Dissertation2009-Salawdeh

8/13/2019 Dissertation2009-Salawdeh

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Istituto Universitario

di Studi Superiori

Universit degli

Studi di Pavia

EUROPEAN SCHOOL FOR ADVANCED STUDIES IN

REDUCTION OF SEISMIC RISK

ROSE SCHOOL

DISPLACEMENT BASED DESIGN OF VERTICALLY

IRREGULAR FRAME-WALL STRUCTURES

A Dissertation Submitted in Partial

Fulfilment of the Requirements for the Master Degree in

EARTHQUAKE ENGINEERING AND ENGINEERING SEISMOLOGY

by

SUHAIB SALAWDEH

Supervisor:Dr. TIMOTHY SULLIVAN

APRIL, 2009


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The dissertation entitled DISPLACEMENT BASED DESIGN OF VERTICALLY

IRREGULAR FRAME-WALL STRUCTURES, by Suhaib Salawdeh, has been approved in

partial fulfilment of the requirements for the Master Degree in Earthquake Engineering and

Engineering Seismology.

TIMOTHY SULLIVAN ____

_________________


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Abstract

i

ABSTRACT

The objective of this work is to investigate and develop seismic design guidelines for two types of

vertical irregular buildings; (i) vertical irregularity associated with steps in building plan area (core

walls full height and frames that have more bays at base of building than at top), and (ii) vertical

irregularity associated with core walls that stop around mid-height of the building. The work develops

a Direct Displacement Based Design (DDBD) approach which is used to design 12 and 4 story case

study buildings of each structural type. Non-linear time-history analyses are then used to verify the

performance of the method and the results indicate that the DBD approach is very effective for frame-

wall structures with setbacks and is reasonably effective for frame-wall structures possessing cores

that stop at intermediate levels.

Keywords; Vertical Irregularity; setback buildings; Core wall termination.


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Acknowledgements

ii

ACKNOWLEDGEMENTS

I would like to express my appreciation to my advisor, Dr. Tim Sullivan, for his time and effort. His

knowledge, direction, and support helped me to progress in this dissertation.

During my study at MEEES program, I had the opportunity to travel to different countries and meet

great professors and colleagues; I would like to thank them for their friendship and support.

Finally, I would like to thank my Parents, who deserve my highest appreciation, my sisters and

brothers for their love and support, with special thanks for my brother Ihab for his endless support and

encouragement.


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Index

iii

Table of Contents

ABSTRACT ............................................................................................................................................ i

ACKNOWLEDGEMENTS .................................................................................................................... ii

Table of Contents ...................................................................................................................................iii

LIST OF FIGURES ................................................................................................................................ v

LIST OF TABLES ................................................................................................................................. ix

1. INTRODUCTION ............................................................................................................................. 1

1.1 Vertical Irregularities in current design codes: .......................................................................... 1

1.2

Eurocode 8: ................................................................................................................................ 2

1.3 International Building Code (IBC): ........................................................................................... 3

1.4 Failures from past earthquakes: ................................................................................................. 4

1.5 Literature Review on Vertical Irregularities: ............................................................................. 7

2. Displacement Based Design of Dual Frame-Wall Vertically Irregular Structures .......................... 11

2.1 General Behaviour ................................................................................................................... 11

2.2 Design Displacement Profile ................................................................................................... 11

2.3 Equivalent SDOF System characteristics ................................................................................ 15

2.4

Equivalent Viscous Damping................................................................................................... 15

2.5 Identification of the required stiffness and strength ................................................................. 16

3. Design Verification Using Non-Linear Time history Analysis ....................................................... 18

3.1 Introduction: ............................................................................................................................. 18

3.2 Modelling approach and assumptions used for analysis: ......................................................... 18

4. Ground Motions used in this study .................................................................................................. 22

5. Investigation of Frame-Wall Structures with Setbacks ................................................................... 27

5.1 Case study structure ................................................................................................................. 27

5.2

Verification of the method with time history analysis: ............................................................ 31

6. Investigation of Frame-Wall Structures Possessing core walls that stop at mid height .................. 35


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Index

iv

6.1 Case study structure ................................................................................................................. 35

6.2 Design Procedure ..................................................................................................................... 36

6.2.1 Contra Flexure Height .................................................................................................... 36

6.2.2Frame Shear Ratio .......................................................................................................... 37

6.2.3 Design Displacement Profile ......................................................................................... 37

6.2.4 Strength Distribution ...................................................................................................... 38

6.3 Verification of the method with time history analysis: ............................................................ 40

6.4 New Approach for Design Displacement Profile and Strength Distribution ........................... 45

7. Summary and Conclusion ................................................................................................................ 51

7.1 Summary .................................................................................................................................. 51

7.2 Conclusion ............................................................................................................................... 51

7.3

Future Research ....................................................................................................................... 52

REFERENCES ..................................................................................................................................... 54

APPENDIX A ....................................................................................................................................... 57


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Index

v

LIST OF FIGURES

Page

Figure 1-1: Criteria for regularity of buildings with setbacks from Eurocode 8 (CEN, 1998). ..3

Figure 1-2: Soft-story mechanism in the ground floor in a commercial building during 1997

Managua Earthquake in Nicaragua. ....................................................................................5

Figure 1-3: Three-story apartment building, El Asnam, Algeria, damaged in the 1980 in El

Asnam Earthquake. .............................................................................................................6

Figure 1-4: Olive View Hospital, San Fernando, California. Partial View of the 5-story

Medical Treatment and Care Unit (at right and back of the graph). ...................................6

Figure 1-5: Severe failure of the first story corner column in Mene Grande Building during

the Cracas earthquake in 1967. ...........................................................................................7

Figure 2-1: Distribution of shear forces between Frames and Walls. Graph (a) shows the Total

shear, graph (b) shows frame shears and graph (c) shows wall shears. ............................14

Figure 2-2: Distribution of overturning moments between Frames and walls. Graph (a) shows

the Total moment, Graph (b) shows frame moments and graph (c) shows wall moments

and contra flexure height, HCF. .........................................................................................14

Figure 2-3: Displacement Response Spectrum. ........................................................................17

Figure 3-1: Rayleigh damping model as shown in Ruaumoko manual (Carr, 2005). ..............20

Figure 3-2: Giberson one-component member model form Ruaumoko manual (Carr, 2005). 20

Figure 3-3: Modified Takeda hysteresis from Ruaumoko manual (Carr, 2005).. ....................21

Figure 4-1: Northridge earthquake, January 17, 1994, EQ3a. ..................................................22

Figure 4-2: Northridge earthquake, January 17, 1994, EQ3b ...................................................22

Figure 4-3: Imperial Valley earthquake, October 15, 1979, EQ4a. ..........................................23

Figure 4-4: Imperial Valley earthquake, October 15, 1979, EQ4b. ..........................................23

Figure 4-5: Hector earthquake, October 16, 1999, EQ5a. ........................................................23


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Index

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Figure 4-6: Hector earthquake, October 16, 1999, EQ5b. ........................................................23

Figure 4-7: Landers earthquake, June 28, 1992, EQ6a. ............................................................23

Figure 4-8: Landers earthquake, June 28, 1992, EQ6b. ............................................................24

Figure 4-9: Scaled elastic displacement response spectra of 5% damping compared with the

design spectrum. ...............................................................................................................24

Figure 4-10: Average of scaled elastic displacement response spectra of 5% damping

compared with the design displacement spectrum. ...........................................................25

4-11: Displacement response spectra of 15% damping compared with the design spectrum of

15% damping. ...................................................................................................................26

Figure 4-12: Average displacement response spectra of 15% damping compared with the

design spectrum of 15% damping. ....................................................................................26

Figure 5-1: plan view of the case studies associated with setbacks along the vertical plan of

the building. ......................................................................................................................27

Figure 5-2: Displacement-spectrum for 5% damping. ..............................................................28

Figure 5-3: 12 story irregular Frame wall structure associated with setbacks on the frames at

the fourth and seventh floor and full height walls. ...........................................................29

Figure 5-4: 4 story irregular Frame wall structure associated with setbacks on the frames at

the second and third floors and full height walls. .............................................................29

Figure 5-5: Maximum recorded displacements for the eight spectrum compatible

accelerograms compared with the design displacements for the 4-story frame-wall

structure with setbacks. .....................................................................................................32




Figure 5-7: Average of the maximum recorded displacements for the eight spectrumcompatible accelerograms compared with the design displacements for the 4-story

frame-wall structure with setbacks. ..................................................................................33

Figure 5-8: Average of the maximum recorded displacements for the eight spectrum

compatible accelerograms compared with the design displacements for the 12-story

frame-wall structure with setbacks. ..................................................................................33

Figure 5-9: Average of the maximum recorded story drifts for the eight spectrum compatible




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Index

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Figure 6-1: plan view of the case studies associated with walls that stop at mid height of the

building. ............................................................................................................................35

Figure 6-2: 12 story irregular Frame-wall structure where the cores stop at mid height. .........36

6-3: 4 story irregular Frame-wall structure where the cores stop at mid height. ......................36



structure where the walls stop at mid height. ....................................................................40






structure where the walls stop at mid height and the top story beam strengths have been

assigned equal to the strength of the story below. ............................................................41



structure where the walls stop at mid height and the top story beam strengths have been

assigned equal to the strength of the story below. ............................................................42


compatible accelerograms for the normal case and for the case where the top story beam

strengths have been assigned equal to the strength of the story below, compared with the

design displacements for the 4-story frame-wall structure where the walls stop at midheight.................................................................................................................................43


compatible accelerograms for the normal case and for the case where the top story beam

strengths have been assigned equal to the strength of the story below, compared with the

design displacements for the 12-story frame-wall structure where the walls stop at mid

height.................................................................................................................................43


accelerograms for the normal case and for the case where the top story beam strengths


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Index

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have been assigned equal to the strength of the story below, compared with the design

displacements for the 4-story frame-wall structure where the walls stop at mid height. ..44


accelerograms for the normal case and for the case where the top story beam strengths

have been assigned equal to the strength of the story below, compared with the design

displacements for the 12-story frame-wall structure where the walls stop at mid height. 44









frame-wall structure where the walls stop at mid height. .................................................47



frame-wall structure where the walls stop at mid height. .................................................48

6-16: Average of the maximum recorded story drifts for the eight spectrum compatible



6-17: Average of the maximum recorded story drifts for the eight spectrum compatible



Figure 6-18: Average of the maximum recorded story drifts for the eight spectrum compatibleaccelerograms compared with the design displacements for the 12-story frame-wall

structure where the walls stop at mid height and the top story beams strengths assigned

as the strengths of the story below it. ................................................................................49



structure where the walls stop at mid height and the top story beams strengths assigned

as half of the strengths of the story below it. ....................................................................50


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Index

ix

LIST OF TABLES

Page

Table 5-1: Design results for the setback irregularity of the frame wall structure. ..................30

Table 6-1: Design results for the irregular frame-wall structure associated with stopping of the

core walls at mid height. ...................................................................................................39


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Chapter 1. Introduction

1

1.INTRODUCTIONMany structures are designed with vertical irregularities due to functional, aesthetic, or

economical reasons. Vertical irregularities are due to sudden changes in stiffness, strength

and/or mass between adjacent stories. Sudden changes in stiffness and strength between

adjacent stories are associated with changes in structural system along the height, changes in

story height, setbacks, changes in materials and unanticipated participation of non-structural

components (Das, 2000). Many structures have suffered unexpected damage or collapse due

to these types of discontinuities.

Vertical irregularities nowadays have a lot of interest in seismic research investigations. This

report will concentrate on the design of this type of structures using the direct displacement

based design method and verifying the performance of this method using non-linear time-

history analyses.

Two types of vertical irregularity will be investigated in this report: (i) vertical irregularity

associated with steps in building plan area (core walls full height and frames that have more

bays at base of the building than at the top), and (ii) vertical irregularity associated with core

walls that stop at intermediate levels within the building.

The following sections in chapter 1 will explain how vertical irregularity is considered in

current design guidelines such as Eurocode 8 (EC8) (CEN, 1998) and International Building

Code (IBC) (ICC, 2003). The work will then give a description of various building failures

that have taken place during past earthquakes, where these failures were caused by the

presence of vertical irregularities in the structure. Finally, a literature review of some of theprevious work on vertical irregular buildings is explained.

1.1Vertical Irregularities in current design codes:Most building codes propose a simplified method called the equivalent lateral force (ELF)

procedure or the multi-mode response spectrum method to compute design forces. These

methods assume that the dynamic forces developed in a structure during an earthquake are

proportional to the maximum ground acceleration and the modal characteristics of the

structure. These forces are approximated as a set of equivalent lateral forces which are

distributed over the height of the structure. However, the ELF method is based on a number of

assumptions which are true for regular structures structures with uniform distribution ofstiffness, strength, and mass over the height. So the current building codes define criteria in


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order to categorize building structures as either regular or irregular as explained in the

following paragraphs.

1.2Eurocode 8:Eurocode 8 (CEN, 1998) design guidelines contain criteria for classification of vertically

regular and irregular structures, where a structure is defined as being irregular when the

ratio of one of the quantities (such as masses or strength) between adjacent stories exceeds a

minimum prescribed value. For a building to be categorised as being regular in elevation, it

shall satisfy the following:

All lateral load resisting systems, such as cores, structural walls, or frames, shall run without

interruption from their foundations to the top of the building or, if setbacks at different heights

are present, to the top of the relevant zone of the building.

Both the lateral stiffness and the mass of the individual storeys shall remain constant orreduce gradually, without abrupt changes, from the base to the top of a particular building.

In framed buildings the ratio of the actual storey resistance to the resistance required by the

analysis should not vary disproportionately between adjacent storeys.

When setbacks are present, the following additional conditions apply:

a) for gradual setbacks preserving axial symmetry, the setback at any floor shall be not greater than

20 % of the previous plan dimension in the direction of the setback as shown in Figures 1-1(a)

and 1-1(b).b) for a single setback within the lower 15 % of the total height of the main structural

system, the setback shall be not greater than 50 % of the previous plan dimension as

illustrated in Figure 1-1(c). In this case the structure of the base zone within the vertically

projected perimeter of the upper stories should be designed to resist at least 75% of the

horizontal shear forces that would develop in that zone in a similar building without the

base enlargement.

c) if the setbacks do not preserve symmetry, in each face the sum of the setbacks at all

stories shall be not greater than 30 % of the plan dimension at the ground floor above the

foundation or above the top of a rigid basement, and the individual setbacks shall be not

greater than 10 % of the previous plan dimension as illustrated in Figure 1-1(d).

For buildings not conforming to the regularity criteria explained above, Eurocode 8 (CEN,

1998) adopts the modal response spectrum analysis procedure for design. However, non-

linear static (pushover) analysis or non-linear time history analysis procedures can be used as

an alternative for designing this type of irregularity.


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Figure 1-1: Criteria for regularity of buildings with setbacks from Eurocode 8 (CEN, 1998).

1.3International Building Code (IBC):The international Building Code (IBC) (ICC, 2003) lists various types of vertical irregularity

as follows:

1a) Stiffness IrregularitySoft Story: is defined to exist when there is a story in which the

lateral stiffness is less than 70% of that in the story above or less than 80% of the averagestiffness of the three stories above.

1b) Stiffness Irregularity -Extreme Soft Story is defined to exist where there is a story in

which the lateral stiffness is less than 60% of that in the story above or less than 70% of the

average stiffness of the three stories above.

2) Weight (Mass) Irregularity is defined to exist where the effective mass of any story is more

than 150% of the effective mass of an adjacent story. A roof that is lighter than the floor

below need not be considered.

3) Vertical geometric irregularity shall be considered to exist where the horizontal dimension

of the lateral force- resisting system in any story is more than 130% of that in an adjacent

story.


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4) In-plane Discontinuity in Vertical Lateral-Force-Resisting Elements is defined to exist

where an in-plane offset of the lateral-force-resisting elements is greater than the length of

those elements or where there is a reduction in stiffness of the resisting element in the story

below.

5) Discontinuity in Capacity-Weak Story where the weak story is one in which the story

lateral strength is less than 80% of that in the story above. The story lateral strength is the

total lateral strength of all seismic-resisting elements sharing the story shear for the direction

under consideration.

Each structure shall be assigned to a seismic design category in accordance with Section

1616.3 in IBC. Seismic design categories are used in IBC to determine permissible structural

systems, limitations on height and irregularity, those components of the structure that must be

designed for seismic resistance and the types of analysis that must be performed.

In the IBC (ICC, 2003), Buildings having one or more of the features of the 5 points listedabove shall be designated as having vertical irregularity except for types 1a, 1b and 2 when no

story drift ratio under design lateral load is greater than 130% of the story drift ratio of the

next story above, also irregularities of these types are not required to be considered for one-

story buildings in any seismic design category or for two-story buildings in Seismic Design

Category A, B, C or D. In these 2 exceptions the structure is deemed to not have the structural

irregularity.

Structures assigned to be vertically irregular in IBC (ICC, 2003) shall comply with specified

requirements depends upon the Seismic Design Category and the type of irregularity

described above. Also Modal Response Spectral Analysis or Non-linear Time HistoryAnalysis procedures are recommended.

1.4Failures from past earthquakes:Experience from past earthquakes shows that irregular buildings are prone to severe damage.

Where the irregularity is due to changes in stiffness, strength, mass or setback of one floor to

that of an adjacent floor. From the study of various structural failures, it was found that a soft

and/or weak story in any building poses a high risk of damage during a seismic event (Das

and Nau, 2003). Some examples of actual structural failures for past earthquakes due to

vertical irregularity in the lateral force resisting system are described here:

Commercial Building Casa Micasa S.A., Managua, Nicaragua. A 2-story reinforced concrete

frame building (Figure 1-2) which suffered significant lateral displacement at the second floor

level during the 1972 Managua Earthquake.


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Figure 1-2: Soft-story mechanism in the ground floor in a commercial building during 1997 Managua

Earthquake in Nicaragua.

As shown in Figure 1-2 the hinging at the top and bottom of the first story columns were

evident at all locations (Das, 2000). This first story was a soft story because, except for glass

partitions all around, it was completely open, while the second story had walls and partitions

that increased significantly the lateral stiffness of this second story relative to the first.

Some of the buildings in a housing development in Algeria were damaged due to El Asnam

Earthquake in 1980 (Figure 1-3). Although most of the buildings in this new housing

development remained standing after the earthquake, some of them were inclined as much as

20 degrees and dropped up to 1 meter, producing significant damage in the structural and non-

structural elements of the first story. The reason for this type of failure was the use of the

Vide Sanitaire, a crawl space about 1 meter above the ground level. This provides space for

plumbing and ventilation under the first floor slab and serves as a barrier against transmission

of humidity from the ground to the first floor. But the way that the vide sanitaires were

constructed created a soft story with inadequate shear resistance. Hence the stubby columnsin this crawl space were sheared off by the inertia forces induced by the earthquake ground

motion (Bertero, 1997).

The olive view medical centre was a 5 story reinforced concrete structure. Figure 1-4

illustrates the damage that olive view hospital suffered during the 1971 San Fernando

Earthquake. As shown in Figure 1-4 a large permanent lateral second floor level displacement

of the main Treatment and Care Unit was found. This large inter-story drift, which induced

significant non-structural and structural damage and which led to the demolishing of the

building, was a consequence of the formation of a soft story at the first story level because of

the existence of a reinforced concrete wall above the second floor level (Bertero, 1997).


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Figure 1-3: Three-story apartment building, El Asnam, Algeria, damaged in the 1980 in El Asnam

Earthquake.

Figure 1-4: Olive View Hospital, San Fernando, California. Partial View of the 5-story Medical

Treatment and Care Unit (at right and back of the graph).

Analysis of building performance during earthquakes has revealed that numerous building

failures have resulted from the fact that basic structural systems are designed neglecting the


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structural modifications induced by the non-structural components, for example, the Mene

Grande building in Caracas, Venezuela suffered severe damage in the Caracas earthquake

1967. This building, a 16-story reinforced concrete frame with a H-shape plan, had tile walls

in the four exterior ends of the building. The design neglected the interaction effects of these

tile walls. During the earthquake, there was not only considerable non-structural damage to

the tile walls in the lower floors of the building, but there was also severe failure in most of

the first story corner columns, as shown in Figure 1-5 (Das, 2000).

Figure 1-5: Severe failure of the first story corner column in Mene Grande Building during the Cracas

earthquake in 1967.

1.5Literature Review on Vertical Irregularities:Studies aimed to predict the behaviour of structures with vertical irregularities are small in

number compared to the studies aimed to predict the behaviour of structures with horizontal

irregularity. Nevertheless, in recent years research activity in this field has been growing.

Researchers have a lot of studies for the effects of vertical irregularities on the seismic

behaviour of structures. These irregularities are characterised by vertical discontinuities in the

distributions of masses, stiffnesses, and strengths. For the next paragraphs some studies that

consider vertical irregularity associated with setbacks of the structure or stopping of the core

wall at different levels of the structure are listed below:

1) Humar and Wright (1977), using one ground motion record in their study, studied the

dynamic behaviour of multi-storey steel rigid frame buildings with setback towers. They


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found that the difference in elastic and inelastic inter-story drifts between set-back and

regular structures depends on the level of the story considered. For the tower, inter-story

drifts were found to be larger than for regular structures. For the base, inter-story drifts

were found to be smaller in set-back structures than in the regular ones. This observation

agrees with the findings of Pekau and Green (1974).

2) Wood (1986) performed an experimental study on two small-scale set-back frames. She

concluded that the behavior of set-back structures did not differ from the behavior of

regular ones.

3) Aranda (1984) found that the ductility demands of columns and beams are higher for set-

back buildings than for regular ones. Arandas study was performed using soft soil

records from the 1980 Mexico earthquake. He concluded that the increase in ductilities is

more pronounced in the stories above the set-back level.

4) Sharooz and Moehle (1990) studied the effects of set-backs on the earthquake response

on multi-story buildings. They observed, based on analytical studies, a concentration of

damage in the tower due to high rotational ductilities. They performed experiments on a

set-back frame structure and concluded that the fundamental mode dominates the

response in the direction parallel to the set-back, and that using static analysis should be

sufficient to predict the response of set-back structures without the need to perform

dynamic analysis.

5) Wong and Tsu (1994), studied the elastic response of setback structures by means of

response spectrum analysis and found that the modal weights of higher order modes for

setback structures are large, leading to a seismic load distribution that is different from

static code procedures. They also found that for set-back structures, although higher

order modes may contribute more to the base shear than the fundamental mode, the first

mode still dominates the displacement response.

6) Pinto and Costa (1995), studied Set-back structures and concluded that the seismic

behavior of regular and irregular structures are similar. In their study the amount of

discontinuity and the ratio of the base height to the total height were small.

7) Duan and Chandler (1995) pointed out that both static and modal spectral analyses were

inadequate to prevent damage concentration in members near the setback level. This

observation support the need for the development of new methods such as the DBD

procedure proposed in this work.

8) Tena-Colunga (2004) studied two irregular (setback and slender) 14-storey RC moment

resisting framed buildings, with one or two-bay frames in the slender direction. In thiscase, structures were designed close to the limiting drift angle of 1.2%, established by the

Mexican code. Results obtained through nonlinear dynamic analyses suggested that the

slender direction of setback buildings with one-bay frames is vulnerable, contrary to

what occurs if a bay is added in the slender direction thanks to the higher redundancy in

framed structures. The author concluded that seismic codes should penalize seismic

design of buildings with single-bay frames in one direction.

9) Khoury et al. (2005) considered four 9-story asymmetric setback perimeter frame

structuresdesigned according to the Israeli steel code SI 1225 (1998)that differed

with special attention on the influence of the setback level, nonlinear dynamic analyses

were performed, and a 3D structural model was used under bi-directional groundmotions. Results showed amplification in response at the upper tower stories, thus


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suggesting that the higher vibration modes have significant influence, particularly the

torsional ones. In this respect, the authors recommended that future research on setback

buildings should be conducted on full plan-asymmetric structures.

10)Athanassiadou and Bervanakis (2005) studied the seismic behavior of reinforced

concrete buildings with setbacks designed to capacity design procedure provided by

Eurocode 8. In their study, two ten-story frames with two and four large setbacks in the

upper floors respectively, as well as a third one, regular in elevation, have been designed

to the provisions of Eurocode 8 for the high (H) ductility class and a common peak

ground acceleration (PGA) of 0.25g. All frames were subjected to inelastic dynamic

time-history analysis for selected input motions. They found that the seismic

performance of the studied multistory reinforced concrete frame buildings with setbacks

in the upper stories designed to EC8 can be considered as completely satisfactory, not

inferior and in some cases even superior of that of the regular ones, even for motions

twice as strong as the design earthquake. Inter-story drift ratios of irregular frames were

found to remain quite low even in the case of the collapse prevention earthquake with

an intensity double that of the design one.

11)Moehle and Sozen (1980), studied frame-wall structures possessing partial-height walls.

Four 9-story model reinforced concrete structures were built, all possessing the same

overall dimensions. To resist the seismic actions, in parallel to two full height frames,

three of the structures used partial height walls of 1, 4 and 9 stories respectively, and the

fourth had only the two frames to resist the seismic response without the walls. They

found that the variations of top displacements with time of the structures with four and

nine-story walls were nearly identical. The base shears that developed in the walls for

both of these structures was approximately 60% of the total base shear. For the structure

with a single story wall, the base shear in the wall was approximately 95% of the total

base shear. Drifts were considerably greater in the lower stories of the single-story wall

and pure frame structures. Due to the sharp change in story shear stiffness it might have

been anticipated that the use of partial height walls would cause large shear demands

around the point of wall termination. However the study showed that because the

deformations of walls are primarily flexural, large story drifts could develop at

intermediate stories (around the points of wall termination) without the development of

large shears in the wall and frames. This point, together with the observation that top

displacements of the structure with a full height wall were nearly identical to those of the

structure with a four story wall, indicate that the use of partial height walls may be anacceptable frame-wall structural configuration.

12)Moehle (1984) studied the seismic response of four irregular reinforced concrete test

structures. These test structures were simplified models of 9-story 3 bay building frames

comprised of moment frames and frame-wall combinations. Irregularities in the vertical

plane of these structures were introduced by discontinuing the structural wall at various

levels. Based upon measured displacements and distributions of storey shears between

frames and walls, it was apparent that the extent of the irregularity could not be gauged

solely by comparing the strengths and stiffnesses of adjacent stories in a structure.

Structures having the same stiffness interruption, but occurring in different stories didnt

perform equally. It was observed that the curvature ductility demand in beams varied


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from 3.9 to 7.2 and for columns from 1.8 to 2.9, for an abrupt termination of shear walls

at different levels along the height.

13)Moehle and Alarcon (1986) presented a combined experimental and analytical study to

examine the seismic response behaviour of reinforced concrete frame-wall structures. In

one of the models, vertical irregularity in the frame-wall system was introduced by

interrupting the wall at the first story level. Inelastic dynamic analysis was capable of

adequately reproducing measured displacement waveforms, but accurate matches of

responses required a trial and error approach to establish the best modelling assumptions.

It was observed that in the vicinity of the discontinuity, the elements exhibited a

curvature ductility demand 4 to 5 times higher than in the case of the model without any

interruption of the wall.

14)Costa (1990) extended the previous work (Costa et al. (1988)) on seismic behavior of

irregular structures. The study was based on twelve, sixteen, and twenty story reinforced

concrete building models. They found the following conclusions: the role of a shear wall

in a mixed structural system was to distribute the frame ductilities uniformly along the

height, the interruption of a shear wall in part or for the total height of the structure led to

a very irregular distribution of frame ductility, also, a significant increase was observed

in the first level above the interruption of the shear wall. Below the interruption, the

behavior was similar to a regular building.

In summary it can be observed that analytical and experimental investigations by previous

researchers have identified differences in dynamic response of regular and irregular buildings.

Even though there are conflicting conclusions regarding the behaviour of set-back structures,

many of the studies indicate that there is an increase in drifts in the tower of this type of

structures. For the types of irregularities where the wall stops at different heights of the

structures the behaviour was more complex, but many researchers observed increase of

ductility demands on the floor above the termination of the wall.


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Chapter 2. Displacement Based Design of Dual Frame-Wall Vertically Irregular Structures

11

2.Displacement Based Design of Dual Frame-Wall VerticallyIrregular Structures

Nowadays displacement based design is widely spreading in the field of seismic design and

extensive research has been done and is ongoing for various types of structures. Direct

Displacement Based Design (DDBD) of Priestley et al. (2007) is becoming more accepted at

the new approaches in the literature, because of its simplicity and its ability to overcome the

deficiencies that exist in traditional force-based design methods (see Priestley et al. 2007)

The buildings investigated in this report are vertically irregular and have both frames and

walls contributing to seismic resistance. A description of the various steps of the DDBD

procedure mainly taken from Sullivan et al. (2006) proposed for the design of the vertically

irregular frame-wall buildings with irregularity associated with steps in building plan area

(core walls extend to the full height of the structures but the frames have more bays at base of

building than at top) is presented in the following paragraphs:

2.1General BehaviourThe large stiffness variation between frames and walls means that the walls typically yield at

significantly lower lateral displacements than the frames, and hence distributions of lateral

force between walls and frames based on initial elastic stiffnesses have little relevance to the

ductile response of the structure. The design displacement is governed by wall-base material

strains or by wall drift at the contra flexure height, HCF, (the height at which the drift will be

maximum, since the moment reversal occurring above this point reduces the drift in the upperstories as shown in Figure 2-2(c)). The proportion between the contra flexure height, HCF, and

the real height of the structure is chosen by the designer based on experience and judgement,

and the proportions of total based shear carried by frames and walls will be dependent upon

this choice as will be explained later in this chapter.

2.2Design Displacement ProfileThe design displacement profile of frame-wall structures can be gauged by considering the

curvature profile in the walls, as demonstrated by Sullivan et al. (2006). The wall

deformations should consider the elastic and inelastic deformation profiles of the wall.


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12

To gauge the elastic deformation profile, the yield curvature of the rectangular walls, y,wall, is

obtained using Equation (2.1) from (Priestley, 2003). The yield curvature for other sectional

shapes can be found in (Calvi and Sullivan, 2009).

, 2 (2.1)

Where lwall is the wall length and yis the yield strain of the longitudinal reinforcement found

from Equation (2.2):

(2.2)

Where fye is the expected reinforcement yield strength and E is the Youngs modulus of the

reinforcement.

The frame yield drift, y,frame , used later to estimate the ductility and equivalent viscous

damping of the frames is found using Equation (2.3) from (Priestley, 2003):

. (2.3)

Where lb is the average beam length, y is the yield strain of the beam longitudinal

reinforcement and hbis the average depth of the beams at the level of interest.

For the yield displacement profile, the wall curvature profile is assumed to be represented aslinear from the yield curvature at the base to zero at the point of contra-flexure and it is

assumed that the curvature above the contra-flexure point is zero when determining the story

yield displacement. On the basis of these assumptions the yield displacement profile of the

walls, , can be established using the wall yield curvature, y,wall, contra-flexure height, HCF,and story height, Hi, as in Equations (2.4a) and (2.4b):

For HiHCF: ,

(2.4a)

For Hi > HCF: ,

(2.4b)

Design displacements will either be limited by material strains in the wall plastic hinges, or by

drift limitations (more commonly), where drift will be maximum at contra-flexure height,

HCF.

First we check if drift limit of the wall at the contra-flexure height is exceeding the design

drift limit:

Drift limit of the wall at the contra-flexure height, HCF, is given by the Equation (2.5)

, , (2.5)


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13

Where y,wall is the yield curvature of the wall, HCF is the contra-flexure, is the damagecontrol curvature given by Equation (2.6):

.

(2.6)

And Lp is Plastic hinge length for wall which taken as Equation (2.7) from Priestley et al.

(2007):

0.1 (2.7)

Where K is a factor for plastic hinge length found by the expression in Equation (2.8):

0.2 1 (2.8)

where fuand fyare the ultimate and yield strengths respectively.

Lspis the strain penetration length found as in Equation (2.9):

0.022(fyein MPA) (2.9)

Where fye and dbl are the expected yield strength and the diameter of the longitudinal

reinforcement.

If the design drift governs (the drift at the contra-flexure height in equation (2.5) exceeds the

design drift, ) then the design displacement profile will be defined by Equation (2.10):

, (2.10)

Where is the design displacement at level i, is the yield displacement of the wall atlevel i, is the design story drift, y,wallis the yield curvature of the wall, HCFis the contra-flexure height and Hiis the height at level i.

If wall base material strains govern, the design displacement profile will be as shown inEquation (2.11):

(2.11)

To calculate the lateral forces proportions and to find the proportions of base shear for frames

and walls that give the assumed contra-flexure height, distribute the total base shear force to

the floor levels in proportion to the product of mass, mi, and displacement i. As such, the

lateral forces, Fi, expressed as a proportion of the base shear, Vbase, at different levels will be

as shown in Equation (2.12):


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14

(2.12)

The strength proportions as a function of the total shear, Vi, are then set in the frames and

walls respectively up the height of the structure.

In the next chapters the details how to distribute the lateral forces between walls and frames

and assure that the proportion chosen will give the assumed contra-flexure height, H CF, will

be explained for each case study. In this chapter, an explanation will be given for the 12 story

irregular case study structure possessing steps in the building plan up the height of the

structure. First an arbitrary value for the proportion, F, of total base shear, Vbase, carried by

the frames is selected. Then the frame proportions of base shear will be found for the different

floor levels depending upon the number of bays (where beams of equal strengths are used up

the height of the structure). Wall shears are obtained as the difference between the total shear

and the frame shear and the proportions of moment for frames and walls can then becalculated. By trial and error (changing the value of proportion of base shear allocated to

frames), the proportions of the lateral loads carried by frames that gives the assumed contra-

flexure height, HCF, will be found. Figures 2-1 and 2-2 show the distribution of lateral forces

and overturning moments between frames and walls illustrated earlier.

Figure 2-1: Distribution of shear forces between Frames and Walls. Graph (a) shows the Total shear,

graph (b) shows frame shears and graph (c) shows wall shears.

Figure 2-2: Distribution of overturning moments between Frames and walls. Graph (a) shows the Total

moment, Graph (b) shows frame moments and graph (c) shows wall moments and contra flexure height,

HCF.


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15

2.3Equivalent SDOF System characteristicsWith the knowledge of the displacement profile, one can obtain various equivalent SDOF

properties of the structure:

The Equivalent SDOF design displacement is given as shown in Equation (2.13):

(2.13)

Effective mass, mewill be found by from Equation (2.14):

(2.14)

And the effective height is given by Equation (2.15):

(2.15)

2.4Equivalent Viscous DampingThe other characteristic required to define the substitute structure is the equivalent viscous

damping. This can be related to the ductility demands on the structure which can be obtained

as explained next.

The displacement ductility demand in the wall, w, is as shown in Equation (2.16):

,, (2.16)

Where is the design displacement given by Equation (2.13) and ,, is the yielddisplacement of the wall at the effective height which is found by substituting the effective

height He(from Equation (2.15)) into Equation (2.4).

The displacement ductility demand on the frames at each level up the height of the structure

can be obtained using the story drifts as Equation (2.17):

,

, (2.17)

Where frame,iis the frame ductility at level i, i, i-1, hi, and hi-1, are the displacements and

heights at level i and level i-1 respectively, andy,frameis the yield drift of the frame given by

Equation (2.3). Because beams of equal depth and strength are used up the height of the

structure, the ductility obtained from Equation (2.17) for each story can be averaged to give

the frame displacement ductility demand.


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16

To find the equivalent viscous damping, eq, the Takeda Thin (TT) model is used for walls

and Takeda Fat (TF) model is used for frames in line with recommendations of PCK (2007)

as shown in Equations (2.18) and (2.19) respectively.

, 0.05 0.444 (2.18)

, 0.05 0.565 (2.19)

Where wis the displacement ductility demand in the walls and fis the average displacement

ductility demand for the frames.

Once the wall and the frame damping components have been established, the value of

damping for the equivalent SDOF system is determined using the overturning moment for the

unit base shear, as in Equation (2.20).

,, (2.20)

Where MOTM,wis the wall overturning resistance, MOTM,fis the frame overturning resistance.

2.5Identification of the required stiffness and strengthAt this point of the design process, all of the substitute structure characteristics required for

DDBD procedure have been established and as such, the design displacement spectrum is

developed at the design level of damping by applying a damping modifier R to the elasticdisplacement spectrum. In this work the expression used in 2003 revision to EC8 shown in

Equation (2.21) has been adopted:

R ...

(2.21)

The new design displacement is then used to read off (or interpolate between known points)

the required effective period from the displacement spectrum developed at the design level of

damping, as shown in Figure 2-3or Equation (2.22):

(2.22)

With the effective period established, the effective stiffness, Ke, is determined as per Equation

(2.23):

(2.23)

Where meis the effective mass found from Equation (2.14) and Teis the effective period.


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17

Figure 2-3:Displacement Response Spectrum.

The base shear is then obtained by multiplying the effective stiffness, Ke, by the design

displacement, d, as shown in Equation (2.24):

(2.24)

Individual member strengths are then determined by multiplying the strength proportions by

the base shear and reinforcement is set so that the design strength develops at the expecteddeformation demand.


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Chapter 3. Design Verification Using Non-Linear Time history Analysis

18

3.Design Verification Using Non-Linear Time history Analysis3.1Introduction:

In order to verify the performance of the DDBD method used in this report, non linear time

history analyses are carried out with time histories which match the design spectrum used in

the DDBD application. The computer program used for the verification is RUAUMOKO

(Carr, 2005).

The computer program RUAUMOKO has been designed to provide a piece-wise time-history

response of non linear two-dimensional and three-dimensional structures to ground

accelerations, ground displacements or more general time varying force excitations. The

program may also be used for static or pushover analyses.

In this computer program RUAUMOKO, several different options can be used for the

modeling of the Mass, Damping and Stiffness matrices, also the program has a wide variety

of modeling options available to represent the structure and its supports and interactions with

adjoining structures, also a wide variety of member types are available as well, like frame

members, quadrilateral members and other ones to model special effects such as spring and

contact or impact members.

The damping exhibited by the structure can be modeled by the commonly assumed Rayleigh

damping models or by a range of models aimed to give a better representation of the variation

of elastic damping with frequency as well as options for different levels of damping in

different parts of the structural system.

There are a wide range of time-history excitations that may be applied to the structure. The

excitation may be in the form of ground accelerations and these may be applied as a rigid-

body ground motion or as a travelling wave acceleration history. The input may be in the form

of time-varying dynamic loading histories or in the form of ground displacement histories.

3.2Modelling approach and assumptions used for analysis:The modelling approaches used in this report are described as the following paragraphs:

The dynamic equation of equilibrium is integrated by the unconditionally stable implicit

Newmark Constant Average Acceleration (Newmark =0.25) method [Clough et al. 1993]

and an integration time step of 0.01 was adopted.

The lateral forces for the model are resisted by walls and frames.


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19

A lumped mass type was adopted for the structural models, where the mass was provided by

specifying nodal weights which contribute only to the diagonal terms of the mass matrix

associated with the three translational degrees of freedom at each end of the member but the

terms associated with the rotational degrees of freedom are taken as zero.

The traditional damping model available in most time history programs is the Rayleigh or

Proportional damping model (Figure 3-1)where the structures damping matrix is given by

Equation (3.1):

(3.1)

where M and K are the mass and stiffness matrices for the structure. The coefficients and

are computed to give the required levels of viscous damping at two different frequencies,

most commonly those of the first and second modes of free vibration. So the reason for its

popularity is that it uses matrices that the analysis already has computed and requires only thecomputation of the two coefficients and in order to form a damping matrix so that the

analysis may be carried out.

For the case study structures under examination, the non-linear time history analysis was

carried out using tangent stiffness Rayleigh damping, which means that the damping matrix is

based on a Rayleigh damping model which uses the current stiffness of the structure at any

time step as the tangent damping matrix (Carr, 2005). When the structure is inelastic then the

tangent damping matrix changes together with the stiffness matrix throughout the time

history. The damping forces of the structure are adjusted in the time step with the increment

of the damping forces being the product of the tangent damping matrix multiplied by theincremental velocities in the structure. In addition to the stiffness dependant damping force,

however the Rayleigh damping model includes a mass dependent damping force. The

incremental damping forces are then added to the damping forces existing in the structure at

the beginning of the time step to give the damping forces at the end of the time step. In order

to achieve the effect of 5% tangent stiffness damping considering the constant mass

dependent component, 5% damping was specified for the second mode of vibration and an

artificially low damping coefficient, * shown in Equation (3.2) was specified for the first

mode damping in line with the recommendations of Priestley (2007).

./ (3.2)

Where sysis the system ductility found from Equation (2.20), the viscous damping, , was

taken as 5% and the value of the coefficient r was taken as 0.05.


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20

Figure 3-1: Rayleigh damping model as shown in Ruaumoko manual (Carr, 2005).

Only X-direction earthquake was used.

Classical small displacement analysis assumed, where the member stiffnesses are not affected

by the deformations of the structure and the nodal coordinates remain unchanged during the

analysis.

Modal analysis is carried out after the static analysis, even though the results of modalanalysis are not generally used during the dynamic analysis (apart from setting damping

coefficient curve) but it gives a good indication of the different mode shapes.

Base nodes are restrained against displacements and rotations in all axes. But all other nodes

are free for displacement in the x (horizontal) and y (vertical) directions, and free for rotation

about z axis.

Columns and beams are modeled as frame elements, the inelastic behavior of the frame

elements are described by Giberson one-component model (Sharpe, 1974) which has a plastic

hinge possible at one or both ends of the elastic central length of the member as shown inFigure 3-2.

Figure 3-2: Giberson one-component member model form Ruaumoko manual (Carr, 2005).


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21

In the model structures described here, plastic hinges are allowed to be formed at the ends of

the beams and at the bottom of the walls and columns of the ground level.

The inelastic response of members in non-linear time history analysis based on line members

is defined by force-deformation equations describing the loading, unloading and reloading ofthe members. The collective equations describing the response for a given member are termed

the hysteresis rule for the member. The hysteresis behaviors of the inelastic sections for our

case studies are modeled by the modified Takeda-Rule (Otani, 1974), which is shown in

Figure 3-3. The modified Takeda rules are characterized by unloading and reloading

stiffnesses that are significantly lower than the initial elastic stiffnesses. The model

parameters used for beams are = 0.3 and =0.6, and for columns and walls = 0.5 and

=0.0.

Figure 3-3: Modified Takeda hysteresis from Ruaumoko manual (Carr, 2005)..

A bilinear approximation to the moment curvature response, consisting of an initial elastic

branch, and a post yield plastic branch was used.

The elastic moment of inertia about the z axis was found using the slope of the initial branch

in accordance with the following formula: , .The dynamic excitation was applied through a ground acceleration history applied to the x

direction earthquake only. Eight accelerograms compatible with the design spectrum

explained in chapter 4 were used and the average value of the results was used to verify the

design procedure.

To provide information on all the remaining modelling aspects, an example of input file used

for the analysis of the 12 story case study structure possessing setbacks is included in

Appendex A.


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Chapter 4. Ground Motions used in this study

23

Figure 4-3: Imperial Valley earthquake,October 15, 1979, EQ4a.

Figure 4-4: Imperial Valley earthquake,October 15, 1979, EQ4b.

Figure 4-5: Hector earthquake, October 16, 1999, EQ5a.

Figure 4-6: Hector earthquake, October 16, 1999, EQ5b.

Figure 4-7: Landers earthquake, June 28, 1992, EQ6a.

Time [sec]

10095908580757065605550454035302520151050

Acceleration[g]

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

-0.8

Time [sec]

10095908580757065605550454035302520151050

Acceleration[g]

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

-0.8

Time [sec]

605550454035302520151050

Acceleration[g]

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

-0.8

Time [sec]

605550454035302520151050

Acceleration[g]

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

-0.8

Time [sec]

44424038363432302826242220181614121086420

Acceleration[g]

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

-0.8


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24

Figure 4-8: Landers earthquake, June 28, 1992, EQ6b.

The response spectrum for each accelerogram was developed at 5% damping using the

program SeismoSignal and compared with the elastic design spectrum of 5% damping in

order to scale the intensity to match the design response spectrum used for this report.

All the time histories were scaled with the proportions that make the response spectra of these

time histories match with the design spectrum. Response spectra for the scaled accelerogramswere found using the program SeismoSignal with 5% damping value and compared with the

design spectrum as shown in Figure 4-9 which shows a good match. Also Figure 4-10shows

the average of the entire earthquakes response spectra and compares it with the design

response spectrum and it is found that the average of the earthquakes response spectrum

perfectly match the design response spectra in the period of interest at 5%.

Figure 4-9: Scaled elastic displacement response spectra of 5% damping compared with the design

spectrum.

Time [sec]

44424038363432302826242220181614121086420

Acceleration[g]

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

-0.8

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.00 1.00 2.00 3.00 4.00 5.00

Displacement(m

)

Period(sec)

Design

Spectrum5%EQ3a

EQ3b

EQ4a

EQ4b

EQ5a

EQ5b

EQ6a

EQ6b


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25

Figure 4-10: Average of scaled elastic displacement response spectra of 5% damping compared with the

design displacement spectrum.

The DBD procedure requires a modification of the elastic displacement response spectrum to

account for ductile response, where the influence of ductility is represented by equivalent

viscous damping. Seismologists have derived formulas for a damping modifier R to be

applied to the elastic displacement spectrum for different levels of damping . As stated in

Chapter 2, the expression used for the design of the case studies was taken from the 2003

revision to EC8 and is shown in equation (4.1):

R ...

(4.1)

To assure the compatibility between the modified displacement spectrum at the required level

of damping and the response spectra generated by the accelerograms at the same level of

damping; a damping level of 15% was chosen and the damping modifier Rwas found and

applied to the elastic displacement spectrum. In parallel to this, the displacement response

spectra for the accelerograms was found using SeismoSignal with 15% damping value and the

spectra were then compared as shown in Figure 4-11. Also the average of the entireearthquakes response spectra at 15% damping was compared with the modified design

spectrum as shown in Figure 4-12. It is apparent that the match at the design level of damping

is not perfect but can be considered as acceptable.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.00 1.00 2.00 3.00 4.00 5.00

Displacement(

m)

Period(sec)

DesignSpectrum

5%damping

Averageforall

accelerograms


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26

4-11: Displacement response spectra of 15% damping compared with the design spectrum of 15%

damping.

Figure 4-12: Average displacement response spectra of 15% damping compared with the design spectrum

of 15% damping.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.00 1.00 2.00 3.00 4.00 5.00

Displacement(

m)

Period(sec)

Designspectrum15%

EQ3a15%

EQ3b15%

EQ4a15%

EQ4b15%

EQ5A15%

EQ5b15%

EQ6a15%

EQ6b15%

0

0.1

0.2

0.3

0.4

0.5

0.6

0.00 1.00 2.00 3.00 4.00 5.00

Displacement(m)

Period(sec)

Design

Spectrum

15%

Averageforall

accelerograms15%


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Chapter 5. Investigation of Frame-Wall Structures with Setbacks

27

5.Investigation of Frame-Wall Structures with Setbacks5.1Case study structure

The first type of case study structure investigated in this report are the frame-wall structures

that possess a vertical irregularity associated with setbacks up the vertical axis of the building;

in other words for these buildings the core walls extend to the full height of the structure and

the frames have more bays at base of the building than at top.

All the structures investigated have the same plan view shown in Figure 5-1, where the lateral

loads acting along the longitudinal axis of the building in the excitation direction are resisted

by two 8 m walls and 2 frames with setbacks as will be explained in more details later. Note

that the scope of this research includes only a study of the response in the setback direction,

and the response in transverse direction should be studied as part of future research taking into

consideration the torsional behaviour.

Figure 5-1: plan view of the case studies associated with setbacks along the vertical plan of the building.


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28

The case study buildings have a uniform story height of 3m, and the total ultimate dead and

live load is uniformly distributed as 10 KPa for all levels including the roof. All frame bays

are 8m, and the wall length is 8m. The expected material strengths are fce = 40 MPa for the

concrete and fye = 500 MPa for both flexural and transverse reinforcement. The flexural

reinforcing steel is assumed to have a diameter, dbl = 25 mm with a ratio of ultimate to yield

strength of fu/fy = 1.35, and a strain at ultimate strength, su= 0.10. It is assumed that the

structure rests on rigid foundations.

The structure is located in a region with peak ground acceleration (PGA) of 0.30g, with a

displacement-spectrum for 5% damping as shown in Figure 5-2.

Figure 5-2: Displacement-spectrum for 5% damping.

For this type of irregularity 2 buildings were investigated; a 12 story building and a 4 story

building. For the 12 story building the core walls extend to the full height of the building and

the frames have setbacks, with 8 bays in the first three stories, 5 bays from the fourth to the

sixth floor and only 3 bays for the seventh to the last story as shown in Figure 5-3. The length

of each bay is 8 m.

For the 4 story building the core walls also extend the full height of the building and the

frames have setbacks at the second and third floors as shown in Figure 5-4. . In this case study

structure, the ratio of the height to length of the wall is less than three, where shear

deformations of the walls must be taken into account, but it was neglected in this work for

simplicity.

The general procedure for the design of these case studies was as explained in chapter 2.

Some important aspects of the design of these case studies are explained in the next

paragraphs.


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Figure 5-3: 12 story irregular Frame wall structure associated with setbacks on the frames at the fourth

and seventh floor and full height walls.

Figure 5-4: 4 story irregular Frame wall structure associated with setbacks on the frames at the second

and third floors and full height walls.

The design story drift limit of 2.5% was selected for these case studies, which is intended to

control damage of non-structural items of the buildings. Damage of structural items iscontrolled by material strains in the wall plastic hinge.

For the 12-story irregular frame-wall building the proportion between the contra flexure

height, HCF, and the real height, H, of the structure was chosen to be 0.9. Based on the contra

flexure height it was found that the design story drift at the contra flexure height was more

critical and the design was controlled by its value. Using the procedure described in Chapter 2

the proportions of base shear for the frames and walls that give the assumed contra-flexure

height was found to occur when 41.5% of the base shear was allocated to the frames and the

rest to the walls. For the 4-story irregular frame-wall building the contra flexure height, HCF,

was taken the same as the real height, and it was decided to allocate 60% of the base shear tothe frames.


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30

Beams of constant strength up the height of the building are assigned and assuming that beam

moments are carried equally by columns above and below a beam-column joint, the beam

strength obtained from the frame shear is found as in equation (5.1).

, , (5.1)

Where Vi,frameis the frame shear at level i, Mb,iare the beame strengths at level i, and hcol, is

the inter-story height.

Design results for both case studies are presented in Table 5-1:

Table 5-1: Design results for the setback irregularity of the frame wall structure.

4 story irregular FW 12 story irregular FW

Height (m) 12 36

Beam height (m) 0.8 0.6

Beam Width (m) 0.3 0.3

Wall dimensions (L*t) (m) 8*0.15 8*0.20

Contra flexure height (m) 12 32.4

Design story drift 1.98% 2.5%

Design Displacement, d,(m) 0.146 0.479

Percent of base shear allocated to frames 60% 41.5%

Effective Height (m) 8.04 23.04

Wall ductility demand 9.3 3.78

Average Frame Ductility 1.48 1.32

System ductility 5.14 2.83

Frames EquivalentViscous damping 9.51% 7.75%

Walls Equivalent Viscous damping 17.3% 14.8%

System Damping 13.2% 12.1%

Effective Period (sec) 1.53 4.86

Effective Mass (tonnes) 4678.7 11969.4

Effective stiffness (KN/m) 79145 19977

Base Shear (KN) 11538 9563

Design Wall strength (KN.m) 21698 67759

Wall Long. Reinforcement percent 0.5% 1%

Design Beam Strength (KN.m) 649 372

Beam Long. Reinforcement percent 1.75% 1.75%


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5.2Verification of the method with time history analysis:

To investigate the performance of the DBD method for the last case study structures, the non-

linear time history method is used, as this is currently the most accurate method for verifying

if inelastic deformations and rotations satisfy the design limits.

The program Ruaumoko (Carr, 2005) was used to undertake the non-linear time history

analyses using 8 different accelerograms as explained in chapter 4.

For each time history analysis the maximum displacement recorded at each floor is found,

which implies that these recorded displacements include the effects of higher modes.

The maximum floor displacements recorded during time-history analyses for the 8

accelerograms are shown in Figures 5-5 and 5-6 and are compared with the design

displacement profile. The average of the maximum recorded displacement during time history

analyses for the eight accelerograms and the design displacement profile are shown in Figures5-7 and 5-8. It is apparent that there is a very good match between the design displacement

and the maximum displacements recorded from the time history analyses for the 12 story

building. However there was approximately 10% difference for the 4 story building and this is

may be because the displacement spectrum for the accelerograms at 15% damping doesnt

match the design spectrum at 15% damping at the corresponding effective period with a

difference of approximately 9.3%.

The average of the maximum story drifts recorded during time-history analyses using the

eight accelerograms compared with the design drift profile for the case studies is shown in

Figures 5-9 and 5-10. It is found that the design drift profile matches the average of themaximum recorded story drifts for the eight accelerograms for the 12 story building relatively

well. In line with the displacement results, the story drifts for the 4 story building have been

overestimated by around 18% and this may be because the spectra of the accelerograms didnt

perfectly match for the design spectrum at the specified effective period of the 4 story

building.


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Figure 5-5: Maximum recorded displacements for the eight spectrum compatible accelerograms

compared with the design displacements for the 4-story frame-wall structure with setbacks.

Figure 5-6: Maximum recorded displacements for the eight spectrum compatible accelerogramscompared with the design displacements for the 12-story frame-wall structure with setbacks.

0

2

4

6

8

10

12

14

0 0.05 0.1 0.15 0.2 0.25

Height(m)

Displacement(m)

DBD

EQ3a

EQ3b

EQ4a

EQ4b

EQ5a

EQ5b

EQ6a

EQ6b

0

5

10

15

20

25

30

35

40

0 0.2 0.4 0.6 0.8 1

Height(m)

Displacement(m)

DBD

EQ3a

EQ3b

EQ4a

EQ4b

EQ5a

EQ5b

EQ6a

EQ6b


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Figure 5-7: Average of the maximum recorded displacements for the eight spectrum compatible

accelerograms compared with the design displacements for the 4-story frame-wall structure with setbacks.

Figure 5-8: Average of the maximum recorded displacements for the eight spectrum compatible

accelerograms compared with the design displacements for the 12-story frame-wall structure with

setbacks.

0

2

4

6

8

10

12

14

0 0.05 0.1 0.15 0.2 0.25

Height(m)

Displacement(m)

DBD

Thistoryaverage

0

5

10

15

20

25

30

35

40

0 0.2 0.4 0.6 0.8 1

DBD

Thistory

Average


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accelerograms compared with the design displacements for the 4-story frame-wall structure with setbacks.


accelerograms compared with the design displacements for the 12-story frame-wall structure withsetbacks.

0

2

4

6

8

10

12

14

0.000 0.005 0.010 0.015 0.020 0.025

Height(m)

Drift

DBD

THistoryAverage

0

5

10

15

20

25

30

35

40

0.000 0.010 0.020 0.030

Height(m)

Drift

DBD

ThistoryAverage


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Chapter 6. Investigation of Frame-Wall Structures Possessing core walls that stop at mid

height

35

6.Investigation of Frame-Wall Structures Possessing core wallsthat stop at mid height

6.1Case study structure

The second type of case study structure investigated in this report are structures with vertical

irregularity associated with core walls that stop at mid-height of the building.

The plan view of the structure is shown in Figure 6-1, and the material properties are the same

as explained in chapter 5.

Figure 6-1: plan view of the case studies associated with walls that stop at mid height of the building.

For this type of irregularity 2 buildings were investigated; a 12 story building and a 4 story

building. For both the 12 and 4 story buildings the core walls stop at mid-height of the


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building and the frames extend the full height with equal number of bays as shown in Figures

6-2 and 6-3.

Figure 6-2: 12 story irregular Frame-wall structure where the cores stop at mid height.

6-3: 4 story irregular Frame-wall structure where the cores stop at mid height.

6.2Design Procedure

The procedure for the design of these case studies is generally the same as explained in

chapter 2, with some specific changes used for this type of irregularity which will be

explained in the next paragraphs.

6.2.1 Contra Flexure Height

The contra flexure height, HCF, is taken as the height of the core walls, which is the maximum

value. Lower values could be adopted but for this case study the contra flexure height, HCF,

was taken as the height of the core walls in order to take advantage of the walls.


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height

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6.2.2 Frame Shear Ratio

The frame proportions of base shear are selected to be the same as the total shear of the story

just above the story where the core stops using Equation (6.1) taken from Sullivan et al.

(2006):

, 1

(6.1)

Where Vi, totalis the total shear at level i, Vbis the total base shear, and n is the total number of

stories in the building.

6.2.3 Design Displacement Profile

The design displacement profile for the first part of the building, the half which has frames

and walls, is defined by equation (6.2):

, (6.2)

Where is the design displacement at level i, yi is the yield displacement of the wall atlevel i found from equation 2.4, is the design story drift, y,wis the yield curvature of thewall, HCFis the contra-flexure height and Hiis the height at level i.

The design displacement profile for the second part of the building, the half which has frames

only, was defined by equation (6.3), which is a modification of the equation used by Pettinga

and Priestley (2005) for normal frames with fixed base, the modification is done in order toaccount for our case study with continuous frame base as will be explained later, adding to it

the design displacement at the floor of wall termination, , , just under the start of the framestructure only.

Dissertation2009-Salawdeh

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