Seismic Forces in Buildings: A Comparative Study with Universal Seismic Codes

A THESIS SUBMITTED TO UNIVERSITY OF KHARTOUM IN PARTIAL FULFILLMENT FOR THE DEGREE OF M.SC. IN STRUCTURAL ENGINEERING

By:

Maha Gaafar Ahmed El-Nourani

(B.Sc. Civil Eng. 2003)

University of Khartoum

Supervisor:

Dr. Mahgoub Osman Mahgoub

Faculty of Engineering

Department of Civil Engineering

August 2010

Dedication

To the coming joy.

To my beloved parents and family.

To myself that I have always doubted.

To a special friend who has encouraged me to start this journey.

To those who have dragged me down and those who have lifted me up.

Because of you all; I am standing here today.

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Acknowledgement

We have been taught that to thank Allah you have to thank people.

I would like to thank some of the people who have helped me through my life and this research in particular.

I would like to pay my gratitude to Dr. Mahgoub Osman Mahgoub for his patience, time and valuable suggestions through the entire research.

I would like also to thank some of my colleagues who have supplied me with unlimited amounts of software books as well as their support.

Finally, I would like to thank my mentor through life, the one who has always believed in the existence of a better me; I would like to thank you father for your unconditional love and support and to you mother all the love.

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Abstract

This research has focussed on the analysis of earthquake forces on buildings using static linear methods by some of the most important universal seismic codes as well as comparing between these codes.

These codes are, the American codes and the European code, EUROCODE 8.

The American code, UBC 1994, is the code used by the Sudanese structural engineers in seismic analysis and design; this code has been studied and discussed in details.

Different illustrative models have been represented in this research:

In the first model, the seismic forces have been computed on a multi-storey reinforced concrete building by the different codes adopted in this research and a comparison between the values have been made.

In the second model, the horizontal distribution of the floor seismic load to the seismic resistant element, shear walls in our case, has been shown by a simplified method.

In the third model, an interior seismic resistant reinforced concrete column have been designed by ACI 318M-05.

The resulting data from seismic analysis computations by the different codes have been discussed in details.

This research has been concluded by focussing on the shared main points adopted by all the seismic codes of our concern in the computation of seismic shear forces on structures as well as discussing some of the differences between these codes.

This study has recommended an update for the seismic data in Sudan which has taken UBC 1994 as a reference code, so as to match the new requirements of UBC 1997 as agreed by the unified Arabic code 2005 for seismic resistant building and structures.

This study has also suggested the application of a min 1% of total dead load of any type of structure at its base as a simple way to include the seismic force in the design.

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ملخصال

الخطية لى تحليل قوى الزXزل على المباني باستخدام الطريقة اXستاتيكيةعتم التركيز في ھذا البحث

.ل و اجراء مقارنة بينھاالكودات العالمية في مجال الزXزباستخدام بعض أھم

.EUROCODE 8 اxوربي الكودو كذلك اxمريكية ھي الكوداتالكوداتھذه

ھو الكود المستعمل في السودان من قبل المھندسيين اXنشائيين في (UBC 1994)الكود اxمريكي

.الي ، ھذا الكود تمت دراسته و مناقشته بالتفصيلالتحليل و التصميم الزلز

:تم تقديم نماذج توضيحية مختلفة

في النموذج اXول تم حساب قوى الزXزل على مبنى خرساني متعدد الطوابق باستخدام الكودات الزلزالية

. المختلفة المعتمدة في ھذا البحث وتمت المقارنة بين القيم المتحصل عليھا

لثاني تم توضيح طريقة مبسطة لتوزيع قوى القص الزلزالية الطابقية على العناصر المقاومة في النموج ا

. جدران القص في ھذه الحالة- للزXزل

مريكيكود اx الفي النموذج الثالث تم تصميم عمود داخلي من الخرسانة المسلحة ليقاوم قوى الزXزل باستخدام

(ACI 318M-05).

.بواسطة الكودات المختلفةلنتائج المتحصل عليھا من التحليل الزلزالي تمت مناقشة تفصيلية ل

اختتم البحث بالتركيز على النقاط اxساسية المشتركة بين الكودات الزلزالية المختلفة في تحليل قوى

.القص الزلزالية على المنشآت وكذلك مناقشة بعض الفروقات بين ھذه الكودات

UBCث على البيانات الزلزالية في السودان والتي اعتمدت على يوصي ھذا البحث باجراء تحدي

و الذي اتفقت الدول العربية على UBC 1997 ككود مرجعي لكي تطابق المتطلبات الجديدة التي أقرھا 1994

. للمباني و المنشات المقاومة للزXزل2005 ككود مرجعي للكود العربي الموحد اعتماده

للمباني على قواعدھا كطريقة الحمل الميت الكلي منعلى اxقل% 1بيق بتطأيضا ھذا البحث يوصي

. مبسطة لتضمين القوى الزلزالية في التصميم

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Table of Contents Acknowledgement ........................................................................................................ i Abstract ........................................................................................................................ ii الملخص .......................................................................................................................... iii Table of Contents ........................................................................................................ iv List of Figures ............................................................................................................ vii List of Plates................................................................................................................ ix List of Tables ................................................................................................................x Notations ................................................................................................................... xiv CHAPTER 1 INTRODUCTION ..................................................................................1 1.1 Introduction ....................................................................................................2 1.2 Causes of Earthquakes....................................................................................4 1.2.1 Natural Induced Earthquakes..................................................................4 1.2.2 Man-Made Earthquakes ..........................................................................6

1.3 The Scales of Earthquakes .............................................................................7 1.4 Seismic Intensity Scale...................................................................................7 1.5 Seismic Magnitude Scale ...............................................................................7 1.6 Seismic Moment Scale ...................................................................................8 1.7 Seismic Instruments .......................................................................................8 1.8 Interpretation of Seismic Data........................................................................9 1.9 Damages Resulting From Earthquakes ..........................................................9 1.10 Objectives: ................................................................................................14 1.11 Research Methodology .............................................................................14

CHAPTER 2 LITERATURE REVIEW .....................................................................15 2.1 Comparison between the Normal Provisions in Building Codes and Those Ones for Earthquake Resistant Design....................................................................16 2.2 Earthquake Resistant Requirements.............................................................17 2.3 Seismic and Wind Design ............................................................................17 2.4 Historical Background about the Development of Earthquake Resistance Provisions in Building Codes..................................................................................17 2.5 The International Seismic Codes References...............................................18 2.6 Early Lateral Force (ELF) Requirements.....................................................18 2.7 The Seismic Codes Used In This Research..................................................19 2.7.1 The UBC ...............................................................................................19 2.7.2 The NEHRP 2003 Edition.....................................................................20 2.7.3 Eurocode 8 ............................................................................................21

2.8 The Sudanese Seismic Studies .....................................................................21 CHAPTER 3 SEISMIC ANALYSIS IN BUILDINGS ..............................................22 3.1 Methods of Seismic Analysis in the Codes..................................................23 3.2 UBC 1994.....................................................................................................23 3.2.1 Estimation of the Minimum Base Shear Force .....................................23 3.2.2 Definition of Seismic Coefficient .........................................................23 3.2.3 The Fundamental Period of the Structure, T.........................................24 3.2.4 Vertical Distribution of the Total Base Shear.......................................25 3.2.5 Overturning Moment.............................................................................26 3.2.6 Modifications on Some of the UBC 1994 Factors to Suit Sudan Conditions ...........................................................................................................26

3.3 1997 UBC Edition........................................................................................29 3.3.1 Site Geology and Soil Characteristics...................................................29

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3.3.2 Occupancy Categories...........................................................................30 3.3.3 Seismic Zone.........................................................................................31 3.3.4 Seismic Zone 4 Near-Source Factor .....................................................32 3.3.5 Seismic Response Coefficients .............................................................34 3.3.6 Configuration Requirements .................................................................34 3.3.7 Selection of Lateral-Force Procedure ...................................................36 3.3.8 Modeling Requirements........................................................................37 3.3.9 Static Force Procedure ..........................................................................37 3.3.10 Vertical Distribution of Force ...........................................................38 3.3.11 Horizontal Distribution of Shear .......................................................38 3.3.12 Horizontal Torsional Moments .........................................................38 3.3.13 Overturning Moments .......................................................................39 3.3.14 Structure Period (T)...........................................................................39 3.3.15 Determination of Seismic Factors .....................................................40

3.4 The NEHRP 2003 Recommended Provisions..............................................41 3.4.1 Site Classification for Seismic Design..................................................41 3.4.2 Seismic Use Groups ..............................................................................43 3.4.3 Occupancy Importance Factor ..............................................................45 3.4.4 Seismic Design Category ......................................................................45 3.4.5 Mapped Acceleration Parameters .........................................................46 3.4.6 Site Coefficients and Adjusted Acceleration Parameters .....................49 3.4.7 Design Acceleration Parameters ...........................................................50 3.4.8 Design Response Spectrum...................................................................50 3.4.9 Irregularity of the Structures .................................................................53 3.4.10 Redundancy:......................................................................................55 3.4.11 Structural Analysis ............................................................................56 3.4.12 Structural Analysis Procedure Selection: ..........................................56 3.4.13 Application of Loading .....................................................................57 3.4.14 Index Force Procedure.......................................................................58 3.4.15 Equivalent Lateral Force Procedure ..................................................58 3.4.16 Vertical Distribution of Seismic Forces ............................................62 3.4.17 Horizontal Shear Distribution ...........................................................63 3.4.18 Overturning Moment.........................................................................63

3.5 EUROCODE 8 .............................................................................................65 3.5.1 Ground Conditions................................................................................65 3.5.2 Seismic Action ......................................................................................66 3.5.3 Criteria for Structural Regularity ..........................................................73 3.5.4 Combinations of the Seismic Action with Other Actions.....................76 3.5.5 Importance Classes and Importance Factors.........................................77 3.5.6 Structural Analysis................................................................................78 3.5.7 Accidental Torsional Effects.................................................................79 3.5.8 Methods of Analysis .............................................................................79 3.5.9 Lateral Force Method of Analysis ........................................................80 3.5.10 Distribution of the Horizontal Seismic Forces ..................................81 3.5.11 Torsional Effects ...............................................................................82

3.6 Comparison between Seismic Provisions Terms in the Specified Code......83 3.7 Design Provisions for R.C Seismic-Resistant Columns by ACI 318M-05..92 3.7.1 Ductility of Reinforced Concrete..........................................................92 3.7.2 R.C Columns Resisting Seismic Forces................................................93 3.7.3 Minimum Flexural Strength of Column................................................93

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3.7.4 Longitudinal Reinforcement .................................................................93 3.7.5 Transverse or Confinement Reinforcement ..........................................94 3.7.6 Shear Strength Requirements................................................................95 3.7.7 Factors Affecting the Behavior of Structures under Seismic Forces ....96

CHAPTER 4 COMPUTATIONAL MODELS.........................................................103 4.1 Comparison between the Specified Codes in Computing the Seismic Base Shear Force of a Multi-Storey Reinforced Concrete Building .............................104 4.2 Computations of Seismic Base Shear Forces .............................................107 4.2.1 UBC 1994 ...........................................................................................107 4.2.2 UBC 1997 ...........................................................................................109 4.2.3 NEHRP 2003.......................................................................................111 4.2.4 EUROCODE 8 2003...........................................................................114

4.3 Vertical Distribution of the Seismic Base Shear Force..............................117 4.3.1 UBC 1994 ...........................................................................................117 4.3.2 UBC 1997 ...........................................................................................118 4.3.3 NEHRP 2003.......................................................................................119 4.3.4 EUROCODE 8 2003...........................................................................120

4.4 Bending Moment and Shear Force Calculations and Diagrams: ...............121 4.5 Distribution of the Floor Seismic Shear Force to the Shear Walls of That Floor 134 4.5.1 Computations of the Horizontal Distribution of the Floor Seismic Force 135

4.6 Design of A Seismic Resistant R.C Column by ACI 318M-05 .................141 4.6.1 R.C Column Seismic Resistant Design by ACI 318M-05 ..................143

CHAPTER 5 DISCUSSION OF RESULTS ............................................................151 5.1 Computation of seismic shear forces by different codes............................152 5.2 Seismic Shear Force Factors ......................................................................153 5.3 Different Factors Effecting the Analysis Accuracy ...................................155 5.4 Seismic analysis using ETABS software ...................................................155 5.5 Vertical distribution of the seismic base shear force to the floors of the structure.................................................................................................................156 5.6 Horizontal distribution of the floor seismic force to seismic resistant elements ................................................................................................................156

CHAPTER 6 CONCLUSIONS & RECOMMENDATIONS...................................158 6.1 Conclusions ................................................................................................159 6.1.1 Seismic Codes Techniques for the Computation of Seismic Forces on Structures ..........................................................................................................159 6.1.2 Seismic Resistant Design For Columns by ACI 318M-05 .................160 6.1.3 Seismic Reference Codes in Sudan and Arab Countries ....................160

6.2 Recommendations: .....................................................................................161 6.2.1 Recommendations for Seismic Design in Sudan ................................161 6.2.2 Recommendations for Future Studies .................................................161

References.................................................................................................................162 Appendices................................................................................................................163

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List of Figures

Figure Page

Figure (1-1) Twentieth century global earthquake fatalities, by

decade. 3

Figure (1-2) Trend of worldwide economic and insured losses, from

Munich Reinsurance. 3

Figure (1-3) Earthquake Fault Lines all over the world 5

Figure (1-4) Fault Types 5

Figure (1-5) Liquefaction Phenomenon 10

Figure (3-1) Seismic Zone Map for USA 32

Figure (3-2) Maximum considered earthquake ground motion for the

conterminous US of 0.2 sec spectral response acceleration (5% of

critical damping), site class B

47

Figure (3-3) Maximum considered earthquake ground motion for the

conterminous US of 1.0 sec spectral response acceleration (5% of

critical damping), site class B

48

Figure (3-4) Maximum considered earthquake response spectrum. 50

Figure (3-5) Long-Period transition Period 51

Figure (3-6) Long-Period transition Period TL(s), for the conterminous

US 52

Figure (3-7) Shape of the elastic response spectrum 69

Figure (3-8) Recommended Type 1 elastic response spectra for

ground types A to E (5% damping) 70

Figure (3-9) Recommended Type 2 elastic response spectra for

ground types A to E (5% damping) 71

Figure (3-10) Criteria for regularity of buildings with setbacks 76

Figure (4-1) Floor plan 105

Figure (4-2) Sectional elevation A-A 106

Figure (4-3) Seismic Bending moment Diagram by UBC 1994 126

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Figure (4-4) Seismic Shear Force Diagram by UBC 1994 127

Figure (4-5) Seismic Bending Moment Diagram by UBC 1997 128

Figure (4-6) Seismic Shear Force Diagram by UBC 1997 129

Figure (4-7) Seismic Bending moment Diagram by NEHRP 2003 130

Figure (4-8) Seismic Shear Force Diagram by NEHRP 2003 131

Figure (4-9) Seismic Bending moment Diagram by EUROCODE 8

2003 132

Figure (4-10) Seismic Shear Force Diagram by EUROCODE 8 2003 133

Figure (4-11) Floor plan 134

Figure (4-12) Centers of gravity and rigidity of shear walls 139

Figure (4-13) Sectional Elevation for the R.C Column 142

Figure (4- 14) Interaction Diagram for ϕPn - ϕMn and Ppr – Mpr 148

Figure (4- 15) Sectional Elevation for the column under design 149

Figure (4-16) Section A-A 150

Figure (4-17) Section B-B 150

Figure (5-1) Seismic base shear force computed by different codes 152

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List of Plates

Plate Page

Plate (1-1) Aerial view of San Andreas Fault, Right-Lateral Strike-

Slip Faults 6

Plate (1-2) Fault rupture – Luzon, Philippines 1990 10

Plate (1-3) Liquefaction – Adapazari, Turkey 1999 11

Plate (1-4) Slope instability – Niigata, Japan 2004 11

Plate (1-5) An example of Mexico City building damage, September

19, 1985 12

Plate (1-6) Hanshin Expressway collapse, January 17, 1995 Hanshin

earthquake.

12

Plate (1-7) Fourth Avenue buildings in downtown Anchorage shows

the damage resulting from the slide in this area.

13

Plate (1-8) Seward at the north end of Resurrection Bay, the total

damage to port and harbor facilities at Seward was estimated at more

than $15,000. Most of this damage was the result of the tsunamis.

Eleven persons lost their lives due to the sea waves at Seward.

13

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List of Tables

Table Page

Table (1-1) Selected Pre-Twentieth Century Earthquakes (Fatalities

greater than 50000) 2

Table (3-1) Seismic Zones and their corresponding PGA’s 27

Table (3-2) Zone number and corresponding seismic zone factor, Z 27

Table (3-3) Soil profile and the corresponding S factor 27

Table (3-4) Importance Factor, I 28

Table (3-5) Soil profile types 30

Table (3-6) Occupancy Category 30-31

Table (3-7) seismic zone Factor Z 32

Table (3-8) —Near-Source Factor Na 32

Table (3-9) —Near-Source Factor Nv 33

Table (3-10)—Seismic Source Type1 33

Table (3-11) Seismic Coefficient, Ca 34

Table (3-12) Seismic Coefficient, Cv 34

Table (3-13) Vertical Structural Irregularities 35

Table (3-14) Plan Structural Irregularities 36

Table (3-15) Site Classification 41

Table (3-16) Seismic use group 43-44

Table (3-17) Occupancy Importance Factors 45

Table (3-18) Seismic Design Category Based on SDS 45

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Table (3-19) Seismic Design Category Based on SD1 46

Table (3-20) Values of Site Coefficient Fa 49

Table (3-21) Values of Site Coefficient Fv 49

Table (3-22) Plan Structural Irregularities 54

Table (3-23) Vertical Structural Irregularities 55

Table (3-24) Structural Methods of Analysis 57

Table (3-25) Coefficient for Upper Limit on Calculated Period 60

Table (3-26) Values of Approximate Period Parameters Cr and x 61

Table (3-27) Ground Types 65

Table (3-28) Values of the parameters describing the recommended

Type 1 elastic response spectra 70

Table (3-29) Values of the parameters describing the recommended

Type 2 elastic response spectra 70

Table (3-30) Recommended values of parameters describing the

vertical elastic response spectra 72

Table (3-31) Consequences of structural regularity on seismic

analysis and design 74

Table (3-32) Values of ϕ for calculating ψEi 77

Table (3-33) Importance classes for buildings 78

Table (3-34) Comparison between Seismic Provisions Terms in the

Specified Codes Concerning the Equivalent Lateral Force (ELF)

Method

83-91

Table (3-35) Comparison between Flexible and Rigid Structures 98

Table (4-1) Seismic forces calculated by static equivalent lateral

force by different codes of practice 116

Table (4-2) Vertical distribution of the seismic base shear by UBC

1994 117

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Table (4-3) Vertical distribution of the seismic base shear by UBC

1997 118

Table (4-4) Vertical distribution of the seismic base shear by

NEHRP 119

Table (4-5) Vertical distribution of the seismic base shear by

EUROCODE 8 120

Table (4-6) Seismic bending moment and shear force calculation by

UBC 1994 122

Table (4-7) Seismic bending moment and shear force calculation by

UBC 1997 123

Table (4-8) Seismic bending moment and shear force calculation by

NEHRP 2003 124

Table (4-9) Seismic bending moment and shear force calculation by

EUROCODE 8 2003 125

Table (4-10) Determination of the stiffnesses of shear walls to

calculate the centre of rigidity 136

Table (4-11) Determination of the centre of gravity, mass 137

Table (4-12) Seismic force components on shear walls 140

Table (4-13) Unfactored loads on column 141

Table (4-14) Factored loads on column 143

Table (5-1) Seismic base shear force computed by different codes 152

Table (5-2) The Dominant Factors in Seismic base Shear force

computations 153

Table (5-3) Factors effecting the computation of the seismic base

shear force 154

Table (5-4) Comparison between the seismic base shear forces

computed manually and by ETABS using the specified codes 156

Table (A-1) Recommended Structural Systems factor Rw and height

limitations for different structural systems 164

Table (A-2) The structural systems factors, R and Ωo and height

limitations 165-166

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Table (A-3) Design Coefficients and Factors for Basic Seismic Force

Resisting Systems 167-172

Table (A-4) Basic value of the behaviour factor, qo, for systems

regular in elevation 173

Table (B-1) Allowable Story Drift, ∆a 178

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Notations

A: Fault surface area or seismic slipping displacement (L*h).

AB: The base area of the structure.

ag : The design ground acceleration on type A ground (ag = γI.agR).

agR: The reference peak ground acceleration on type A ground.

Ac: The total effective area of the shear walls in the first storey of the building,

in m2.

Ai: The effective cross-sectional area of the shear wall i in the first storey of the

building, in m2.

Ach: Column core area (confined by the external hoops).

Ag: Total gross area of column.

Ast: Area of longitudinal reinforcement

Ash: Sum of legs cross areas over bc.

an, ax: The accelerations of the structure at level x and the roof of the structure

respectively.

bc: The cross sectional dimension of the core, measured centre to centre of the

hoops .

C: The spectral shape coefficient.

Cd : The deflection amplification factor from Table(B-1).

Cv, Ca: Seismic Coefficients.

Cs: The seismic response coefficient.

Cw: A coefficient related to the effective shear wall area and hn is as defined

above.

Cvx: Vertical distribution factor.

D: Average slipping along seismic fault.

DF: Moment Distribution factor at the top and bottom.

D(x,y): Slipping along seismic fault.

di: The thickness of any layer of soil (between 0 and 100 ft [30 m]).

ds: The total thickness of cohesionless soil layers in the top 100 ft (30 m).

dc: The total thickness of cohesive soil layers in the top 100 ft (30 m).

E: The resulting energy as measured by Joule.

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E: The earthquake load on an element of the structure resulting from the

combination of the horizontal component, Eh, and the vertical component, Ev.

Eh: The load effect resulting from the horizontal component of the earthquake

ground motion.

Em: The estimated maximum earthquake force that can be developed in the

structure.

Ev : The load effect resulting from the vertical component of the earthquake

ground motion and is equal to an addition of 0.5CaID to the dead load effect, D, for

Strength Design, and may be taken as zero for Allowable Stress Design.

eox, eoy: The natural eccentricities .

eox: The distance between the centre of stiffness and the centre of mass,

measured along the x direction, which is normal to the direction of analysis

considered.

eai: The accidental eccentricity of storey mass i from its nominal location,

applied in the same direction at all floors.

Fx: The floor equivalent horizontal force.

Fi: The portion of the seismic base shear, V, induced at Level i.

Fb: The seismic base shear (a notation used by EUROCODE 8 =V in the

other codes)

G: Shear factor for the medium in earthquake center.

g: The ground acceleration(9.81m/s2).

hn, hx: The heights of the structure at level x and the roof of the structure

respectively.

hi, hx: Height from the base to levels i and x.

hn: The height in feet (meters) above the base to the highest level of the

structure and the values of Cr and x shall be determined from Table (3-26).

hi: The height of shear wall i.

hwi: The height of wall i.

hsx: The story height below Level x.

hx: The horizontal spacing of crossties or legs of overlapping hoops and hx≤350mm on centre.

I: The importance factor, UBC 1994.

I: Seismic importance factor, UBC 1997.

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I: The occupancy importance factor, NEHRP.

k: An exponent related to the effective fundamental period of the structure.

kw: The factor reflecting the prevailing failure mode in structural systems with

walls.

Le: The distance between the two outermost lateral load resisting elements,

measured perpendicularly to the direction of the seismic action considered.

Li: The length of shear wall.

Li: The floor-dimension perpendicular to the direction of the seismic action.

Lwi: The length of the shear wall i in the first storey in the direction parallel to

the applied forces, in m, with the restriction that lwi/H should not exceed 0.9.

Lmax, Lmin: The larger and smaller in plan dimension of the building, measured in

orthogonal directions.

ls: The radius of gyration of the floor mass in plan (square root of the ratio of

(a) the polar moment of inertia of the floor mass in plan with respect to the centre of

mass of the floor to (b) the floor mass).

M: Earthquake degree according to Richter’s.

Mprctop, btm: The probable moment capacities of the column and obtained from

interaction diagram for probable strength Ppr- Mpr of the column, for the range of

factored loads on the member for the load combination under consideration.

∑Mnc: Sum of nominal flexural strengths of columns framing into the joint,

evaluated at the faces of the joint.

∑Mnb: Sum of nominal flexural strength of the beams framing into the joint,

evaluated at the face of the joint.

m: The total mass of the building, above the foundation or above the top of a

rigid basement.

mi, mj: The storey masses at level i and j respectively.

�: Number of stories.

n: The number of shear walls in the building effective in resisting lateral forces

in the direction under consideration.

�i: The Standard Penetration Resistance determined in accordance with ASTM

D 1586, as directly measured in the field without corrections, and shall not be taken

greater than 100blows/ft.

PI: The plasticity index, determined in accordance with ASTM D 4318.

xvii

Px : The total vertical design load at and above Level x. Where calculating the

vertical design load for purposes of determining P-delta effects, the individual load

factors need not exceed 1.0.

q: The behaviour factor.

qo : The basic value of the behaviour factor, dependent on the type of the

structural system and on its regularity in elevation .

Rw: The numerical structural system factor, UBC 1994.

R: The structural system factor, UBC 1997.

R: The response modification factor, NEHRP.

rmax: The maximum element-story shear ratio. For a given direction of loading,

the element-story shear ratio is the ratio of the design story shear in the most heavily

loaded single element divided by the total design story shear.

rx , ry: The square root of the ratio of the torsional stiffness to the lateral stiffness

in the y and x direction respectively (“torsional radius”).

S: The site coefficient, UBC 1994.

S: The soil factor, EUROCODE 8.

S: The spacing between the hoops, measured centre to centre of the hoops.

si , s j: The displacements of masses mi, mj in the fundamental mode shape.

Ss: The mapped acceleration parameter at short period.

S1: The mapped acceleration parameter at a period of 1.0 second

SDS: The design spectral response acceleration parameter at short periods.

SD1: The design spectral response acceleration parameter at a period of 1.0

second.

SMS, SM1: The maximum considered earthquake (MCE) spectral response

acceleration parameters, adjusted for site class effects, for short and long period

respectively.

Sd (T1): The ordinate of the design spectrum at period T1.

sui : The undrained shear strength in psf (kPa), determined in accordance with

ASTM D 2166 or D 2850, and shall not be taken greater than 5,000psf (250kPa).

Sd (T): The design spectrum.

Se (T): The elastic response spectrum.

T: The fundamental period of vibration of the structure or the vibration

period of a linear single-degree-of-freedom system.

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TB: The lower limit of the period of the constant spectral acceleration branch.

TC: The upper limit of the period of the constant spectral acceleration branch.

TD: The value defining the beginning of the constant displacement response

range of the spectrum.

T1: The fundamental period of vibration of the building for lateral motion in the

direction considered, EUROCODE 8.

TL: Long-period transition period.

T0: 0.2SD1/SDS TS: SD1/SDS V: Total design lateral force or shear at the base of the structure.

Vx: The seismic shear force acting between Level x and x - 1.

Vsi: The shear wave velocity in ft/sec (m/s).

W: Normally the total dead load of the building.

Wi, Wx: Portions of W assigned to levels i and x, respectively; that is, the weight at

or adjacent to levels i and x.

w: The moisture content in percent, determined in accordance with ASTM D

2216.

wi, wx : The portion of the total gravity load of the structure, W, located or assigned

to Level i or x.

x: The distance of the element under consideration from the centre of mass of

the building in plan, measured perpendicularly to the direction of the seismic action

considered.

Z: Seismic zone Factor.

zi, zj: The heights of the masses mi, mj above the level of application of the

seismic action (foundation or top of a rigid basement).

λ: The correction factor.

δ : The lateral elastic displacement of the top of the building, in m, due to the

gravity loads applied in the horizontal direction.

iδ : Calculated deflection using applied lateral force at level i.

δmax: The maximum displacement at Level x.

δavg: The average of the displacements at the extreme points of the structure at

Level x.

δx, δn: The lateral displacements at level x and the roof of the structure

respectively.

xix

δxe : The deflections determined by an elastic analysis.

η: The damping correction factor with a reference value of η = 1 for 5%

viscous damping.

ξ: The viscous damping ratio of the structure, expressed as a percentage.

ψE,i : The combination coefficient for variable action i.

α1: The value by which the horizontal seismic design action is multiplied in

order to first reach the flexural resistance in any member in the structure, while all

other design actions remain constant.

αu: The value by which the horizontal seismic design action is multiplied, in

order to form plastic hinges in a number of sections sufficient for the development of

overall structural instability, while all other design actions remain constant. The

factor αu may be obtained from a nonlinear static (pushover) global analysis.

β: The lower bound factor for the horizontal design spectrum.

γI: The importance factor, EUROCODE 8.

Ωo: The seismic force amplification factor that is required to account for

structural overstrength.

∆: The design story drift.

ρ: Reliability/Redundancy Factor.

CHAPTER 1

I TRODUCTIO

2

1.1 Introduction

Earthquakes have caused so much loss in human lives, constructions as well as economy through the years and left nothing but destruction and devastation. The following Tables and charts give a clear vision about the severity of the earthquake disaster.

Table (1-1) selected pre-twentieth century earthquakes

(fatalities greater than 50000)(4)

Year Month Day Location Deaths

856 12 22 Iran, Damghan 200000

839 3 23 Iran, Ardabil 150000

1138 8 9 Syria, Aleppo 230000

1268 Asia minor, Silicia 60000

1290 9 China, Chilhi 100000

1556 1 23 China, Shansi 830000

1667 11 Caucasia, Shemakha 80000

1693 1 11 Italy, Sicily 60000

1727 11 18 Iran, Damghan 77000

1755 11 1 Portugal, Lisbon 70000

1738 2 4 Italy, Calabria 50000

3

Figure (1-1) Twentieth century global earthquake fatalities, by decade(4)

Decade

Fatalities

Figure (1-2) Trend of worldwide economic and insured losses,

from Munich Reinsurance(4)

4

1.2 Causes of Earthquakes

Ancients had thought that legendary reasons are behind earthquakes. Some of them believed that, animals of different types carry the earth and keep it steady; the type of animals differs from one culture to the other. Whereas Phithagourth believed that what causes earthquakes are wars between dead people! Probably, the first scientific interpretation refers to the Arabic philosopher and scientist Ibn-Sina who thought the action of the earthquake refers to a movement of what lies beneath the ground. In our recent world the American scientist Reid is the first scientist to find the physics basis to explain the process of earthquakes and has published it in 1910 in a paper under the title ‘Elastic rebound theory of earthquake sources ‘, the following definition can be extracted from that theory:

Earthquake is a sudden breakage and faulting of huge volume and masses of rocks inside the lithosphere because they have been stressed to limits that exceed their ability of enduring the tectonic forces applied on them; as a result of that a massive movement energy is released mainly in the form of vibrations that move in different speeds inside the ground and on its surface causing disasters and destructions to both environment and humans.

The main shake corresponding to the earthquake action is called ‘the main shock’ and it is sometimes preceded by a group of minor shakes that are called ‘the foreshocks ‘; however the main shock is always followed by a big group of small and moderate shakes that may reach 100 and are called ‘the aftershocks’ and may last for a long period of time between few months to few years depending on the volume of the energy released through the earthquake .Another form of seismic activity is called earthquake swarms and is characterized by gradual releasing of the stored seismic energy within limited areas and through time periods varying between few weeks to few months in the form of mini earthquakes without the existence of the main shock.

Generally earthquakes can be divided into two types:

1.2.1 Natural Induced Earthquakes Many natural phenomena can induce earthquakes and they are summarized

as follows:

1. Tectonic earthquakes

Tectonic earthquakes result from the relative movement of the plates forming the earth crust resulting in what is known as faults. Usually the faults start to form in a deep zone of the rocks that is called the ‘hypocenter’ and the center on the surface is called the ‘epicenter’. The closer the hypocenter to the earth surface the greater is the proportion of the destruction in the area. The relative displacement on the slipping fault sides, as a result of an earthquake can reach few meters whereas the same fault length can reach hundreds of kilometers depending on the amount of the liberated seismic energy and generally tectonic earthquakes spread close to the faults of the main plates forming the earth crust.

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5

Figure (1-3) Earthquake Fault Lines all over the world(15)

Figure (1-4) Fault Types(15)

6

Plate (1-1) Aerial view of San Andreas Fault, Right-Lateral Strike-Slip Faults

2. Volcanic earthquakes

Volcanic earthquakes result from cumulating pressures and excessive heat because the rocks released from the deep lava are pushed under a weak zone of the crust which leads to sudden cracks that will release lava in excessive speed and pressure, this type of earthquakes has the same effect of explosions.

Volcanic earthquakes can be categorized into three groups:

i. Level (a): the hypocenter depth varies between 1 to10km

ii. Level (b): the hypocenter depth is less than 1km.

iii. Volcanic earthquakes similar to explosions: these earthquakes happen almost on the earth surface; this is the reason they sound like explosions in their effect and continue to a relatively long period of time causing continuous volcanic shakes and usually the inner flow of lava causes the volcanic gases to explode.

3. Collapse earthquakes

They result from the collapse of cave roofs and usually they generate low seismic energy and therefore small earthquakes with local effects.

1.2.2 Man-Made Earthquakes Many human activities can lead to earthquakes. Some of these activities can

be completely controlled such as explosions both traditional and nuclear. Whereas other activities may initiate uncontrolled earthquakes to happen such as those

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7

resulting from filling dams and fluids injection in some mining areas or oil extraction; the magnitude of these earthquakes can reach 5.5 degree on Richter scale.

1.3 The Scales of Earthquakes

It is very difficult to measure the magnitude of an earthquake and that is due to a number of factors related to the process of the earthquake in itself such as intensity, occurrence period, earthquake magnitude and the degree of destruction resulting from it. A lot of scales were suggested to estimate the magnitude of an earthquake and define the destruction range resulting from it but all these scales are lacking some important elements. In spite of that; two terms are universally widely used, these are; intensity and magnitude terms and in some other cases seismic moment term is used.

1.4 Seismic Intensity Scale

Intensity scale is considered as a descriptive scale as the seismic intensity is defined by the degree of shaking resulting from it, also the damages in the field and the constructions; this is investigated by field observations. This is achieved by drawing maps that show ranges in a specific area and for this purpose Modified Mercalli Intensity Scale is used and it grades from I (mild intensity that can not be felt by humans but registered through sensitive seismic registration instruments) to XII (severe destructive intensity where devastating losses for humans, materials and environment are encountered as a result of the complete destruction of structures, public facilities as well as the disconnection of transportations roads) to indicate the severity of damages related to the earthquake.

1.5 Seismic Magnitude Scale

The American scientist Charles Richter has developed a physical scale technique to compare between the liberated energy from the different earthquakes that have affected California State. This scale depends on measuring the range of the biggest seismic wave registered in the seismic registration for any earthquake and this has to be from a specific distance from the epicenter (the surface center of the earthquake).

The magnitude of an earthquake M is defined according to this scale as the logarithm (log10 )of the greatest wave range registered from an earthquake 100km far and the frequency range is measured by micrometer (10-6m). Although this system is used in almost a universal pattern to define the seismic degree, but it contains deficiencies such as; the greatest wave frequency can be identified for the P, S, (pressure and shear waves, together they are called body waves as they are spreading inside the earth), or surface waves generated by an earthquake, which makes it difficult to define the magnitude and more than a single estimation of the same event can be found. In addition to that most magnitude equations don’t take into consideration the period of earthquake shaking and so the mechanics and dynamics of faults and seismic energy liberating remains uncounted.

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8

�otes

a. As a result of studying a large number of earthquakes, both scientists Gutenberg and Richter have reached a descriptive relation between earthquakes degree and the resulting energy as follows:

Log E=1.5M+11.4 (1-1)

Where,

E: The resulting energy as measured by Joule

M: earthquake degree according to Richter’s

The greatest degree registered for earthquakes by Richter’s scale is between 8.6 and 8.8, practically can not exceed 9 because it is impossible for rocks to endure an energy that exceeds this value.

b. Mercalli’s scale depends on the intensity of the damages resulting from earthquakes whereas Richter scale depends on measuring the frequency of the widest seismic waves corresponding to earthquakes. So there is no logical basis to relate these two scales together in a scientific way; yet a lot of trials have been made in this area.

1.6 Seismic Moment Scale

As Richter’s scale system is lacking some elements; a number of seismic scientists have suggested a scale that depends on the faulty slipping phenomenon that results from earthquakes, this scale is called the seismic moment scale and is calculated by the following formula:

Mo=G∫AD (x, y) dA=GAD (1-2)

Where;

G: shear factor for the medium in earthquake center

A: fault surface area or seismic slipping displacement (L*h)

D(x,y): slipping along seismic fault

D: average slipping along seismic fault

The value of Mo is related to the earthquake volume as it depends on the seismic fault state before and after the earthquake. So it gives a physical evidence for the destructive energy related to the earthquake.

1.7 Seismic Instruments

Nowadays instruments are used to register seismic waves and identify their properties. These instruments are called seismographs and their concepts are based on a free hanged weight connected to a needle that touches a cylinder with a graph wrapped around it and electronically controlled, the seismograph base is reinforced concrete and is fixed on a rocky layer. When the seismic waves reach the seismograph the earth below it shakes whereas the hanged weight inertia forces maintain its stability which enables a special needle on the rotating cylinder surface

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9

to register the earth shaking.

Recent instruments are more improved as the needle is replaced by light rays and the light reflects on a layer of sensitive photo paper by a mirror hanged precisely and these new instruments contain amplifications that show and register even the smallest vibrations.

1.8 Interpretation of Seismic Data

As the speed of the different models of the seismic waves varies, scientists are able to specify the distance between the epicenter and the used registration area; this is done by determining the time of arrival of the different seismic waves that come from the center. The epicenter is specified by determining the earthquake center from 3 seismic registration stations and this is done by drawing at least 3 circles whose radii are equal to the epicenter estimated distances from these seismic registration stations and the epicenter is the point where the three drawn circles intersect. For identifying the magnitude of the earthquake according to Richter’s scale, special curves are used that connect the measured seismic frequency in the seismic registration station and its degree according to Richter’s scale and this is done by determining the distance between the epicenter and the registration station.

1.9 Damages Resulting From Earthquakes

The main damages resulting from earthquakes can be summarized as follows: 1. Collapse of buildings. 2. Horizontal or vertical offset or both at the region. 3. Soil liquefaction:

Liquefaction phenomenon occurs when the soil beneath the ground water level or saturated soils in general lose their strength and behave as liquids and this occurs when the seismic waves, in particular shear waves, pass through the soil and this leads the soil particles to be loose and that increases the water pressure in those strata (layers) to a degree greater than the weight of the loose soil; this leads the saturated soil particles to be pushed up and the saturated part of the soil will be temporary transformed to a viscous liquid and so the liquefaction phenomenon occurs and huge universal earthquakes damages refer to it.

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10

Figure (1-5) Liquefaction Phenomenon

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4. Damages to life line systems:

a. Water and sanitary networks damages b. Roads and bridges damages

5. Communications network damages 6. Energy and electricity constructions damages. 7. Earthquake induced fires. 8. Tsunamis:

When the epicenter lies in sea region gaily-force waves develop as a result of the sudden vertical movement of the earth crust in the region due to earthquakes; these sea waves are generally called Tsunami which can reach tens of meters in height which risk the coastal cities and islands and cause fatal losses in lives and money. Therefore, many regulations in oceans exist in the form of seismic stations to alert locals from the danger of tsunamis when an earthquake hits the region. Plates (1-2) ___ (1-8) show some of the destruction made by earthquakes around the world.

Plate (1-2) Fault rupture – Luzon, Philippines 1990

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Plate (1-3) Liquefaction – Adapazari, Turkey 1999

Plate (1-4) Slope instability – iigata, Japan 2004

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12

Plate (1-5) An example of Mexico City building damage, September 19, 1985

Plate (1-6) Hanshin Expressway collapse, January 17, 1995 Hanshin

earthquake(15)

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13

Plate (1-7) Fourth Avenue buildings in downtown Anchorage shows the

damage resulting from the slide in this area(15)

Plate (1-8) Seward at the north end of Resurrection Bay, the total damage to port and harbor facilities at Seward was estimated at more than $15,000. Most of this damage was the result of the tsunamis. Eleven persons lost their lives due

to the sea waves at Seward(15)

14

1.10 Objectives:

The objective of this research is to discuss the seismic analysis provisions and implementations on structures by different codes of practice.The primary purpose of seismic building codes is to provide a uniform method to determine the seismic forces for any location with enough accuracy to ensure a safe and economical design. Here emphasis will be on the provisions of two of the most adopted codes in the United States in the seismic field, the NEHRP 2003 (National Earthquake Hazard Program) and the UBC 1994 and 1997 (Uniform Building Code), which the Sudanese trials in this field are based mainly on its 1994 edition, as well as the EUROCODE8. Only the linear static method of analysis will be discussed in details as it lacks analysis complications and is applicable for most buildings as long as the regularity of the building on its both projections is maintained and the severity of the earthquake in the region is relatively low. This method applies a lateral force on the base of the building to represent the seismic action on the building under consideration.

1.11 Research Methodology

The main task of this research is to compute the seismic shear forces on buildings by different codes of practice and compare the results.

In order to achieve that the following points were followed: 1. Detailed seismic analysis provisions were provided, but focussing was on the linear elastic static methods in different universal codes. These codes are, the American codes UBC (Uniform Building Code) Editions 1994 and 1997, NEHRP (National Earthquake Hazard Reduction Program) Edition 2003, as well as EUROCODE 8 Edition 2003.

2. Seismic resistant design provisions for R.C columns by ACI 318M-05 were provided as an example; to show some of the techniques used in seismic resistant design.

3. These Analysis and Design provisions were applied to the following illustrative models: i. In the first model, R.C office building, the seismic shear forces were

computed by the different seismic codes. ii. In the second model, floor slab with R.C shear walls, the floor seismic

shear force were distributed on the seismic resistant elements of that floor which are shear walls in this case.

iii. For the third model, Seismic resistant design for an interior R.C column was made by ACI 318M-05.

4. The results were discussed in details and a comparison was made between the four seismic codes mentioned above.

CHAPTER 2

LITERATURE REVIEW

16

(4) 2.1 Comparison between the ormal Provisions in Building

Codes and Those Ones for Earthquake Resistant Design

Building codes are made to protect the public welfare that includes safety of individual citizens as well as economy.

This is accomplished by setting:

i. Minimum standards for construction materials to be used by different types of structures and occupancy.

ii. Minimum permissible strength of these structures.

iii. Acceptable amount of deformations under design loadings.

Design and construction practice would vary widely if building code criteria are not united. This can be forced by the governments.

Design loading levels in the codes have moderate to low probability of occurrence during the structure’s life, each hazard has its own probability of exceedance and the building must be designed to withstand all of them. So the same building may be designed for an earthquake that is expected to occur every 500 years, wind load every 100 years and snow load every 20 years.

Two main objectives are accomplished when designing for such loads:

1. Provide low probability of failure and this is fulfilled by defining minimum required levels of structural strength.

2. Provide sufficient stiffness to insure that deflections do not affect the serviceability of the structure or result in cracking or other damage that would require repair following routine loading.

The resulting structures are capable of resisting the design loading with either elastic or near-elastic behavior. Consequently, engineered buildings rarely experience structural damage as a result of the effects of dead, live, wind, or snow loads, and rarely completely fail under such loading.

Here appears the uniqueness of the Building code provisions for earthquake-resistant design, unlike the provisions for other load conditions. They do not intend that structures be capable of resisting design loading within the elastic or near-elastic range of response, which means some level of damage is permitted. Building codes intend only that buildings resist large earthquake loading without life-threatening damage and, in particular, without structural collapse or creation of large, heavy falling debris hazards. This unique earthquake design philosophy evolved over time based primarily on two factors: 1. Most buildings will never experience a design earthquake and, therefore, design to resist such events without damage would be economically impractical for most structures. Even in zones of relatively frequent seismic activity, such as regions around the Pacific Rim, intense earthquakes are rare events, affecting a given region at intervals ranging from a few hundreds to thousands of years.

2. The development history for building code seismic provisions has also lead to this philosophy.

17

2.2 Earthquake Resistant Requirements

According to this design philosophy, earthquake resistant requirements by the different codes are summarized as follows:

1. The structure should be capable of resisting moderate intensity earthquake without allowing the stresses in its members to exceed the elastic limit. Which means the structure should not be affected by the earthquake force with the allowance of the probability of easily maintainable damages in some non-structural elements.

2. The structure should enter the plastic zone, when subjected to severe earthquake which means the allowance of some repairable structural and non-structural damages without occurrence of any partial collapse in the structure.

3. The structure should withstand severe and destructive earthquake. So the structure is not allowed to collapse completely, but it is acceptable to have severe and irreparable damages. This is to assure safety of residence and to minimize human life loss, if the area is subjected to severe earthquake in different periods of time.

2.3 Seismic and Wind Design

In load combinations seismic and wind forces do not exist simultaneously. The codes prescribe that when wind design produces greater effects, the wind design shall govern, but detailing requirements and limitations prescribed in the chapter to come and referenced sections in codes of practice shall be followed.

2.4 Historical Background about the Development of Earthquake Resistance Provisions in Building Codes

Building code provisions governing design for earthquake resistance may be traced back as far as building regulation enacted in Lisbon, Portugal, following the great earthquake of 1755. Building code provisions for earthquake resistance design are generally traced to one of three bases:

i. The experience basis: involves the observation of the behaviour of real structures in earthquakes and the development of rules preventing the construction of buildings that are repeatedly observed to behave poorly during earthquakes.

ii. The theoretical basis: contains the body of analytical and laboratory research that has been developed over the years, mainly by the academic community.

iii. The designer judgment: the building design community, especially, structural engineers have historically taken the leadership role in:

a. The development of these building code provisions.

(1, 4 & 12)

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18

b. Tempering and moderating the information obtained from the experience and theoretical bases, with their independent design judgment, assuring political acceptability of the building code within the design community, if not completely rational or justifiable provisions.

Early building code provisions for seismic resistance focussed on prohibiting certain types of constructions observed to behave poorly in past earthquakes, and to require the use of certain construction details and techniques observed to provide better performance. These features remain an important part of modern codes. However, modern codes supplement these prescriptive requirements with specifications of minimum permissible structural strength and stiffness.

2.5 The International Seismic Codes References

Most developed countries develop and enforce their own building codes; however the seismic provisions currently used throughout the world generally follow one of four basic models: a. NEHRP (National Earthquake Hazard Reduction Program) Recommended Provisions, developed by the Building Seismic Safety Council in the United States [BSSC, 1997]

b. Building Standards Law of Japan c. New Zealand Building Standards Law d. EUROCODE8

Although each individual code has many unique requirements and provisions, in general all are based on and incorporate similar concepts.

2.6 Early Lateral Force (ELF) Requirements

In the early 20th century, building codes around the world began to introduce that structures resisting earthquakes must be provided with special requirements to insure sufficient strength to resist a specified lateral force. These requirements, though substantially refined, are retained in most building codes today as a basic design method and are frequently termed the equivalent lateral force (ELF) technique.

Perhaps the first of these requirements appeared in the building code published by the City of San Francisco, following the great 1906 earthquake. This code required all buildings to be designed for a lateral pressure of 30lb/ft2 on the projected area of the building facade, as a protection against both wind and earthquake. Following a devastating magnitude 7.5earthquake in Messina, Italy, that caused 80,000 casualties in 1908, a special committee of practicing engineers and engineering professors was commissioned to recommend improved construction requirements. The resulting report recommended that the first story of structures shall be designed for a horizontal force equal to1.5% of the weight above and the second and third stories shall be designed for one eighth of the building weight above. This appears to have been the first formal recommendation to provide earthquake resistance by providing lateral strength equal to a fraction of the structure’s supported weight. The ELF concept was introduced in Japan in 1914, but not required.

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19

(2)

Following the great 1923 Tokyo earthquake, the Japanese Urban Building Law Enforcement Regulations were revised to require lateral design for a strength equal to 10% of the structure’s supported weight.

2.7 The Seismic Codes Used In This Research

The codes adopted in USA and Europe shall be discussed here.

In the United States of America different regions have adopted different codes to deal with the differing levels of seismic risk. Here the two most popular references in the seismic resistant design in USA, as well as many countries around the world, will be discussed. These are the UBC and NEHRP.

In Europe the provisions of EUROCODE 8 are widely adopted in most of the continent, as well as many countries around the world.

Only the linear static method at each code shall be discussed in details.

2.7.1 The UBC The Uniform Building Code (UBC) is used in the western regions of the

United States, in particular, California design practice. It is based on the earthquake code of the structural engineers association of California. Many codes around the world are based on its regulations, some of them are Arab countries such as Egypt, Syria as well as the Sudanese trials in the seismic field .It is also very important to emphasize that the 1997 UBC edition is the reference base for the united seismic Arab code for buildings and seismic resistant structures.

Here we will go through the provisions of UBC 1994 edition, as the Sudanese trials are based on it, as well as the 1997 edition as a substantial change has been made to its provisions.

2.7.1.1 The UBC 1994

The seismic base shear force is calculated as follows:

V=ZIC W (2-1) RW C= 1.25S (2-2)

T 2/3

Where:

Z: the seismic zone coefficient

I: the importance factor

C: the spectral shape coefficient

T: the fundamental period of vibration of the structure

S: the site coefficient

20

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Rw: the numerical structural system factor

W: normally the total dead load of the building.

2.7.1.2 The UBC 1997 The total design base shear in a given direction shall be determined from the following formula:

WRT

ICV

v= (2-3)

And V calculated above shall satisfy the following:

i. WR

ICa5.2≤ (2-4)

ii. IWCa11.0≥ (2-5)

iii. WR

IZ�v8.0≥ (2-6) In addition, for Seismic Zone 4

Where, Cv and Ca: Seismic Coefficients Nv: near-source factor I: seismic importance factor R: the structural system factor T: the structure fundamental period of vibration

W: the total dead load of the building plus portions of other loads, (live and snow loads).

Z: seismic zone Factor

2.7.2 The NEHRP 2003 Edition Although not a code, the NEHRP (National Earthquake Hazard Reduction

Program) provisions are designed to assist in code development and it is the source for many recent editions of different codes such as the seismic regulations in IBC (International Building Code) and the NFPA (National Fire Protection Association) 5000 Building Code, as well as, many design codes in the countries that base their design regulations on those of the United States practice.

The seismic base shear force is calculated as follows:

V = C s W (2-7)

IR

SCs

DS

/= (2-8)

The value of Cs shall satisfy the following:

i. LD

TforTIRT

S≤≤

)/(1

(2-9)

ii. LLD

TforTIRT

TS>≤

)/(21

(2-10)

(3)

21

(9)

(6)

iii. ≥ 0.01 (2-11)

iv. )/(

5.0 1

IR

S≥ (2-12) (for buildings and structures located where S1 ≥0.6g)

Where: Cs = the seismic response coefficient W = the total dead load and applicable portions of other loads SDS = the design spectral response acceleration parameter in the short period range R = the response modification factor from Table 4.3-1, and I = the occupancy importance factor SD1 = the design spectral response acceleration parameter at a period of 1.0 second T = the fundamental period of the structure (in seconds) TL = Long-period transition period (in seconds) S1 = the mapped maximum considered earthquake spectral response acceleration parameter

2.7.3 Eurocode 8 The seismic base shear force is calculated as follows:

F b = Sd (T1).m.λ (2-13) Where: Sd (T1) = the ordinate of the design spectrum at period T1 T1 = the fundamental period of vibration of the building for lateral motion in the direction considered m = is the total mass of the building, above the foundation or above the top of a rigid basement λ= is the correction factor

2.8 The Sudanese Seismic Studies

It is very important to draw attention to the seismic hazard in Sudan as there is an increase in the magnitude & frequency of seismic events in many parts of Sudan, yet no consideration for seismic action when designing buildings. Most seismic sources are located in the southern most part of the country, northern Kordofan state in center of the country, the red sea area in north-east, the afar depression in neighbouring Eritrea that affects the eastern part of Sudan and finally the induced source in the lake Nasir in southern Egypt. The southern portion of Sudan is very active; it has experienced one of the largest earthquakes in recent history on May 20, 1990 with a magnitude of 7.4 degree on Richter scale and that is one of the largest recorded earthquakes in Africa. In northern Kordofan state in August and November of the year 1993, earthquakes of magnitudes 5.4 and 4.4 respectively were recorded. Also there is a noticeable recent increase in the seismic activity in the Nile Basin that covers most of Sudan. There are some Sudanese trials in the seismic design field, Reference (8), and mainly based on the UBC 1994.

CHAPTER 3

SEISMIC A ALYSIS I BUILDI GS

23

(1&2)

3.1 Methods of Seismic Analysis in the Codes

Seismic load analysis on structures is divided into two groups linear and nonlinear which can be done through either static or dynamic approaches. These methods are summarized as follows:

1. Equivalent Lateral Force Method (linear, static).

2. Modal analysis using response spectrum procedure (linear, dynamic).

3. Non-linear static (pushover) analysis.

4. Non-linear time history (dynamic) analysis.

5. Linear response time history procedure (dynamic).

Hereafter emphasis will be on the linear static method of analysis in different codes of practice.

3.2 UBC 1994

Many codes are used in the different regions of the United States of America. Here we will start by discussing the equivalent lateral force method (ELF) in the Uniform Building Code (UBC) which is used in the western regions of the United States, in particular, California design practice. Two editions of this code shall be discussed here, edition 1994 and 1997. Here the provisions of 1994 edition shall be discussed first.

The Equivalent Lateral Force, ELF, approach is based on the 1994 earthquake code of the structural engineers association of California; it shall be discussed here as the Sudanese trials in the seismic field is based mainly on its provisions.

3.2.1 Estimation of the Minimum Base Shear Force The UBC states that the structure must be designed to resist a minimum total

lateral seismic load V, which will be assumed to act nonconcurrently in orthogonal directions parallel to the main axes of the structures, V is calculated from the following formula,

V=ZIC W ……. (3-1) RW

& C= 1.25S …….. (3-2)

T 2\3

3.2.2 Definition of Seismic Coefficient 1. Z: the seismic zone coefficient is proportionate to the effective peak ground acceleration (EPA) of a region which is given by a map dividing US into regions of five levels of ground motion. For other countries depending on this code national zoning maps should be developed.

24

2. I: the importance factor, proportionate to the number of people in the building whose safety is directly at risk and whether the structure has an immediate post earthquake role in the safety and recovery of the community.

3. C: the spectral shape coefficient, it scales the response of the particular structure to the earthquake acceleration spectrum. The curve given by equation (3-2) is a simplified multi mode acceleration response spectrum normalized to an effective peak ground acceleration of 1 basis.

4. T: the fundamental period of vibration of the structure, it can be determined by the use of empirical formulas or by the results of an elastic dynamic analysis.

5. S: the site coefficient, adjusts the shape of the appropriate frequency response content of the site soil conditions, the UBC has divided the soil characteristics into four types with a site coefficient S for each of these depending on the soil type and depth.

6. Rw: the numerical structural system factor, measures the ability of the structural system to sustain cyclic inelastic deformations without collapse. It is the denominator of the design base shear equation, so the design loads decrease for systems with large inelastic deformation capabilities. Its magnitude depends on the ductility of the type and material of the structure, the possibility of failure of the vertical load system, the degree of redundancy of the system that would allow some localized failures without overall failure, and the ability of the secondary system, in the case of dual systems, to stabilize the building when the primary system suffers significant damage.

7. W: usually the total dead load of the building.

�otes:

a. For design projects where it is not practical to evaluate the site soil condition and the structure period, a maximum limit on C=2.75 is used for any structure and soil site condition to provide a simple seismic load evaluation. Also, a lower limit of C/Rw = 0.075 is given to assure that a minimum base shear of 3% of the building weight is used in seismic zone 4, with proportional values in the lower zones.

b. As an EPA value is used to scale the spectral shape given by the coefficient C, so the product of the coefficients Z and C represents an acceleration response spectrum envelope having a 10% probability of being exceeded in 50 years.

3.2.3 The Fundamental Period of the Structure, T The recommended value of T may be determined from the following methods: a. T= Ct (hn)

3/4 (3-3) Where: Ct= 0.085 for steel moment resistant frames Ct= 0.073 for R.C moment resistant frames Ct= 0.049 for all other frames hn= height in meters above the base to level n.

25

D

hnTa

09.0= (For concrete shear walls)(3-4)

b.

÷= ∑ ∑

= =

n

i

n

i

iiii fgwT1 1

22 δδπ (3-5)

Where, wi= concentrated structure weight at level i. fi= distributed seismic lateral force at level i.

iδ = calculated deflection using applied lateral force at level i. g: the ground acceleration(9.81m/s2) The value of C given by equation (C=1.25 S/ T 2/3) shall not be less than 80% of the value obtained using T from equation (3-3)

3.2.4 Vertical Distribution of the Total Base Shear As the value of the total base shear is now estimated. So to continue with the

static analysis, the base shear should be distributed as horizontal loads at the various floor levels. To decide the correct distribution for the horizontal load the following factors are considered:

1. The effective load at a floor level is equal to the product of the mass assigned to the floor and the horizontal acceleration at that level. 2. The maximum acceleration at any level of the structure in the fundamental mode is proportional to its horizontal displacement in that mode. 3. The fundamental mode for a regular structure, consisting of shear walls and frames, is approximately linear from the base.

So the linear acceleration distribution of the total base shear V through the height is given by the following formula,

∑=

=

n

ii

xxx

i

hW

hWVF

1

……. (3-6)

Where, Fx: the floor equivalent horizontal force V: the equivalent total shear force Wi &Wx: those are portions of W assigned to levels i and x, respectively; that is, the weight at or adjacent to levels i and x. hi & hx: height from the base to levels I and x. The structures whose weight is distributed uniformly over their height, the horizontal load distribution resulting from the previous equation forms a triangle, with a maximum value at the top, this distribution is appropriate for those buildings of relatively stocky proportions where only the fundamental mode is significant. In more slender, longer period buildings, however, higher modes become significant causing a greater proportion of the total horizontal inertia forces to act near the top, the intensity of this effect is related to the period of the building, this is reflected in

26

(8 & 9)

UBC as well as other codes by applying a part of the total loading as a concentrated horizontal force Ft at the top of the building by the following formula:

∑=

+=n

i

t iFFV1

……….. (3-7)

And Ft = 0.07TV≤ 0.25V ………. (3-8) What remains of the total base shear is then distributed over the height of the building as an inverted triangle as follows:

∑−=

=

n

ii

xxtx

i

hW

hWFVF

1

)( … (3-9)

Torsion in any story is to be taken of the product of the story shear and an eccentricity resulting from the addition of a calculated eccentricity of the mass above, from the center of rigidity of the story, and an accidental eccentricity of 5% of the plan dimension of the building perpendicular to the direction of the force under consideration. In the presence of torsional irregularities, the accidental eccentricity is to be increased by an amplification factor relating the maximum story drift at one end of the structure to the average of the story drifts of the two ends of the structure.

3.2.5 Overturning Moment All structures are expected to resist overturning moments resulting from the shear forces Ft and Fx which act above or under the story level under consideration. This moment is then distributed over all resisting elements and these moments shall be carried down to the foundation.

3.2.6 Modifications on Some of the UBC 1994 Factors to Suit Sudan Conditions

3.2.6.1 The seismic zone factor, Z The seismic hazard analysis carried by Abdalla et. al. is the only work done in this area so far. The iso-acceleration maps resulted in the hazard analysis were used to delineate Sudan into 5 macro-seismic zones. As the expected life time in the Sudan is 50 years for most buildings; the seismic zone map is generated based on time of exposure equals 50 years (457 years return period) and probability of exceedance of 10% as shown in Appendix C, the generated zone map given also in Appendix C is based on the PGA (peak ground acceleration) levels. Zone’s numbers and their corresponding PGA’s are shown in Table (3-1)

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Table (3-1) Seismic Zones and their corresponding PGA’s

Zone umber PGA(in g’s)

0 Less than 0.04 1 0.04- 0.10 2A 0.10 -0.15 2B 0.15- 0.20 3 > 0.20

The PGA in this Table is going to be replaced by EPA (effective peak ground acceleration) which defines the seismic zone factor Z as stated in the provisions of the UBC. This is done by multiplying the PGA by 0.82. As in Table (3-2)

Table (3-2) Zone number and corresponding seismic zone factor Z

Zone o. Z 0 0.05 1 0.08 2A 0.12 2B 0.16 3 0.20

3.2.6.2 The soil factor, S The Nile valley which is the most densely populated area in Sudan is characterized by heavy expansive stiff clays at varying depths resting on silty clay strata. Similar soil strata dominate the Gazira area, Gadarif, Upper Nile Province, part of Bahr El- Gazal and Equatoria Provinces. A layer of dense sand overlain by a layer of loose fine sand dominates most of the North and West of Sudan. Rock is encountered in the Red Sea region and in scattered areas in the south and west Sudan. No study has been done to investigate the response of soils in Sudan to ground movement. So it has been recommended to use Table (3-3) that shows the different soil profiles and the corresponding S-factors until additional information in this area is available.

Table (3-3) Soil profile and the corresponding S factor

Soil Profile umber

Soil Profile Description S Factor

S1 Rock or stiff soil conditions or stable deposits sands gravel or stiff clays of depth less than 20m.

1

S2 Deep Cohesionless or stiff clays exceeding 20m in

depth. 1.25

S3 Soft to medium stiff clays and sands 1.5 For case of very soft clays a site-specific study should be performed to develop seismic design criteria.

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3.2.6.3 The spectral shape coefficient, C As there are no strong motion records for earthquake in the Sudan; it is recommended to use the definition of C as explained in the UBC provisions (C=1.25 S/T 2/3) with the proposed values of S and T until adequate data is recorded and further investigation is done in this area.

3.2.6.4 Importance factor, I In Sudan it is recommended to use UBC approach in determining the importance factor of the structure as it is more direct and easier. Table (3-4) shows the recommended importance factors for the different buildings in Sudan.

Table (3-4) Importance Factor, I

Occupancy Categories Importance Factor, I

(1) Essential building to be used immediately after earthquakes such as hospitals, fire stations, broad casting buildings, power

stations etc.

1.25

(2) Hazardous facilities such as structures housing toxic or explosive substances.

1.25

(3) building of high occupancy such as schools, stadiums, theaters etc.

1.10

(4) Buildings of low occupancy such as residential buildings, hotels, office buildings

etc.

1.00

3.2.6.5 The fundamental period of the structure, T For moment resisting frames UBC (1985) define the empirical period as follows: T= 0.1N (3-10) It is more appropriate to recommend the UBC (1994) formula to be used in the case of Sudan until investigation is done for the structure period of the construction systems adopted in Sudan.

3.2.6.6 The structural system factor, Rw Engineering judgment and behaviour of structural systems during earthquakes play a major part of assessment of the value of Rw. In Sudan no such observations for the structural systems have been recorded, so assigning values for Rw will depend on the experts’ judgment. The values assigned by UBC for Rw must be lowered substantially because of the low standards of detailing of reinforced concrete and structural steel as well as the comparatively poor control of construction. The recommended structural system factor Rw as well as the height limitation for the different structural systems commonly used in Sudan are defined in Table (A-1) in the Appendices.

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(3)

3.3 1997 UBC Edition

It is important to go through the provisions of this edition of the UBC for the following reasons: i. Many provisions have changed substantially ii. Along with the NEHRP ,they reflect the final vision in the understanding and

interpretation of the earthquake phenomenon iii. The united Arabic code (2003) is based on it, as most of the data required by

this code is available in many Arabic countries.

The procedures and the limitations for the design of structures shall be determined considering seismic zoning, site characteristics, occupancy, configuration, structural system and height in accordance with this section. Structures shall be designed with adequate strength to withstand the lateral displacements induced by the Design Basis Ground Motion, considering the inelastic response of the structure and the inherent redundancy, overstrength and ductility of the lateral-force resisting system. The minimum design strength shall be based on the Design Seismic Forces determined in accordance with the static lateral force procedure.

3.3.1 Site Geology and Soil Characteristics

Each site shall be assigned a soil profile type based on properly substantiated geotechnical data using the site categorization procedure set forth in the following section. Exception:

When the soil properties are not known in sufficient detail to determine the soil profile type, Type SD shall be used. Soil Profile Type SE or SF need not be assumed unless the building official determines that Type SE or SF may be present at the site or in the event that Type SE or SF is established by geotechnical data.

3.3.1.1 Soil profile type The Soil Profile Types SA, SB, SC, SD and SE are defined in the following

Table and Soil Profile Type SF is defined as soils requiring site-specific evaluation are the same as A,B,C,D,E and F in NEHRP, so reference should be made to NEHRP provisions for further details.

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Table (3-5) Soil profile types

Site Class

Site Description

sV (m/s)

(Shear wave velocity)

� or ch� (number of blows by SP