Paper No. D013 SEISMIC PERFORMANCE OF STEEL MOMENT RESISTING FRAMES DESIGNED WITH: DISPLACEMENT-BASED AND

STRENGTH-BASED APPROACHES

Dr. S.B. Kharmale1, Dr. V.B. Patil2 and V.S. Revankar3

1Corresponding author, Assistant Professor, Government College of Engineering and Research, Avasari, Maharashtra, E-mail:- kharmale.swapnil@gmail.com Contact (+91)8308456141.

2 Professor, BVB College of Engineering and Technology, Hubli, Karnataka E-mail:- vbpatil.iitb@gmail.com Contact (+91)9164398816.

3 Postgraduate student, BVB College of Engineering and Technology, Hubli, Karnataka, E-mail:- vinodrevankar@gmail.com Contact (+91)9886666869.

ABSTARCT

Steel moment resisting frame (MRF) is still most efficient and favored system among new as well as conventional lateral load resisting systems, for high to medium seismic regions of globe. Significant inelastic deformation capacity offered by this system render it as an effective earthquake resisting structure. Existing design standards/specification for this system still based on elastic force/strength based approach where inelastic behavior is accounted implicitly. Over this last decade performance-based seismic design (PBSD) method has emerged as a promising and efficient seismic design method which explicitly accounts for the inelastic behavior of structural system in the design process. This paper presents a case study of seismic performance comparison of nine-story steel MRF designed with conventional and performance-based design approach. The seismic performance of MRF is evaluated under a suit of various ground motion representing high to medium seismicity using nonlinear static pushover analysis and nonlinear incremental dynamic analysis. The findings of evaluation study showed that the displacement based seismic design method for MRF is significantly more efficient in achieving a certain inelastic displacement/ductility for a given seismic hazards when compared to the existing design standards/specification for this system. Keywords: moment resisting frame, performance-based seismic design, nonlinear static pushover analysis, nonlinear incremental dynamic analysis.

INTRODUCTION

Steel moment resisting frames (MRF) offer high elastic stiffness, substantial ductility and significant inelastic deformation capacity, hence it is considered as efficient earthquake resisting system. A great number of modern mid- and high rise buildings have MRF as the primary lateral load resisting system. The elastic force/strength-based design procedure for this system as per existing design standards have following limitations:- i. Significant inelastic deformation capacity (ductility) of MRF system can not be fully utilized as

the seismic force calculation is based on force/strength based approach where inelasticity is implicitly accounted through response modification factor, R.

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ii. This design procedure lacks in specifying yielding hierarchy and specific provisions to attain selected yielding hierarchy.

In order to overcome these limitations of the elastic force/strength-based design method, the performance-based seismic design (PBSD) philosophy (SEAOC, 1995; BSSC, 2006) proposed various design approaches which consider the inelastic behaviour of the structure explicitly. In performance-based seismic design, the main objective is to achieve a predefined structural response for a specified earthquake intensity level by considering the inelastic response of the structure. The various possible design approaches like the comprehensive design approach, displacement-based design approach, energy-based design approach, perspective design approach, etc can be found in the Vision 2000 (SEAOC, 1995) document and in FEMA 445(BSSC, 2006). Among these approaches displacement-based seismic design is more favored as the use of displacement as performance quantifier is more rational (Ghobarah, 2001). A displacement-based approach of PBSD of various lateral load resisting systems using target inelastic drift and pre-selected yield mechanism, named the performance-based plastic design (PBPD), were recently developed in the University of Michigan. These design methods were based on the concept of modified energy balance equation (Lee and Goel, 2001) where the inelastic energy demand on structural system was equated to inelastic work done when the structure was subjected to monotonic loading up to target drift. These methods utilized the plastic theory in the design process in order to satisfy the desired performance objectives. Details of PBSD methods and step-by- step performance-based plastic design (PBPD) for different earthquake resisting structural system can also be found in the book by Goel and Chao (2009). In order to comment on the benefits and limitations of the PBPD method versus the standard practice till date, it is very much essential to compare the proposed design method with the existing design guidelines practiced in the globe. The primary theme of work presented in this paper is to compare the seismic performance of steel MRF designed with force/strength based approach of existing standards and displacement-based design approach of PBSD. For this purpose, typical nine-storey steel MRF located in high seismic region, is designed for the same seismic hazard using AISC Seismic Provision (AISC 2005a) as a more general existing design standard and PBPD method developed by Lee and Goel (2001). The seismic performance of these designs is evaluated using nonlinear static pushover analysis (NSPA), nonlinear dynamic analyses (NLRHA) under high to medium seismicity and nonlinear incremental dynamic analysis (NIDA). On the basis of results of evaluation study the concluding remarks are summarized in the last sections of this paper. DESIGN OF STEEL MRF USING STRENGTH-BASED AND DISLPACEMENT-BASED APPROACH As per AISC Seismic Provision (AISC 2005 a), steel MRF expected to withstand significant inelastic deformations under the action of strong motion are termed as special moment frames (SMF). Chapter 9 of AISC Seismic Provision (AISC 2005 a) provides detailed provisions for design of this SMF. The seismic force calculations are based on ASCE 7 for minimum design loads in buildings (ASCE, 2005), and inelasticity is only implicitly accounted for through response modification factor, R. For the design of steel MRF system for a high seismic scenario (i.e. SMF), ASCE 7(ASCE, 2005) specifies a response modification factor, R = 8 and a system overstrength factor, Ωo = 3. Therefore, steel MRF are implicitly designed for a target displacement ductility ratio, t (= R/ Ωo =2.67), which is the ratio of response reduction factor and system overstrength factor.

Strength-Based Design of Nine-storey MRF Fig. 1 shows the plan and elevation of a nine-storey study building. Five exterior bays of steel MRF comprises the primary lateral load resisting system and are considered for design by both the approaches. This 9-storey MRF resembles similar geometric configuration as that of 9-storey SAC frames (Gupta and Krawinkler 1999). The building is assumed to have seismic weights of 5000kN per floor, except for the roof, where it is 3500 kN. For the seismic force calculation the study building is assumed to be located in downtown San Francisco. The soil at the site is considered to be Site Class D (stiff soil) and the building occupancy category is assumed as I, based on its use as an office building.

The values of spectral acceleration (for 5% damping) for maximum considered earthquake (MCE) for said locations are Ss = 1.75g at a period of 0.2 second and S1 = 0.870g at a period of 1.0 second. The design spectral acceleration parameters for a period of 0.2 second and 1 second are calculated as per ASCE7: SDS = 1.17g and SD1 = 0.870g. Considering a high seismic design scenario, the value of R and Ωo are taken as 8 and 3, respectively. Thus implicitly this design is for target displacement ductility ratio t = 2.67. The seismic response coefficient, Cs as per ASCE 7 (ASCE, 2005) is

DSs

SCRI

(1)

Thus design base shear, Vb is

b sV C W (2) where, W is total seismic weight. The equivalent lateral forces, Fi at each floor level is obtained by distributing the design base shear, Vb as per IBC (ICC, 2006) specified lateral force distribution. Strength-based approach specifies the elastic analysis of steel MRF with trial sections for floor beams and columns under the gravity load and lateral load combination. For the design of lateral load resisting steel MRF considered in this study contribution of gravity load is very less as compare to lateral load (since gravity load is equally shared by all frames) and hence neglected. Following to elastic analysis, beam and columns sizes are determined by force/strength-based approach (Strength Action). The design method as per AISC Seismic Provision (AISC 2005a) follows the iterative process as outlined in design flow chart (Fig. 2). This strength-based design is designated as “AISC design”.

Figure 2:- Design flow chart as per strength-based approach of AISC Seismic Provision (AISC, 2005a) and ASCE 7 (ASCE, 2005)

Figure 1:- Plan and elevation of nine-storey study building with MRF in exterior bays as lateral load resisting system.

Displacement-Based Design of Nine-storey MRF Performance-based plastic design (PBPD) method for steel MRF by Lee and Goel (2001) considers pre-selected yield mechanism and uniform target drift as performance objectives. The pre-selected yield mechanism for a single bay of steel MRF under the action of unidirectional monotonic loading up to the target drift consists of plastic hinges formation at column bases and at both ends of all floor beams as shown in Fig.3. As discussed earlier, this design method based on modified energy balance equation. In this concept, the inelastic energy demand on a structural system is equated with the

inelastic work done through the plastic deformations resulted from the unidirectional monotonic loading up to the target drift. This principle, with various modifications, was also used earlier by Chao et al. (2007) for the design of steel braced frames, and by Ghosh et al. (2009) and Kharmale (2011) for the design of steel plate shear walls (SPSW) with pinned and rigid beam to column connections. As per displacement-based design approach (Lee and Goel, 2001) the design base shear, Vb for MRF system is

22 2

21 1

84 where

2

npeb

vi ii

CV C hW T g

(3)

where, Ce (= Sa/g) is normalized design pseudo-acceleration, is energy modification factor, T1 is fundamental time period, hi is the height of ith floor measured from ground, and Cvi (= Fi/Vb) is the lateral force distribution factor, p is the plastic drift. For the design of steel MRF with specific target drift (or target displacement ductility ratio, t) p can be evaluated by assuming suitable value of yield drift, y (in range of 1.0% to 1.1%). As design consider inelastic state of response of structure, the fundamental time period of elastic system can be suitably increased and preliminary estimate for this can be made using the expression for Teq given by Chopra and Goel (2001). The lateral force distribution specifically developed for PBPD method by Chao et al. (2005) can be used for evaluating, Cvi. However considering the recent study by Kharmale and Ghosh (2012) on lateral force distribution for ductility-based design of SPSW any code-based lateral force distribution can also be suitable for PBPD of structures. After evaluating Vb and its floorwise distribution, beam and column sizes are obtained as per design steps mentioned flow chart (Fig.4).

Figure 3:- Pre-selected yield mechanism

for PBPD of MRF

Figure 4:- Design flow for PBPD of MRF (Lee and Goel, 2001)

In order to compare the seismic performance of steel MRF designed with two different approaches, same nine-storey MRF is also designed with displacement-based approach (Lee and Goel, 2001). This design is based on same ASCE 7 (ASCE, 2005) elastic response spectra as used for AISC design and is for target displacement ductility ratio, t = 2.66. This value of t (= 2.66) corresponds to the same displacement ductility ratio which is implicitly prescribed in ASCE 7. The design of MRF follows the design flow chart given in Fig.4. This displacement-based design is designated as “PBPD design”.

Figure 5 provides the sectional details for MRF designed with both approaches. Table 2 provides various design parameters for both designs.

Figure 5:- Sectional details of: - (a) AISC design, (b) PBPD design

Table 1:- Various design parameters for AISC and PBPD designs

Parameters AISC design PBPD design

Total seismic weight, W (kN) 43500 43500 Fundamental time period, T1 (s) 1.27 1.48 Pseudo-acceleration, Sa/g for (T1, = 5%) from ASCE7 (ASCE,2005) spectra

0.683 0.588

Design base shear, Vb (kN) 6344 4677

Lateral force distribution and equivalent lateral forces at each floor level, Fi (kN)

IBC (ICC, 2006) F1 = 24.3, F2 = 97.7, F3= 219, F4 = 389,

F5 = 608, F6 = 876, F7 = 1192, F8 = 155,

F9 = 1380.

Chao et al. (2005) F1 = 52, F2 = 105, F3= 162, F4 = 229,

F5 = 309, F6 = 414, F7 = 573, F8 = 894,

F9 = 1939.

SEISMIC PERFORMANCE EVALUATION OF STEEL MRF DESIGNED USING STRENGTH-BASED AND DISLPACEMENT-BASED APPROACH There exist inherent uncertainties in probable earthquake loading and corresponding response. Hence, any design process should involve a demand/capacity evaluation at different performance level like immediate occupancy, life safety, and collapse prevention. Seismic performance evaluation includes the estimation of capacity and demand of structural system in terms of forces and or displacements. This section deals with seismic performance evaluation of nine-storey steel MRF which is designed in previous section by two different design approaches. This evaluation is carried out through nonlinear static pushover analysis (NSPA), nonlinear response history analysis (NLRHA) and nonlinear incremental dynamic analysis (NIDA) on the analytical models of nine-storey steel MRF.

Analytical Model of Nine-Storey Steel MRF A centerline lumped mass model of both designs of nine-storey steel MRF is developed using nonlinear beam-column element of the structural analysis program DRAIN-2DX (Prakash et al.,

(a) (b)

1993). For all the elements, the material is assumed to be elastic perfectly plastic steel with yield stress (Fy) = 344.74 MPa and without any overstrength factor. For all analyses the geometric nonlinearity and the nominal lateral stiffness from gravity frames are neglected. The hysteresis behaviour of the structure is assumed without strength and stiffness degradation.

Nonlinear Static Pushover Analysis (NSPA) NSPA is used to evaluate the expected performance of a structural system by estimating its strength and deformation demands in design earthquakes. This evaluation is based on an assessment of important performance parameters, including global drift, interstory drift, and inelastic element deformations. The IBC 2006 (ICC, 2006) recommended lateral force distribution is used for NSPA of both design model. Each model of design is subjected to the unidirectional monotonic push till the respective target displacement so as to induce significant inelastic deformations in the system. The roof displacement versus base shear plot is bilinearized by equating the areas under the actual pushover curve and the approximate one and yield point (yield displacement, Dy; yield base shear, Vby) is obtained for each design. For each design, yield drift, y (the ratio of yield displacement, Dy and total height, H of MRF system) and yielding hierarchy is obtained from NSPA. This y is later used for the calculation of achieved displacement ductility ratio, a.

Nonlinear Response History Analysis (NLRHA) The method consists of performing a time-history analysis in the non-linear domain. The seismic action is directly applied, by means of accelerograms, at the base of the structure. In order to investigate the performance of MRF in high to medium seismicity, NLRHA is performed under the ground motion records of 1940 El Centro, 1967 Koyna, 1995 Northridge, and 1999 Chamoli (NW Himalaya) earthquakes. Details of these ground motion record is given in Table 2 and Fig. 6

Table 2:- Details of ground motion records for NLRHA (source:- http://peer.berkeley.edu and http://db.cosmos-eq.org )

Earthquake Station PGA Scale Factor AISC design PBPD design

1940 El Centro IMPERIAL VALLEY 0.215g 2.12 3.14 1967 Koyna ----- 0.474g 7.00 5.50 1995 Northridge SEPULVEDA VA 0.939g 1.57 2.21 1999 Chamoli (NW Himalaya) GOPESHWAR 0.360g 5.78 6.70

MRF system is assumed to be a lumped mass model with 5% Rayleigh damping in the first two modes of vibration. For NLRHA of each design under specific record, the acceleration time history of each earthquake is scaled through scale factor (Table 2) so as to have the same design spectral acceleration at the fundamental period T1. Figure 7 gives calculation of typical scale factor for 1967 Koyna earthquake. The ultimate drift (ratio of ultimate displacement, Dm to total height of MRF, H) and the absolute floor displacement at an instant of ultimate roof displacement are obtained from NLRHA of both designs under four different ground motion records. The floor displacement profiles at an instant of maximum roof displacement are obtained by plotting the absolute floor displacement across the height of MRF.

Figure 7:- Scale factor calculation for NLRHA under 1967 Koyna earthquake

Figure 6:- Acceleration time history of ground motions for NLRHA of MRF designs

Nonlinear Incremental Dynamic Analysis (NIDA) Nonlinear incremental dynamic analysis provides thorough estimation of structural performance under seismic loads. It involves subjecting a structural model to one (or more) ground motion record(s), each scaled to multiple levels of intensity, thus producing one (or more) curve(s) of response parameterized versus intensity level (Vamvatsikos and Cornell, 2005). For the scope of work presented in this paper, a single record IDAs are obtained by subjecting both designs of MRF to 1995 Northridge earthquake which is relatively strong motion record among other earthquake record considered in this study. This single record IDA has peak ground acceleration as an intensity measure and maximum inter-storey drift as a damage measure. For each design incremental dynamic analysis is carried out till the maximum inter-storey drift reaches to 5%.

RESULTS AND DISCUSSION

This section presents results obtained from NSPA, NLRHA and NIDA. On the basis of these results, seismic performance of both (force/strength-based and displacement-based) designs of nine-storey steel MRF is discussed.

As discussed before, the roof displacement versus base shear plot obtained from NSPA of both design models is bilinearized to obtain yield point (Dy, Vby). For AISC design the yield point is (0.371 m, 5552 kN) and same for PBPD design is (0.426 m, 5053 kN). For PBPD design, initial assumption of yield drift, y is required in the range of 1.0% to 1.1% (design flow chart of Fig.4) and the yield drift obtained (y = 1.18%) from NSPA is near to its initial assumption which indicates the PBPD model exhibit exactly same lateral load resisting behaviour as assumed in design formulation. In addition to y calculation, NSPA provides the information regarding the inelastic activity in each member of MRF system. Fig. 8 provides pushover plot along with yielding hierarchy for both design as obtained respective NSPA. From these yielding hierarchies, it can be observed that PBPD design exhibit more gradual and sequential yield pattern as compare to that of AISC design. There is no soft-storey collapse mechanism till the end of analysis for PBPD model whereas a soft storey collapse mechanism at sixth storey of AISC design model limits its reserve inelastic deformation capacity. Fig 8.b also proves that the pre-selected yield mechanism as assumed in PBPD design is almost achieved and hence one of the performance criteria is satisfied for the case of PBPD.

Figure 8:- Pushover plots with yielding hierarchy from NSPA of (a) ASIC design, (b) PBPD design.

The ultimate roof displacement, Dm obtained from NLRHA of each design under specific ground motion record is used to obtain the achieved displacement ductility, a as ratio of Dm to Dy. Table 3 provides the calculation of a and percentage difference between a and t for each design against each ground motion record. It should be noted that for AISC design there is no direct recommendation for t however, the use R = 8 and Ωo = 3 as per ASCE 7 implicitly accounts for t = R/ Ωo. = 8/3 =2.67. For comparison of seismic performances of designs by both approaches, PBPD design is also achieved for t = 2.67. From this table it can be observed that PBPD design is more effective in achieving the intended ductility ratio as percentage difference between a and t is comparatively less than that for AISC design for which average percentage difference is −46.0 %.

Table 3:- Result summary for achieved displacement ductility ratio, a for AISC and PBPD designs from NLRHA under different earthquakes

Earthquake t AISC design PBPD design

Dm (m)

Dy (m)

a = Dm/ Dy

%Diff. Dm (m)

Dy (m)

a = Dm/ Dy

%Diff.

El Centro 2.67 0.528 0.371 1.42 −46.5 0.982 0.426 2.31 −13.3 Koyna 2.67 0.496 0.371 1.34 −49.7 0.671 0.426 1.58 −40.8 Northridge 2.67 0.541 0.371 1.46 −45.2 0.901 0.426 2.12 −20.5 Chamoli 2.67 0.568 0.371 1.53 −42.4 0.779 0.426 1.83 −31.3

Average % Diff. −46.0 −26.5 In addition to the ductility achieved in terms of the peak roof displacement, the displacement profiles are also studied in order to check for any localized concentration of plasticity in any storey. Fig. 9 presents displacement profiles from NLRHA at the instant of peak roof drift for both the designs. From this figure it is clearly observed that displacement profile for PBPD design resembles nearly same profile as assumed initially in design process and thus follow assumed plastic mechanism. Fig. 10 presents single record IDA for both the design under 1995 Northridge earthquake. Both AISC and PBPD design shows the hardening although hardening of PBPD design model is more sever than AISC design model. As per AISC Seismic Provision (AISC, 2005a) special moment resisting frames (SMF) should withstand at least 0.04 radian inter-storey drift. From the IDA plot of Fig.10 it is observed that, PBPD design is capable of fulfilling this limit even the time history of Northridge earthquake is scaled by thrice where as AISC design can bear only 1.75 times unscaled (original) seismic hazard of Northridge earthquake.

Figure 9:- Displacement profiles for both designs at the instant of peak roof drift. from NLRHA under (a) Northridge, (b) El Centro, and (c) Chamoli (NW Himalaya) earthquakes.

Figure 10:- Single record IDA for AISC and PBPD designs under Northridge earthquake

CONCLUDING REMARKS

The objective of work presented in this paper is to compare the seismic performance of steel MRF designed with conventional force/strength-based and advanced displacement-based approach. For this purpose nine-storey steel MRF is designed by AISC Seismic Provision (AISC, 2005a) as a more general existing design standard and by PBPD method developed by Lee and Goel (2001). The seismic performance of these designs is evaluated through NSPA, NLRHA and NIDA. The concluding remarks on the seismic performance of these designs are summarized as follows:- 1. The force/strength-based approach lacks in including the actual inelastic deformation capacity of

MRF in design seismic force calculation and hence unable to achieve the specified displacement ductility ratio (R/Ωo).

2. The displacement-based approach include actual inelastic target drift and an energy-based formulation in the design procedure thus, it is found to be very effective in achieving a certain inelastic displacement for a given earthquake scenario.

3. The use of plastic design method in displacement-based approach leads structures to meet a pre-selected performance objective in terms of yield mechanism and target drift.

4. The displacement-based design procedure prevents structures from developing undesirable collapse mechanism (such as a soft-story mechanism) even under action of strong motion record.

5. The displacement-based approach of design offer very simplistic design solution while satisfying an advanced earthquake resisting design criterion hence this approach should be treated as prospective candidate for design codes.

REFERENCES

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