Reinforced Concrete buildings, Engineering Structures Vol 30 (2008) pp804820

7. 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.