Chapter

A DEVELOPED FEM-BEM PRACTICAL TECHNIQUE TO CONSIDER SSI IN THE LATERAL ANALYSIS FOR MULTISTORY BUILDINGS By Abdelrahman Mohamed Ibrahiem Ali Elmeliegy

A Thesis Submitted to the Faculty of Engineering at Cairo University In Partial Fulfillment of the Requirements for the Degree of Master of Science In Structural Engineering

FACULTY OF ENGINEERING, CAIRO UNIVERSITY GIZA, EGYPT 2017

A DEVELOPED FEM-BEM PRACTICAL TECHNIQUE TO CONSIDER SSI IN THE LATERAL ANALYSIS FOR MULTISTORY BUILDINGS By Abdelrahman Mohamed Ibrahiem Ali Elmeliegy

A Thesis Submitted to the Faculty of Engineering at Cairo University In Partial Fulfillment of the Requirements for the Degree of Master of Science In Structural Engineering Under the Supervision of

Prof. Dr. Youssef F. Rashed Professor of Structural Analysis and Mechanics Structural analysis and mechanics Deptartment Faculty of Engineering Cairo University

FACULTY OF ENGINEERING, CAIRO UNIVERSITY GIZA, EGYPT 2017

A DEVELOPED FEM-BEM PRACTICAL TECHNIQUE TO CONSIDER SSI IN THE LATERAL ANALYSIS FOR MULTISTORY BUILDINGS By Abdelrahman Mohamed Ibrahiem Ali Elmeliegy A Thesis Submitted to the Faculty of Engineering at Cairo University In Partial Fulfillment of the Requirements for the Degree of Master of Science In Structural Engineering Approved by the Examining Committee Prof. Dr. Youssef Fawzy Rashed, Thesis Advisor (Professor at Faculty of Engineering; CairoUniversity) ____________________________

Prof. Dr. Sameh S. Fahmy Mehanny, Internal Examiner (Professor at Faculty of Engineering; CairoUniversity) ____________________________ Prof. Dr. Ibrahiem Mahfouz, External Examiner (Professor at Faculty of Engineering; Benha University)

____________________________

FACULTY OF ENGINEERING, CAIRO UNIVERSITY GIZA, EGYPT 2017

DEDICATION

To whom I would never be without their guidance and support To my mother, father, brother and sisters A.M.Elmeliegy Feb.2017

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ACKNOWLEDGEMENT First of all due thanks go to God the most merciful and most graceful. Who without his guidance and inspiration nothing could have been accomplished. I also wish to express my deep indebtedness to Prof. Dr. Youssef Fawzy Rashed, Professor of Structural Analysis and Mechanics, Structural Engineering Department, Faculty of Engineering, Cairo University, for his generous guidance and encouraging, sincere help, consistent support by all means and asking, valuable suggestions, and precise advice through all stages of this research work, I express my true thanks and gratitude for opening my mind to the true values of sincere and creativity. I have learned many lessons in working under his guidance and leadership that I will remember for an extremely long time. My thanks also go to my colleagues, especially Dr.Taha Abou Elnaga, Eng. Ahmed Fady, Eng. Anas Abu Rawash and all friends who supported me all the way to achieve this work. A.M.Elmeliegy….February,2017

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Engineer: Abdelrahman Mohamed Ibrahiem Ali Elmeliegy Date of Birth: 27/05/1991 Nationality: Egyptian E-mail: [email protected] Phone:0127 321 5801 Address: 27 Yasser Elgeheny - Omrania - Giza - Egypt Registration Date: 1/10/2013 Awarding date: 2017 Degree: Master of Science Department: Structural Engineering Supervisor: Prof. Dr. Youssef Fawzy Rashed Examiners: Prof. Dr. Youssef Fawzy Rashed Prof. Dr. Sameh S. Fahmy Mehanni, (Internal Examiner) Prof. Dr. Ibrahiem Mahfouz, (External Examiner) Title of Thesis: A DEVELOPED FEM-BEM PRACTICAL TECHNIQUE TO CONSIDER SSI IN THE LATERAL ANALYSIS FOR MULTISTORY BUILDINGS Keywords: BEM; Soil-structure interaction; static condensation; foundation-soil flexibility; static soil-structure interaction.

Summary: In this thesis, a new practical technique for the analysis of buildings including soilstructure interaction is suggested. The new analysis is based on sub-structuring approach where the system is partitioned into two main parts which are the superstructure part and the raft-soil part. A static condensation technique is implemented at the column-raft interface. A developed algorithm representing the column-raft interface is implemented to ensure compatibility and equilibrium at that interface. Current practical analysis of SSI is implementing the static condensation at the raft-soil interface which is time consuming and tediously job. The new analysis has shown less time and effort in the modeling and analyses. This technique of analysis is presented here only for linear analysis. However, this technique can be extended to include nonlinear analysis such as no tension SSI, soil nonlinearity SSI.

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Table of Contents Table of Contents .......................................................................................... vii Chapter 1 Introduction and Background......................................................... 1 1.1 General ...................................................................................................................... 1 1.2 Sources of Soil structure interaction ......................................................................... 1 1.2.1 Kinematic interaction: .................................................................................................... 2 1.2.2 Inertial interaction: ......................................................................................................... 2

1.3 Methods of soil structure interaction modeling ........................................................ 3 1.3.1 The direct approach [15-16] ........................................................................................... 3 1.3.2 The Substructure approach [17] ..................................................................................... 5

1.4 Methods of soil representation: ................................................................................. 7 1.4.1 The Winkler model ......................................................................................................... 7 1.4.2 The multi-Parametric model [19-20] .............................................................................. 7 1.4.3 The elastic half space model ........................................................................................... 8

1.5 Available solutions in practice .................................................................................. 8 1.5.1 The uncoupled manually iterative method ..................................................................... 9 1.5.2 The conventional method in practice............................................................................ 11

1.6 Thesis objectives ..................................................................................................... 12 1.7 Thesis outline .......................................................................................................... 14 1.8 Conclusions ............................................................................................................. 14

Chapter 2 Used Numerical Methods And Softwares.................................... 15 2.1 Introduction ............................................................................................................. 15 2.2 The finite element method (FEM) [31] ................................................................... 15 2.2.1 Advantage of the FEM: ................................................................................................ 15 2.2.2 Disadvantage of the FEM: ............................................................................................ 15

2.3 The ETABS software [33] ...................................................................................... 16 2.3.1 ETABS modeling and simulation capabilities.............................................................. 16 2.3.2 ETABS analysis capabilities ........................................................................................ 16 2.3.3 Used ETABS files ........................................................................................................ 17

2.4 Used structural objects and terminology in ETABS building model ..................... 19 2.4.1 Joint objects: ................................................................................................................. 19 2.4.2 Support object:.............................................................................................................. 19 2.4.3 Line objects: ................................................................................................................. 19

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2.4.4 Area / shell objects: ...................................................................................................... 19 2.4.5 Meshes / divisions: ....................................................................................................... 19 2.4.6 Body Constraint: ........................................................................................................... 20 2.4.7 Diaphragm constraint: .................................................................................................. 20

2.5 The boundary element method (BEM) [36]............................................................ 20 2.6 Raft terminology used in BEM/PLPAK ................................................................. 21 2.6.1 Raft foundation: ............................................................................................................ 21 2.6.2 Boundary elements: ...................................................................................................... 21 2.6.3 Nodes: ........................................................................................................................... 21 2.6.4 Extreme points: ............................................................................................................. 21 2.6.5 Colum load modeling: .................................................................................................. 21 2.6.6 Wall load modeling in PLPAK: ................................................................................... 22 2.7 Soil terminology used in BEM/PLPAK .......................................................................... 23 2.7.1 Subgrade reaction (K): ................................................................................................. 23 2.7.2 Elastic modulus (E): ..................................................................................................... 23 2.7.3 Poison’s ratio (v): ......................................................................................................... 23 2.7.4 Soil layers: .................................................................................................................... 23 2.7.5 Soil cells/divisions: ....................................................................................................... 23 2.8 The PLPAK software package [40] ................................................................................. 25 2.8.1The PlGen: .................................................................................................................... 27 2.8.2 PLView:........................................................................................................................ 27 2.8.3 PL.exe: .......................................................................................................................... 27 2.8.4 PLPost: ......................................................................................................................... 27 2.8.5 PLCoreman: .................................................................................................................. 28 2.8.6 Used PLPAK files ........................................................................................................ 28

2.9 Soil modeling in PLPAK: ....................................................................................... 31 2.9.1 Winkler model: ............................................................................................................. 31 ............................................................................................................................................... 32 2.9.2 EHS modeling: ............................................................................................................. 33

2.6 Conclusions ............................................................................................................. 34

Chapter 3 The Proposed New Technique ..................................................... 35 3.1 Introduction ............................................................................................................. 35 3.2 The developed translator ......................................................................................... 35 3.2.1 Translator.exe ............................................................................................................... 35

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3.3 Rotational stiffness implementation in SSIPAK/PLPAK ....................................... 38 3.4 Illustrative Example ................................................................................................ 39 1-

Structural drawings........................................................................................................ 39

2-

ETABS 3D Model ......................................................................................................... 39

3-

Data base file ................................................................................................................. 42

3.5 Methodology and automation ................................................................................. 44 3.6 The graphical user interface SSIPAK ..................................................................... 48 3.7 Conclusions ............................................................................................................. 49

Chapter 4 Numerical examples ..................................................................... 50 4.1 Introduction ............................................................................................................. 50 4.2 Example set 1 .......................................................................................................... 50 4.3 Example set 2 .......................................................................................................... 71 4.4 Example set 3 .......................................................................................................... 92 Bare frame results: ........................................................................................................ 93 Shear wall results .......................................................................................................... 96 4.5 Example set 4 .......................................................................................................... 99

Chapter 5 Summary, Conclusions and Recommendations for Future Work ..................................................................................................................... 102 4.1 Summary ............................................................................................................... 102 5.2 Conclusions ........................................................................................................... 102 5.3 Recommendations for future work ....................................................................... 103

ARABIC SUMMARY .................................................................................... 2

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LIST OF TABLES Table 4.1The fundamental periodic time in seconds for example 1 – with rotational stiffness ............................................................................................................................. 70 Table 4.2 The fundamental periodic time in seconds for example 1 – without rotational stiffness ............................................................................................................................. 70 Table 4.3 The fundamental periodic time in seconds for example 2 – without rotational stiffness. ............................................................................................................................ 91 Table 4.4 The fundamental periodic time in seconds for example 2 – without rotational stiffness. ............................................................................................................................ 91 Table 4.5 Section properties for example set 3 [8]. .......................................................... 92 Table 4.6 The soil properties according to work done by [8]. .......................................... 92 Table 4.7 Time period for different modes of shape – 4 floors. ....................................... 95 Table 4.8 Time period for different modes of shape - 16 floors. ...................................... 95 Table 4.9 Time period for different modes of shape - 4 floors. ........................................ 98 Table 4.10 Time period for different modes of shape - 16 floors. .................................... 98 Table 4.11 Section properties according to work done by [12]. ....................................... 99 Table 4.12 The soil properties according to work done by [12]. ...................................... 99 Table 4.13 The fundamental time period for 6-floors multi-story framed building. ...... 100 Table 4.14 The fundamental period for 12-floors multi-story framed building. ............ 101

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LIST OF FIGURES Figure 1.1(a) The effect of soil flexibility on the lateral deformation. (b) The effect of neglecting soil flexibility.---------------------------------------------------------------------------- 3 Figure 1.2The direct approach of soil-structure interaction.. ----------------------------------- 4 Figure 1.3 The substructure method of soil-structure interaction.. ---------------------------- 6 Figure 1.4 Soil representation using Winkler springs.. ------------------------------------------ 7 Figure 1.5 The Uncoupled iterative technique used in design firms.------------------------ 10 Figure 1.6 The conventional method used in practicaldesign firms (a),(b).. --------------- 11 Figure 1.7 The proposed new method of static condensation.. ------------------------------- 13 Figure 2.1 The structure of the ETABS .e2k file. ---------------------------------------------- 17 Figure 2.2 The structure of point coordinates .txt ETABS file. ------------------------------ 18 Figure 2.3 The structure of static load cases .txt file. ------------------------------------------ 18 Figure 2.4 The structure Support Restraint .txt file. ------------------------------------------- 18 Figure 2.5 the structure of Support Reactions.txt file. ----------------------------------------- 18 Figure 2.6 The structure of Point Spring Force.txt file ---------------------------------------- 19 Figure 2.7 Soil and boundary elements discretization for a typical raft on Winkler foundation. ------------------------------------------------------------------------------------------- 22 Figure 2.8 Soil and boundary elements discretization for a typical raft on EHS. --------- 24 Figure 2.9Flow chart show the PLPAK components ------------------------------------------ 26 Figure 2.10 The structure of the model.txt file. ------------------------------------------------ 28 Figure 2.11 The structure of the material .txt file. --------------------------------------------- 29 Figure 2.12 The structure of the slab .txt file. -------------------------------------------------- 29 Figure 2.13 The structre of the soil support .txt file.------------------------------------------- 29 Figure 2.14 The structure of the .aip file. ------------------------------------------------------- 30 Figure 2.15 The structure of the .ipu file. ------------------------------------------------------- 30 Figure 2.16 The structure of the .run file. ------------------------------------------------------- 30 Figure 2.17 The Winkler cell discretization in the PLView. --------------------------------- 32 Figure 2.18 Practical raft on Winkler modeled using PLGen -------------------------------- 32 Figure 2.19EHSPAk add-on start menu --------------------------------------------------------- 33 Figure 3.1 he structure of . c file. ----------------------------------------------------------------- 36 Figure 3.2 The structure of the .k file. ----------------------------------------------------------- 36 Figure 3.3 The structure of the LC.txt file. ------------------------------------------------------ 36 Figure 3.4 The structure of the column load.txt file. ------------------------------------------ 37 Figure 3.5 The structure of the $Runstiff$ file. ------------------------------------------------ 37 Figure 3.6 The input and output files used by translator. ------------------------------------- 38 Figure 3.7 The rotational stiffness implementation procedure. ------------------------------ 39 Figure 3.8 The structural drawings using AutoCAD.------------------------------------------ 40 Figure 3.9 The ETABS 3D model. --------------------------------------------------------------- 41 Figure 3.10 a & b The steps to export the database file containing the required text files. --------------------------------------------------------------------------------------------------------- 42 Figure 3.11 The database file containing the required text files. ---------------------------- 43 Figure 3.12 The raft model in PLGEN. ---------------------------------------------------------- 44 Figure 3.13 The raft model in PLVIEW. -------------------------------------------------------- 44 Figure 3.14 Flow chart shows the proposed technique. --------------------------------------- 47

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Figure 3.15 The graphical user interface (SSIPAK). ------------------------------------------ 48 Figure 4.1. Exapmle 1 plan ------------------------------------------------------------------------ 51 Figure 4.2 ETABS 3D modeling of example 1 super structure. ----------------------------- 52 Figure 4.3 PLPAK 2D modeling of example 1 raft foundation. ----------------------------- 52 Figure 4.4 SAP2000 3D modeling of example 1- Direct method. --------------------------- 53 Figure 4.5 SAP2000 3D modeling of example 1- Direct method. --------------------------- 53 Figure 4.6 Lateral Deflection in X-direction for example 1- E=2000 t/m2 (with rotational stiffness). --------------------------------------------------------------------------------------------- 54 Figure 4.7 Lateral Deflection Ratio SSI/NSSI in X-direction for example 1- E=2000 t/m2 (with rotational stiffness). ------------------------------------------------------------------------- 54 Figure 4.8 Drift SSI/NSSI ratio in X-direction for example 1 E=2000 t/m2 (with rotational stiffness).--------------------------------------------------------------------------------- 55 Figure 4.9 Inter story drift in X-direction for example 1- E=2000 t/m2 (with rotational stiffness). --------------------------------------------------------------------------------------------- 55 Figure 4.10 Lateral Deflection in X-direction for example 1 E=2000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 56 Figure 4.11 Lateral Deflection SSI/NSSI in X-direction for example 1 E=2000 t/m2 (without rotational stiffness).---------------------------------------------------------------------- 56 Figure 4.12 Inter story drift in X-direction for example 1 E=2000 t/m2 (without rotational stiffness). --------------------------------------------------------------------------------------------- 57 Figure 4.13 Drift SSI/NSSI ratio in X-direction for example 1- E=2000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 57 Figure 4.14 Lateral Deflection Ratio SSI/NSSI in X-direction for example 1- E=5000 t/m2 (with rotational stiffness). ------------------------------------------------------------------- 58 Figure 4.15 Lateral Deflection in X-direction for example 1- E=5000 t/m2 (with rotational stiffness).--------------------------------------------------------------------------------- 58 Figure 4.16 Inter story drift in X-direction for example 1- E=5000 t/m2 (with rotational stiffness). --------------------------------------------------------------------------------------------- 59 Figure 4.17 Drift SSI/NSSI ratio in X-direction for example 1- E=5000 t/m2 (with rotational stiffness).--------------------------------------------------------------------------------- 59 Figure 4.18 Lateral Deflection in X-direction for example 1- E=5000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 60 Figure 4.19 Lateral Deflection Ratio SSI/NSSI in X-direction for example 1- E=5000 t/m2 (without rotational stiffness). --------------------------------------------------------------- 60 Figure 4.20 Inter story drift in X-direction for example 1- E=5000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 61 Figure 4.21 Drift SSI/NSSI ratio in X-direction for example 1- E=5000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 61 Figure 4.22 Lateral Deflection in X-direction for example 1- E=10000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 62 Figure 4.23 Lateral Deflection Ratio SSI/NSSI in X-direction for example 1- E=10000 t/m2 (without rotational stiffness). --------------------------------------------------------------- 62 Figure 4.24 Drift SSI/NSSI ratio in X-direction for example 1- E=10000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 63

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Figure 4.25 Inter story drift in X-direction for example 1- E=10000 t/m2 (with rotational stiffness). --------------------------------------------------------------------------------------------- 63 Figure 4.26 Lateral Deflection in X-direction for example 1- E=10000 t/m2(without rotational stiffness).--------------------------------------------------------------------------------- 64 Figure 4.27 Lateral Deflection Ratio SSI/NSSI in X-direction for example 1- E=10000 t/m2 (without rotational stiffness). --------------------------------------------------------------- 64 Figure 4.28 Inter story drift in X-direction for example 1- E=10000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 65 Figure 4.29 Drift SSI/NSSI ratio in X-direction for example 1- E=10000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 65 Figure 4.30 Lateral Deflection in X-direction for example 1- E=20000 t/m2 (with rotational stiffness).--------------------------------------------------------------------------------- 66 Figure 4.31 Lateral Deflection Ratio SSI/NSSI in X-direction for example 1- E=20000 t/m2 (with rotational stiffness). ------------------------------------------------------------------- 66 Figure 4.32 Drift SSI/NSSI ratio in X-direction for example 1- E=20000 t/m2 (with rotational stiffness).--------------------------------------------------------------------------------- 67 Figure 4.33 Inter story drift in X-direction for example 1- E=20000 t/m2 (with rotational stiffness). --------------------------------------------------------------------------------------------- 67 Figure 4.34 Lateral Deflection in X-direction for example 1- E=20000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 68 Figure 4.35 Lateral Deflection Ratio SSI/NSSI in X-direction for example 1- E=20000 t/m2 (without rotational stiffness). --------------------------------------------------------------- 68 Figure 4.36 Drift SSI/NSSI ratio in X-direction for example 1- E=20000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 69 Figure 4.37 Inter story drift in X-direction for example 1- E=20000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 69 Figure 4.38 Exapmle 2 plan. ---------------------------------------------------------------------- 72 Figure 4.39 ETABS 3D modeling of example 2 super structure. ---------------------------- 73 Figure 4.40 PLPAK 2D modeling of example 2 raft foundation. ---------------------------- 73 Figure 4.41 SAP2000 2D view.------------------------------------------------------------------- 74 Figure 4.42 SAP2000 3D modeling of example 2- Direct method. ------------------------- 74 Figure 4.43 Lateral Deflection in X-direction for example 2- E=2000 t/m2 (with rotational stiffness).--------------------------------------------------------------------------------- 75 Figure 4.44 Lateral Deflection Ratio SSI/NSSI in X-direction for example 2- E=2000 t/m2 (with rotational stiffness). ------------------------------------------------------------------- 75 Figure 4.45 Inter story drift in X-direction for example 2- E=2000 t/m2 (with rotational stiffness). --------------------------------------------------------------------------------------------- 76 Figure 4.46 Drift SSI/NSSI ratio in X-direction for example 2- E=2000 t/m2 (with rotational stiffness).--------------------------------------------------------------------------------- 76 Figure 4.47 Lateral Deflection in X-direction for example 2- E=2000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 77 Figure 4.48 Lateral Deflection Ratio SSI/NSSI in X-direction for example 2- E=2000 t/m2 (without rotational stiffness). --------------------------------------------------------------- 77

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Figure 4.49 Inter story drift in X-direction for example 2- E=2000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 78 Figure 4.50 Drift SSI/NSSI ratio in X-direction for example 2- E=2000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 78 Figure 4.51 Lateral Deflection Ratio SSI/NSSI in X-direction for example 2- E=5000 t/m2 (with rotational stiffness). ------------------------------------------------------------------- 79 Figure 4.52 Lateral Deflection in X-direction for example 2- E=5000 t/m2 (with rotational stiffness).--------------------------------------------------------------------------------- 79 Figure 4.53 Drift SSI/NSSI ratio in X-direction for example 2- E=5000 t/m2 (with rotational stiffness).--------------------------------------------------------------------------------- 80 Figure 4.54 Inter story drift in X-direction for example 2- E=5000 t/m2 (with rotational stiffness). --------------------------------------------------------------------------------------------- 80 Figure 4.55 Lateral Deflection in X-direction for example 2- E=5000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 81 Figure 4.56 Lateral Deflection Ratio SSI/NSSI in X-direction for example 2- E=5000 t/m2 (without rotational stiffness) . -------------------------------------------------------------- 81 Figure 4.57 Inter story drift in X-direction for example 2- E=5000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 82 Figure 4.58 Drift SSI/NSSI ratio in X-direction for example 2- E=5000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 82 Figure 4.59 Lateral Deflection in X-direction for example 2- E=10000 t/m2 (with rotational stiffness).--------------------------------------------------------------------------------- 83 Figure 4.60 Lateral Deflection Ratio SSI/NSSI in X-direction for example 2- E=10000 t/m2 (with rotational stiffness). ------------------------------------------------------------------- 83 Figure 4.61 Drift SSI/NSSI ratio in X-direction for example 2- E=10000 t/m2 (with rotational stiffness).--------------------------------------------------------------------------------- 84 Figure 4.62 Inter story drift in X-direction for example 2- E=10000 t/m2 (with rotational stiffness). --------------------------------------------------------------------------------------------- 84 Figure 4.63 Lateral Deflection in X-direction for example 2- E=10000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 85 Figure 4.64 Lateral Deflection Ratio SSI/NSSI in X-direction for example 2- E=10000 t/m2 (without rotational stiffness) . -------------------------------------------------------------- 85 Figure 4.65 Inter story drift in X-direction for example 2- E=10000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 86 Figure 4.66 Drift SSI/NSSI ratio in X-direction for example 2- E=10000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 86 Figure 4.67 Lateral Deflection in X-direction for example 2- E=20000 t/m2 (with rotational stiffness).--------------------------------------------------------------------------------- 87 Figure 4.68 Lateral Deflection Ratio SSI/NSSI in X-direction for example 2- E=20000 t/m2 (with rotational stiffness). ------------------------------------------------------------------- 87 Figure 4.69 Inter story drift in X-direction for example 2- E=20000 t/m2 (with rotational stiffness). --------------------------------------------------------------------------------------------- 88 Figure 4.70 Drift SSI/NSSI ratio in X-direction for example 2- E=20000 t/m2 (with rotational stiffness).--------------------------------------------------------------------------------- 88

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Figure 4.71 Lateral Deflection in X-direction for example 2- E=20000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 89 Figure 4.72 Inter story drift in X-direction for example 2- E=20000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 89 Figure 4.73 Drift SSI/NSSI ratio in X-direction for example 2- E=20000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 90 Figure 4.74 Inter story drift in X-direction for example 2- E=20000 t/m2 (without rotational stiffness).--------------------------------------------------------------------------------- 90 Figure 4.75 The structural layout and dimensions [8]. ---------------------------------------- 92 Figure 4.76 The time period for mode 1- 4 floors. --------------------------------------------- 93 Figure 4.77 The time period for mode 3 - 4 floors. -------------------------------------------- 93 Figure 4.78 The time period for mode 4 - 4 floors. -------------------------------------------- 93 Figure 4.79 The time period for mode 1- 16 floors. ------------------------------------------- 94 Figure 4.80 The time period for mode 3 - 16 floors.------------------------------------------- 94 Figure 4.81 The time period for mode 4 - 16 floors.------------------------------------------- 94 Figure 4.82 The time period for mode 1 - 4 floors. -------------------------------------------- 96 Figure 4.83 The time period for mode 3 - 4 floors. -------------------------------------------- 96 Figure 4.84 The time period for mode 4 - 4 floors. -------------------------------------------- 96 Figure 4.85 The time period for mode 1 - 16 floors.------------------------------------------- 97 Figure 4.86 The time period for mode 3 - 16 floors.------------------------------------------- 97 Figure 4.87 The time period for mode 4 - 16 floors.------------------------------------------- 97 Figure 4.88 The structural layout and dimensions according to work done by [12]. ----- 99 Figure 4.89 The fundamental time period for 6-floors mutli-story framed building. --- 100 Figure 4.90 The fundamental period for 12-floors multi-story framed building. --------- 101

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Chapter 1 Introduction and Background 1.1 General According to many reports [1], construction industry has witnessed a very rapid growth particularly in multi-story buildings because of tendency to urbanization and industrial development. Considering multi-story building from 3 to 20 stories with raft foundations , it is common – in structural engineering – mainly in the analysis of building at design firms not taking into account the flexibility of the sub structure (foundations and underneath soil) in the analysis of the superstructure. They often carry out design as two parts independently. Generally, buildings are assumed to be fixed or hinged at the ground level. As a consequence, the evaluated responses due to different types of load cases especially the lateral loads (earthquakes and wind loads) do not truly present the accurate behavior of the structure. Raft and soil stiffness will add more flexibility to the structure; so that the overall stiffness will be decreased and a more realistic and economic designs could be achieved. On the other hand, the lateral deflection and the inter-story drift will increase with increasing the soil flexibility. Although this is more conservative for the structures, the safety of the structure due to lateral deflection should be re-evaluated so, it is important to consider soil-structure interaction in the analysis.

1.2 Sources of Soil structure interaction In the structural analysis, the assumption of fixed base for the building especially for the building on soft or medium soil is not realistic [2-14]. Usually designers are assuming fixed or hinged base for the sake of simplicity. This assumption may be accepted if the structure will be constructed on rock layer or if the relative stiffness of the substructure (soil-foundation system) compared to the superstructure is high. In the most occasions, existence of soil induces two separate effects on the structure, first, the amplitude and the direction of the free ground motion from the bed rock will be adjusted ( amplified or degraded) at the level of structure’s base [3]. Second, hence the underneath soil is flexible, the forces acting on the masses of the structures will enforce the supporting systems (raft foundation..etc.) and the underneath soil to deform. These two phenomena are referred to as kinematic interaction and inertial interaction, respectively. In fact, kinematic interaction is the inability of the foundation to match the soil deformations due to the free field ground motion. On the other hand, the inertial interaction can change the structure periodic time (T) hence the structure response to the seismic loading. These two effects are discussed in more detail in the following sections.

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1.2.1 Kinematic interaction: Kinematic interaction is the inability of rigid foundation to match the movement of soil under ground motion. Due to the effect of existence of soil mass, the ground motion amplitude and frequency will change at each point depending on soil and ground motion characteristics. Also, the ground motion decreases with the increasing of depth. Moreover, due to the existence of raft foundation which is much more stiffn relative to soil stiffness, the ground motion waves may suffer from scattering at foundations corners and deviation so, the base of super structure will be exposed to different ground motion than the free field motion. So, there is need to use some transformation to transform the free field motion into foundation input motion using some mathematical transformation techniques. Yet, the kinematic interaction plays an important role in case of loose soil with high level of ground water table and in soft soils. In this thesis, only the inertial interaction will be considered.

1.2.2 Inertial interaction: In the second type of interaction, the existence of flexible material under the foundation of the super structure is denoted as inertial interaction. Inertial forces which are induced by foundation motion during the lateral loading can cause the underneath soil to deform figure 1.1 (a). Hence more flexibility will be added to the super structure. That means the dynamic characteristics of the structure such as fundamental periodic time and structure responses such as lateral deflection, base shear and inter-story drifts will differ from those of the fixed/hinged base structure figure 1.1 (b). So, base shear, story shear, lateral deflection and inter-story drift should be re-computed. The soil-structure interaction effect can be evaluated and assessed by comparing the same structure responses subjected to lateral loading with and without soil underneath the foundation systems. This is usually causing increasing in natural periodic time due to flexibility of existing soil added to the system. In most cases, inertial interaction has beneficial effect on the structure as base shear and story shear will decrease with gaining more ductility in the structure which allow for more energy dissipation. However, in some rare cases, it has detrimental effects on the structure especially for low rise buildings [5]. Gazetas & Mylonakis, [2-4] demonstrated the possible severities of neglecting soil structure interaction for a certain soil and seismic characteristics. They demonstrated that the increase in the natural periodic time may cause an increase in the seismic demand of the structure.

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(a)

Figure 1.1(a) The effect of soil flexibility on the lateral deformation. (b) The effect of neglecting soil flexibility.

1.3 Methods of soil structure interaction modeling Basically there are two approaches for the soil structure interaction analysis.

1.3.1 The direct approach [15-16] In this approach, the structure, foundation system, and the underneath soil are modeled together as a unit. The entire system is solved in a single step as shown in figure 1.2. In this method, soil is modeled as a finite solid element with the corresponding elastic modulus (E) and Poisson’s ratio (v), also it can be modeled using boundary element method taking the advantages of no meshing in the domain and less computational time [16]. The boundary conditions are implemented so that the soil continua almost represent the soil block under the structure. The structure is modeled using the beam elements for the beams and columns whereas the slabs; raft and shear walls are modeled using shell elements. The advantage of that method is that it can be used for complex geometries and different material properties. Also it can be used for the nonlinear interaction analysis [15].

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However, the preparation of data and modeling complexity makes it difficult to be implemented in the field of engineering practice besides, if the size of the structure is big which is the case for practical buildings, the user cannot use this method efficiently. Another disadvantage of this method is the modeling of an infinite media as a finite one with artificial boundary conditions. This can cause energy trapping within the model and cause error in the computation process. So, there are some techniques that have been developed to solve this problem such as using non-reflecting boundaries [15] to absorb energy or using dampers [15] to prevent energy from reflecting back into the model.

Figure 1.2The direct approach of soil-structure interaction.

Since most of the ground motions are usually recorded on the ground surface without considering the existence of the structure, therefore, in constructing a finite element modeling to model soil-structure interaction, all ground motions must be refined to obtain the bedrock motion before using those as the input motions for such modeling approach. So it is very complex to obtain the bedrock ground motion especially in case of complex soil profiles.

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In this thesis, the direct method is used as verification for the proposed technique with only static lateral loads to overcome the problem of preventing energy. This method can be used as verification for small problems only, practical examples cannot be solved as it requires large computers which are not available.

1.3.2 The Substructure approach [17] In the substructure approach the soil-structure interaction problem is divided into two independently substructures as shown in figure 1.3. The substructure number one is the structure itself including the raft foundation. The substructure number two is the soil half space. The coupling process between the substructure no.1 and the substructure no.2 is undertaken with various algorithms [17] which basically ensures the equilibrium and compatibility at the interface between the soil and the structure. In this approach, it is assumed that no separation and slippage occur at the interface between the structure and the soil subdomain. In static interaction analysis, the entire structure is initially considered rested on an initial value of linear springs. After the analysis is done, the reaction forces are equilibrated at the interface and are hence subjected with the same values and in opposite direction on the soil subdomain as external forces. Then, the analysis of soil subdomain under the predefined loads is carried out. The response of the soil subdomain in terms of deformation can be computed. Using iterative technique with an acceptable tolerance, the compatibility and equilibrium can be achieved [17]. In case of the static soil-structure interaction analysis, only the inertial interaction is regarded in the analysis where kinematic interaction has no effect. As demonstrated previously, the main advantage of the substructure method of soil-structure interaction is its flexibility which makes it efficient. Also, nonlinear soil-structure interaction analysis can be done in an appropriate way [17] .

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The substructure no.1

The substructure no.2

Figure 1.3 The substructure method of soil-structure interaction.

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1.4 Methods of soil representation: There are different methods to represent and model the soil. From these methods we can mention the Winkler method, two parameter method and elastic half space method [15].

1.4.1 The Winkler model The Winkler Model [18] is the most used model for soil-structure interaction analysis by structural engineers. This is due to its simplicity. It is considered as the oldest method to model the underneath soil. This model depends on representing the soil as finite number of springs on a rigid base as shown in figure (1.4).

Figure 1.4 Soil representation using Winkler springs.

In this model, no coupling between springs which means deformation will be immediately under each spring individually where the deflection at the other point is zero. The springs have only the vertical degree of freedom. The stiffness of uncoupled springs can be evaluated using different methods, all of these methods are based on the linear relationship between force (Ri) and deflection (δi)at a certain point as shown in equation (1). Ki= Ri / δi. (1) Although the Winkler model is one of the simplest ways of soil modeling, it is also the least accurate. The primary deficiency of the model is that there is no unique value of K for a certain type of soil. This means that the subgrade reaction is not considered as a property among the different soil properties.

1.4.2 The multi-Parameter model [19-20] The multi-parameter models have been developed to refine the Winkler soil representations. In these models two or more independent constants with elastic behavior are predefined. These constants are used to consider the shear deformation of the soil, hence Winkler springs will be coupled. Most of these models use elastic beam, elastic membrane or springs as an elastic interaction element which can transfer the load in the transversal direction. Examples of these models are illustrated in the work of Filonenko-

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Borodich [21-22] who used deformed pre-tensioned membrane as an interaction element between Winkler springs, Pasternak [23] who used a shear layer to couple the spring elements, Loof and kerr [24] who used a shear layer with springs to couple the springs elements, Haber- Shaim who used a plate as an interaction element, Hetenyi [25] who used a plate-spring system for coupling between springs and Rhines [26] who used a system of springs-plate-shear layer to couple springs. These models have also the deficiency of that they are not considered a property among the different soil properties.

1.4.3 The elastic half space model Continuum is defined in continuum mechanics by a continuously distributed mass through the space. The simplest elastic continuum is described with linear elastic isotropic behavior given by Hook’s law. Without failure criteria the elastic medium has infinite tension and compression capacity, which is not real for soil. Several constitutive relations exist, with different failure criteria in tension and compression. Several analytical solutions due to different loading cases have been developed for the elastic half space. Boussinesq [20] and Mindlin [27] considered the soil as an elastic, homogenous, isotropic, , and infinite half space. Steinbrenner [28] considered the presence of a rigid layer under the considered surface soil finite layer. For all previous models, normal stresses in horizontal direction and shear stresses are neglected as well as the horizontal displacements at top and bottom of the medium. Due to these assumptions, these methods are not suitable to study stresses inside the medium. Several numerical methods can be used to analyze the elastic semi-finite continuum such as finite element method and boundary element method.

1.5 Available solutions in practice In practice, the most common method is the Winkler spring model despite of its several shortcomings previously presented. The ACI committee [29] suggested using elastic half space technique with Boussinesq theory instead of Winkler model for accurate modeling. Unlike the Winkler and the twoparameter models, the elastic half space method uses data obtained from geotechnical investigations such as elastic modulus E and Poison’s ratio v. Nowadays, the uncoupled iterative method [30] is used widely in many design companies and they make use of EHS to represent the soil medium. However, it takes a long time and huge effort through structural and geotechnical analyses to still obtain an approximate solution [30].

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1.5.1 The uncoupled manually iterative method In this section the uncoupled iterative method is discussed. In this method the substructure approach is used. In other words the structure including the raft foundation and soil is modeled separately where the soil is modeled as a continuum elastic half space. The sub-structuring is done at the soil-raft interface. The method is based on manual iterative procedure which is done at the soil-raft interface to ensure that compatibility and equilibrium have been achieved. At each stage of the iterative process, the results of one analysis form the boundary conditions for the subsequent analysis using the vertical equilibrium as shown in figure 1.5. This method is used by some consultant and design firms [30]. However, this method of coupling requires much time and efforts to be done properly. This is because the static condensation which is done at the soil-raft interface results in many degrees of freedoms unlike the case of doing condensation at the raftcolumns interface. Another method of sub-structuring to overcome these shortcomings is the core of this thesis and presented in details in chapter 3. The steps of this method are demonstrated in cycles as follow: a. The first iteration (n) 1- The soil flexibility matrix [F] is computed from EHS program such as Pdisp [42]. 2- The vertical structural loads {Q} are applied directly to the ground surface, and the vertical surface displacements {ws }1 are obtained as follow {ws}1 = [ F ] x {Q}. Such displacements are computed using a software package called the VDisp – a software package for elastic half space problems. 3- The raft is founded on bed of springs of vertical nodal stiffness as follow {Ks}1 = {Q/(ws)1}. However, most of design companies use a preliminary suggested formulate to get the subgrade reaction which can be evaluated as 100-120 of soil bearing capacity in t/m/m2. 4- The entire structural loading {L} - including any imposed moments – is applied to the raft on springs, and the vertical spring forces {P}1 are obtained by conventional methods of structural analysis. Initial values of vertical raft displacement {wk }1 are also computed to be compared to the corresponding ground displacement profile.

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Figure1.5The Uncoupled iterative technique used in design firms.

The second iteration (n+1) 5- The vertical spring forces {P}1 are applied directly to the ground surface, and the vertical surface displacements {ws}2are obtained as follow {ws}2 = [ F ] x {P}1. . 6- The raft is founded on bed of springs of vertical nodal stiffness as follow {Ks}2 = {P/(ws)2}. 7- The entire structural loading {L} is applied to the raft on springs, and the vertical spring forces {P}2 are obtained as before. Values of vertical raft displacement {wk}2 are also computed to be compared to the corresponding ground displacement profile. The iterative process is continued until satisfactory convergence is achieved.

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1.5.2 The conventional method in practice Although the previous method in section 1.5.1 is used by some design firms, the most of design firms uses the method presented in the current section. In this method, the superstructure is modeled on fixed/hinged base and analysis is carried out based on this assumption. The reactions from the superstructure are reversed into the foundation system and then the analysis is done

(a) [12]

(b) [12]

Figure 1.6 The conventional method used in practicaldesign firms (a),(b).

as shown in figure 1.6 (a). So, the interaction between the underneath soil and the foundation is taken but the effect of the foundation-soil flexibility on the superstructure is omitted. Moreover, the common method to represent the soil is Winkler uncoupled springs, which means that there is no realistic representation of soil and hence less accurate results than modeling soil as elastic half space.

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In some rare cases, the entire structure is modeled including the raft foundation [12]. The soil is modeled as Winkler uncoupled springs as shown in figure 1.6 (b).

1.6 Thesis objectives The main objective of this work is to develop a practical tool to consider soil-structure interaction in the analysis of building rested on raft foundation which can be used by design engineers in design firms easily and efficiently. The new idea is based on the availability of the ETABS program [32] which is widely used in design firms for the analysis and design of building as presented in chapter 2 in section 2.3. Also, there is a program called PLPAK [40] see chapter 2 section 2.5 through which soil can be modeled as elastic half space. The soil-structure interaction procedure is carried out using an iterative technique. Unlike the uncoupled iterative technique presented in section 1.5.1, this technique is based on a static condensation at the raft - columns interface as shown in figure 1.7. This will produce much less degrees of freedom and hence much less effort and computation time. The new practical technique is aimed to be automated, also a graphical user interface for the work is going to be developed to ease the use for engineers in the practice. The thesis objectives can be summarized as below.  To develop a new algorithm to couple the structure with the soil in the analysis of multi-story buildings rested on raft foundations to consider the effect of static soil-structure interaction.  To implement this tool to couple the well-known commercial finite element program named ETABS which is used for the analysis of buildings with a boundary element based program named PLPAK which is used for the analysis of slabs and foundation on elastic half space.  To develop graphical user interface for the code to be efficiently used used in practice.

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Figure 1.7 The proposed new method of static condensation.

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1.7 Thesis outline A very short overview for each chapter in this thesis is presented as follows. Chapter 1: introduces briefly the problem, presents the background of the problem and previous work done in that area. Chapter 2: introduces the finite element method and its disadvantages, the ETABS software and its main components. The boundary elements method’s advantages and disadvantages are also listed. PLPAK components and its adds-on are presented. Chapter 3: the proposed technique is presented with detailed explanation and flow chart showing how to automate and use this technique in practice. Also the developed GUI main buttons are demonstrated in details. Chapter 4: numerical examples and results are presented. A comparison and verification to internationally published papers are shown. Framed and shear wall structures are used in this chapter. Lateral deflection, lateral deflection ratio SSI/NSSI, Drift, Drift Ratio SSI/NSSI are used for the comparisons. Chapter 5: summary, conclusion and recommendation for future work are presented.

1.8 Conclusions In this chapter, an overview for the thesis was discussed followed by an introduction about the soil structure interaction sources, methods of soil structure interaction, models used to represent the soil and available solutions in practice. The advantages and disadvantages for such a method were reviewed. Finally, the objectives of this thesis were stated. In the next chapter, the boundary element method is reviewed. Soil modeling in BEM and PLPAK is also reviewed. Finally The PLPAK software package is presented with its available methods to model soil.

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Chapter 2 Used Numerical Methods And Softwares 2.1 Introduction In this chapter a brief review about finite element method FEM is presented. The ETABS program as a software applying the FEM is also reviewed with its main components and capabilities. The ETABS files with different extensions are presented in details. The boundary element method is also reviewed. The PLPAK program – A BEM Based program as an application for the direct BEM for Reissner’s plate is also presented. Soil modeling methods in PLPAK is reviewed as well.

2.2 The finite element method (FEM) [31] The finite element method is a numerical method for solving linear partial differential equations. According to the FEM [31], the entire domain of the considered problem is discretized into smaller subdomains which only are connected at their corner nodes. The unknowns of the problem are the deflections and rotations in the directions of prescribed degrees of freedom. The values of these unknowns are obtained from the solution of equilibrium and compatibility equations assembled from all elements. Due to the wide usage of the FEM, there are many established commercial programs that are based on the method such as ETABS [32], SAP2000 [33], ANSYS [34] etc.

2.2.1 Advantage of the FEM: The advantages of the FEM can be summarized into, a) ability to model different geometries and nonlinear materials b) obtained system matrices are positive definite, banded, and sparse c) Widely tested approach d) Commercial availability e) Flexibility

2.2.2 Disadvantage of the FEM: The disadvantages of the FEM can be summarized into, a) The FEM requires the use of powerful computers of considerable speed and storage capacity. b) It is difficult to ascertain the accuracy of numerical results when large structural systems are analyzed. c) The method is poorly adapted to a solution of the so-called singular problems (e.g., plates and shells with cracks, corner points, discontinuity internal actions, etc.), and of problems with unbounded domains. d) The method presents many difficulties associated with problems of C1 continuity and nonconforming elements in plate (and shell) bending analysis.

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e) Large effort and time consuming in discretization of the domain and no flexibility in modification

2.3 The ETABS software [33] The ETABS stands for Extended (Three-Dimensional) Analysis of Building Software. It is one of the most well-known and commercially available analysis software which is used widely in the structural analysis of buildings. ETABS software is developed using the finite element method as a numerical modeling technique in the analysis of structures. Unlike SAP2000, ETABS has more advanced computation algorithms which are implemented to analyze any complex high rise structure in lesser time and memory. Also ETABS has more user friendly input options to generate the complex high rise structure's model. The model can include different or integrated structural systems with the ability to solve complex problems easily [35]. In addition to that, ETAB software has design features according to many codes of design with unique calculation notes that is widely used by design firms.

2.3.1 ETABS modeling and simulation capabilities ETAB software has a friendly graphical user interface GUI. Modeling capabilities that can be done using ETABS GUI are summarized below. a) Different types of structural elements such as frame and shell elements. b) Different types of support restraints simulation including roller, hinged and fixed supports. c) Different types of nonlinear support element such as gap element. d) Different types of constraints including body, plate, weld, diaphragm constraints. e) Different types of load cases and conditions including gravity loads and lateral loads.

2.3.2 ETABS analysis capabilities ETAB software solver can do the following analyses.

a) b) c) d) e)

Static and dynamic analyses. Linear and nonlinear analyses. Seismic and pushover analyses. Construction staged analysis. Geometric nonlinearity analysis.

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2.3.3 Used ETABS files In this section, important input and output files that are used in this thesis are presented in details. 2.3.3.1 ETABS model file (.e2k) This file contains all ETABS model data including name of the model, saving date, coordinate system, point coordinates, point assignments, line assignments, load cases..etc. this file can be exported directly from the ETABS GUI and re-imported again. The structure of the .e2K file is shown in figure 2.1.

Figure 2.1 The structure of the ETABS .e2k file.

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2.3.3.2 ETABS data base file (.txt) This data base file contains model data as well as the analysis data in separate text formatting files. This file can be exported directly from the ETABS model after analysis is done. Only in this thesis, five files are used in the proposed technique. These files structures are shown in figures 2.2 – 2.6. 1- Point Coordinates .txt file: This file contains the points labels and X,Y, and Z coordinates as shown in figure 2.2.

Figure 2.2 The structure of point coordinates .txt ETABS file.

2- The Static Load Cases.txt file: This file contains the different load cases that were entered by user and the selfweight multiplier for each case as shown in figure 2.3.

Figure 2.3 The structure of static load cases .txt file.

3- The Supports (Restraints).txt file: This file contains the support labels and restrained directions as shown in figure 2.4.

Figure 2.4 The structure Support Restraint .txt file.

4- The Supports Reactions.txt file: This file contains the support labels, load case and the corresponding reactions in each direction as shown in figure 2.5.

Figure 2.5 the structure of Support Reactions.txt file.

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5- The Point Spring Forces.txt file: This file contains the spring labels, load cases and the spring forces in each direction as shown in figure 2.6.

Figure 2.6 The structure of Point Spring Force.txt file

2.4 Used structural objects and terminology in ETABS building model In this section, different objects and terminologies used in ETABS building model are reviewed. These can be divided to the following: 2.4.2 Joint objects: Joints are automatically generated at the corners and ends of all other types of other objects mentioned below. 2.4.2 Support object: Used to model and represent supporting conditions. It includes roller, hinge, fixation and Winkler supports. It can be modified to restraint degree of freedom in customized directions.

2.4.3 Line objects: There are four types of line objects used in modeling. 1- Frame element: used to model beams, frames, trusses and bracing systems. 2- Cable element: used to model cables. 3- Tendon element: used to model pre-stressing tendons in pre-stressed concrete.

2.4.4 Area / shell objects: Used to model slabs, walls and other two dimensional elements. This includes thin and thick shells.

2.4.5 Meshes / divisions: Each area object is divided into a number of relatively small subareas. The dimensions of these subareas depend on the problem type and dimensionality and the degree of accuracy pursued.

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2.4.6 Body Constraint: A body constraint causes all of its constrained joints to move together as a threedimensional rigid body. By default, all degrees of freedom at each connected joint participate. However, you can select a subset of the degrees of freedom to be constrained. This Constraint can be used to: 1- Model rigid connections, such as where several beams and/or columns frame together. 2- Connect together different parts of the structural model that were defined using separate meshes. 3- Connect Frame elements that are acting as eccentric stiffeners to Shell elements.

2.4.7 Diaphragm constraint: A diaphragm Constraint causes all of its constrained joints to move together as a planar diaphragm that is rigid against membrane deformation. Effectively, all constrained joints are connected to each other by links that are rigid in the plane, but do not affect out-ofplane (plate) deformation. This constraint can be used to model concrete floors in building structures, which typically have very high in-plane stiffness especially in lateral analysis.

2.5 The boundary element method (BEM) [36] The boundary element method is a numerical method for solving linear partial differential equations which have been formulated as boundary integral equations. It can be applied in many disciplines in engineering and science including solid mechanics, fluid mechanics, acoustics, electromagnetism, fracture mechanics, and plasticity. In contrast with other energy methods like finite element method, the boundary element method discretization is only on the problem boundaries. The direct and indirect boundary element methods are the two branches of the BEM. The direct BEM formulates the problem in terms of variables that have definite physical meanings, such as displacements of the boundary nodes of the plate. In contrast, the indirect BEM uses variables whose physical meanings cannot always be clearly specified. The advantages of the boundary element method are reducing problem dimensionality, requiring low memory, it focuses on the body boundary, good for incompressible materials, easy to define and vary boundary elements, accurate and good for stress concentrations. In practicality, there are already several programs which are developed using boundary element method and adopted for the solution of many engineering problems [37-40].

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2.6 Raft terminology used in BEM/PLPAK In this section, important terminologies used in modeling of raft foundation in BEM/PLPAK are presented. Consider figures 2.7 and 2.8.

2.6.1 Raft foundation: In the PLPAK, raft foundation is modeled using flat Reisinner’s plate theory [36] (flat shear deformable plate) with 3 DOF; two rotational D.O.Fs about X and Y axes and the third D.O.F is a translation in Z axis as shown in figure 2.7 and 2.8.

2.6.2 Boundary elements: Consider an arbitrary raft with the plan shown in figure 2.7. In the boundary element method, the problem is discretized only on the boundaries. In the PLPAK, boundaries can be discretized into customized numbers upon user preferences and problem conditions. The solution in terms of displacement and tractions is carried out only on the boundary elements then using other numerical techniques, the internal displacements and tractions can be calculated.

2.6.3 Nodes: These nodes are the nodes which define the type of the boundary element whether it is constant, linear or quadratic boundary element. See figure 2.7.

2.6.4 Extreme points: These are the points which separate a boundary element from another one. See figure 2.7.

2.6.5 Colum load modeling: In the proposed technique, there are two methods of modeling columns load. These two methods are column load modeling without rotational stiffness and column load modeling with rotational stiffness. 2.6.5.1 Column load modeling without rotational stiffness: In this case, each column load is located using the coordinates of each corner of the load area. The loaded area is the interface between raft and column cross section. This area is considered a square with length of (L) where L is the minimum dimension of the column cross section. There are three types of loads that can be represented at each loaded area: 1- Force in direction of axis Z distributed on that area. This force represents the action of the column in the direction of Z-axis. 2- Moment about X-axis. 3- Moment about Y-axis. 21

2.6.5.2 Column load modeling with rotational stiffness: In this case, each column loaded area is divided into 9 equal squared areas. Each square has a dimension of L/3. The only load is acting on each subarea is the force in Z-axis. The resultant forces/moments for the total 9 subareas definitely equal the applied force, moment about X-axis and moment about Y-axis.

2.6.6 Wall load modeling in PLPAK: In this section, wall load modeling in PLPAK is presented. There are two methods of modeling wall load in PLPAK similar to that of column load modeling. The difference is that wall load is not considered as an assembled load at the interface between the wall and raft. In this thesis, the wall load is considered as a number of neighboring column loads. The number of column loads depends on the number of divisions/meshes that wall is divided in the ETABS model. Each column load can be represented as in section (2.6.5.1) and (2.6.5.2) depending on the type of analysis wanted to be carried out.

Figure 2.7 Soil and boundary elements discretization for a typical raft on Winkler foundation.

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2.7 Soil terminology used in BEM/PLPAK In this section, the important terminologies and objects used in modeling of soil in the PLPAK is presented.

2.7.1 Subgrade reaction (K): It is an approximate value representing the stiffness of the soil. This value does not depend on geotechnical investigation so, it is not unique for a certain soil. The subgrade reaction is based on approximate relationships.

2.7.2 Elastic modulus (E): It is a unique property for a certain soil type. This property is retrieved from the geotechnical investigation and does not depend on approximate relationships.

2.7.3 Poison’s ratio (v): It is the ratio between the transverse strain to the longitudinal strain. In soil modeling within the PLPAK, soil poison’s ratio must be entered only if soil is going to be modeled using elastic half space.

2.7.4 Soil layers: As will be mentioned later in section 2.9.2, soil can be modeled as elastic continuum half space coupled with stiffness method. This continua can be modeled as several layers as shown in figure. For each layer, it is required to enter the total depth, Poison’s ration and the Young’s modulus of that layer. Then each layer’s stiffness are computed and assembled at the interface between soil and raft. The only degree of freedom that is considered in the layering is the vertical one.

2.7.5 Soil cells/divisions: There are two methods for modeling foundation-soil system in BEM/PLPAK. The first method is to model the soil as Winkler. The second method is to model the soil as elastic half space.

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In the following subsection, the direct boundary integral equation for shear deformable plate rested on Winkler/elastic half space is reviewed. The applications of these integral equations in the PLPAK software are presented.

Figure 2.8 Soil and boundary elements discretization for a typical raft on EHS.

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2.8 The PLPAK software package [40] The PLPAK software [40] is a developed research program which is developed by a research group named CUFE-BE at faculty of engineering Cairo university. PLPAK uses the direct boundary element method as a numerical method to solve linear partial differential equation which governs the shear deformable plate bending problems named Reissner’s plate [36]. It can solve slabs and foundations on elastic foundation such as Winkler and E.H.S. The program has a unique graphical user interface (GUI) for structural 2-D modeling analysis of building slabs and foundations. The program consists mainly of five integrated parts: 1- Model Generator executive file (PLGen). 2- Visualization and simulation executive file (PLView). 3- The command line solver. (Pl.exe). 4- Post-processing and results executive file (PLPost). 5- The core manager executive file (PLCoreMan). And there are other adds-on packages for the PLPAK such as (PLDesign, EHSPAK, PTPAK, and LTPAK). The four parts are integrated together to solve and visualize the results as in the following flow chart shown in figure 2.9.

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Figure 2.9Flow chart show the PLPAK components

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The main purposes of each part are listed below:

2.8.1The PlGen: The main object of this part is to generate the input files. The input files Includes material properties, columns locations, column loads, load cases, patch loads, wall support, wall support assembly , wall load assembly, soil support ( EHS-Winkler), slabs thickness, slabs geometry, boundary discretization, boundary condition, soil support discretization, opening and beams data.

2.8.2 PLView: The main purpose of the PLView is to simulate and visualize the boundary element models generated later using the PLGen module or from user text input. It can be used to show and hide the boundary elements, boundary element numbering, extreme nodes, node numbering, points, points numbering, elements directions, loads, supports, boundary conditions, internal points, additional internal points. Also, the entire model can be viewed in tables. Each table can be edited easily. Also, a check button is available to check if the model is geometrically and algorithmically valid or not.

2.8.3 PL.exe: Simply, it is the executable file containing the solver. The required input files for Pl.exe are the files containing the entire data of the boundary element model ( .in) file, The mode of run and the destination of the model on the hard disk (.run) and other input files such $run$, Lic, $Plcontl$. The output file , definitely are the solution of the problems in terms of displacement (.u) files and traction (.t) files at the boundary elements. There are other files accompanied by the output files like (.out), ( .stt) , (.log), (.bs), (.ber), (.ipu), (ips) text files.

2.8.4 PLPost: The PLPost is a post-processing tool of the PLPAK. It takes the output files obtained from PL.exe and present the results in many ways as follows: 1- Demonstrates result at certain point. 2- Demonstrates result along a certain strip. 3- Demonstrates result over certain area as contour map. 4- Demonstrates soil reactions or soil contact pressure. 5Demonstrates results in a tabulated form. Also, in the PLPost any required load combination could be performed. This part is responsible for presenting the results of the boundary element model. This part shares the same graphical interface with the PLView, because it represents the results over the graphical representation of the boundary element model.

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2.8.5 PLCoreman: The PLCoreMan is the head of the PLPAK program. It is the manager of all files and the caller of the executable files and other subroutines, through which, you may run the other PLPAK components. It reads the input data files then calls the command-line solver PL.exe which - as mentioned above - solves the problem and generates output files. PLCoreMan also connect all parts of the PLPAK package. Also, through PLCoreMan, modes of run and solution can be changed if needed.

2.8.6 Used PLPAK files In this section, important input and output files that are used in this thesis are presented in details. 2.8.6.1 PLGEN text format files In this section, the PLGEN text format files are described in details. These are 14 files named as follows.

1- model.txt : This file contains the name of the other 13 files to be read later as shown in figure 2.10.

Figure 2.10 The structure of the model.txt file.

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2- Material .txt: In this thesis, material name and its properties is defined as shown in figure 2.11.

Figure 2.11 The structure of the material .txt file.

3- Slab.txt : This file contains raft data as shown in figure 2.12.

Figure 2.12 The structure of the slab .txt file.

4- Soil support .txt : This file contains the soil support data as shown in figure 2.13.

Figure 2.13 The structre of the soil support .txt file.

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The column load.txt and Lc.txt structure are presented later in chapter 3. The other files contain zero as they will not be used. 2.8.6.2 Other files 1- .aip file : This file contains the number of additional internal points needed to carry out post processing. Also contains the coordinates of each internal point as shown in figure 2.14.

Figure 2.14 The structure of the .aip file.

2- .ipu file : This file contains the post processing results at the internal points. The results are presented in terms of Uz , Rx and Ry as shown in figure 2.15.

Figure 2.15 The structure of the .ipu file.

3- .run file : This file contains the path of the input and output files generated by PL.exe as shown in figure 2.16

Figure 2.16 The structure of the .run file.

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2.9 Soil modeling in PLPAK: In PLPAK, soil can be represented as Winkler continous springs or as elastic half space. The later is based on Mindlin [20], Boussinesq [27], and Steinbrenner [28] equation are coupled with boundary element method to represent the soil as an elastic continuum stiffness cells [30] as reviewed in section 2.3.2.

2.9.1 Winkler model: In BEM, soil is modeled as a continuous Winkler spring cells with vertical DOF only [41] as shown in figure 2.7. In the Winkler model, soil cells are considered uncoupled. Each soil cell deflection is function only of the applied load. There is no contribution of the other Winkler patches in the behavior of a certain patch. Soil underneath a raft is modeled as Winkler springs in PLPAK by directly drawing soil patches underneath the corresponding raft domain only. Hence, stiffness of soil and its divisions in two directions are defined. These procedures are shown in Figures 2.17 and 2.18.

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Figure 2.17 The Winkler cell discretization in the PLView.

Figure 2.18 Practical raft on Winkler modeled using PLGen

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2.9.2 EHS modeling: In BEM, soil can be represented as an elastic continuum half space using many methods [30]. In the PLPAK, the BEM coupled with the stiffness matrix approach are implemented in order to model soil as a continuous coupled media. In this method of modeling, soil is only modeled at the interface between raft and soil as a continuous coupled soil cells or patches. Each single patch has stiffness in direction of the Z-axis only. This interface is considered as a condensation of the entire stiffness of the soil continuum at the top layer of the soil. Soil underneath a raft is modeled as elastic half space in PLPAK by directly drawing four side polygon containing raft domain, define stiffness of soil and divide it to specified number in two directions. Soil underneath raft is modeled by defining stiffness of soil in PLPAK by –ve value then the EHSPAK package is triggered to define the soil profile as shown in Figure 2.7. This package can export stiffness matrix of soil hence the rest of solution procedures are carried out to get results in the PLPost.

Figure 2.19EHSPAk add-on start menu

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2.6 Conclusions In this chapter, an overview about the finite element method is presented. The ETABS program is presented with its main components and some modeling terminologies. Also, the boundary element method and its two branches were reviewed.. The PLPAK software package and its main components were presented with its available methods to model soil with modeling terminology about SSI modeling. In the next chapter, the proposed technique is presented. Each file structure is also illustrated.

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Chapter 3 The Proposed New Technique 3.1 Introduction In the previous chapter, the finite element method and its applications were discussed. The ETABS software and its components were illustrated. Also, BEM was reviewed. The PLPAK software and its main components were presented. Modeling of Soil as Winkler uncoupled springs and as EHS was also discussed. In this chapter, the proposed technique of including the SSI in the lateral analysis of buildings is discussed. The developed Translator.exe is illustrated in detail followed by an illustrative example. The entire methodology of the work is illustrated in details with flow chart presentation. The developed graphical user interface is presented as a method to automate the proposed analysis technique.

3.2 The developed translator In this section, the developed translator is illustrated in detail. The methodology of the translation is discussed. The proposed technique to implement translation stiffness is illustrated. Also, the proposed technique to implement the rotational stiffness in the analysis is illustrated. The input and output files are presented in detail.

3.2.1 Translator.exe The main object of this executable file is to translate the required data from the superstructure model in ETABS to be modeled in the PLPAK software. The translation procedure is carried out after the analysis of the superstructure in ETABS is done. The user has to export five files which will be used by translator to generate the PLPAK raftsoil model. The input and output files the that translator uses are presented in details in the below subsections. 3.2.1.1 Input files In this section, the translator input files are presented. 1- IterID.txt file: This file contains the number of iterations that has been done. In the beginning, no iteration is done, so the value written in the file is zero. This file will be used in later section if it is required to carry out more than one iteration. 2- ETABS database file: These five files are presented in section 2.3.3.2 in details.

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3- MDim.txt file: This file contains the minimum dimension of the columns in the structural plan. This will be used later to define and locate the loaded area of each column/wall in PLGEN model. 3.2.1.2 Output files 1- Load case name .aip files : These files are generated for each load case exported from ETABS model. The structure of this file is presented previously in section 2.3.3.2 2- Load Case name .c files: These files are generated for each load case exported from ETABS model. Each file contains the support reactions of a certain load case. The structure of this file is shown in figure 3.1.

Figure 3.1 he structure of . c file.

3- Load Case name .k files: These files are generated for each load case exported from ETABS model. Each file contains the support label and Winkler spring stiffness value. This file is used as a data updater for the ETABS model data. The structure of this file is shown in figure 3.2.

Figure 3.2 The structure of the .k file.

4- LC.txt file : This file is written in PLPAK format. This file contains the number of the load cases translated from ETABS and the name of each load case. The structure of this file is shown in figure 3.3.

Figure 3.3 The structure of the LC.txt file.

36

5- Column Load .txt file: This is written in PLPAK format. This file contains the number of column load and the column load values for each load case. The number of column loads can be the same number of the supports; this is the case of column load modeling without rotational stiffness or can be the number of supports multiplied by 9; in this case, the rotational stiffness is implemented. The structure of this file is shown in figure 3.4.

Case load 1

Case load n Figure 3.4 The structure of the column load.txt file.

6- $Runstiff$ file: This file is generated from translator. This file contains the path of the .c file, .k file and .ipu file mentioned previously in section 2.8.6.2. The structure of this file is shown in figure 3.5.

Figure 3.5 The structure of the $Runstiff$ file.

37

The input and output files that are used by the translator can be illustrated in a flow chart diagram as shown in figure 3.6.

Figure 3.6 The input and output files used by translator.

3.3 Rotational stiffness implementation in SSIPAK/PLPAK In this section the assumption and the procedure to implement the rotational stiffness in the proposed analysis is illustrated. Consider a part of a raft surrounding a column as shown in figure 3.7. In order to consider the rotational stiffness of the raft-soil system in the analysis of buildings with SSI, a relatively small segment of the raft is considered. This segment is assumed to have linear behavior. This means that it tends to rotate as a rigid body. This assumption is acceptable as long as the dimensions of this segment does not exceed the column dimensions. Knowing the deflection of two points on the line and assuming the rotational angle is very small so that Ø = sin Ø = tan Ø. The rotation about Y-axis can be estimated as Ryy = (Uz9 –Uz5) /L where the rotation about X-axis can be estimated as Rxx=(Uz7 –Uz3) /L.

38

Figure 3.7 The rotational stiffness implementation procedure.

3.4 Illustrative Example In this section, an illustrative example is presented with detailed steps. This is to show the process to translate the data of the super-structure ETABS model and construct the raftsoil PLGEN model in PLPAK. 1- Structural drawings: In most cases, the designers have the structural drawings in cad formatting. It is the key to begin the modeling on ETABS as shown in figure 3.8. 2- ETABS 3D Model: Designers always use the structural drawings to construct the ETABS 3d modeling as shown in figure 3.9. ETABS model have to be modeled in a correct way. All load cases should be included. For the first iteration, the end conditions for each column will be fixed or hinged.

39

Figure 3.8 The structural drawings using AutoCAD.

40

Figure 3.9 The ETABS 3D model.

41

3- Data base file: in this step, the user have to open the data base of the ETABS and begin to select some important files which will be used later as shown in figure 3.10 (a & b).

Figure 3.10 a & b The steps to export the database file containing the required text files.

42

It should be noted that different load cases can be selected. Also, user has to export the following files. The structure of these file was presented in section 2.3.3.2. These files are a- Point coordinates b- Static load cases figure c- Support (Restraints) Assignments figure d- Support reactions figure The database file which will be exported from ETABS is shown in figure 3.11.

Figure 3.11 The database file containing the required text files.

4- Run translator.exe: In this step, translator .exe is executed. The input and output files that required for the translation process is presented previously in section 3.2.1. 5- PLPAK model: In this step, PLGEN model is generated. The generated files from translator are then imported in text formatting. The model is shown in figure 3.12-3.13.

43

Figure 3.12 The raft model in PLGEN.

Figure 3.13 The raft model in PLVIEW.

44

3.5 Methodology and automation In this section, a flow that chart describes the entire process of including soil-structure interaction in the analysis of building is presented as shown in figure 3.14. A detailed description of thte function of each part is presented. The proposed new technique can be summarized in the following steps. These steps can generally be divided into 4 main groups of steps. a- The preparation of the models This includes the preparation of the ETABS and PLPAK model. 1- Prepare the structural drawing as discussed in section 3.4-1. 2- Import the structural drawing to ETABS and create ETABS model as discussed in section 3.4-2. 3- Run analysis for the ETABS model and check results. 4- Export the required files listed below: i. Model.e2k. ii. Point coordinates .txt. iii. Support (Restraint).txt. iv. Static load cases.txt. v. Support reactions.txt. vi. Point spring reactions.txt. 5- Save the ETABS files in one folder. 6- Create the raft model on PLGEN. This model includes only the raft, soil data. No loads are included in this step. 7- Export the PLGEN into text formatting and generate the 14 files described in section 2.8.6. 8- Save the PLGEN model and the text formatting files in one folder.

b- Analysis 1- The analysis starts with executing the translator.exe file. 2- First, the IterID.txt is read. If zero, the support reactions file will be read besides the other files. If not, it means the first iteration is done. So, the translator will read the point spring force.txt besides the other files. 3- The user will be asked about the minimum dimension of the column. It is required to distribute the load on an adequate area. Also to define the small segment which is important for the rotational stiffness’s calculation. 4- The translator.exe will translate the ETABS and generate two file in PLPAK text formatting. 5- Also, load case name . k , load case name . c , load case name. aip and $RunStiff$ files are generated.

45

c- Post processing 1- Modify the run mode of PL.exe from 1 to 2 in the load case name. run file. This file is located at each load case folder. 2- Copy the load case .aip file and paste it in its corresponding load case file. 3- Run again from the PLCorman the PL.exe. 4- Load case name.ipu file is generated for each load case. 5- Execute the spring stiffness calculator.exe 6- The load case name.k for each load case is generated. d- Edit the model.e2k 1- Run the edit etabs .e2k.exe. 2- The new model.e2k file is generated. 3- Import the new model.e2k file and check the new model.

46

47 Figure 3.14 Flow chart shows the proposed technique.

3.6 The graphical user interface SSIPAK In this section, a graphical user interface for the work done in this thesis is presented. The aim of the GUI SSIPAK is to automate the previous processes described in section 3.5 to be easy for practical use. The GUI SSIPAK consists of 12 main buttons and controls as shown is figure 3.15. A detailed explanation for each control is presented as below.

1

8

2

9

3 4

7

5

11 0 12 0

6

10

Figure 3.15 The graphical user interface (SSIPAK).

1- Control 1 : a browse button to define the path of the ETABS model and the exported files from ETABS. 2- Control 2 : a browse button to define the path of the PLPAK/PLGEN model and the PLPAK text format files. 3- Control 3 : the minimum column dimension has to be entered by theuser in this box. 4- Control 4 : execute the translator. 5- Control 5 : copy and replace the old LC.txt and Column load.txt. 6- Control 6 : open new window of the PLGEN.

48

7- Control 7 : copy the .aip files into corresponding load case folder and modify the run mode from 1 to 2. 8- Control 8 : a drop down menu to select which load case for which spring stiffness is to be calculated. 9- Control 9 : run the spring stiffness calculator 10- Control 10 : shows the new values of Kz ,Krx and Kry in tabulated format. 11- Control 11 : execute the edit etabs .e2k file. 12- Control 12 : open new window of ETABS.

3.7 Conclusions In this chapter, the translator .exe is presented. The input and output files required for the translator are described in detail. An illustrative example that shows the detailed steps to translate the required model data from ETABS model to PLPAK model is presented. The rotational stiffness implementation technique to include the rotational stiffness in the soilstructure interaction is also illustrated. The methodology used to include soil-structure interaction in the analysis of buildings is illustrated with flow chart. Finally, a graphical user interface to automate the entire process is developed to facilitate the use of this technique.

49

Chapter 4 Numerical examples 4.1 Introduction In the previous chapter, the proposed technique to account for the soil structure interaction in the analysis of multi-story building resting on raft foundation was discussed. In this chapter, several Numerical example sets are tested and results are compared to numerical methods and previously published results to verify the proposed technique. In addition, results are also compared to those obtained from the finite element method.

4.2 Example set 1 It is as 10 Story framed building with symmetric plan subjected to static lateral force. In this example, a typical framed building with symmetric plan and elevation as shown in figure 4.1 consists of 10 stories, 5 meter for the first story and 3m for the 9 remaining stories remaining. This structure is subjected to static lateral loading. A 0.5 t/m static lateral distributed load is applied in the positive direction of X- axis. All columns of the building are 0.4 x 0.7 m except the corner columns that are 0.5 x 0.5 m. Also, all slabs are 0.18 m with beams 0.3 x 0.7 m as shown in figure 4.1. The raft foundation thickness is 1.2 m. Analyses were carried out using substructure approach where the super structure is modeled using ETABS - the well-known finite element commercial program – figure 4.2. The raft foundation and the underneath soil are modeled using PLPAK – a developed package for solving shear deformable plates on Winkler and elastic half space based on boundary element method and stiffness method figure 4.3. Lateral deflection, lateral deflection ratios (SSI/NSSI), Drift and drift ratios (NSSI/SSI) are obtained. The results are compared to the same structure modeled using the direct method. SAP2000 – finite element well known commercial program is used figure 4.4– where the soil is modeled as isotropic, elastic material using solid element with 8 nodes in each corner, at each corner 3 translation degree of freedom. Different types of soil (E=2000, 5000, 10000 and 20000 t/m2) with ν = 0.4, 0.4, 0.25 and 0.25 respectively are used. Also two types of equivalent Winkler method are used in the comparison. The subgrade reactions corresponding to a certain value of E are obtained using Boit and Vesic equation shown below.

50

Figure 4.1. Exapmle 1 plan

51

Figure 4.2 ETABS 3D modeling of example 1 super structure.

Figure 4.3 PLPAK 2D modeling of example 1 raft foundation.

52

Figure 4.4 SAP2000 3D modeling of example 1- Direct method.

Figure 4.5 SAP2000 3D modeling of example 1- Direct method.

53

Example 1 Results: For E=2000 t/m2 (With rotational stiffness) 35

Lateral Deflection (m)

30

Story Height (m)

25 20 15

CONTINUM MODEL FIXED BASE

10

Proposed technique ًWinkler according to Boit equation

5

Winkler according to Vesic equation 0 0

0.05

0.1

0.15

Lateral Deflection Figure 4.6 Lateral Deflection in X-direction for example 1- E=2000 t/m2 (with rotational stiffness).

35 30

Story Height (m)

25 20 15 CONTINUM MODEL FIXED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0

0.5

1 1.5 2 2.5 Lateral Deflection Ratio SSI/NSSI

3

3.5

Figure 4.7 Lateral Deflection Ratio SSI/NSSI in X-direction for example 1- E=2000 t/m2 (with rotational stiffness).

54

35

INTER STORY DRIFT

30 CONTINUUM MODEL Fixed Base Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

Story Height (m)

25 20 15 10 5 0 0

0.001

0.002

0.003

0.004

0.005

0.006

Drift Figure 4.9 Inter story drift in X-direction for example 1- E=2000 t/m2 (with rotational stiffness). 35

Drift Ratio

30

Story Height (m)

25 20 15 CONTINUM MODEL FIXED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

Drift Ratio Figure 4.8 Drift SSI/NSSI ratio in X-direction for example 1 E=2000 t/m2 (with rotational stiffness).

55

For E=2000 t/m2 (without rotational stiffness): Lateral Deflection (m)

35 30

Story Height (m)

25 20 15

CONTINUM MODEL HINGED BASE Proposed technique without rotational stiffness Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0

0.05

0.1 Lateral Deflection (m)

0.15

0.2

Figure 4.10 Lateral Deflection in X-direction for example 1 E=2000 t/m2 (without rotational stiffness).

35

Lateral deflection ratio

30

Story Height (m)

25 20 15 10

CONTINUM MODEL HINGED BASE Proposed technique without rotational stiffness Winkler according to Boit equation Winkler according to Vesic equation

5 0 0

0.5

1 1.5 2 Lateral Deflection Ratio SSI/NSSI

2.5

Figure 4.11 Lateral Deflection SSI/NSSI in X-direction for example 1 E=2000 t/m2 (without rotational stiffness).

56

35

INTER STORY DRIFT

30

Story Height (m)

25 20 Continuum Model Hinged base Proposed technique without rotational stiffness Winkler according to Boit equation Winkler according to Vesic equation

15 10 5 0 0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

Interstory drift Figure 4.12 Inter story drift in X-direction for example 1 E=2000 t/m2 (without rotational stiffness).

35

Drift Ratio

30

Story Height (m)

25 20 15 CONTINUM MODEL HINGED BASE Proposed technique without rotational stiffness Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0.00

1.00

2.00

3.00 4.00 Drift Ratio

5.00

6.00

7.00

Figure 4.13 Drift SSI/NSSI ratio in X-direction for example 1- E=2000 t/m2 (without rotational stiffness).

57

-

For E=5000 t/m2 (with rotational stiffness):

35

Lateral Deflection (m)

30

Story Height (m)

25 20 15 10

CONTINUM MODEL FIXED BASE Proposed Technique Winkler according to Boit equation Winkler according to Vesic equation

5 0 0

0.01

0.02

0.03

0.04 0.05 Lateral Deflection

0.06

0.07

0.08

0.09

Figure 4.15 Lateral Deflection in X-direction for example 1- E=5000 t/m2 (with rotational stiffness).

Lateral Deflection ratio SSI/NSSI

35 30

Story Height (m)

25 20 15 CONTINUM MODEL FIXED BASE Proposed Technique Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0.00

0.50 1.00 1.50 Lateral Deflection Ratio SSI/NSSI

2.00

Figure 4.14 Lateral Deflection Ratio SSI/NSSI in X-direction for example 1- E=5000 t/m2 (with rotational stiffness).

58

35

INTER STORY DRIFT

30

Story Height (m)

25 20 15 10

CONTINUM MODEL FIXED BASE Proposed Technique Winkler according to Boit equation Winkler according to Vesic equation

5 0 0

0.001

0.002

0.003

0.004

0.005

Drift Figure 4.16 Inter story drift in X-direction for example 1- E=5000 t/m2 (with rotational stiffness). 35

Drift Ratio

30

Story Height (m)

25 20 15 10

CONTINUM MODEL FIXED BASE Proposed Technique Winkler according to Boit equation Winkler according to Vesic equation

5 0 0.00

0.50

1.00

1.50 2.00 Drift Ratio

2.50

3.00

3.50

Figure 4.17 Drift SSI/NSSI ratio in X-direction for example 1- E=5000 t/m2 (with rotational stiffness).

59

-

For E=5000 t/m2 (without rotational stiffness):

35

Lateral Deflection (m)

30

Story Height (m)

25 20 15 CONTINUM MODEL HINGED BASE Proposed Technique without rotational stiffness Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0

0.02

0.04

0.06 0.08 Lateral Deflection (m)

0.1

0.12

0.14

Figure 4.18 Lateral Deflection in X-direction for example 1- E=5000 t/m2 (without rotational stiffness).

35

Lateral deflection ratio

30

Story Height (m)

25 20 15 CONTINUM MODEL HINGED BASE Proposed technique without rotational stiffness Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0.00

0.50

1.00

1.50

2.00

Lateral Deflection Ratio SSI/NSSI Figure 4.19 Lateral Deflection Ratio SSI/NSSI in X-direction for example 1- E=5000 t/m2 (without rotational stiffness).

60

35

INTER STORY DRIFT

30

Story Height (m)

25 CONTINUM MODEL

20

HINGED BASE Proposed technique without rotational stiffness

15

Winkler according to Vesic equation 10

Winkler according to Vesic equation

5 0 0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

Drift Figure 4.20 Inter story drift in X-direction for example 1- E=5000 t/m2 (without rotational stiffness). 35

Drift Ratio

30

Story Height (m)

25 20 15 CONTINUM MODEL HINGED BASE Proposed technique without rotational stiffness Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0.00

0.50

1.00

1.50

2.00

2.50

3.00

Drift Ratio Figure 4.21 Drift SSI/NSSI ratio in X-direction for example 1- E=5000 t/m2 (without rotational stiffness).

61

For E=10000 t/m2 (with rotational stiffness):

-

35

Lateral Deflection (m)

30

Story Height (m)

25 20 15 CONTINUM MODEL FIXED BASE Proposed Technique Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Lateral Deflection (m) Figure 4.22 Lateral Deflection in X-direction for example 1- E=10000 t/m2 (without rotational stiffness). 35

Lateral deflection ratio

30

Story Height (m)

25 20 15 CONTINUM MODEL FIXED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0.00

0.50

1.00

1.50

2.00

Lateral Deflection Ratio SSI/NSSI Figure 4.23 Lateral Deflection Ratio SSI/NSSI in X-direction for example 1- E=10000 t/m2 (without rotational stiffness).

62

35

INTER STORY DRIFT

30

Story Height (m)

25

CONTINUM MODEL Fixed BASE proposed technique Winkler according to Boit equation Winkler according Vesic equation

20 15 10 5 0 0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

Drift Figure 4.25 Inter story drift in X-direction for example 1- E=10000 t/m2 (with rotational stiffness). 35

Drift Ratio

30

Story Height (m)

25 20 15 CONTINUM MODEL FIXED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0.00

0.50

1.00

1.50

2.00

Drift Ratio Figure 4.24 Drift SSI/NSSI ratio in X-direction for example 1- E=10000 t/m2 (without rotational stiffness).

63

For E=10000 t/m2 (without rotational stiffness):

35

Lateral Deflection (m)

30

Story Height (m)

25 20 15 CONTINUM MODEL HINGED BASE Proposed technique without rotational stiffness Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0

0.02

0.04 0.06 0.08 Lateral Deflection (m)

0.1

0.12

Figure 4.26 Lateral Deflection in X-direction for example 1- E=10000 t/m2(without rotational stiffness).

35 30

Story Height (m)

25 20 15 CONTINUM MODEL HINGED BASE Proposed technique without rotational stiffness Winkler according Boit equation Winkler according to Vesic equation

10 5 0 0

0.5

1

1.5

Lateral Deflection Ratio SSI/NSSI Figure 4.27 Lateral Deflection Ratio SSI/NSSI in X-direction for example 1- E=10000 t/m2 (without rotational stiffness).

64

35

INTER STORY DRIFT

30

Story Height (m)

25 20 CONTINUM MODEL Hinged base Proposed technique without rotational stiffness Winkler according to Boit equation Winkler according to Vesic equation

15 10 5 0 0

0.002

0.004

0.006

0.008

0.01

0.012

Drift Figure 4.28 Inter story drift in X-direction for example 1- E=10000 t/m2 (without rotational stiffness).

35

Drift Ratio

30

Story Height (m)

25 20 15 10

CONTINUM MODEL HINGED BASE Proposed technique without rotational stiffness Winkler according to Boit equation Winkler according to Vesic equation

5 0 0.00

0.50

1.00 1.50 Drift Ratio

2.00

2.50

Figure 4.29 Drift SSI/NSSI ratio in X-direction for example 1- E=10000 t/m2 (without rotational stiffness).

65

-

For E=20000 t/m2 (with rotational stiffness):

35

Lateral Deflection (m) 30

Story Height (m)

25 20 15 CONTINUM MODEL FIXED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0

0.01

0.02

0.03 0.04 Lateral Deflection

0.05

0.06

Figure 4.30 Lateral Deflection in X-direction for example 1- E=20000 t/m2 (with rotational stiffness).

35

Lateral deflection ratio

30

Story Height (m)

25 20 15

CONTINUM MODEL FIXED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0

0.5 1 Lateral Deflection Ratio SSI/NSSI

1.5

Figure 4.31 Lateral Deflection Ratio SSI/NSSI in X-direction for example 1- E=20000 t/m2 (with rotational stiffness).

66

35

INTER STORY DRIFT 30

Story Height (m)

25 20 Continuum Model Fixed base Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

15 10 5 0 0

0.0005

0.001

0.0015 0.002 Drift

0.0025

0.003

0.0035

Figure 4.33 Inter story drift in X-direction for example 1- E=20000 t/m2 (with rotational stiffness).

35

Drift Ratio

30

Story Height (m)

25 20 15 CONTINUM MODEL FIXED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0.00

0.50

1.00 Drift Ratio

1.50

2.00

Figure 4.32 Drift SSI/NSSI ratio in X-direction for example 1- E=20000 t/m2 (with rotational stiffness).

67

-

For E=20000 t/m2 (without rotational stiffness):

35

Lateral Deflection (m)

30

Story Height (m)

25 20 15 10

CONTINUM MODEL HINGED BASE Proposed technique without rotational stiffness Winkler according to Boit equation Winkler according to Vesic equation

5 0 0

0.02

0.04

0.06

0.08

0.1

Lateral Deflection (m) Figure 4.34 Lateral Deflection in X-direction for example 1- E=20000 t/m2 (without rotational stiffness). 35

Lateral deflection ratio

Story Height (m)

30 25 20 15 CONTINUM MODEL FIXED BASE Proposed technique without rotational stiffness Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0.95

1 1.05 1.1 Lateral Deflection Ratio SSI/NSSI

1.15

Figure 4.35 Lateral Deflection Ratio SSI/NSSI in X-direction for example 1- E=20000 t/m2 (without rotational stiffness).

68

35

INTER STORY DRIFT

30

Story Height (m)

25 20 Continuum Model Hinged base Proposed technique without rotational stiffness Winkler according to Boit equation Winkler according to Vesic equation

15 10 5 0 0

0.002

0.004

0.006

0.008

0.01

0.012

Drift Figure 4.37 Inter story drift in X-direction for example 1- E=20000 t/m2 (without rotational stiffness).

35

Drift Ratio

30

Story Height (m)

25 20 15 CONTINUM MODEL FIXED BASE

10

Proposed technique without rotational stiffness Winkler according to Boit equation

5

Winkler according to Vesic equation 0 0.00

0.50

1.00

1.50

2.00

Drift Ratio Figure 4.36 Drift SSI/NSSI ratio in X-direction for example 1- E=20000 t/m2 (without rotational stiffness).

69

Table 4.1The fundamental periodic time in seconds for example 1 – with rotational stiffness

Continuum Model NSSI

1.8776

Proposed technique 1.8776

Boit

Vesic

1.8776

1.8776

E=2000

2.54

2.22

2.74

3.25

Ratio

1.35

1.18

1.46

1.73

E=5000

2.141

2.06

2.13

2.27

Ratio

1.14

1.10

1.13

1.21

E=10000

2.04

1.96

2.13

2.27

Ratio

1.09

1.04

1.13

1.21

E=20000

1.98

1.94

2.05

2.09

Ratio

1.05

1.03

1.09

1.11

Table 4.2 The fundamental periodic time in seconds for example 1 – without rotational stiffness

Continuum Model

Proposed technique

Boit

Vesic

NSSI

2.643

2.643

2.643

2.643

E=2000

3.05

2.94

3.29

3.71

Ratio

1.15

1.11

1.24

1.40

E=5000

2.836

2.8

2.82

2.92

Ratio

1.07

1.06

1.07

1.10

E=10000

2.77

2.74

2.82

2.92

Ratio

1.05

1.04

1.07

1.10

E=20000

2.71

2.69

2.67

2.8

Ratio

1.03

1.02

1.01

1.06

70

4.3 Example set 2 It is a 10 Story shear wall framed building subjected to static lateral force. In this example, a typical shear wall framed building shown in figure 4.38 consists of 10 stories, 5 meter for the first story and 3m for the 9 story remaining. This structure is subjected to static lateral loading. A 0.5 t/m static lateral distributed load is applied in the positive direction of X- axis. All columns of the building are 0.4 x 0.7 m except the corner columns are 0.5 x 0.5 m. Also, all slabs are 0.18 m with beams 0.3 x 0.7 m as shown in figure 4.38. The raft foundation thickness is 1.2 m. Analyses were carried out using substructure approach where the super structure is modeled using ETABS - the wellknown finite element commercial program – figure 4.39. The raft foundation and the underneath soil are modeled using PLPAK – a developed package for solving shear deformable plates on Winkler and elastic half space based on boundary element method and stiffness method figure 4.40. Lateral deflection, lateral deflection ratios (SSI/NSSI), Drift and drift ratios (NSSI/SSI) are obtained. The results are compared against the same structure modeled using direct method. SAP2000 – finite element well known commercial program is used figure 4.41 – where the soil is modeled as isotropic, elastic material using solid element with 8 nodes in each corner, at each node 3 translation degree of freedoms. Different types of soil ( E=2000,5000,10000 and 20000 t/m2) with ν = 0.4,0.4,0.25 and 0.25 respectively are used. Also two types of equivalent Winkler method are used in the comparison. The subgrade reactions corresponding to a certain value of E are obtained using Boit and Vesic equation previously mentioned.

71

Figure 4.38 Exapmle 2 plan.

72

Figure 4.39 ETABS 3D modeling of example 2 super structure.

Figure 4.40 PLPAK 2D modeling of example 2 raft foundation.

73

Figure 4.42 SAP2000 3D modeling of example 2- Direct method.

Figure 4.41 SAP2000 2D view.

74

Example 2 Results: For E=2000 t/m2 (with rotational stiffness) 35

lateral Deflection m

30

Story Height m

25 20 15 CONTINUM MODEL FIXED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0

0.01

0.02 0.03 0.04 Lateral Deflection (m)

0.05

0.06

Figure 4.43 Lateral Deflection in X-direction for example 2- E=2000 t/m2 (with rotational stiffness). 35

Lateral deflection ratio

30

Story Height m

25 CONTINUM MODEL FIXED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

20 15 10 5 0 0

1 2 3 Lateral Deflection Ratio SSI/NSSI

4

Figure 4.44 Lateral Deflection Ratio SSI/NSSI in X-direction for example 2- E=2000 t/m2 (with rotational stiffness).

75

35

INTER STORY DRIFT

Story Height (m)

30 25

CONTINUM MODEL Fixed Base

20

Proposed technique Winkler according to Boit equation

15

Winkler according to Vesic equation 10 5 0 0

0.001

0.002

0.003

Drift Figure 4.45 Inter story drift in X-direction for example 2- E=2000 t/m2 (with rotational stiffness).

Drift Ratio

35 30

Story Height m

25 CONTINUM MODEL

20

FIXED BASE Proposed technique

15

Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0

1

2 Drift Ratio

3

4

Figure 4.46 Drift SSI/NSSI ratio in X-direction for example 2- E=2000 t/m2 (with rotational stiffness).

76

For E=2000 t/m2 (without rotational stiffness)

-

35

lateral Deflection m

30

Story Height m

25 20 15 CONTINUM MODEL FIXED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0

0.02

0.04

0.06 0.08 0.1 Lateral Deflection (m)

0.12

0.14

Figure 4.47 Lateral Deflection in X-direction for example 2- E=2000 t/m2 (without rotational stiffness). 35

Lateral deflection ratio

30

Story Height m

25 20 15 10 5 0 0

1

2 3 Lateral Deflection Ratio SSI/NSSI

CONTINUM MODEL HINGED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation 4 5

Figure 4.48 Lateral Deflection Ratio SSI/NSSI in X-direction for example 2- E=2000 t/m2 (without rotational stiffness).

77

INTER STORY DRIFT

35 30

Story Height (m)

25 CONTINUM MODEL Hinged Base Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

20 15 10 5 0 0

0.001

0.002

0.003 Drift

0.004

0.005

0.006

Figure 4.49 Inter story drift in X-direction for example 2- E=2000 t/m2 (without rotational stiffness). 35

Drift Ratio

30

Story Height m

25 20 15

CONTINUM MODEL HINGED BASE

10

Proposed technique 5

Winkler according to Boit equation Winkler according to Vesic equation

0 0

2

4

6

8

10

Drift Ratio Figure 4.50 Drift SSI/NSSI ratio in X-direction for example 2- E=2000 t/m2 (without rotational stiffness).

78

For E=5000 t/m2 (Rotations are fixed)

35

lateral Deflection (m)

30

Story Height (m)

25 20 15 CONTINUM MODEL FIXED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0

0.01

0.02 Drift

0.03

0.04

Figure 4.52 Lateral Deflection in X-direction for example 2- E=5000 t/m2 (with rotational stiffness).

Lateral defelction ratio

35

Story Height m

30 25 CONTINUM MODEL FIXED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

20 15 10 5 0 0

0.5 1 1.5 2 Lateral Deflection Ratio SSI/NSSI

2.5

Figure 4.51 Lateral Deflection Ratio SSI/NSSI in X-direction for example 2- E=5000 t/m2 (with rotational stiffness).

79

35

INTER STORY DRIFT

30

Story Height m

25 CONTINUM MODEL FIXED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

20 15 10 5 0 0

0.0005

0.001 Drift

0.0015

0.002

Figure 4.54 Inter story drift in X-direction for example 2- E=5000 t/m2 (with rotational stiffness). 35

Drift Ratio

30

Story Height m

25 20 15

CONTINUM MODEL FIXED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0

0.5

1

1.5 Drift Ratio

2

2.5

3

Figure 4.53 Drift SSI/NSSI ratio in X-direction for example 2- E=5000 t/m2 (with rotational stiffness).

80

For E=5000 t/m2 (without rotational stiffness)

-

35

lateral Deflection m

30

Story Height m

25 20 15 CONTINUM MODEL HINGED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0

0.01

0.02

0.03 0.04 0.05 Lateral Deflection (m)

0.06

0.07

Figure 4.55 Lateral Deflection in X-direction for example 2- E=5000 t/m2 (without rotational stiffness). 35

Lateral deflection ratio

30

Story Height m

25 20 15 CONTINUM MODEL HINGED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0

0.5 1 1.5 2 Laterl Deflection Ratio SSI/NSSI

2.5

Figure 4.56 Lateral Deflection Ratio SSI/NSSI in X-direction for example 2- E=5000 t/m2 (without rotational stiffness) .

81

35

INTER STORY DRIFT

30

Story Height (m)

25 CONTINUM MODEL HINGED BASE

20

Proposed technique 15

Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

Drift Figure 4.57 Inter story drift in X-direction for example 2- E=5000 t/m2 (without rotational stiffness).

35

Drift Ratio

30

Story Height m

25 20 15 CONTINUM MODEL HINGED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0

1

2 3 4 Drift Ratio Figure 4.58 Drift SSI/NSSI ratio in X-direction for example 2- E=5000 t/m2 (without rotational stiffness).

82

For E=10000 t/m2 (Rotations are fixed)

-

35

lateral Deflection m

30

Story Height m

25 20 15 CONTINUM MODEL FIXED BASE

10

Proposed technique 5

Winkler according to Boit equation Winkler according to Vesic equation

0 0

0.005

0.01

0.015 0.02 0.025 Lateral Deflection (m)

0.03

0.035

Figure 4.59 Lateral Deflection in X-direction for example 2- E=10000 t/m2 (with rotational stiffness).

Lateral deflection ratio

35

Story Height m

30 25 20

CONTINUM MODEL FIXED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

15 10 5 0 0

0.5 1 1.5 Lateral Deflection Ratio SSI/NSSI

2

Figure 4.60 Lateral Deflection Ratio SSI/NSSI in X-direction for example 2- E=10000 t/m2 (with rotational stiffness).

83

35

INTER STORY DRIFT

30 25 Story Height (m)

CONTINUM MODEL Fixed Base Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

20 15 10 5 0 0

0.0005

0.001

0.0015

Drift Figure 4.62 Inter story drift in X-direction for example 2- E=10000 t/m2 (with rotational stiffness). 35

Drift Ratio

30

Story Height m

25 20

CONTINUM MODEL FIXED BASE Proposed technique Winkler aacording to Boit equation Winkler according to Vesic equation

15 10 5 0 0

0.5

1 Drift Ratio

1.5

2

Figure 4.61 Drift SSI/NSSI ratio in X-direction for example 2- E=10000 t/m2 (with rotational stiffness).

84

For E=10000 t/m2 (without rotational stiffness)

35

lateral Deflection m

30

Story Height m

25 20 15 CONTINUM MODEL HINGED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0

0.01

0.02 0.03 0.04 0.05 Lateral Deflection (m) Figure 4.63 Lateral Deflection in X-direction for example 2- E=10000 t/m2 (without rotational stiffness).

35

Lateral deflection ratio

30

Story Height m

25 20 15 CONTINUM MODEL HINGED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0

0.5 1 1.5 Lateral Deflection Ratio SSI/NSSI

2

Figure 4.64 Lateral Deflection Ratio SSI/NSSI in X-direction for example 2- E=10000 t/m2 (without rotational stiffness) .

85

35

INTER STORY DRIFT

30

Story Height (m)

25 Continum Model Hinged Base Proposed technique Winkler according to Vesic equation Winkler according to Boit equation

20 15 10 5 0 0

0.0005

0.001

0.0015 Drift

0.002

0.0025

0.003

Figure 4.65 Inter story drift in X-direction for example 2- E=10000 t/m2 (without rotational stiffness). 35

Drift Ratio

30

Story Height m

25 20 15 CONTINUM MODEL HINGED BASE Proposed technique Winkler according to Boit equation Winkler accoding to Vesic equation

10 5 0 0

0.5

1

1.5 Drift Ratio

2

2.5

3

Figure 4.66 Drift SSI/NSSI ratio in X-direction for example 2- E=10000 t/m2 (without rotational stiffness).

86

-

For E=20000 t/m2 (with rotational stiffness)

35

lateral Deflection m

30

Story Height m

25 20 15 CONTINUM MODEL FIXED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0

0.005

0.01

0.015 0.02 0.025 Lateral Deflection (m)

0.03

0.035

Figure 4.67 Lateral Deflection in X-direction for example 2- E=20000 t/m2 (with rotational stiffness). 35

Lateral deflection ratio

30

Story Height m

25 CONTINUM MODEL FIXED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

20 15 10 5 0 0

0.5 1 1.5 Lateral Deflection Ratio SSI/NSSI

2

Figure 4.68 Lateral Deflection Ratio SSI/NSSI in X-direction for example 2- E=20000 t/m2 (with rotational stiffness).

87

35

INTER STORY DRIFT

30

Story Height (m)

25

CONTINUM MODEL Fixed base

20

Proposed technique Winkler according to Boit equation

15

Winkler according to Vesic equation

10 5 0 0

0.0002

0.0004

0.0006 0.0008 Drift

0.001

0.0012

0.0014

Figure 4.69 Inter story drift in X-direction for example 2- E=20000 t/m2 (with rotational stiffness).

35

Drift Ratio

30

Story Height m

25 CONTINUM MODEL FIXED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

20 15 10 5 0 0

0.5

1 Drift Ratio

1.5

2

Figure 4.70 Drift SSI/NSSI ratio in X-direction for example 2- E=20000 t/m2 (with rotational stiffness).

88

-

For E=20000 t/m2 (Rotations are free)

35

lateral Deflection (m)

30

Story Height m

25 20 15 CONTINUM MODEL HINGED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

10 5 0 0

0.01

0.02

0.03

0.04

0.05

Lateral Deflection (m) Figure 4.71 Lateral Deflection in X-direction for example 2- E=20000 t/m2 (without rotational stiffness).

35

Lateral deflectionj ratio

30

Story Height (m)

25 20 15 CONTINUM MODEL 10

FIXED BASE Proposed technique

5

Winkler according to Boit equation Winkler according to Vesic equation

0 0

0.5 1 1.5 2 Lateral Deflection Ratio SSI/NSSI Figure 4.72 Inter story drift in X-direction for example 2- E=20000 t/m2 (without rotational stiffness).

89

35

INTER STORY DRIFT

30 CONTINUM MODEL

Story Height (m)

25

Fixed base Proposed technique

20

Winkler according to Boit equation Winkler according to Vesic equation

15 10 5 0 0

0.0005

0.001

0.0015

0.002

0.0025

Drift Figure 4.74 Inter story drift in X-direction for example 2- E=20000 t/m2 (without rotational stiffness). 35

Drift Ratio

30

Story Height m

25 20 CONTINUM MODEL FIXED BASE Proposed technique Winkler according to Boit equation Winkler according to Vesic equation

15 10 5 0 0

0.5

1 Drift Ratio

1.5

2

Figure 4.73 Drift SSI/NSSI ratio in X-direction for example 2- E=20000 t/m2 (without rotational stiffness).

90

Table 4.3 The fundamental periodic time in seconds for example 2 – with rotational stiffness.

Continuum Fixed Base

1.13

Proposed technique 1.13

Boit

Vesic

1.13

1.13

E=2000

1.94

1.71

1.46

1.48

Ratio

1.72

1.51

1.29

1.31

E=5000

1.66

1.41

1.42

1.51

Ratio

1.47

1.25

1.26

1.34

E=10000

1.43

1.33

1.38

1.41

Ratio

1.27

1.18

1.22

1.25

E=20000

1.34

1.31

1.33

1.36

Ratio

1.19

1.16

1.18

1.20

Table 4.4 The fundamental periodic time in seconds for example 2 – without rotational stiffness.

Continuum Hinged Base

1.14

Proposed technique 1.14

E=2000

1.99

1.72

1.718

1.8

Ratio

1.75

1.51

1.51

1.58

E=5000

1.6

1.47

1.718

1.76

Ratio

1.40

1.29

1.51

1.54

E=10000

1.47

1.38

1.53

1.68

Ratio

1.29

1.21

1.34

1.47

E=20000

1.37

1.33

1.42

1.489

Ratio

1.20

1.17

1.25

1.31

91

Boit

Vesic

1.14

1.14

4.4 Example set 3 This example set consists of 4 examples; two of these examples are bare framed multistory building with 4 and 16 stories while the other two examples are framed-shear wall multi-story building with 4 and 16 stories. The results in terms of time period (T) per seconds are compared and verified with respect to the work done by B.R. Jayalekshmi and H.K.Chinmayi [8]. The structural layout and dimensions are taken as shown in figure 4.75. The section properties and soil properties are considered due to the shown values in table 4.5 and 4.6 respectively.

Figure 4.75 The structural layout and dimensions [8]. Table 4.5 Section properties for example set 3 [8].

No. of stories

Column Dimensions(m)

Shear wall thickness (m)

Upto3 stories

Above 3 stories

4

0.32x0.32

0.32x0.32

0.15

16

0.6x0.6

0.5x0.5

0.25

Table 4.6 The soil properties according to work done by [8].

Soil Type

Description

Poission's ratio

Sb Sc Sd Se

Rock Dense soil Stiff soil Soft soil

0.3 0.3 0.35 0.4

92

Young's modulus E (kn/m2) 8.40E+06 1.91E+06 4.46E+05 1.03E+05

Bare frame results:

Fundamental Period - Mode 1 - 4 Floors

Time Period (sec)

1.2 1 0.8 0.6 0.4

continuum model [8] Proposed technique

0.2 0 Soil type

Figure 4.76 The time period for mode 1- 4 floors. T - Mode 3 - 4 Floors

Time Period (sec)

1.2 1 0.8 0.6 0.4

Continuum model [8]

0.2

Proposed technique

0 Soil type Figure 4.77 The time period for mode 3 - 4 floors.

Time Period (sec)

T - Mode 4- 4 Floors 1.2 1 0.8 0.6 0.4 0.2 0

Continuum model [8] Proposed technique

Soil type Figure 4.78 The time period for mode 4 - 4 floors.

93

Time Period (sec)

Fundamental Period - Mode 1 - 16 Floors 4 3.5 3 2.5 2 1.5 1 0.5 0

Continuum model [8] Proposed technique

Soil type Figure 4.79 The time period for mode 1- 16 floors.

Time Period (sec)

T - Mode 3 - 16 Floors 3 2.5 2 1.5 1 0.5 0

Continuum model [8] Proposed technique

Soil type Figure 4.80 The time period for mode 3 - 16 floors.

Time Period (sec)

T - Mode 4 - 16 Floors 1.2 1 0.8 0.6 0.4 0.2 0

Continuum model [8] Proposed technique

Soil type Figure 4.81 The time period for mode 4 - 16 floors.

94

Table 4.7 Time period for different modes of shape – 4 floors.

Continuum model [8]

Proposed technique

Ratio

Mode 1

Mode 3

Mode 4

Mode 1

Mode 3

Mode 4

Fixed

0.85

0.71

0.26

0.857

0.72

0.26

1.01

sb

1

0.75

0.29

0.86

0.72

0.26

0.86

sc

1

0.75

0.29

0.868

0.72

0.26

0.87

sd

1

0.75

0.29

0.872

0.72

0.26

0.87

se

1.01

0.76

0.29

0.88

0.72

0.263

0.87

Table 4.8 Time period for different modes of shape - 16 floors.

Continuum model [8]

Proposed technique

Ratio

Mode 1

Mode 3

Mode 4

Mode 1

Mode 3

Mode 4

Fixed

3

2.28

0.89

2.97

2.42

0.94

0.99

sb

3.51

2.5

1.01

3.02

2.42

0.95

0.86

sc

3.52

2.5

1.01

3.17

2.42

0.95

0.90

sd

3.55

2.5

1.02

3.24

2.42

0.95

0.91

se

3.66

2.51

1.02

3.33

2.42

0.95

0.91

95

Shear wall results:

Fundamental Period - Mode 1 - 4 Floors

Time Period (sec)

1.2 1 0.8

Continuum model [8] Proposed technique

0.6 0.4 0.2 0 Soil type

Figure 4.82 The time period for mode 1 - 4 floors. T- Mode 3 - 4 Floors

Time Period (sec)

1.2 1 0.8 0.6

Continuum model [8] Proposed technique

0.4 0.2 0 Soil type

Figure 4.83 The time period for mode 3 - 4 floors. T - Mode 4- 4 Floors Time Period (sec)

1.2 1 0.8 0.6

Continuum model [8]

0.4

Proposed technique

0.2 0 Soil type Figure 4.84 The time period for mode 4 - 4 floors.

96

Fundamental Period - Mode 1 - 16 Floors

Time Period (sec)

2.5 2

Continuum model [8]

1.5

Proposed technique

1 0.5 0 Soil type

Figure 4.85 The time period for mode 1 - 16 floors. T - Mode 3 - 16 Floors

Time Period (sec)

1.2 Continuum model [8]

1

Proposed technique

0.8 0.6 0.4 0.2 0 Soil type

Figure 4.86 The time period for mode 3 - 16 floors.

T - Mode 4 - 16 Floors Time Period (sec)

1.2 1 0.8

Continuum model [8]

0.6

Proposed technique

0.4 0.2 0 Soil type Figure 4.87 The time period for mode 4 - 16 floors.

97

Table 4.9 Time period for different modes of shape - 4 floors.

Mode

Continuum [8]

Proposed technique

Ratio

Mode 1

Mode 3

Mode 4

Mode 1

Mode 3

Mode 4

Fixed

0.18

0.159

0.055

0.165

0.16

0.06

0.917

Sb

0.19

0.158

0.045

0.199

0.17

0.06

1.04

Sc

0.22

0.158

0.045

0.25

0.17

0.06

1.13

Sd

0.29

0.158

0.046

0.31

0.17

0.08

1.06

Se

0.41

0.158

0.046

0.44

0.19

0.15

1.07

Table 4.10 Time period for different modes of shape - 16 floors.

Mode

Continuum [8]

Proposed technique

Ratio

Mode 1

Mode 3

Mode 4

Mode 1

Mode 3

Mode 4

Fixed

1.28

0.5

0.27

1.279

0.48

0.264

1.00

Sb

1.34

0.52

0.28

1.47

0.48

0.28

1.10

Sc

1.46

0.52

0.3

1.61

0.48

0.28

1.10

Sd

1.76

0.53

0.33

1.93

0.48

0.3

1.10

Se

2.25

0.54

0.35

2.28

0.48

0.327

1.01

98

4.5 Example set 4 This example consists of 2 examples; one of these examples is bare framed multi-story building with 6 stories while the other example is framed multi-story building with 12 stories. The results in terms of time period (T) per seconds are compared and verified with respect to the work done by [12]. The structural layout and dimensions are taken as shown in figure 4.88. The soil properties are considered due to the shown values in table.

Figure 4.88 The structural layout and dimensions according to work done by [12]. Table 4.11 Section properties according to work done by [12].

Model

Beam Size (cm)

Slab thickness (cm)

Column (cm)

Raft thickness (cm)

6-Story

25x60

15

60x60

60

12-Story

25x60

15

80x80

100

Table 4.12 The soil properties according to work done by [12].

Soil condition

Poisson's ratio

Kx (t/m2/m)

Kyb (t/m2/m)

Kz (t/m2/m)

0.33

Modulus of elasticity E (t/m2) 24480

Stiff soil

1127.21

1127.21

1417.29

Medium soil Soft soil

0.33

12240

563.6

563.6

708.64

0.33

6120

281.8

281.8

354.32

99

6-floors multi-story framed building results:

Time Period T (sec)

1.50

Time period (sec) - 6 Stories

1.00 Raft on Winkler [12] Proposed technique

0.50

0.00 Fixed

Stiff Soil Medium Soil End Condition

Soft Soil

Figure 4.89 The fundamental time period for 6-floors mutli-story framed building.

Table 4.13 The fundamental time period for 6-floors multi-story framed building.

Time (sec)

Raft on Winkler [12]

Proposed technique

Ratio

Fixed

0.98

0.98

1.00

Stiff Soil

1.07

1.00

0.93

Medium Soil

1.12

1.04

0.93

Soft Soil

1.21

1.09

0.90

100

12-floors multi-story building results:

3.00

Time period (sec) - 12 Stories

Time Period T (sec)

2.50 2.00 1.50

Raft on Winkler [12] Proposed technique

1.00 0.50 0.00 Fixed

Stiff Soil Medium Soil End Condition

Soft Soil

Figure 4.90 The fundamental period for 12-floors multi-story framed building.

Table 4.14 The fundamental period for 12-floors multi-story framed building.

Time (sec)

Raft on Winkler [12]

Proposed technique

Ratio

Fixed

1.92

1.87

0.97

Stiff Soil

2.15

1.98

0.92

Medium Soil

2.32

2.08

0.90

Soft Soil

2.60

2.24

0.86

101

Chapter 5 Summary, Conclusions and Recommendations for Future Work 4.1 Summary This thesis presents a new method to consider soil-structure interaction in the analysis of the multi-story buildings. This is done by coupling the 3D modelling tool of ETABS and the EHS in PLPAK to consider SSI in the lateral analysis of multi-storey buildings. This coupling technique is considered as a modified sub-structuring technique. This coupling technique has advantages over the current technique in practice. These advantages are mainly the static condensation is carried out at the columns-raft interface not at the raftsoil interface, this can produce much less degrees of freedom for which the static condensation is carried out compared to the number of degrees of freedom that can be produced from the case of applying contestation at raft-soil interface. Also, the number of iterations required to achieve a certain convergence in the proposed technique is one or two iterations compared to non-convergence iterations in case of using the available technique in practice. A practical graphical user interface is developed to ease the use of this technique in practice by engineers.

5.2 Conclusions -

-

New practical technique based on FEM-BEM is introduced to consider SSI in the lateral analysis for multistory building rested on raft foundation. This technique has shown a good agreement with FEM continuum models with different types of structures and with two internationally published papers. The fundamental periods of buildings (T) increases with increasing substructure flexibility. The Lateral Deflection and Inter story drift are increasing with increases substructure flexibility. The effect of soil is increasing with height increase. Vertical stiffness of soil-raft system is the predominate factor. Rotational stiffness of soil-raft system has small participation in the structure response due to lateral loads (10-15 %). Rotational stiffness participation is increasing with the decrease of E of soil. Rotational stiffness has more influence in case of framed structure than structures with shear walls. For shear wall structure, translation stiffness in X-Y direction has more influence than rotational stiffness. Finally, it can be concluded that although conventional design procedure omitting SSI is conservative it is required to ensure the structural safety due to lateral deflection.

102

5.3 Recommendations for future work The future work can be considered in the following directions: 1) No tension SSI. 2) Structures Pounding including SSI. 3) Soil-Pile-Raft-Structure interaction. 4) Nonlinear SSI (Iterative – Elastoplastic – Actual Curve). 5) Nonlinear/Pushover analysis including SSI. 6) Progressive collapse including SSI.

103

REFERENCES [1] Informs web site, http://www.construction-ic.com/ [2] George Gazetas, Grorge Mylonakis; Seismic soil-structure interaction: new evidence and emerging issues- Soil Dynamics III, ASCE, Special Geotechnical Publication, 1998, Vol. 2. [3] George mylonakis and George Gazetas; seismic soil-structure interaction: beneficial or detrimental?, Journal of Earthquake Engineering- Journal of Earthquake Engineering 4(3):277-301 · July 2000 with 269 Reads. DOI: 10.1080/13632460009350372. [4] George Gazetas, Grorge Mylonakis, Soil-Structure Interaction Effects on Elastic and Inelastic Structures; Fourth international Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics-2001. [5] Bhattacharya, K., Dutta, S. C., and Dasgupta, S., (2004), “Effect of Soil Flexibility on Dynamic Behaviour of Building Frames on Raft Foundation”, Journal of Sound and Vibration, Elsevier, Vol.274, pp.111-135. [6] Nateghi-A, F. and Rezaei-Tabrizi, A. (2013), Nonlinear dynamic response of tall buildings considering structure–soil–structure effects. Struct. Design Tall Spec. Build., 22: 1075–1082. doi:10.1002/tal.753 [7] B. R. Jayalekshmi and H. K. Chinmayi, “Effect of Soil Flexibility on Seismic Force Evaluation of RC Framed Buildings with Shear Wall: A Comparative Study of IS 1893 and EUROCODE8,” Journal of Structures, vol. 2014, Article ID 493745, 15 pages, 2014. doi:10.1155/2014/493745 [8] Mengke Li, Xiao Lu, Xinzheng Lu; Influence of soil-structure interaction on seismic collapse resistance of super-tall buildings-2014. [9] Halkude S.A, Kalyanshetti M.G., Bareklikar S.M; Seismic Response of R.C. Frames with Raft Footing Considering Soil Structure Interaction-2014. [10] B. R. Jayalekshmi and H. K. Chinmayi, “Effect of Soil Flexibility on Seismic Force Evaluation of RC Framed Buildings with Shear Wall: A Comparative Study of IS 1893 and EUROCODE8,” Journal of Structures, vol. 2014, Article ID 493745, 15 pages, 2014. doi:10.1155/2014/493745 [11] Abdel Raheem, S.E., Ahmed, M.M. & Alazrak, T.M.A. Int J Adv Struct Eng (2015) 7: 11. doi:10.1007/s40091-014-0078-x [12] Hemet S. Chore, P.A.Dode; Soil Structure Interaction of Tall Buildings-2015 [13] VivekGarg and M.S.Hora, (2012) “A review Interaction Behavior of StructureFoundation-Soil System”. International Journal of Engineering Research and Applications (IJERA) ISSN:224-9622 www.ijera.com vol.2,Issue 6, Novemberdecember 2012, pp.639-644 [14] Siddhath G. Shah, Solanki C.H., Desai J.A; Soil structure interaction analysis methods-State of art- Review-2011. [15] M.N. Viladkar, Karisiddappa, P. Bhargava, P.N. Godbole; Static soil-structure interaction response of hyperbolic cooling towers to symmetrical wind loads2005. [16] Jahromi HZ, Izzuddin BA, Zdravkovic L, 2009, A domain decomposition approach for coupled modelling of nonlinear soil-structure interaction, Computer

104

[17] [18] [19] [20] [21]

[22]

[23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40]

[41]

Methods in Applied Mechanics and Engineering, Vol:198, ISSN:0045-7825, Pages:2738-2749 Winkler E. Die lehr von elastizität und festigkeit. Dominicus: Prague; 1867 Caselunghe Aron, Eriksson Jonas; Structural element approach for soil-structure interaction-2012. Selvadurai APS. Elastic analysis of soil foundation interaction. Elsevier: Amsterdam; 1979. Filonenko-Borodich MM. Some approximate theories of elastic foundation. Uch, Zap,Mosk, Gos, Uni. Mekh, 46: 3-18, Russia; 1940. Filonenko-Borodich MM. A very simple model of an elastic foundation capable ofspreading the load.Sb, Tr, Mosk, Elektro, Inst.Inzh, Trans, No: 53 Transzheldorizdat,Russia; 1945. Pasternak PL. On a new method of analysis of an elastic foundation by means of twofoundationconstants.GosudartvennoeIzdatelstroLiberaturipoStroitelstvuiArkht ekture,Moscow, Russia; 1954. Kerr AD. Elastic and viscoelastic foundation models. J. Appl. Mech. ASME, 31: 491-498; 1964. Hetenyi M. Beams on elastic foundation. University of Michigan Press, Ann Arbor,Michigan; 1946. Rhines’s Model 1969. Wang CM, Chow YK, How YC. Analysis of rectangular thick rafts on an elastic half space.Computers and Geotechnics 2001; 28: 161-184. Bowels JE. Foundation analysis and design, 5th Edition. McGraw-Hill: New York;1996. ACI. Suggested analysis and design procedures for combined footings and mats. ACI Struct J 1988;304–24. Ahmed Mostafa Shaaban, Youssef F. Rashed, A coupled BEM-stiffness matrix approach for analysis of shear deformable plates on elastic half space, Engineering Analysis with Boundary Elements, Vol.37, Issue 4, Pages 699–707, April 2013. Bathe K.J., (1982), "Finite Element Procedure in Engineering Analysis", Englewood Cliffs, NJ, Prentice-Hall. https://www.csiamerica.com/products/etabs https://www.csiamerica.com/products/sap2000 http://www.ansys.com/products/Structures http://www.comp-engineering.com/products/ETABS/etabs.html Vander Weeën, F., Application of the boundary integral equation method to Reissner’s plate model. Int. J. Numerical Methods in Engineering, 18, 1–10, 1982. https://www.integratedsoft.com/ http://www.beasy.com/ http://www.gpbest.com/ PLPAK, BE4E: www.be4e.com Rashed YF.A boundary/domain element method for analysis of building raft foundations.Engineering analysis with boundary elements.2005; 29:859-877. http://www.oasys-software.com/products/engineering/pdisp.html

105

ARABIC SUMMARY

‫محتىي انزســبنت‬ ‫حخُبٔل انشسبنت يٕػٕع الخشاح ؽش‪ٚ‬مت عًه‪ٛ‬ت نألخز ف‪ ٙ‬االعخببس انخأث‪ٛ‬ش انًخببدل ب‪ ٍٛ‬انخشبت ٔانًُشأ‬ ‫نهًببَ‪ ٙ‬انًعشػت ألدًبل جبَب‪ٛ‬ت ‪ٔ ،‬حذخٕٖ انشسبنت عهٗ خًست أبٕاة ب‪ٛ‬بَٓب كًب ‪ٚ‬هٗ ‪:‬‬

‫انببة األول ‪ :‬مقذمــت‬ ‫‪ٚ‬خؼًٍ ْزا انببة يمذيت عٍ انخأث‪ٛ‬ش انًخببدل ب‪ ٍٛ‬انخشبت ٔانًُشأ ‪ ،‬اسببة ٔجٕد ْزا انخأث‪ٛ‬ش‪ ،‬ؽشق حًث‪ٛ‬م‬ ‫انخأث‪ٛ‬ش انًخببدل ب‪ ٍٛ‬انخشبت ٔانًُشأ ٔكزنك انطشق انًخخهفت نخًث‪ٛ‬م انخشبت‪.‬‬

‫انببة انثبوً ‪ :‬انطزق انعذدَت وانبزامج انمستخذمت‬ ‫‪ٚ‬عشع ْزا انببة يمذيت ثى حعش‪ٚ‬ف بطش‪ٚ‬مت انعُبطشانًذذٔدة ٔانذذٔد‪ٚ‬ت انذذٔد‪ٚ‬ت ٔاسخخذايبث ٔع‪ٕٛ‬ة‬ ‫ٔيً‪ٛ‬ضاث كم ؽش‪ٚ‬مت عه‪ ٙ‬دذة‪ .‬كًب اَّ حطشق ان‪ ٙ‬حمذ‪ٚ‬ى بشَبيج ال ‪ٔ PLPAK‬بشَبيج ال‬ ‫‪ٔ ETABS‬انخعش‪ٚ‬ف بًكَٕبث كم يًُٓب‪.‬‬

‫انببة انثبنث ‪ :‬انطزَقت انجذَذة انمقتزحت‬ ‫‪ٚ‬مذو ْزا انفظم ٔطفب خطٕة بخطٕة نهطش‪ٚ‬مت انًمخشدت يع انخٕػ‪ٛ‬خ بظٕس نخهك انخطٕاث‪.‬‬

‫انببة انزابع ‪ :‬أمثهت عذدَت‬ ‫‪ٚ‬مذو ْزا انببة عذة يسبئم يخؼًُت يمبسَت عبيت ب‪ ٍٛ‬انطش‪ٚ‬مت انًمخشدت ٔانطشق االخشٖ ‪.‬‬

‫انببة انخبمس‪ :‬انخالصت واالستىتبجبث واقتزاحبث نهعمم انمستقبهٍ‬ ‫‪ٚ‬هخض ْزا انببة يب حى اَجبصِ ف‪ ٙ‬انبذث ببالػبفت إنٗ سشد نبعغ اإللخشادبث نُمبؽ انبذث انًسخمبه‪ٛ‬ت‬

‫‪2‬‬

‫مهىذس‪ :‬عبذانشدًٍ دمحم ابشاْ‪ٛ‬ى عه‪ ٙ‬انًه‪ٛ‬ج‪ٙ‬‬ ‫تبرَخ انمُالد‪1991/05/27 :‬‬ ‫انجىسُت‪ :‬يظش٘‬ ‫تبرَخ انتسجُم‪2013/10/1:‬‬ ‫تبرَخ انمىح‪2017 :‬‬ ‫انقسم‪:‬انُٓذست االَشبئ‪ٛ‬ت‬ ‫انذرجــــت‪ :‬يبجسخ‪ٛ‬ش انعهٕو‬ ‫انمشـــــــــزف‪:‬‬ ‫أ‪.‬د‪َ .‬ىسف فىسٌ راشذ‬ ‫انممتحىىن‪:‬‬ ‫أ‪.‬د‪َ .‬ىسف فىسٌ راشذ‬ ‫أ‪.‬د‪ .‬سبمح سمُز فهمٍ مهىٍ (ممتحه داخهٍ)‬ ‫أ‪.‬د‪ .‬ابزاهُم محفىظ (ممتحه خبرجٍ)‬ ‫عىىان انزسبنت‪:‬‬ ‫طزَقت عمهُت مبتكزة رابطت بُه طزَقتٍ انعىبصز انحذودَت وانمحذودة نالخذ فٍ االعتببر تأثُز انتزبت‪-‬انمىشأ‬ ‫انمتببدل عهٍ انمىشئبث انمعزضت الحمبل جبوبُت‪.‬‬ ‫كهمبث دانت‪:‬‬ ‫ؽش‪ٚ‬مت انعُبطش انذذٔد‪ٚ‬ت ‪ -‬أنخأث‪ٛ‬ش انًخببدل ب‪ ٍٛ‬انخشبت ٔانًُشأ‪ -‬انخكث‪ٛ‬ف االسخبح‪ٛ‬ك‪ -ٙ‬اَؼغبؽ‪ٛ‬ت (انخشبت‪-‬انهبشت) –‬ ‫انخأث‪ٛ‬ش االسخبح‪ٛ‬ك‪ ٙ‬انًخببدل ب‪ ٍٛ‬انخشبت ٔانًُشأ‬ ‫مهخص انزسبنت‪:‬‬ ‫ف‪ْ ٙ‬زا انبذث حى الخشاح ؽش‪ٚ‬مت عًه‪ٛ‬ت جذ‪ٚ‬ذة كفء الخز انخأث‪ٛ‬ش انًخببدل ب‪ ٍٛ‬انخش‪ٚ‬ت ٔانًُشئبث انًعشػت الدًبل جبَب‪ٛ‬ت‪.‬‬ ‫حعخًذ ْزِ انطش‪ٚ‬مت ف‪ ٙ‬االسبط عه‪ ٙ‬ؽش‪ٚ‬مت انخمسى ( ‪ٔ )Sub structuring‬انخ‪ ٙ‬ف‪ٓٛ‬ب ‪ٚ‬خى حمسى انًسأنت ان‪ ٙ‬جضئ‪ٍٛ‬‬ ‫يُفظه‪ٍٛ‬؛ جضء خبص ببنجضء انعهٕ٘ نهًُشأ (غ‪ٛ‬ش شبيم انهبشت) ٔانجضء االخش جضء خبص ببنخشبت ببالػبفت ان‪ ٙ‬انهبشت‪.‬‬ ‫حى اسخخذاو ؽش‪ٚ‬مت انخكث‪ٛ‬ف االسخبح‪ٛ‬ك‪ ) Static condensation( ٙ‬عه‪ ٙ‬انًسخٕ٘ انًبس ب‪ ٍٛ‬انهبشت ٔاالعًذة‪ .‬كًب اَّ حى‬ ‫بشيجت ْزِ انطش‪ٚ‬مت عُذ انًسخٕ٘ انًبس ب‪ ٍٛ‬انهبشت ٔاالعًذة نهخأكذ يٍ حذم‪ٛ‬ك االحضاٌ ٔانخٕافك االصاد‪ ٙ‬عُذ رنك انًسخٕ٘‪.‬‬ ‫دبن‪ٛ‬ب ‪ٚ‬خى اسخخذاو ؽش‪ٚ‬مت يشببّ يٍ انخكث‪ٛ‬ف االسخبح‪ٛ‬ك‪ٔ ٙ‬نكٍ عُذ انًسخٕ٘ انًبس ب‪ ٍٛ‬انهبشت ٔانخشبت ْٕ بذٔسِ ‪ٚ‬سخٓهك جٓذا‬ ‫ٔٔلخب يمبسَت ببنطش‪ٚ‬مت انًمخشدت‪.‬‬ ‫ف‪ْ ٙ‬زا انبذث حى اسخخذاو ْزِ انطش‪ٚ‬مت ف‪ ٙ‬انخذه‪ٛ‬م انخط‪ ٙ‬فمؾ ٔيع رنك ‪ًٚ‬كٍ اسخخذايٓب ف‪ ٙ‬انخذه‪ٛ‬م انالخط‪ ٙ‬الدمب‬ ‫بسٕٓنت ٔبطش‪ٚ‬مت يببششة‪.‬‬

‫‪1‬‬

‫طزَقت عمهُت مبتكزة رابطت بُه طزَقتٍ انعىبصز انحذودَت وانمحذودة نالخذ فٍ‬ ‫االعتببر تأثُز انتزبت‪-‬انمىشأ انمتببدل عهٍ انمىشئبث انمعزضت الحمبل جبوبُت‬ ‫إعـذاد‬ ‫مهىذس ‪ /‬عبذانزحمه دمحم ابزاهُم عهٍ انمهُجٍ‬ ‫سسـبنت يمذيت إنٗ كه‪ٛ‬ت انُٓذسـت ‪ -‬جبيعت انمبْشة‬ ‫كجضء يٍ يخطهببث انذظـٕل عهٗ دسجت‬ ‫يبجسخ‪ٛ‬ش انعهٕو‬ ‫ف‪ٙ‬‬ ‫انُٓذست اإلَشبئ‪ٛ‬ت‬

‫‪ٚ‬عخًذ يٍ نجُت انًًخذُ‪:ٍٛ‬‬ ‫أ‪.‬د‪َ .‬ــىسف فىسي راشــذ‬

‫(انًششف انشئ‪ٛ‬سٗ)‬

‫(أسخبر لسى انُٓذست اإلَشبئ‪ٛ‬ت ‪ -‬كه‪ٛ‬ت انُٓذست ‪ -‬جبيعت انمبْشة)‬

‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬ ‫أ‪.‬د‪ .‬سبمح سمُز فهمٍ مهىٍ‬

‫(انًًخذٍ انذاخه‪)ٙ‬‬

‫(أسخبر لسى انُٓذست اإلَشبئ‪ٛ‬ت ‪ -‬كه‪ٛ‬ت انُٓذست ‪ -‬جبيعت انمبْشة)‬

‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬ ‫أ‪.‬د‪ .‬إبزاهُم محفىظ‬

‫(انًًخذٍ خبسج‪)ٙ‬‬

‫(أسخبر لسى انُٓذست اإلَشبئ‪ٛ‬ت ‪ -‬كه‪ٛ‬ت انُٓذست ‪ -‬جبيعت بُٓب)‬

‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬

‫كليــة الهندســة ‪ -‬جامعــة القاهــرة‬ ‫الجيـزة ‪ -‬جمهوريـة مصـرالعربيــة‬ ‫‪2017‬‬

‫طزَقت عمهُت مبتكزة رابطت بُه طزَقتٍ انعىبصز انحذودَت وانمحذودة نالخذ فٍ‬ ‫االعتببر تأثُز انتزبت‪-‬انمىشأ انمتببدل عهٍ انمىشئبث انمعزضت الحمبل جبوبُت‬ ‫إعـذاد‬ ‫مهىذس ‪ /‬عبذانزحمه دمحم ابزاهُم عهٍ انمهُجٍ‬ ‫سسـبنت يمذيت إنٗ كه‪ٛ‬ت انُٓذسـت ‪ -‬جبيعت انمبْشة‬ ‫كجضء يٍ يخطهببث انذظـٕل عهٗ دسجت‬ ‫يبجسخ‪ٛ‬ش انعهٕو‬ ‫ف‪ٙ‬‬ ‫انُٓذست اإلَشبئ‪ٛ‬ت‬

‫حذج إشـشاف‬ ‫أ‪.‬د‪َ .‬ــىسف فىسي راشــذ‬ ‫أسخبر حذه‪ٛ‬م ٔي‪ٛ‬كبَ‪ٛ‬كب االَشبءاث‬ ‫كه‪ٛ‬ت انُٓذست ‪ -‬جبيعت انمبْشة‬

‫كليــة الهندســة ‪ -‬جامعــة القاهــرة‬ ‫الجيـزة ‪ -‬جمهوريـة مصـرالعربيــة‬ ‫‪2017‬‬

‫طزَقت عمهُت مبتكزة رابطت بُه طزَقتٍ انعىبصز انحذودَت وانمحذودة نالخذ فٍ‬ ‫االعتببر تأثُز انتزبت‪-‬انمىشأ انمتببدل عهٍ انمىشئبث انمعزضت الحمبل جبوبُت‬ ‫إعـذاد‬ ‫يُٓذط ‪ /‬عبذانزحمه دمحم ابزاهُم عهٍ انمهُجٍ‬

‫سسـبنت يمذيت إنٗ كه‪ٛ‬ت انُٓذسـت ‪ -‬جبيعت انمبْشة‬ ‫كجضء يٍ يخطهببث انذظـٕل عهٗ دسجت‬ ‫يبجسخ‪ٛ‬ش انعهٕو‬ ‫ف‪ٙ‬‬ ‫انُٓذست اإلَشبئ‪ٛ‬ت‬

‫كليــة الهندســة ‪ -‬جامعــة القاهــرة‬ ‫الجيـزة ‪ -‬جمهوريـة مصـرالعربيــة‬

‫‪2017‬‬