a simplified modal pushover analysis procedure based on

Paper ID # The 7th

Asia Conference on Earthquake Engineering, 22-25 November 2018, Bangkok, Thailand

XXX-X-XXXX-XXXX-X/XX/$XX.00 ©20XX 7ACEE

A Simplified Modal Pushover Analysis Procedure

based on Displacement Modification Approach

Fawad Ahmed Najam

NUST Institute of Civil Engineering

National University of Sciences and

Technology (NUST)

Islamabad, Pakistan

[email protected]

Pennung Warnitchai

Department of Civil and Infrastructure

Engineering

Asian Institute of Technology (AIT)

Bangkok, Thailand

line 5: email address

Tahir Mehmood

Department of Civil Engineering

COMSATS Institute of Information

Technology (CIIT)

Wah Cantt, Pakistan

[email protected]

Muhammad Irshad Qureshi

Department of Civil Engineering

University of Engineering and

Technology (UET)

Taxila, Pakistan

[email protected]

Abstract—This study presents and evaluates a simplified

Modal Pushover Analysis (MPA) procedure for predicting the

nonlinear seismic demands of high-rise buildings with RC

shear walls. This procedure is based on the assumption that the

maximum inelastic displacement of every significant vibration

mode of a structure can be estimated by applying a

modification factor to the corresponding peak elastic

displacement of that mode. This assumption provides a

convenient way to determine the pushover target displacement

for every significant vibration mode. The peaks values of

individual modal responses can be obtained from the multi-

mode pushover analyses at the corresponding target

displacements, which can be combined using a modal

combination rule to approximately determine the overall

nonlinear seismic demands. The seismic demands of three case

study buildings are evaluated using this procedure, while those

obtained from the detailed Nonlinear Response History

Analysis (NLRHA) procedure are used as benchmark. It is

shown that the presented simplified analysis procedure is able

to predict the overall seismic demands as well as individual

modal contributions of case study buildings with a reasonable

accuracy. Therefore, it can serve as a relatively quicker and

convenient analysis option for performance evaluation of high-

rise buildings.

Keywords—Seismic demand, shear wall buildings, modal

pushover analysis, NLRHA, displacement modification

I. INTRODUCTION

Over last several decades, the research efforts for the simplified estimation of nonlinear seismic demands for practically convenient applications have resulted in the conception of two main approaches. These are referred as the “equivalent linearization” and the “displacement modification”. The procedures based on the displacement modification approach are based on the idea that maximum response of the nonlinear single-degree-of-freedom (SDF) system can be estimated by multiplying the displacement of its elastic counterpart with a suitable modifying factor. This modifying factor (which corresponds to the expected ratio of the peak inelastic displacement to the peak elastic displacement) may further be represented as a product of several coefficients, each accounting for a specific aspect of inelastic action. These coefficients are generally derived from the statistical analysis of the results obtained from a

large number of nonlinear and corresponding linear SDF systems subjected to the ground motion records. Using this approach, the nonlinear static procedure (NSP) prescribed in ASCE/SEI 41-13 [1] provides a practical procedure for determining the nonlinear force and displacement demands. This procedure is based on the pushover analysis of nonlinear structural model using the modal inertia force pattern of first vibration mode. Therefore, it is not applicable to high-rise buildings whose response may have significant contributions from higher vibration modes.

This study aims to extend the idea of displacement modification to every significant vibration mode of the structure. For this purpose, an approximate analysis procedure referred to as the Uncoupled Modal Response History Analysis (UMRHA) procedure will be used as theoretical basis. The UMRHA procedure was originally formulated by Chopra and Goel [2] and later simplified into the modal pushover analysis (MPA) procedure. It allows to decompose the complex nonlinear dynamic response of buildings in to contributions from few individual vibration modes. Recently, Ahmed and Warnitchai [3], Mehmood et al. [4, 5], and Najam and Warnitchai [6] have applied the UMRHA procedure to various buildings with RC shear walls and gravity frame systems. These studies have shown that this procedure is able to provide reasonably accurate predictions of story shears, story overturning moments, inter-story drifts, and floor accelerations. Moreover, it also provides an opportunity to clearly understand the individual modal behavior as well as their relative contributions to total response. In this study, using this procedure as a theoretical background, the proposed simplified MPA procedure is applied to various case study high-rise buildings subjected to different types of input ground motions. The accuracy of the proposed procedure is evaluated for demand contributions from individual vibration modes as well as for the combined seismic demands.

II. THE PROPOSED SIMPLIFIED MODAL PUSHOVER

ANALYSIS PROCEDURE – FORMULATION AND BASIC

ASSUMPTIONS

As mentioned in earlier, the UMRHA procedure can be used to approximately decompose the combined dynamic response of buildings in to modal contributions, even when

Paper ID # The 7th


they exceed the elastic limits. This study uses the UMRHA procedure as a theoretical background to propose a convenient and practical analysis procedure for the estimation of nonlinear seismic demands. Therefore, it is necessary to first briefly review the theoretical concepts and underlying assumptions of the UMRHA procedure.

A. The Uncoupled Modal Response History Analysis

(UMRHA) Procedure

The UMRHA procedure can be viewed as an extended version of the classical modal analysis procedure. In the latter, the complex dynamic responses of a linear multi-degree-of-freedom (MDF) structure are considered as a sum of many independent vibration modes. The response behavior of each mode is essentially similar to that of a SDF system, which is governed by a few modal properties, making it easier to understand. Furthermore, only a few vibration modes can accurately describe the complex structural responses in most practical cases. This classical modal analysis procedure is applicable to any linear elastic structures. However, when the responses exceed the elastic limits, the governing equations of motion become nonlinear and consequentially, the theoretical basis for modal analysis becomes invalid. Despite this, the UMRHA procedure assumes that even for inelastic responses, the vibration modes still exist, and the complex inelastic responses can be approximately expressed as a sum of these modal responses. In this procedure, the behavior of each vibration mode is represented by a nonlinear SDF system governed by Equation (1).

�̈�𝑖(𝑡) + 2𝜉𝑖𝜔𝑖�̇�𝑖(𝑡) + 𝐹𝑠𝑖(𝐷𝑖 , �̇�𝑖)/𝐿𝑖 = −�̈�𝑔(𝑡) (1)

Where 𝐿𝑖 is the product of modal participation factor (𝛤𝑖)

and modal mass (𝑀𝑖) of any 𝑖𝑡ℎ mode, while 𝜔𝑖 and 𝜉𝑖 are the natural circular frequency and the damping ratio of the

𝑖𝑡ℎ mode, respectively. To compute the response time history of 𝐷𝑖(𝑡) against a ground acceleration vector (�̈�𝑔(𝑡)), one

needs to know the nonlinear force-deformation function

𝐹𝑠𝑖(𝐷𝑖 , �̇�𝑖) which describes the restoring force produced by

the structure under a deformed shape of 𝑖𝑡ℎ mode. This restoring force function is a combined result of lateral response contributions from all structural components, and is usually selected by idealizing the actual modal cyclic pushover curve for each mode with a suitable hysteretic model. Further details of this procedure and its validation can be seen in Chopra and Goel [2], Ahmed and Warnitchai [3], Mehmood et al. [4, 5] and Najam and Warnitchai [6].

B. From the UMRHA Procedure to the Simplified MPA

Procedure

The underlying assumption of the UMRHA procedure is that the complex dynamic response of MDF structures can be approximately determined from the superposition of few significant vibration modes, and the response of each can be described by a nonlinear modal SDF system. Using this procedure, several studies [3-6] have shown that the response of each vibration mode undergoes a different level of nonlinearity, and therefore, should be treated differently. This realization serves as the primary theoretical rationale for the conception and development of proposed simplified procedure in the current study. The underlying idea is that the peak modal inelastic displacements can be more conveniently obtained by applying the displacement

modification approach separately to the corresponding elastic modal SDF systems. Unlike the first-mode-based displacement coefficient method (DCM) [7], where the full structure is idealized as an equivalent SDF system, the concept can be separately applied to every significant vibration mode of the MDF structure. The suitable modifiers (or coefficients) can be applied to the elastic displacement of all modal SDF systems to estimate the corresponding peak nonlinear displacements, which can then be used as the target displacements for modal pushover analysis (MPA) procedure. The modal combination of peak responses obtained from the multi-mode pushover analyses at the corresponding inelastic modal (target) displacements is expected to provide a reasonably accurate estimate of nonlinear demands. This scheme will be referred onwards as the simplified MPA procedure (abbreviated as SMPA).

Fig. 1 shows a schematic overview of the proposed SMPA procedure as resulted from conceptual simplification of the UMRHA procedure. Following the ASCE/SEI 41-13

[1] NSP guidelines, for any 𝑖𝑡ℎ vibration mode, the monotonic pushover curve of the building can be approximated by the idealized force vs. deformation relationship. The base shear corresponding to the idealized yield point ( 𝑉𝑦,𝑖 ) can be estimated from the idealized

pushover curves of each mode. Extending the ASCE/SEI 41-

13 [1] (or FEMA 440 [7]) expression to any 𝑖𝑡ℎ vibration mode, the value of normalized yield strength factor (𝑅𝑦,𝑖) can

be determined using Equation (2).

𝑅𝑦,𝑖 =

𝐶𝑚,𝑖𝑆𝐴,𝑖

𝑉𝑦,𝑖/𝑊 (2)

Where 𝐶𝑚,𝑖 is the effective modal mass participation

factor and 𝑆𝐴,𝑖 is the spectral acceleration at the initial natural

period (𝑇𝑖) of any 𝑖𝑡ℎ vibration mode. 𝑊 is the total seismic weight of the structure. ASCE 41-13 [1] denotes the yield strength factor as 𝜇𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ instead of 𝑅𝑦 . However, being

consistent with generally used notation, this factor will be denoted onwards as 𝑅𝑦 in the current study. For each

significant 𝑖𝑡ℎ vibration mode, the value of yield strength factor ( 𝑅𝑦,𝑖 ) can be determined and (along with other

affecting parameters e.g. the post-yield stiffness ratio, 𝛼𝑖 ) can be used to estimate the suitable displacement modification factors. For the most common nonlinear hysteretic behaviors, a considerable amount of research [8-12] has been conducted already in recent years to derive the peak inelastic-to-elastic displacement ratios (IDRs, denoted as 𝑥𝑖𝑛/𝑥𝑒𝑙 ). These IDRs can be used as a suitable

displacement modification factors for any 𝑖𝑡ℎ vibration mode. Similar to the ASCE/SEI 41-13 [1] expression, the

target displacement (𝛿𝑇𝑖) for any ith vibration mode can then be determined using Equation (3).

𝛿𝑇𝑖 = 𝛤𝑖 (

𝑥𝑖𝑛

𝑥𝑒𝑙

) 𝑆𝐴,𝑖

𝑇𝑒𝑖2

4𝜋2𝑔 (3)

Where 𝛤𝑖 is the modal participation factor and 𝑇𝑒𝑖 is the effective time period corresponding to the initial slope of

idealized pushover curve for any 𝑖𝑡ℎ vibration mode. The peak modal responses ( 𝑟𝑖 ) at the corresponding target displacements (𝛿𝑇𝑖) are extracted from the pushover results

Paper ID # The 7th


and are combined using the SRSS modal combination rule to get the overall peak response (𝑟) using Equation (4).

𝑟 = (∑ 𝑟𝑖2

𝑚

𝑖=1

)

1/2

(4)

Where 𝑚 is the number of significant vibration modes.

In the current study, the results from another detailed parametric study conducted by Najam et al. [13] will be used to determine the suitable displacement modifying coefficients for every significant vibration mode of selected case study buildings. This study aimed to derive the peak inelastic-to-elastic displacement ratios (IDRs) for the hysteretic behaviors and their controlling parameters describing the cyclic behavior of selected case study buildings.

III. CASE STUDY BUILDINGS AND GROUND MOTIONS

In this study, the simplified MPA procedure is applied to three existing high-rise case study buildings. These buildings (20-, 33- and 44-story high, denoted as B1, B2 and B3, respectively) are located in Bangkok, the capital city of Thailand, and are only designed for gravity and wind loads. They are selected to represent a range of typical existing RC shear wall buildings in many countries around the world. All three case study buildings have a podium (for first few stories) and a tower continued up to the roof level. The primary gravity-load-carrying system in B1 is RC beam-column frame with RC slabs, while B2 and B3 have the flat plate system (RC column-slab frame). The lateral load in all three buildings is mainly resisted by a number of RC walls and cores. All three buildings have mat foundation resting on piles. Masonry infill walls are also extensively used in these buildings. Salient structural and architectural features of these buildings are given in Table 1.

TABLE 1: BASIC GEOMETRY AND CHARACTERISTICS OF CASE STUDY BUILDINGS

Building B1 B2 B3

Height (𝑚) 60 116 152

No. of stories 20 33 44

Typical story height (𝑚) 2.8 3.5 3.5

Height of podium (𝑚) 14 22 43

Natural periods of

first three

translational vibration

modes (sec)

𝑥 direction

𝑇1 1.44 2.81 2.79

𝑇2 0.38 0.60 0.71

𝑇3 0.17 0.31 0.33

𝑦 direction

𝑇1 2.12 3.21 3.61

𝑇2 0.63 0.97 1.12

𝑇3 0.21 0.47 0.31

RC wall section area/total building

footprint area (%) 0.40 1.22 0.99

RC column section area/total building

footprint area (%) 1.20 2.20 1.80

The detailed nonlinear response history analysis (NLRHA) procedure is carried out using a suite of compatible ground motion records. The 3D inelastic finite element models of case study buildings are created in Perform 3D [15]. Each RC wall is modeled by nonlinear concrete and steel fiber elements over the entire height since flexural cracking and yielding may occur at any location due to the higher-mode effects. Each RC column is modeled by a combination of a linear elastic beam-column element with nonlinear plastic zones at its two ends. The concrete slabs are

assumed to remain elastic and are modeled by elastic thin shell elements. Each masonry infill wall is modeled by two equivalent compression-only diagonal struts following the FEMA 356 [14] guidelines. The inherent modal damping ratio of 2.5% is assigned to every significant vibration mode.

Fig. 1. The basic concept of the simplified modal pushover analysis procedure

A set of seven ground motion records (𝑀𝑤 6.5 – 7.5) are selected from the PEER [16] strong ground motion database. They are recorded on relatively near-source sites (< 50 Km) with site class D. The ground motions are scaled and adjusted by spectral matching [17] to match with a 5% damped design basis earthquake (DBE-level) target response spectrum prescribed in ASCE 7-05, corresponding to a building site with 𝑆𝑠 = 1.5g and 𝑆1 = 0.75g. Fig. 3 shows the target and matched acceleration response spectra of the selected ground motions.

F

DF

D

F

D

Mode 1Mode 2

Mode 3

Uncoupled Modal Response History Analysis (UMRHA)

NLNL NL

…

Modal Pushover Analysis (MPA)

The Simplified MPA Procedure

Paper ID # The 7th


IV. RESULTS AND DISCUSSION

The nonlinear models of case study buildings are first subjected to the detailed NLRHA procedure to compute the true inelastic seismic demands. These demands are used as a benchmark to gauge the overall accuracy of the proposed simplified MPA procedure. To obtain further insight to the composition of these demands, the UMRHA procedure is also carried out. The modal contributions of various key response quantities (obtained from the UMRHA procedure) are used to evaluate the demand predictions of the proposed simplified MPA procedure for individual vibration modes.

For the proposed procedure, the multi-mode pushover analysis for few significant vibration modes is carried out for case study buildings. The monotonic modal pushover curves were obtained and approximated as a bilinear 𝑉𝑦,𝑖 − 𝑥𝑖

𝑟

relationship by following the pushover idealization scheme prescribed in ASCE 41-13 [1]. The following approximation scheme is used to locate the idealized yield point and to determine the post-yield stiffness [1].

For any 𝑖𝑡ℎ -mode pushover curve, the first line of the idealized force–displacement relationship starts from origin and have a slope equal to the effective lateral stiffness (𝐾𝑒,𝑖).

This effective stiffness is defined as the secant stiffness corresponding to the 60% of the effective yield strength ( 𝑉𝑦,𝑖 ) of that mode of the structure. The effective yield

strength (𝑉𝑦,𝑖 ) cannot be taken greater than the maximum

base shear (𝑉𝑏). The second line represents the positive post-

yield stiffness (𝛼𝐾𝑒,𝑖) and connects the point corresponding

to the target displacement (𝛿𝑇𝑖) on actual pushover curve and the point at the intersection with the first line such that the areas above and below the actual pushover curve are approximately balanced. For the post-peak behavior, the ASCE 41-13 [1] also recommends a third line having the negative post-yield stiffness slope determined by the point corresponding to the target displacement (𝛿𝑇𝑖) (or the peak base shear) and the point at which the base shear degrades to 60% of the effective yield strength ( 𝑉𝑦,𝑖 ). However, the

computed target displacements for case study buildings were smaller than those corresponding to the onset of negative stiffness and therefore, the bilinear approximation was

enough for their response evaluation using the proposed simplified MPA procedure.

For every significant vibration mode of case study buildings, the yield strength factor (𝑅𝑦 ) is obtained using

Equation (2). This is the most important factor affecting the ratio of peak inelastic displacement to the corresponding elastic displacement of the SDF systems. Table 2 shows the lateral yield strength factor (𝑅𝑦) determined for first three

translational vibration modes of case study buildings in strong (𝑥) direction, subjected to the selected ground motion set.

TABLE 2: THE LATERAL YIELD STRENGTH FACTOR (𝑅𝑦) OBTAINED FROM THE

IDEALIZATION OF MONOTONIC PUSHOVER CURVES OF CASE STUDY BUILDINGS

Mode No. B1 (20-story) B2 (33-story) B3 (44-story)

1 8 6.8 2.9 2 2.5 3.9 2.4

3 <1 <1 <1

The lateral yield strength factor (𝑅𝑦 ) for some cases

(mostly for the higher modes) are less than 1, indicating that their idealized yield strength is higher than the elastic strength demand imposed by the ground motions. The response of such cases will remain linear elastic and therefore, the elastic displacement (without any modification) is used as the target displacement in the simplified MPA procedure. For cases with 𝑅𝑦 > 1, the

suitable modifying coefficients were picked from the detailed database of IDRs developed in Najam et al. [13]. As an example, Fig. 4 shows the peak inelastic-to-elastic displacement ratios for SDF systems modeled using two hysteretic behaviors (bilinear flag-shaped and elastic perfectly-plastic).

Once the displacement modifying coefficients (𝑥𝑖𝑛/𝑥𝑒𝑙) are estimated, the elastic spectral displacement of every significant vibration mode is modified into the corresponding peak inelastic displacement of roof (i.e. target displacement) using Equation (3) and the modal responses (𝑟𝑖 ) from the multi-mode pushover analysis are obtained. The combined

Fig. 2. The acceleration response spectra of ground motions, and 3D views of three case study buildings

(a) 20-story building (B1) (b) 33-story building (B2)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.5 1 1.5 2 2.5 3 3.5 4

Spe

ctr

al A

cce

lera

tio

n (

g)

Period (sec)

5%-damped Target Response Spectrum

Mean of Matched Ground MotionsIndividual Ground Motions

𝜉 = 2.5%

𝜉 = 10%

𝜉 = 5%

44-story

building (B3)

33-story

building (B2)

20-story

building (B1)

Paper ID # The 7th


responses (𝑟) are then determined using the SRSS rule for combining the peak modal demands using Equation (4).

For the three case study buildings, the individual modal story shears obtained from the simplified MPA procedure are compared with envelops of modal contributions obtained from the UMRHA procedure. The results for the first three translational modes in their strong (𝑥) directions are shown in Fig. 4. It can be seen that for B1 and B2, the responses of first and third mode are matching reasonably well with those obtained from the UMRHA procedure. However, the difference in second mode is relatively higher. For B3, all three vibration modes are showing a good agreement with the UMRHA procedure. This shows that the simplified MPA procedure is able to provide a reasonably accurate prediction of nonlinear seismic shear demands for every important mode.

Fig. 5 shows the detailed comparison between the seismic demands of all three case study buildings obtained

by the simplified MPA procedure and the UMRHA procedure with the benchmark NLRHA values for the input ground motions. The story displacement, inter-story drift ratio (IDR), story shear and overturning moment distributions are shown for all cases. It can be seen that the seismic demand estimations from the simplified MPA procedure are reasonably matching with those obtained from the detailed NLRHA procedure (except a slight underestimation in base shear for B1). Similarly, a sufficient agreement between the seismic demands obtained from the simplified MPA procedure and the UMRHA procedure can also be observed for all three buildings.

The presented results show that the simplified MPA procedure can serve as an appropriate analysis option for a convenient and quicker estimation of nonlinear seismic demands in situations where the detailed NLRHA may not be practical. It can provide results of reasonable accuracy with significantly less effort, resources and computational

Fig. 3. The peak inelastic-to-elastic displacement ratios for SDF systems modeled using two hysteretic behaviors (bilinear flag-shaped and elastic

perfectly-plastic).

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 1 2 3 4

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 1 2 3 4

= 2

= 4

= 6= 8

= 2

= 4

= 6= 8

Mean of 30 GMs ( = 0.05) Mean of 30 GMs ( = 0.05)

Time Period (sec)Time Period (sec)

Fig. 4. The performance of the simplified MPA procedure for individual vibration modes. The comparison of modal story shears of all three case study

building subjected to input ground motions

0

5

10

15

20

25

30

35

40

45

0 20 40 60

Story Shear (x106 N)

0

2

4

6

8

10

12

14

16

18

20

0 5 10 15 20

Peak Story Shear (x106 N)

0

5

10

15

20

25

30

35

0 10 20 30 40

Peak Story Shear (x106 N)

SMPA

UMRHA

B1

SMPA

UMRHA

SMPA

UMRHA

B2 B3

Mode 3

Mode 1

Mode 2

Mode 3

Mode 1

Mode 2

Mode 3

Mode 1

Mode 2

Level N

o.

Paper ID # The 7th


cost. Nowadays, various commercially available software packages provide the automated facility of applying the monotonically increasing modal inertia load vectors and obtaining all the response quantities at any desired target displacement of control node (usually at the roof level). This makes it very convenient to perform the multi-mode pushover analysis using such computer-aided analysis packages.

This study is an initial attempt towards evaluating the basic concept of the proposed simplified MPA procedure (i.e. the extension of displacement modification approach to determine the pushover target displacement of every significant vibration mode) for the selected case study buildings. This idea can be expanded in future to other types of structures (exhibiting different hysteretic behaviors). The

use of more detailed investigations for deriving the displacement modifying coefficients may also increase the accuracy of the simplified MPA procedure. Although the current study is limited to structures with cyclic behaviors close to the selected case study buildings, it provides a general understanding of the factors affecting the displacement modifying coefficients and can help in identifying many practical situations where the use of equal-displacement assumption can be highly non-conservative.

V. CONCLUSIONS

This study presented a simplified analysis procedure for the convenient estimation of nonlinear seismic demands of high-rise buildings. It is based on the basic notion of using the mode-by-mode understanding of the dynamic response

Fig. 5. The comparison between the seismic demands obtained by the simplified MPA procedure (SMPA) and the UMRHA procedure with the benchmark

NLRHA values for input ground motions (strong direction (𝑥) of all three case study buildings)

0

2

4

6

8

10

12

14

16

18

20

0 10 20 30 40 50

0

5

10

15

20

25

30

35

0 0.5 1 1.5 2 2.5 3

0

5

10

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20

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30

35

0 500 1000 1500 2000 2500

0

5

10

15

20

25

30

35

0 10 20 30 40 50 600

5

10

15

20

25

30

35

0 0.5 1 1.5 2 2.5

0

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4

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18

20

0 300 600 900 1200

0

2

4

6

8

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14

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18

20

0 0.25 0.5 0.75 1

0

2

4

6

8

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20

0 1 2 3

0

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0 0.5 1 1.5

0

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0 25 50 75 1000

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0 0.5 1 1.5 2 2.5 3

Peak Displacement (mm) Peak Inter-story Drift Ratio (%) Peak Story Shear (x 106 N) Peak Moment (x 106 KN m)



B1

B2

NLRHA Mean

UMRHA Mean

SMPA

NLRHA Mean

UMRHA Mean

SMPA

B3

NLRHA Mean

UMRHA Mean

SMPA

NLRHA Mean

UMRHA Mean

SMPA

NLRHA Mean

UMRHA Mean

SMPA

NLRHA Mean

UMRHA Mean

SMPA

NLRHA Mean

UMRHA Mean

SMPA

NLRHA Mean

UMRHA Mean

SMPA

NLRHA Mean

UMRHA Mean

SMPA

NLRHA Mean

UMRHA Mean

SMPA

NLRHA Mean

UMRHA Mean

SMPA

NLRHA Mean

UMRHA Mean

SMPA

Le

ve

l N

o.

Le

ve

l N

o.

Le

vel N

o.

Paper ID # The 7th


(offered by the UMRHA procedure) as its conceptual basis and motivation. The underlying idea is that the displacement modification approach used in the nonlinear static procedure of ASCE/SEI 41-13 [1] can be extended to every significant vibration mode of the structure. The suitable displacement coefficients can be separately applied to the peak elastic displacement of each mode to estimate the corresponding inelastic displacement, which can then be used as the target displacements for the multi-mode pushover analysis to determine all the response quantities. The accuracy of the proposed procedure is examined by using three case study buildings subjected to seven input ground motion. In this examination, the modal contributions determined from the UMRHA procedure and the overall seismic demands obtained from the detailed NLRHA procedure are used as benchmarks. It is observed that the proposed procedure can provide reasonably accurate estimates of the true seismic demands, either for individual vibration modes or for their sum (total demands), while requiring significantly less computational time and effort compared to the detailed NLRHA procedure. Therefore, it can be considered and developed further as a convenient analysis option for the seismic performance evaluation of high-rise buildings.

REFERENCES

[1] ASCE/SEI 41-13, Seismic evaluation and retrofit of existing buildings. American Society of Civil Engineers. ASCE/SEI, 2013, DOI: 10.1061/9780784412855

[2] A. K. Chopra, R. K. Goel, “A modal pushover analysis procedure for estimating seismic demands for buildings,” Earthquake Engineering & Structural Dynamics, 31(3), 561–582, 2002, DOI: 10.1002/eqe.144

[3] M. Ahmed, Optimal reduction of inelastic seismic demands in high-rise RC core wall buildings using energy dissipating devices. PhD Thesis, Department of Civil and Infrastructure Engineering, 2011.

[4] T. Mehmood, Investigation of nonlinear seismic response of high-rise RC wall structures using modal decomposition technique. PhD Thesis, Department of Civil and Infrastructure Engineering, 2016.

[5] T. Mehmood, P. Warnitchai & P. Suwansaya, “Seismic evaluation of tall buildings using a simplified but accurate analysis procedure,” J. of Earthq. Eng., 1–26, 2017, DOI: 10.1080/13632469.2016.1224742

[6] F. A. Najam & P. Warnitchai, “A modified response spectrum analysis procedure to determine nonlinear seismic demands of high‐rise buildings with shear walls,” The Structural Design of Tall and Special Buildings, Volume27, Issue1, 2018, DOI: 10.1002/tal.1409

[7] FEMA 440, Improvement of nonlinear static seismic analysis procedures. Federal Emergency Management Agency. Redwood City, California, 2005.

[8] A. K. Chopra & C. Chintanapakdee, “Inelastic deformation ratios for design and evaluation of structures: Single-degree-of-freedom bilinear systems,” J. of Structural Engineering, 130(9), 1309–1319, 2004.

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a simplified modal pushover analysis procedure based on

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