UNIVERSITY OF CALIFORNIA, THESIS MASTER OF SCIENCE

UNIVERSITY OF CALIFORNIA,

IRVINE

Effect of Vertical Component of Ground Motion on Dual System Tall Buildings

THESIS

submitted in partial satisfaction of the requirements

for the degree of

MASTER OF SCIENCE

in Civil Engineering

by

Shima Ebrahimi

Thesis Committee:

Associate Professor Farzin Zareian, Chair

Adjunct Professor Farzad Naeim

Professor Lizhi Sun

2016

© 2016 Shima Ebrahimi

ii

DEDICATION

To

My parents and husband

In recognition of their worth

iii

Table of Contents Table of Figures ......................................................................................................................................... v

Table of Tables......................................................................................................................................... vii

ACKNOWLEDGMENTS ............................................................................................................................ viii

ABSTRACT OF THE THESIS ..................................................................................................................... ix

Chapter 1 ..................................................................................................................................................... 1

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

1.1 Literature Review ....................................................................................................................... 3

1.2 Scope and Organization of This Study .................................................................................... 6

Chapter 2 ..................................................................................................................................................... 8

Structural Modeling .................................................................................................................................. 8

2.1 Building Overview: ......................................................................................................................... 8

2.2 Modeling Technique: ..................................................................................................................... 8

2.2.1 Modeling Technique to Capture Effect of VCGM: ............................................................. 11

2.2.3 Core Wall Modeling: .............................................................................................................. 15

2.2.4 Coupling Beams Modeling: .................................................................................................. 18

2.2.5 Moment Frame Beam and Column Modeling: .................................................................. 19

2.2.6 Basement Wall and Below Second Floor Slab Modeling: ............................................... 19

2.3 Model Validation:.......................................................................................................................... 20

2.3.1 Modal Analysis: ...................................................................................................................... 20

2.3.2 Time History Analysis: ......................................................................................................... 21

2.4 Revised Perform 3D Model for Slab Response: ...................................................................... 24

Chapter 3 ................................................................................................................................................... 25

3.1 Time History Analysis:................................................................................................................. 25

3.2 Ground Motions: ........................................................................................................................... 25

3.3 Defining Intensity Measure: ....................................................................................................... 35

3.4 Response to Earthquake Ground Motions: .............................................................................. 36

3.4.1 Axial Force: ............................................................................................................................. 37

3.4.2 Inter-Story Drifts: .................................................................................................................. 43

3.4.3 Story Shear: ............................................................................................................................ 46

3.4.4 Slab Response analysis:........................................................................................................ 49

Chapter 4 ................................................................................................................................................... 60

SUMMARY AND CONCLUSIONS.............................................................................................................. 60

iv

4.1 Summary ........................................................................................................................................ 60

4.2 Conclusion and observations ..................................................................................................... 61

Bibliography ............................................................................................................................................. 63

v

Table of Figures

Figure 2-1: Three-Dimensional Rendering of Structure From OpenSees Model ................................. 10

Figure 2-2: Typical Plan View at Level 2 and Above .............................................................................. 11

Figure 2-3: Difference Between 1st- and 2nd-Order P-Delta ................................................................... 15

Figure 2-4: Material Stress-Strain Relationships (Tuna 2012). ............................................................ 17

Figure 2-5: Sketch of Core Walls Modeling in OpenSees ........................................................................ 17

Figure 2-6: Coupling Beams Shear-Displacement Backbone Curve (Moehle, et al. 2011) .................. 18

Figure 2-7: Below-Ground Diaphragm Meshing ..................................................................................... 20

Figure 2-8: Comparison of Inter-Story Drift Ratios in H1 (East–West) Direction. .............................. 22

Figure 2-9: Comparison of Inter-Story Drift Ratios in H2 (North–South) Direction. .......................... 23

Figure 2-10: Typical Floor Diaphragm Meshing ..................................................................................... 24

Figure 3- 1: Axial Force on Exterior and Interior Columns for Group 1 ............................................... 38



Figure 3- 4: Axial Force on Exterior and Interior Columns for Group 4 .............................................. 39

Figure 3- 5: Axial Force on Shear Walls for Group 1 .............................................................................. 40




Figure 3- 9: Max Inter-Story Drift Ratio for Group 1 .............................................................................. 44

Figure 3- 10: Max Inter-Story Drift Ratio for Group 2 ............................................................................ 44



Figure 3- 13: Max Story Shear Ratio for Group 1 .................................................................................... 47

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Figure 3- 17: Vertical Acceleration at Mid-Span at Corner Slab for Group 1 .......................................... 51

Figure 3- 18: Vertical Acceleration at Mid-Span at Corner Slab for Group 2 ........................................ 52



Figure 3- 21: Vertical Displacement at Mid-Span at Corner Slab for Group 1 ...................................... 56




vii

Table of Tables

Table 3-1: Ground Motion Groups Summary .......................................................................................... 26

Table 3-2: Summary of Ground Motions of Group 1: Acceleration Information .................................. 27

Table 3-3: Summary of Ground Motions of Group 1: Moment Magnitude and

Closest Distance ......................................................................................................................................... 28


Table 3-5: Summary of Ground Motions of Group 2: Moment Magnitude and Closest Distance ....... 30





Table 3- 10: Equations for magnification factor of Interior column axial load due to vertical

component of ground motions ................................................................................................................. 42

Table 3- 11: Equations for magnification factor of exterior column axial load due to vertical

component of ground motions ................................................................................................................. 42

Table 3- 12: Equations for magnification factor of shear wall axial load due to vertical component of

ground motions ......................................................................................................................................... 42

Table 3- 13: Equations for magnification factor of max IDR ratio due to vertical component of

ground motions ......................................................................................................................................... 46

Table 3- 14: Equations for magnification factor of story shear ratio due to vertical component of

ground motions ......................................................................................................................................... 49

viii

ACKNOWLEDGMENTS

I would like to express the deepest appreciation to my committee chair, Professor Farzin

Zareian, who has the attitude and the substance of a genius: he continually and convincingly

conveyed a spirit of adventure in regard to research, and an excitement in regard to teaching.

Without his guidance and persistent help, this dissertation would not have been possible.

I would also like to thank Professor Farzad Naeim and Dr.Zeyneb Tuna whose vast

knowledge in the area of computational modeling and structural behavior provided

direction and a source of inspiration.

I would like to thank Professor Lizhi Sun, whose work demonstrated to me and concern the

support in Structural Engineering and Technology. His work in this field was always

transcend academia and provide a quest for our times.

Lastly, I would like to thank my family , friends, and colleagues for their continuous

support. Their love and encouragement is unprecedented.

ix

ABSTRACT OF THE THESIS

Effect of Vertical Component of Ground Motion on Dual System Tall Buildings

By

Shima Ebrahimi

Master of Science in Civil Engineering

University of California, Irvine, 2016

Associate Professor Farzin Zareian, Chair

This study presents the influence of vertical component of ground motion on the response

of a tall building; earthquakes with reverse fault and strike-slip with short or far distance to

the fault are considered. The main focus has been on the change of structural response due to

inclusion of vertical exitation in the analysis.

The first part of this study discusses the description of the structural model and modeling

techniques in detail which is based on Model 2B of PEER’s Case Studies of the Seismic

Performance of Tall Buildings (Moehle, et al. 2011). All elements are modeled with specific

effective stiffness and nonlinear materials to capture the accurate behavior of the building

under the nonlinear response history analysis. Backbone curves of the components is

presented. The model is validated by comparing the behavior of the structural model for this

x

study and the response of the Model 2B of PEER’s Case Studies of the Seismic Performance

of Tall Buildings (Moehle, et al. 2011).

The second part of this thesis focuses on the nonlinear response history analysis, the ground

motion selection and information on the selected records. The effect of vertical component

of the ground motion on the structural behavior is discussed in detail by comparing the

structural response due to the lateral components of the ground motion and the structural

response due to all three components of the ground motion. The structural response includes

the following parameters: maximum inter-story drift ratio, the axial force of columns and

shear walls, story shear, peak floor vertical acceleration and peak floor vertical displacement.

Equations for estimating the effect of vertical components of ground motions on tall

buildings are presented based on the results.

1

Chapter 1

INTRODUCTION

The standard practice in earthquake analysis of buildings is to ignore the vertical component

of ground motions and analyze the structure under the horizontal components of the ground

motion. However, an emerging body of evidence shows that the vertical component of

ground motions can have a destructive effect on structures, especially given individual site

conditions.

The vertical-to-horizontal ratio (V/H) of peak ground acceleration (PGA), is a strong function

of the source to site distance, local site conditions and natural periods as well as relativity

weaker function of the faulting mechanism, magnitude, and sediment depth (Bozorgnia &

Campbell, 2004).

The standard engineering rule-of-thumb for estimating vertical component of ground

motion for design of structure is assuming V/H =2/3. However, this “rule of thumb” is

imprecise for near-fault moderate and large-magnitude earthquakes (Friedland, Power, &

Mayes, 1997). In fact, acceleration records from the January 17, 1994, Northridge

earthquake in the United States, the January 17, 1995, Hyogoken earthquake in Japan, and

the February 22, 2011, Christchurch earthquake in New Zealand, among others, clearly show

that the vertical component of ground motion magnitude can be as large as or exceed the

horizontal component.

The reason for the traditional privileging of horizontal ground motion is that the attenuation

relationship was always performed for the entire range of magnitudes and epicentral

2

distances instead of concentrating on individual intervals. Thus, the outcomes had a smaller

V/H ratio (Papazoglou & Elnashai, 1996). The use of a constant value of 2/3 for V/H over the

entire period range of engineering interest is still recommend in united states by some

engineering guideline (FEMA-356 2000) even with all the evidence that have refuted this

assumption . Although, European Communities (1993), permitted V/H to vary with period

in the European Building Code (EC8), but primarily for reducing V/H from 2/3 at short

periods to 1/2 at long periods. The 1997 Uniform Building Code (UBC-97) acknowledged the

fact that V/H is dependent on source-to-site distance at relatively short distances and

suggested using site-specific vertical response spectra for sites located close to active faults.

However, neither Uniform Building Code (UBC-97) nor International Building Code (IBC-

2000) offers guidance on the design of the vertical spectrum (Bozorgnia and Campbell 2004)

In the past, two arguments have been made against the importance of the effect of the

vertical component of the ground motion. First, standard, properly designed structures are

already designed with a large factor of safety in the vertical direction. Second, the peaks of

strong vertical motion have low energy content. Both of these claims can be refuted. It is

contended that the relationship between structural and excitation periods are more

important than energy content. Also, from observation, it is evident that structures designed

base on code requirement can fail due to strong vertical ground motion (Papazoglou &

Elnashai, 1996).

Many experienced engineers think that vertical earthquake motion should be factored into

the design of structures. Consideration of vertical earthquake motions in the design of

3

bridges in high seismic zones was recommended by Friedland, Power, and Mayes (Friedland,

Power and Mayes 1997). Bozorgnia and Campbell say that modified spectra must be used

for vertical component of ground motion because calculating the vertical spectrum by using

2/3 of the horizontal spectrum underestimates the effect of the vertical component for short-

and long-period structures and overestimates that effect for medium-period structures

(Bozorgnia and Campbell 2016).

1.1 Literature Review

Earthquakes like Kobe 1995, Northridge 1994, Loma Prieta 1989, and Kalamata 1986

changed our perspective on the vertical component of ground motion. One of the most

comprehensive studies of these records has been done by Papazoglou and Elnashai(1996).

In Northridge, where a V/H as high as 1.79 was recorded, a Holiday Inn which had sustained

structural damage was investigated. A significant number of columns experienced shear

failure. This analysis was based on the fact that the RC frame vibrated in the first mode of

the structure, and there was no sign of torsional failure. Papazoglou and Elnashai (1996)also

concluded that larger reduction in column shear capacity is projected for higher stories

because they experience a greater relative change in preexisting axial force specially in

vibration in the first vertical mode.

The Kobe earthquake was a unique earthquake with respect to observing strong vertical

motion. Large V/H ratios, as well as PGA, were recorded over long epicentral distances (≥ 45

km). After this earthquake, considerable attention was given to a large number of steel box

4

columns. It was concluded that because there was no evidence of bending deformation of

the plates in the box columns, the axial response in the box columns was mainly tensile. The

Kalamata earthquake was a near-field earthquake (< 9km) with a focal depth of 7 km and a

magnitude of 5.7 on the Richter scale. The result of these unique conditions was a V/H ratio

as high as 1.26. The field records indicated noticeable structural damage due to the vertical

component of ground motion. This damage included an RC pedestal cracked at mid-height,

signifying possible tensile failure. Moreover, there were significant number of shear-

compression failures in columns and shear walls, despite the fact that in those buildings,

bending failure was expected. In addition to studying field evidence, researchers have made

efforts toward analyzing the effects of vertical ground motions. Some of the main ones are

explained briefly below:

Iyengar and Shinozuka (1972) investigated the behavior of self-weight and vertical

acceleration on medium-tall structures. The structures were modeled as cantilevers. Their

primary findings were that self-weight and acceleration could either increase or decrease

the peak response. In most cases this difference is considerable. In a frame structure, a

vertical acceleration effect could be more prominent in beam behavior

Iyengar and Sahia (1977) used modal superposition to evaluate the effect of vertical ground

motion on the response of cantilever structures. They concluded that in the analysis of

towers, the vertical component should be included in the design.

Antoniou (1997)Analyzed an eight-story RC building which was designed based on a design

acceleration of 0.3 g and a high ductility class of EC8 (CEN 2005a). The author concluded

that on roof displacement and inter-story drift, vertical acceleration has no effect, and the

results are the same as if one had solely considered horizontal acceleration. However, a

5

significant increase in axial force in columns can lead to the growth of tensile force. The

fluctuation of axial force due to vertical acceleration can cause shear failure in columns.

Munshi and Ghosh (1998) studied the nonlinear behavior of a 12-story RC building in

earthquake conditions. The building showed accelerating motions in both the horizontal and

vertical planes. A minor rise in the maximum deformation was seen when the vertical

ground motion was included. According to this study, the wall-frame system is not sensitive

to vertical acceleration

Collier and Elnashai (2001)investigated the behavior of a four-story reinforced concrete

structure by a particular simplified method for a combination of vertical and horizontal

acceleration. The primary purpose of this study was to determine the influence of ground

motions in conjunction with various V/H and time intervals between peak acceleration of

vertical and horizontal motions on the vertical period of the structure. This study showed

that the amplitude of both horizontal and vertical motion can have a major effect on the

vertical period of vibration.

Shakib and Fuladgar (2003), by modeling a 2D one-story structure resting on a sliding

support, studied the behavior of pure-friction base isolated asymmetric building affected by

the vertical component of ground motion. Based on this study, the lateral behavior of the

pure-friction base, when isolated, is significantly affected by vertical acceleration. Moreover,

when the structure is subjected to vertical and horizontal accelerations simultaneously, the

torsional behavior of the structure increases noticeably in the moderate range of

eccentricities.

Mwafy and Elnashai (2006) did a substantial study on three RC frame groups with different

characteristics, including a 12-story regular frame, an eight-story frame-wall building, and

6

an eight-story irregular structure. Each structure has four different design levels, generating

a total of 12 structures. This study showed that vertical acceleration has more effect on high-

rise buildings than low-rise buildings. The authors indicated that the axial load in columns,

as well as curvature ductility demand, will increase up to 45% and 60% higher, respectively,

when the vertical component of an earthquake is included.

1.2 Scope and Organization of This Study

The purpose of this study is to investigate the sensitivity of structural response to the strong

vertical ground motion. Specifically, this thesis will compare the structural response to

lateral ground accelerations (X and Y) against the structural response to all orthogonal

components of ground accelerations (X, Y, and Z). In other words, what difference does the

inclusion of the vertical component make in a time history analysis.

The parameters of interest are:

Story drift

Story shear

Axial force of critical columns

Slab vertical displacement at mid-span

Slab vertical acceleration at mid-span

Chapter 2 explores the analytical modeling and summary of response results for modeling

validation. Chapter 3 focuses on the nonlinear response history analysis, the ground motion

selection procedure, and information on the selected records. The structural response of the

7

structure under the selected ground motion is then evaluated in detail. Chapter 4 then

presents the conclusions of this study.

8

Chapter 2

Structural Modeling

In order to investigate the effects of vertical components of earthquakes on the responses of

tall buildings, Model 2B of PEER’s Case Studies of the Seismic Performance of Tall Buildings

(Moehle, et al. 2011) has been modeled in the OpenSees program. This Chapter describes

details of this model.

2.1 Building Overview:

The building includes 42 stories above ground and four stories below ground, with a roof

and penthouse. A core wall and four-bay SMFs at the building’s perimeter on all sides were

considered as a lateral-force resisting system. Core walls were built with L-shaped walls

connected by coupling beams. The four-story podium has a 16-inch-thick basement wall

around it. Figures 2-1 and 2-2 show the 3-D view and typical plan view of the structure,

respectively.

2.2 Modeling Technique:

According to Model 2B of PEER’s Case Studies of the Seismic Performance of Tall Buildings

(Moehle, et al. 2011) , a three-dimensional nonlinear model of the building was modeled

using OpenSees software. The model only contains the building’s lateral force-resisting

system (i.e., the gravity system was excluded). The seismic masses equivalent to the dead

load have been assigned to tops of columns and shear walls in proportion to their tributary

9

area. The mass associated with the ground level and below is ignored. Concrete shear walls

and concrete special moment frames are modeled from the foundation level to the penthouse

and roof levels, respectively. The diaphragms at the ground floor and below are modeled

with a finite element mesh to account for their in-plane stiffness. The diaphragms above

ground level are modeled as rigid diaphragms by slaving the horizontal translation degrees

of freedom. Ground motions are input at the top of the mat foundation. The foundation is

idealized as rigid by providing lateral and vertical supports at the top of the foundation. The

lateral resistance of the soil surrounding the subterranean walls is ignored.

10

Figure 2-1: Three-Dimensional Rendering of Structure From OpenSees Model

11

Figure 2-2: Typical Plan View at Level 2 and Above

2.2.1 Modeling Technique to Capture Effect of VCGM:

2.2.1.1 Second-order P-Delta:

Structural engineers usually would not ignore the P-Delta effect while performing the

stability analysis and design slender member, tall structure or any structure which

experiences significant gravity loads along with lateral force. In the conventional first-order

structural analysis, the equilibrium is expressed by the un-deformed structure’s geometry.

For a linearly elastic structure, since the relationship between external force and

displacement is proportional, the unknown deformation can be computed directly.

However, second-order analysis requires an iterative procedure to obtain the solution.

Linear elastic analysis is not accurate because it does not account for the permanent

deformation of the building. Therefore, the analysis progresses in a step-by-step incremental

12

method, using the structure’s deformed geometry acquired by iterative cycles of the

calculation. Figure-2-3 shows the significant difference between first-order and second-

order analysis. A simple method, known as the amplification method, and which is

commonly used to capture second-order effects, is to magnify just the response obtained

from the first-order analysis by an magnification factor is 1/ (1-P/Pcr), where P is the axial

load and Pcr is the elastic buckling load of the considered member. In the case of massive

gravity loading—e.g., during an earthquake, with a strong vertical component of ground

motion—the accuracy of capturing the actual P-Delta effect reduces significantly, and the

result which was obtained from the Amplification Method becomes unreliable. In such a

case, the iterative P-delta analysis must be performed to predict the actual effect on the

structure. OpenSees is capable of performing the iterative P-Delta analysis to represent the

actual second-order effect on the structure. A simple example of a cantilever column has

been analyzed by this means in OpenSees; it has been verified by hand-calculation for up to

three iteration cycles.

13

Example:

Height, L =240 in

E = 29000 ksi

I = 40000 in^4

Vertical Load, P =600 Kips

Horizontal Load, H = 300 Kips

First Iteration

M = H × L = 72000 Kips − in

the lateral displacement (Δ1) at the column top is:

Δ1 = ML2

3EI = 1.1917 in

Also, the vertical load P acting on displaced Δ1 column tip resulting in the generation of the

additional moment M1 at the base.

M1 = P × Δ1 = 715.02 Kips − in

the total moment “Mt1” at the base of the column = (M+M1) = 72715.02 Kips-in

The modified horizontal displacement “Δ2” experiences the first modified moment Mt1

Δ2 = Mt1L2

3EI= 1.203 in

14

Second Iteration

Now, “P” which stands for vertical load takes action on the newly displaced column tip; (Δ2 -

Δ1) causes an additional moment M2 at the base

M2 = P × (Δ2 − Δ1) = 67.8 Kips − in

𝑀𝑡2 = (M + M1 + M2) = (Mt1 + M2) = 72782.82 Kips − in

Δ3 = Mt2 L

2

3EI = 1.2046 in

Third Iteration

M3 = P × (Δ3 – Δ2) = 0.96 Kips − in

Mt3 = M + M1 + M2 + M3 = 72783.78 Kips − in

Δ4 =𝑀𝑡3𝐿2

3𝐸𝐼= 1.2047 in

15

Figure 2-3: Difference Between 1st- and 2nd-Order P-Delta

2.2.3 Core Wall Modeling:

Flexural behavior of the core walls was captured by using nonlinear vertical fiber elements

which represent the behavior of steel reinforcement and concrete. The shear behavior was

counted by modeling it as elastic perfectly plastic stress-strain curve. For fiber elements, the

section’s unconfined cover was ignored. A modified Mander model (Mander et al., 1988) was

used for the confined concrete stress-strain relationship. The tensile strength of the concrete

was ignored. Confining ratios were calculated according to ACI 318 (2008), section21.4.4.

The steel stress-strain relationship is based on the material specifications for A706

reinforcing steel. The expected yield strength of 70 ksi and an ultimate strength of 105 ksi

in both compression and tension were considered. Steel properties were modeled based on

the Giuffre-Menegotto-Pinto model. For the core wall’s inelastic in-plane shear behavior, the

effective shear modulus was chosen to be 20% of the concrete expected elastic modulus 𝐸𝐶 ,

which has been defined in ACI 318–08. (ACI 318-08. 2008) To characterize the core walls’

16

expected shear strength, the ultimate shear strength 𝑉𝑢𝑙𝑡was determined as 1.5 times 𝑉𝑛,

which the nominal shear capacity is as defined in ACI 318-08. The described modeling

approach is based on Model 2B of PEER’s Case Studies of the Seismic Performance of Tall

Buildings (Moehle, et al. 2011). Figure 2-4 shows material stress-strain relationships which

were used in modeling. Each Shear wall was modeled as a column with fiber elements and

rigid beams with very large I and A (100 times stiffer than shear walls). Figure2-5 describes

how the walls were modeled in OpenSees. Displacement-based elements were used to model

shear wall elements. All elements were divided into three elements for results Accuracy.

17

Figure 2-4: Material Stress-Strain Relationships (Tuna 2012).

Column

Rigid Beam Node

Rigid Beam

Figure 2-5: Sketch of Core Walls Modeling in OpenSees

18

2.2.4 Coupling Beams Modeling:

Coupling beams were modeled with the same approach as Model 2B of PEER’s Case Studies

of the Seismic Performance of Tall Buildings (Moehle, et al. 2011) using two elastic beam–

column elements connected at midspan by a nonlinear shear spring with envelope

properties defined based on test results by Naish (2010). The effective stiffness of elastic

portion is 𝐸𝐼𝑒𝑓𝑓 = 0.20𝐸𝐼𝑔. Figure 2-6 shows properties of the shear hinge. More details

on material properties can be obtained in (Deger and Yang 2015); (Tuna 2012), and (Ghodsi,

et al. 2010).

Figure 2-6: Coupling Beams Shear-Displacement Backbone Curve (Moehle, et al. 2011)

19

2.2.5 Moment Frame Beam and Column Modeling:

Components of Moment resisting frames were modeled with elastic elements with nonlinear

fiber section as concentrated plasticity hinges and plastic length zones at each end. The

elastic portions of the moment frame elements were modeled with the cross-section

properties and the stiffness modification factors based on ASCE 41-06, such that 𝐸𝐼𝑒𝑓𝑓 =

0.35𝐸𝐼𝑔 (flexural, for beams), 𝐸𝐼𝑒𝑓𝑓 = 0.70𝐸𝐼𝑔 (flexural, for columns), and GA = 1.0GAg

(shear). Plastic hinge length was calculated based on the work of Paulay and Priestley

(1992) with the Radau Hinge Integration method based on the work of Scott and Fenves

(2006).

2.2.6 Basement Wall and Below Second Floor Slab Modeling:

Basement walls are modeled as elastic finite elements with their effective stiffness values

𝐸𝐼𝑒𝑓𝑓 = 0.80𝐸𝐼𝑔 .Slabs were modeled as elastic shell elements with 25 percent of total

stiffness. Both basement walls and slabs were modeled based on Model 2B of PEER’s Case

Studies of the Seismic Performance of Tall Buildings (Moehle, et al. 2011). The figure shows

how the diaphragms were meshed to capture the structure’s true behavior. Figure 2-7 shows

below-ground diaphragm meshing.

20

Figure 2-7: Below-Ground Diaphragm Meshing

2.3 Model Validation:

As previously mentioned, this building is Model 2B of PEER’s Case Studies of the Seismic

Performance of Tall Buildings (Moehle, et al. 2011). For the purpose of this research, this

building was remodeled in OpenSees. The OpenSees program analyzes data more quickly

and in a more advanced way than Peform3D. As well, it can capture the iterative P-Delta

effect, a capability missing from Perform3D.

2.3.1 Modal Analysis:

Both periods were obtained by the programs Perform 3D (2007) and OpenSees from the

models before the nonlinear analyses were performed. The frame beams, columns, and

coupling beams reflected a reduced stiffness, as described in above sections when calculating

the period. However, the core shear walls were modeled using the uncracked properties of

concrete. Table 2-1 shows a summary of the periods obtained for Building2B.

21

Table 2: Period Summary from the Computer Models

Period

Vibration Mode Perform 3D OpenSees Dominant direction

1 4.27 sec. 4.30 sec. Translation mode on X

direction

2 3.87 sec. 3.91 sec. Translation mode on Y

direction

3 2.34 sec. 2.36 sec. Torsional mode

2.3.2 Time History Analysis:

Systematic analyses were conducted to validate structural responses of the OpenSees’s

model using Perform3D’s model at four levels of ground shaking intensity, namely, SLE25,

SLE43, DBE, and MCE, with return periods of 25, 43, 475, and 2475 years, respectively. Each

hazard level includes 15 pairs (i.e., two horizontal components) of ground motions.To

compare the overall responses of these two models, inter-story drifts were investigated.

Inter-story drift profiles of OpenSees’s model and Perform 3D’s model (Figures 2-8 and 2-9)

showed that each engine’s mean and individual GM results are very to each other.

22

Mean Individual GM

Figure 2-8: Comparison of Inter-Story Drift Ratios in H1 (East–West) Direction.

23

Mean Individual GM

Figure 2-9: Comparison of Inter-Story Drift Ratios in H2 (North–South) Direction.

24

2.4 Revised Perform 3D Model for Slab Response:

In order to assess the effect of the vertical components of ground motions on slabs, a model

was built in Perform3D which had semi-rigid diaphragms on the roof, the 24th floor, the 10th

floor, and the 2nd floor. The diaphragms were modeled with a finite element mesh to account

for their in-plane stiffness and out-of-plane response. By modeling the selected floors, not

only the difference in slab responses can be evaluated in terms of change of floor levels but

also, it would help preventing numerical issues on analysis as well as reducing the analysis

time significantly with respect to the full semi-rigid model. The slabs were reinforced

concrete and were assumed to behave like horizontal shear walls. Therefore, as ASCE 41-13

suggests, the Effective Stiffness of 50% was assumed for in-plane and out-of-plane stiffness.

Figure 2.10 shows how these floors were meshed in Perform3D.

Figure 2-10: Typical Floor Diaphragm Meshing

25

Chapter 3

Analyses, Results, and Discussion 3.1 Time History Analysis:

Nonlinear response history analysis (NRHA) was performed on the model both including and

excluding the vertical component of ground motions. This has been done in OpenSees and

using Newmark’s integration method. Unconditional stability in Newmark’s method is

satisfied, where β= 0.25 and ϒ= 0.5. Furthermore, 2.5% damping is assumed. The first

horizontal mode and the 20% of the first period were used to calculate damping coefficients.

3.2 Ground Motions:

Papazoglou et al. (1996) have provided a broad review of structural damage attributable to

the vertical motion for analysis of typical structures under horizontal and combined

horizontal-vertical excitation based on previous earthquake records. These records have

shown the importance of the vertical component of ground motion, which is currently

ignored in the conventional design of buildings. These field observations can be used to

compute the response of structures under these real earthquake records using dynamic time

history analysis. The records were selected with respect to their fault type (strike-slip;

reverse) and their distance to the fault (near-field ground motions, far-field ground

motions). Only records from earthquakes with magnitude 6 and above which are recorded

on soil class C or D have been considered. Table 3-1 shows the group records in more detail.

26

Table 3-1: Ground Motion Groups Summary

Group Distance Fault

1 0-10 Strike-Slip

2 10-25 Strike-Slip

3 0-10 Reverse

4 10-25 Reverse

Among 190 usable records, 120 records were selected, 30 per group. The following tables

display essential characteristics of the ground motions, including magnitude, PGAs, V/H, and

the closest distance to the fault.

27

Table 3-2: Summary of Ground Motions of Group 1: Acceleration Information

Year Event Station PGA (g) Hor.1 Hor.2 Vert

V/H

1992 "Erzican_ Turkey" "Erzincan" 0.50 0.39 0.23 0.47

1995 "Kobe_ Japan" "KJMA" 0.83 0.63 0.34 0.41

1995 "Kobe_ Japan" "Takarazuka" 0.70 0.61 0.43 0.61

2002 "Denali_ Alaska" "TAPS Pump Station #10" 0.33 0.30 0.24 0.72

2000 "Tottori_ Japan" "SMNH01" 0.62 0.73 0.64 0.87

2000 "Tottori_ Japan" "TTRH02" 0.77 0.94 0.79 0.84

2003 "Bam_ Iran" "Bam" 0.81 0.63 0.97 1.20

2010 "Darfield_ New

Zealand" "GDLC" 0.76 0.71 1.25 1.63

2010 "Darfield_ New

Zealand" "HORC" 0.45 0.48 0.81 1.70

1995 "Kobe_ Japan" "Nishi-Akashi" 0.48 0.46 0.39 0.80

1999 "Duzce_ Turkey" "Lamont 1058" 0.11 0.08 0.07 0.69

1999 "Duzce_ Turkey" "Lamont 1059" 0.14 0.15 0.10 0.66

1999 "Duzce_ Turkey" "IRIGM 487" 0.28 0.30 0.23 0.76

1979 "Imperial Valley-06" "Agrarias" 0.29 0.19 0.47 1.64

1979 "Imperial Valley-06" "Bonds Corner" 0.60 0.78 0.53 0.68

1979 "Imperial Valley-06" "Chihuahua" 0.27 0.25 0.22 0.80

1979 "Imperial Valley-06" "EC County Center FF" 0.21 0.24 0.24 1.04

1979 "Imperial Valley-06" "El Centro Array #5" 0.53 0.38 0.59 1.12




1979 "Imperial Valley-06" "El Centro Differential

Array" 0.35 0.48 0.77 1.60

1979 "Imperial Valley-06" "Holtville Post Office" 0.26 0.22 0.26 1.00

1995 "Kobe_ Japan" "Port Island (0 m)" 0.35 0.29 0.57 1.63

1999 "Kocaeli_ Turkey" "Yarimca" 0.23 0.32 0.24 0.75

1999 "Duzce_ Turkey" "Duzce" 0.40 0.51 0.35 0.67

2010 "Darfield_ New

Zealand" "DSLC" 0.26 0.24 0.32 1.23

2010 "Darfield_ New

Zealand" "LINC" 0.46 0.39 0.91 1.98

2010 "Darfield_ New

Zealand" "ROLC" 0.39 0.32 0.71 1.82

2010 "Darfield_ New

Zealand" "IWTH20" 0.30 0.21 0.87 2.92

28

Table 3-3: Summary of Ground Motions of Group 1: Moment Magnitude and Closest Distance

Year Event Station Mw Distance

1992 "Erzican_ Turkey" "Erzincan" 6.69 0

1995 "Kobe_ Japan" "KJMA" 6.9 0.94

1995 "Kobe_ Japan" "Takarazuka" 6.9 0

2002 "Denali_ Alaska" "TAPS Pump Station #10"

7.9 0.18

2000 "Tottori_ Japan" "SMNH01" 6.61 5.83

2000 "Tottori_ Japan" "TTRH02" 6.61 0.83

2003 "Bam_ Iran" "Bam" 6.6 0.05

2010 "Darfield_ New Zealand"

"GDLC" 7 1.22


"HORC" 7 7.29

1995 "Kobe_ Japan" "Nishi-Akashi" 6.9 7.08

1999 "Duzce_ Turkey" "Lamont 1058" 7.14 0.21

1999 "Duzce_ Turkey" "Lamont 1059" 7.14 4.17

1999 "Duzce_ Turkey" "IRIGM 487" 7.14 2.65

1979 "Imperial Valley-06" "Agrarias" 6.53 0

1979 "Imperial Valley-06" "Bonds Corner" 6.53 0.44

1979 "Imperial Valley-06" "Chihuahua" 6.53 7.29

1979 "Imperial Valley-06" "EC County Center FF" 6.53 7.31

1979 "Imperial Valley-06" "El Centro Array #5" 6.53 1.76

1979 "Imperial Valley-06" "El Centro Array #6" 6.53 0



1979 "Imperial Valley-06" "El Centro Differential Array"

6.53 5.09

1979 "Imperial Valley-06" "Holtville Post Office" 6.53 5.35

1995 "Kobe_ Japan" "Port Island (0 m)" 6.9 3.31

1999 "Kocaeli_ Turkey" "Yarimca" 7.51 1.38

1999 "Duzce_ Turkey" "Duzce" 7.14 0


"DSLC" 7 5.28


"LINC" 7 5.07


"ROLC" 7 0


"IWTH20" 7 6.11

29



V/H

1979 "Imperial Valley-06" "Cerro Prieto" 0.17 0.16 0.21 1.25

1992 "Landers" "Coolwater" 0.28 0.42 0.18 0.42

1992 "Landers" "Joshua Tree" 0.27 0.28 0.18 0.64

1992 "Landers" "Morongo Valley Fire

Station" 0.22 0.16 0.16 0.73

2000 "Tottori_ Japan" "OKY004" 0.82 0.54 0.17 0.21

2010 "Darfield_ New Zealand" "DFHS" 0.47 0.51 0.37 0.73

2010 "Darfield_ New Zealand" "Heathcote Valley Primary

School " 0.58 0.63 0.30 0.48

1990 "Manjil_ Iran" "Abbar" 0.51 0.50 0.54 1.05

2000 "Tottori_ Japan" "SMNH02" 0.32 0.58 0.37 0.65

1979 "Imperial Valley-06" "Calexico Fire Station" 0.28 0.20 0.19 0.70

1987 "Superstition Hills-02" "El Centro Imp. Co. Cent" 0.36 0.26 0.13 0.36

1987 "Superstition Hills-02" "Westmorland Fire Sta" 0.17 0.21 0.23 1.10

1987 "Superstition Hills-02" "Imperial Valley Wildlife

Liquefaction Array" 0.18 0.21 0.40 1.94

1995 "Kobe_ Japan" "Amagasaki" 0.28 0.33 0.34 1.05

1995 "Kobe_ Japan" "Fukushima" 0.18 0.22 0.20 0.92

1999 "Kocaeli_ Turkey" "Duzce" 0.31 0.36 0.21 0.57

1999 "Duzce_ Turkey" "Bolu" 0.74 0.81 0.20 0.25

2000 "Tottori_ Japan" "SMN002" 0.18 0.15 0.11 0.60

2010 "El Mayor-Cucapah_ Mexico" "Chihuahua" 0.25 0.20 0.28 1.12

2010 "El Mayor-Cucapah_ Mexico" "MICHOACAN DE OCAMPO" 0.54 0.41 0.80 1.49

2010 "El Mayor-Cucapah_ Mexico" "RIITO" 0.40 0.38 0.67 1.69

2010 "El Mayor-Cucapah_ Mexico" "EJIDO SALTILLO" 0.15 0.15 0.18 1.15

2010 "El Mayor-Cucapah_ Mexico" "El Centro -Imperial & Ross" 0.37 0.38 0.27 0.71

2010 "El Mayor-Cucapah_ Mexico" "El Centro Differential Array" 0.51 0.55 0.31 0.56

2010 "Darfield_ New Zealand" "Christchurch Cashmere

High School" 0.23 0.25 0.30 1.18

2010 "Darfield_ New Zealand" "Pages Road Pumping

Station" 0.22 0.20 0.32 1.42

2010 "Darfield_ New Zealand" "Christchurch Resthaven " 0.26 0.24 0.21 0.81

2010 "Darfield_ New Zealand" "Riccarton High School " 0.19 0.23 0.31 1.32

2010 "Darfield_ New Zealand" "Styx Mill Transfer Station " 0.18 0.17 0.23 1.33

2010 "El Mayor-Cucapah_ Mexico" "Westside Elementary

School" 0.28 0.26 0.24 0.86

30



1979 "Imperial Valley-06" "Cerro Prieto" 6.53 15.19

1992 "Landers" "Coolwater" 7.28 19.74

1992 "Landers" "Joshua Tree" 7.28 11.03

1992 "Landers" "Morongo Valley Fire Station" 7.28 17.36

2000 "Tottori_ Japan" "OKY004" 6.61 19.72

2010 "Darfield_ New Zealand" "DFHS" 7 11.86

2010 "Darfield_ New Zealand" "Heathcote Valley Primary School "

7 24.36

1990 "Manjil_ Iran" "Abbar" 7.37 12.55

2000 "Tottori_ Japan" "SMNH02" 6.61 23.64

1979 "Imperial Valley-06" "Calexico Fire Station" 6.53 10.45

1987 "Superstition Hills-02" "El Centro Imp. Co. Cent" 6.54 18.2

1987 "Superstition Hills-02" "Westmorland Fire Sta" 6.54 13.03

1987 "Superstition Hills-02" "Imperial Valley Wildlife Liquefaction Array"

6.54 23.85

1995 "Kobe_ Japan" "Amagasaki" 6.9 11.34

1995 "Kobe_ Japan" "Fukushima" 6.9 17.85

1999 "Kocaeli_ Turkey" "Duzce" 7.51 13.6

1999 "Duzce_ Turkey" "Bolu" 7.14 12.02

2000 "Tottori_ Japan" "SMN002" 6.61 16.6

2010 "El Mayor-Cucapah_ Mexico" "Chihuahua" 7.2 18.21

2010 "El Mayor-Cucapah_ Mexico" "MICHOACAN DE OCAMPO" 7.2 13.21

2010 "El Mayor-Cucapah_ Mexico" "RIITO" 7.2 13.7

2010 "El Mayor-Cucapah_ Mexico" "EJIDO SALTILLO" 7.2 14.8

2010 "El Mayor-Cucapah_ Mexico" "El Centro -Imperial & Ross" 7.2 19.39

2010 "El Mayor-Cucapah_ Mexico" "El Centro Differential Array" 7.2 22.83

2010 "Darfield_ New Zealand" "Christchurch Cashmere High School"

7 17.64

2010 "Darfield_ New Zealand" "Pages Road Pumping Station"

7 24.55

2010 "Darfield_ New Zealand" "Christchurch Resthaven " 7 19.48

2010 "Darfield_ New Zealand" "Riccarton High School " 7 13.64

2010 "Darfield_ New Zealand" "Styx Mill Transfer Station " 7 20.86

2010 "El Mayor-Cucapah_ Mexico" "Westside Elementary School"

7.2 10.31

31



V/H

1994 "Northridge-01" "Jensen Filter Plant

Administrative Building" 0.41 0.62 0.35 0.56

1994 "Northridge-01" "Pardee -SCE" 0.56 0.30 0.39 0.69

1994 "Northridge-01" "Sylmar -Converter Sta East" 0.85 0.45 0.48 0.56

1994 "Northridge-01" "Sylmar -Olive View Med FF" 0.60 0.84 0.54 0.64

2003 "San Simeon_ CA" "Cambria -Hwy 1 Caltrans

Bridge" 0.18 0.13 0.09 0.49

2003 "San Simeon_ CA" "Templeton -1-story Hospital" 0.44 0.48 0.26 0.55

2004 "Niigata_ Japan" "NIG019" 1.33 1.17 0.80 0.60



2004 "Niigata_ Japan" "NIGH01" 0.67 0.84 0.38 0.45


1979 "Montenegro_

Yugoslavia" "Bar-Skupstina Opstine" 0.37 0.37 0.24 0.65

1979 "Montenegro_

Yugoslavia" "Ulcinj -Hotel Albatros" 0.18 0.23 0.23 0.99

1979 "Montenegro_

Yugoslavia" "Ulcinj -Hotel Olimpic" 0.29 0.25 0.46 1.57

1978 "Tabas_ Iran" "Tabas" 0.85 0.86 0.64 0.74

1985 "Nahanni_ Canada" "Site 1" 1.11 1.20 2.28 1.90

1985 "Nahanni_ Canada" "Site 3" 0.18 0.17 0.14 0.79

1992 "Cape Mendocino" "Cape Mendocino" 1.49 1.04 0.74 0.49

1994 "Northridge-01" "Jensen Filter Plant Generator

Building" 0.57 0.99 0.76 0.77

1994 "Northridge-01" "LA Dam" 0.43 0.32 0.32 0.75

1994 "Northridge-01" "Pacoima Kagel Canyon" 0.30 0.43 0.17 0.39

1979 "Montenegro_

Yugoslavia" "Petrovac -Hotel Olivia" 0.46 0.30 0.21 0.45

2008 "Iwate_ Japan" "IWTH25" 1.43 1.15 3.84 2.68

1976 "Gazli_ USSR" "Karakyr" 0.70 0.86 1.70 1.97

1994 "Northridge-01" "Arleta -Nordhoff Fire Sta" 0.35 0.31 0.55 1.60

1994 "Northridge-01" "Newhall -Fire Sta" 0.58 0.59 0.55 0.93

1994 "Northridge-01" "Newhall -W Pico Canyon Rd." 0.42 0.36 0.30 0.71

1994 "Northridge-01" "Rinaldi Receiving Sta" 0.87 0.47 0.96 1.10

1994 "Northridge-01" "Sylmar -Converter Sta" 0.62 0.92 0.61 0.66

2008 "Iwate_ Japan" "IWT011" 0.22 0.15 0.21 0.96

32



1994 "Northridge-01" "Jensen Filter Plant

Administrative Building" 6.69 0

1994 "Northridge-01" "Pardee -SCE" 6.69 5.54

1994 "Northridge-01" "Sylmar -Converter Sta East" 6.69 0

1994 "Northridge-01" "Sylmar -Olive View Med FF" 6.69 1.74

2003 "San Simeon_ CA" "Cambria -Hwy 1 Caltrans

Bridge" 6.52 6.97

2003 "San Simeon_ CA" "Templeton -1-story Hospital" 6.52 5.07

2004 "Niigata_ Japan" "NIG019" 6.63 0.21



2004 "Niigata_ Japan" "NIGH01" 6.63 0.49


1979 "Montenegro_

Yugoslavia" "Bar-Skupstina Opstine" 7.1 0

1979 "Montenegro_

Yugoslavia" "Ulcinj -Hotel Albatros" 7.1 1.52

1979 "Montenegro_

Yugoslavia" "Ulcinj -Hotel Olimpic" 7.1 3.97

1978 "Tabas_ Iran" "Tabas" 7.35 1.79

1985 "Nahanni_ Canada" "Site 1" 6.76 2.48

1985 "Nahanni_ Canada" "Site 3" 6.76 4.93

1992 "Cape Mendocino" "Cape Mendocino" 7.01 0

1994 "Northridge-01" "Jensen Filter Plant Generator

Building" 6.69 0

1994 "Northridge-01" "LA Dam" 6.69 0

1994 "Northridge-01" "Pacoima Kagel Canyon" 6.69 5.26

1979 "Montenegro_

Yugoslavia" "Petrovac -Hotel Olivia" 7.1 0

2008 "Iwate_ Japan" "IWTH25" 6.9 0

1976 "Gazli_ USSR" "Karakyr" 6.8 3.92

1994 "Northridge-01" "Arleta -Nordhoff Fire Sta" 6.69 3.3

1994 "Northridge-01" "Newhall -Fire Sta" 6.69 3.16

1994 "Northridge-01" "Newhall -W Pico Canyon Rd." 6.69 2.11

1994 "Northridge-01" "Rinaldi Receiving Sta" 6.69 0

1994 "Northridge-01" "Sylmar -Converter Sta" 6.69 0

2008 "Iwate_ Japan" "IWT011" 6.9 8.41

33



V/H

1971 "San Fernando" "Castaic -Old Ridge

Route" 0.32048 0.27516 0.1666 0.51984

1971 "San Fernando" "LA -Hollywood Stor

FF" 0.22476 0.19493 0.16427 0.73084

1994 "Northridge-01" "Canyon Country -W

Lost Cany" 0.40361 0.47163 0.30349 0.64349

1994 "Northridge-01" "LA -Brentwood VA

Hospital" 0.18536 0.16424 0.13807 0.74484

1994 "Northridge-01" "LA -UCLA Grounds" 0.27788 0.47381 0.26497 0.55923

1994 "Northridge-01" "Sunland -Mt Gleason

Ave" 0.13298 0.15724 0.20335 1.2933


2007 "Chuetsu-oki_

Japan" "Shiura Nagaoka" 0.22909 0.21551 0.11629 0.50761

2007 "Chuetsu-oki_

Japan" "NIG028" 0.13068 0.13945 0.076164 0.54619

2008 "Iwate_ Japan" "AKTH04" 2.4685 1.3433 1.1058 0.44796

2008 "Iwate_ Japan" "AKTH06" 0.18967 0.18449 0.14258 0.75172

2008 "Iwate_ Japan" "MYG005" 0.53551 0.53551 0.65675 1.2264

2008 "Iwate_ Japan" "Iwadeyama" 0.35409 0.26871 0.23008 0.64978

1971 "San Fernando" "Lake Hughes #12" 0.38215 0.28217 0.19418 0.50813

1971 "San Fernando" "Lake Hughes #9" 0.16988 0.14345 0.094275 0.55493

1976 "Friuli_ Italy-01" "Tolmezzo" 0.35713 0.31512 0.27704 0.77576

1994 "Northridge-01" "Beverly Hills -12520

Mulhol" 0.62092 0.44991 0.32582 0.52474

1994 "Northridge-01" "Lake Hughes #12A" 0.17445 0.25713 0.12055 0.46882

1994 "Northridge-01" "Topanga -Fire Sta" 0.32469 0.19247 0.19474 0.59977

2003 "San Simeon_ CA" "San Antonio Dam -Toe" 0.092985 0.12103 0.059472 0.49139

2007 "Chuetsu-oki_

Japan" "Kashiwazaki City Takayanagicho"

0.36207 0.72686 0.40537 0.5577

2007 "Chuetsu-oki_

Japan" "Oguni Nagaoka" 0.62535 0.51331 0.23961 0.38315

2008 "Iwate_ Japan" "AKT023" 0.3658 0.36784 0.25009 0.6799

2008 "Iwate_ Japan" "IWT015" 0.24339 0.2002 0.12186 0.50069

2008 "Iwate_ Japan" "Minase Yuzawa" 0.21533 0.244 0.13913 0.57018

2008 "Iwate_ Japan" "Kurihara City" 0.70268 0.42199 0.28619 0.40728

2008 "Iwate_ Japan" "Ichinoseki Maikawa" 0.33839 0.39224 0.16527 0.42134

1994 "Northridge-01" "LA -N Faring Rd" 0.27998 0.26365 0.18433 0.65837

2007 "Chuetsu-oki_

Japan" "NIG017" 0.24619 0.20681 0.1668 0.67751

2008 "Iwate_ Japan" "IWTH20" 0.24453 0.25434 0.13837 0.54403

34



1971 "San Fernando" "Castaic -Old Ridge

Route" 6.61 19.33

1971 "San Fernando" "LA -Hollywood Stor FF" 6.61 22.77

1994 "Northridge-01" "Canyon Country -W Lost

Cany" 6.69 11.39

1994 "Northridge-01" "LA -Brentwood VA

Hospital" 6.69 12.92

1994 "Northridge-01" "LA -UCLA Grounds" 6.69 13.8

1994 "Northridge-01" "Sunland -Mt Gleason

Ave" 6.69 12.38


2007 "Chuetsu-oki_ Japan" "Shiura Nagaoka" 6.8 10.61

2007 "Chuetsu-oki_ Japan" "NIG028" 6.8 15.32

2008 "Iwate_ Japan" "AKTH04" 6.9 13.07

2008 "Iwate_ Japan" "AKTH06" 6.9 19.15

2008 "Iwate_ Japan" "MYG005" 6.9 10.71

2008 "Iwate_ Japan" "Iwadeyama" 6.9 20.77

1971 "San Fernando" "Lake Hughes #12." 6.61 13.99

1971 "San Fernando" "Lake Hughes #9." 6.61 17.22

1976 "Friuli_ Italy-01" "Tolmezzo" 6.5 14.97

1994 "Northridge-01" "Beverly Hills -12520

Mulhol" 6.69 12.39

1994 "Northridge-01" "Lake Hughes #12A" 6.69 20.77

1994 "Northridge-01" "Topanga -Fire Sta" 6.69 10.31

2003 "San Simeon_ CA" "San Antonio Dam -Toe" 6.52 16.17

2007 "Chuetsu-oki_ Japan" "Kashiwazaki City Takayanagicho"

6.8 10.38

2007 "Chuetsu-oki_ Japan" "Oguni Nagaoka" 6.8 10.31

2008 "Iwate_ Japan" "AKT023" 6.9 11.68

2008 "Iwate_ Japan" "IWT015" 6.9 17.05

2008 "Iwate_ Japan" "Minase Yuzawa" 6.9 17.34

2008 "Iwate_ Japan" "Kurihara City" 6.9 12.83

2008 "Iwate_ Japan" "Ichinoseki Maikawa" 6.9 23.01

1994 "Northridge-01" "LA -N Faring Rd" 6.69 12.42

2007 "Chuetsu-oki_ Japan" "NIG017" 6.8 11.2

2008 "Iwate_ Japan" "IWTH20" 6.9 18.74

35

3.3 Defining Intensity Measure:

The purpose of this research is to show the difference between the building’s response under

two horizontal components and one vertical component, and the structure’s response under

only horizontal components. To present these changes in the response of structure, it is

crucial to determine the properties of a recorded earthquake that are most directly related

to the structures behavior. A value that quantifies the effect of a ground motion on the

structure is often called an Intensity Measure (IM). A record’s Peak Ground Acceleration has

frequently been used as an IM. However, ratio of PGAV to PGAH is not a good IM because it

can not show the strength of the ground motion.In other words, the structural response

cannot be presented correctly because PGAV/PGAH cannot presents the difference between

the strength of earthquakes which have similar V/H .

The efficiency of the estimation of the structural response can be enhanced if the correlation

between vertical and horizontal motions could be accounted for by an improved intensity

measure. In this research, the IM considered consists of the ratio of PGAV to PGAH along with

a third set of parameters: the magnitude (M), distance (R), and 30-m shear-wave velocity

(V30)associated with the ground motion. The resulting IM is called Ɛ (“epsilon”), which is

calculated as follows:

)ln(

)ln()ln(

/

/

HV

HV

H

V

PGA

PGA

The parameters PGAV and PGAH are obtained from empirical earthquake data. The

predicted median value of V/H, /V H , and the total aleatory standard deviation of the V/H

prediction, /V H , are calculated using CB16 ground motion model Bozorgnia and Campbell

36

(2016), using M, R, and V30 as input. The logarithms of all values in the ratio are taken, and

the result is Ɛ.

3.4 Response to Earthquake Ground Motions:

Each set of earthquakes cosidered in this study has 30 ground motions. Nonlinear response

history analysis has been performed for all of the individual ground motions in each group

with and without vertical component of ground motions.The Engineering demand

parameters (interstory drift ratio, peak floor acceleration, story shear and etc) were

obtained for all individual motions including vertical component (EDPV+H) as well as for all

individual motions without vertical excitation(EDPH).The ratios of EDPV+H and EDPH is called

𝛼 and is calculated as follows for each ground motion.

𝛼 =𝐸𝐷𝑃𝑉+𝐻

𝐸𝐷𝑃𝐻

Based on the individual ratios 𝛼, a linear equation (per Table 3-10 to 3-14) has been

established to estimate a magnification factor(�̂�) as a function of Ɛ. In this study, axial force

on columns and shear walls, maximum inter-story drifts ratio, story shear, peak floor vertical

acceleration and peak floor vertical displacement were investigated.

37

3.4.1 Axial Force:

Figure 3-1 through 3-4 compare the axial force on exterior and interior columns, with and

without vertical excitation for each group respectively. Based on these figures, it can be

concluded that interior columns are significantly more influenced by vertical excitation than

exterior columns and shear walls. The motions with reverse fault type and a short distance

to a fault have a significant effect on the axial force of columns and shear walls. As seen in

Figure 3-3, the axial load in interior columns is amplified by 35% at the median level. As the

ratio PGAv/PGAH increases, the magnification factor increases significantly. There is less

change in axial force ratio (H+V/H) from median level for motions with short distance to

strike-slip fault than with motions at a short distance to reverse fault. The change in �̂� is

very small for both far-field groups as compared to the near-field groups resulting

comparatively small change in axial force in the interior columns. The same pattern, with

smaller magnification values, can be seen for exterior columns and shear walls. It can thus

be concluded that in general, earthquakes with a reverse fault have more effect on the axial

load of columns and shear walls than earthquakes with a strike-slip fault. The effect of the

vertical component is more on the interior columns than the exterior columns and shear

walls since interior columns carry more gravity load than exterior columns and shear walls.

Tables 3-9 through 3-12 present the summary of equations of magnification factor for axial

load in columns and shear walls due to the effect of vertical excitation.

38

Figure 3- 1: Axial Force on Exterior and Interior Columns for Group 1


39



40

Figure 3- 5: Axial Force on Shear Walls for Group 1


41



42

Table 3- 10: Equations for magnification factor of Interior column axial load due to vertical component of ground motions

Strike-Slip Reverse

Near Field

�̂�𝑎𝑥𝑖𝑎𝑙 𝑙𝑜𝑎𝑑 = 1.23 − 0.22𝜀𝑉𝐻 𝜎𝑎𝑥𝑖𝑎𝑙 𝑙𝑜𝑎𝑑 = 0.20


Far Field



Table 3- 11: Equations for magnification factor of exterior column axial load due to vertical component of ground motions

Strike-Slip Reverse

Near Field



Far Field



Table 3- 12: Equations for magnification factor of shear wall axial load due to vertical component of ground motions

Strike-Slip Reverse

Near Field



Far Field



43

3.4.2 Inter-Story Drifts:

Figure 3-9 through 3-12 represent the maximum inter-story drift ratio (IDR) of the

structure’s response under the vertical and horizontal components of ground motions to the

response of the structure under only horizontal components. The figures show that there is

no significant contribution to story drift from inclusion of vertical component in the analysis.

As with axial load ratio, near-field ground motions with reverse faults have the most effect

on the maximum IDR. Table 3-13 shows that IDR magnification factor (𝛼 ) is very small for

all groups. To calculate the inter story drift, one need only consider the horizontal

components of ground motion.

44

Figure 3- 9: Max Inter-Story Drift Ratio for Group 1


45



46

Table 3- 13: Equations for magnification factor of max IDR ratio due to vertical component of ground motions

Strike-Slip Reverse

Near Field

�̂�𝑀𝑎𝑥 𝐼𝐷𝑅 = 1.04 − 0.05𝜀𝑉𝐻 𝜎𝑀𝑎𝑥 𝐼𝐷𝑅 = 0.035


Far Field



3.4.3 Story Shear:

Figure 3-9 through 3-12 represent the maximum story shear ratio of the structure’s response

under both the vertical and the horizontal components of ground motions to the response of

the building under only horizontal components. The figures show no significant change in

story shear when the vertical component is factored in. As with the axial load ratio, near-

field earthquakes with reverse faults have the most effect on the story shear. Table 3-14

shows that story shear magnification factor (𝛼) is very small for all groups.

47

Figure 3- 13: Max Story Shear Ratio for Group 1


48



49

Table 3- 14: Equations for magnification factor of story shear ratio due to vertical component of ground motions

Strike-Slip Reverse

Near Field

�̂�𝑠𝑡𝑜𝑟𝑦 𝑠ℎ𝑒𝑎𝑟 = 1.06 − 0.05𝜀𝑉𝐻

𝜎𝑠𝑡𝑜𝑟𝑦 𝑠ℎ𝑒𝑎𝑟 = 0.04



Far Field





3.4.4 Slab Response analysis:

From 30 records of each group, 6 records were selected with different V/H ratios to

calculated vertical displacement and acceleration of the slab at 2nd, 10th and 24th floors

along with the roof. The vertical acceleration and vertical displacement ratio (V+H/H) are

not a good EDPs for showing the effect of the vertical component of ground motions on slabs

because the vertical acceleration and the vertical displacement experienced by slab under

only horizontal components are negligible. Therefore only the results of the model under

ground motions including the vertical excitation are presented in the following sections.

3.4.4.1 Slab Vertical Acceleration:

Figures 3-17 through 3-20 present the peak floor acceleration of slab including vertical

excitation from the nonlinear response history analysis when the slab is accelerated

vertically. As seen in the figures, the near-field earthquakes have much more effect on the

slab vertical acceleration than far-field motions. The figures show that the vertical

acceleration of slab is around 2.2g for near-field with reverse fault earthquakes. It can be

concluded that the vertical component of ground motion is very important for slab design.

50

The peak floor vertical acceleration decreases gradually when floor level increases. In other

words, the peak floor vertical acceleration and floor level are inversely proportional to each

other. It must be emphasized that the slope of the linear regression line for near-field ground

motions are very sharp. This means that the slab vertical acceleration value is significantly

different for various potential earthquakes in each group.

51

`

Figure 3- 17: Vertical Acceleration at Mid-Span at Corner Slab for Group 1

52


53


54


55

3.4.4.2 Slab Vertical Displacement:

Figures 3-21 through 3-24 present the vertical displacement of the slab when vertical

excitation is included. As with other EDPs, the near-field earthquakes have much more effect

on the magnification factor than far-field earthquakes. The figure 3-23 show that the vertical

displacement of the slab is approximately 2.4 inch in the second floor for motions at near-

field to reverse fault. As with the absolute vertical acceleration, the relative vertical

displacement decreases gradually when floor level increases.

56

Figure 3- 21: Vertical Displacement at Mid-Span at Corner Slab for Group 1

57


58


59


60

Chapter 4

SUMMARY AND CONCLUSIONS

4.1 Summary

With the increasing interest in understanding the effect of the vertical component of ground

motion on structures, modeling the buildings to simulate the effects of the vertical motions

remains a major challenge for the earthquake engineering community. This study presents

the influence of vertical component of ground motions on the response of a tall building;

earthquakes with reverse fault and strike-slip with short or far distance to the fault are

considered. In addition, equations for estimating the effect of vertical component of ground

motions on tall buildings were developed based on the results. This was done by modeling

Model 2B of PEER’s Case Studies of the Seismic Performance of Tall Buildings (Moehle, et al.

2011). which is a high-rise, reinforced concrete, dual-system building located at a highly

seismic site, and which was designed using the performance-based seismic design

procedures of the TBI Guidelines. Time history analysis was performed for near-field and

far-field records which had either reverse or strike-slip fault type. These records were

obtained from the NGA-West2 database.

61

4.2 Conclusion and observations

The results of the present study can be summarized as follows.

1. The vertical component of an earthquake increased the axial force on the columns

over that of the horizontal components by 20% to 120%. This increase was higher for

interior columns than exterior columns and shear walls. Earthquakes with reverse

faults have a stronger effect on a column’s axial load than strike-slip faults. Moreover,

earthquakes in the near field have a significantly higher effect on axial load than

earthquakes in the far-field.

2. Maximum inter-story drifts and story shear response do not change considerably due

to vertical excitation consideration. For in the median sense and for strong

earthquakes with a short distance to the fault, story drifts and story shears increase

only around 6%.; there is a small increase in magnification factor for rare records

with higher𝑃𝐺𝐴𝑉 𝑃𝐺𝐴𝐻⁄ . This means that vertical components are unnecessary for

calculating the inter-story drift and story-shear.

3. The vertical component of ground motion has a significant effect on slab vertical

acceleration. For near-field and far-field records, it is really important to include the

vertical component of ground motion in the analysis when designing a slab. The peak

floor vertical acceleration and floor level are inversely proportional to each other. For

near-field ground motions, the absolute vertical acceleration experienced by slab for

rare earthquakes is significantly different than the most likely events.

62

4. Slab vertical displacement is highly influenced by vertical excitation. The floor

relative vertical displacement decreases gradually when floor level increases. The

relative vertical displacement experienced by slab for rare earthquakes is

significantly different than the most likely events for all ground motions

63

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