Solutions for Soil and

Structural Systems usingExcel and VBA Programs

Robert L. Sogge

PE, PhD, Civil Engineering Consultant, Tucson, USA

WILEYAJohn Wiley & Sons, Ltd., Publication

Contents

About the Author xxi

Preface xxiii

Acknowledgments xxv

PART ONE COMPUTER SOFTWARE 1

1 Microsoft Excel Spreadsheet 31.1 History of Spreadsheet Development 3

1.2 Excel 2010 4

1.2.1 File Conversion and Compatibility 4

1.3 Transmitting Cell Values Not Formulas 5

1.4 Accuracy 5

1.5 Saving 61.6 Implementation of Excel Features 6

1.6.1 General Tips 6

1.6.2 Fonts 7

1.6.3 =IF Statements 7

1.6.4 Naming Cells 8

1.6.5 Functions 8

1.6.6 Drawing 91.6.7 Charting 9

Related Workbook on DVD 11

Further Readings 11List of Workbook available in the DVD

eCalc

viii Contents

2 Microsoft VBA Programming Language 13

2.1 History of the BASIC Computer Language 13

2.1.1 Stage I - BASIC with CP/M and DOS 13

2.1.2 Stage II - Visual BASIC with Windows 14

2.1.3 Stage III - VBA and Excel with Windows 15

2.2 Justification for Using Excel with VBA Macros 15

2.3 Difference between a Workbook and a VBA Macro 16

2.4 VBA Macro Nomenclature 16

2.5 Generating a Procedure 17

2.6 Security Level Required to Open VBA Macros 19

2.7 VBA Code Statements that Differ from Previous BASIC Versions 19

2.8 Implementation of VBA Macro Programming 20

2.8.1 Type and Size Declaration of Variables for Subs

and Functions 20

2.8.2 Integer Variables 20

2.8.3 Floating Point Variables 21

2.8.4 Double-Precision Variables 21

2.8.5 Currency Variables 222.8.6 String Variables 222.8.7 Variant Variables 22

2.8.8 Declaring Data Types in Sub or Function Procedures 232.8.9 Dimensioning Variables 23

2.8.10 Option Explicit Statement 242.8.11 ReDim Statement 24

2.8.12 Sub Procedure 24

2.8.13 Function Procedure 25

2.9 Inputting Data to a VBA Procedure 26

2.9.1 In Worksheet Cells 26

2.9.2 From a Sequential Data File 272.9.3 From Input Boxes 30

2.10 Output Data from a VBA Procedure 302.10.1 Output to Worksheet Cells 302.10.2 Output to a Sequential Data File 31

2.11 Running a Macro 322.11.1 Using a Start Button 322.11.2 Alternative Start Methods 33

2.12 Code Debugging 332.13 Charting in a Worksheet 342.14 Line Plots in a Worksheet 34

2.15 Macro Sub Program Showing Output to Worksheet 352.16 Computer Hardware/Software Requirements 36

2.16.1 Memory Requirements 362.16.2 Processing Speed 37

Contents ix

Related Workbooks on DVD 38

Further Readings 39

List of Workbooks available in the DVD

For-Next Demo

LogoOutput4

PframeMemSpacePiTwoSeries

PART TWO STRUCTURES 41

3 Finite Element Method - The Theory 433.1 Theory 433.2 Developing the Element Stiffness Matrix 44

3.2.1 Equilibrium 44

3.2.2 Force-Deformation (Stress-Strain) 46

3.2.3 Deformation Compatibility 46

3.3 Creating the Global Stiffness Matrix by Assembling Element Stiffnesses 47

3.4 Solving Simultaneous Equations for Displacements 47

3.5 Element Displacements and Forces 483.6 Flowchart of Steps 49

Related Workbook on DVD 49

References 49

List of Workbook available in the DVD

Load Distribution to Rebar-Concrete

4 Finite Element Analysis VBA Program PFrame 51

4.1 Program PFrame - Finite Element Analysis (FEA) of Beam-Bar

Structural Systems 51

4.2 Creating an Input Data Worksheet 52

4.3 Input Data 52

4.3.1 Member Axis Orientation and Conversion of Moment

of Inertia 54

4.4 Joint Numbering and Dimensions 56

4.5 Load Application 584.5.1 Applied Joint Loads 584.5.2 Applied Member Loads 58

4.5.3 Applied FEFs 58

4.6 Imposed Joint Displacements 59

4.7 Unstable or Improperly Supported Configurations 60

4.8 Running Program PFrame 60

4.9 Output Data 62

4.10 Alternate Solution Approach to Macro Program PFrame 63

4.11 Significant Aspects of Excel Worksheet & VBA Macro

Program Construction 63

X Contents

List of Workbook and Examples available in the DVDPFrame

Example 4.1 Beam on Pinned SuptsExample 4.2a - PFIbm2a

Example 4.2b - PFIbm2b

Example 4.2c - PFIbm2c

5 Beams 65

5.1 Beam Member Types 655.2 Bar Members as Pinned-End Beams 65

5.3 Moment of Inertia Conversion for Different Member Axis Orientation 67

5.4 Load Application 69Related Workbooks on DVD 69

List of Examples available in the DVD

Example 5.1a - Beam 1 mbr 2 jts

Example 5.1b - Beam 2 mbrs 3 jtsExample 5.2 - PFIbm

Example 5.3a - Pinned Beam on SuptsExample 5.3b - Pinned Beam on Column SuptsExample 5.4 - Cantilevered Beam with Dist Ld

6 Frames 716.1 Analysis of Frames 716.2 Rigid Joints 716.3 Joint Numbering 716.4 Pinned-End Beam 736.5 Supports 74

6.5.1 Inclined or Skewed 74

6.5.2 Elastic 746.5.3 Imposed Support Displacements 75

6.6 Varying EI of Members Comprising a Frame 756.7 Stability - The P-A Effect 766.8 Load Case Combinations of Load Groups 766.9 Interior Member Forces 776.10 Examples 77Related Workbooks on DVD 79References 80List of Examples available in the DVD

Example 6.1a Fixed FrameExample 6.1b Fixed Frame

Example 6.2a Portal Frame

Example 6.2b Portal Frame

Example 6.3 Frame Pinned SuptExample 6.4 PFIfram

Contents xi

Example 6.5 Bike Frame

Example 6.6 Bridge Bent

Example 6.7a Bar Arch

Example 6.7b Beam Arch

Example 6.8 ArchElasSupt

7 Trusses 81

7.1 Theory for Bar Members 817.2 Analysis of Bar Assemblage 81

7.3 Load Application 82

7.4 Initial Member Length Changes 82

7.5 Support Displacements 82

Reference 82

List of Examples available in the DVD

Example 7.1a Bars

Example 7.1b Bars

Example 7.2a Truss

Example 7.2aa Truss

Example 7.2b Truss

Example 7.2c Truss

Example 7.2cc Truss

8 Reinforced Concrete 83

8.1 Concrete and Reinforcing Steel Properties 83

8.2 Design Capacity and Reinforcing Requirements 84

8.2.1 Shear Design Capacity 858.2.2 Moment Design Capacity 85

8.2.3 Beam-Column Capacity 86

8.2.4 Shrinkage and Temperature Reinforcement (AASHTO 5.10.8) 87

8.2.5 Reinforcement to Control Cracking 87

8.3 Strength Properties for a Soil-Structure Interaction Analyses 89

8.4 Cracked-Section Concrete Properties 90

8.5 Excel Workbooks 91

8.5.1 Workbook Reinf Concrete 91

8.5.2 Workbook Beam-LFD 92

8.5.3 Workbook Beam-Col ID 92

8.5.4 Workbook PMEIX-VBA 92

Related Workbooks on DVD 92

8.6 Notation 92

References 93

List of Workbooks and Example available in the DVDBeam-Col ID(4)

Beam-LFD(2)

PMEIX-VBA(5)

xii Contents

Reinf Concrete(2)

Example 8.1 Rect8thk

PART THREE SOILS 95

9 Soil Classification 97

9.1 Field Geotechnical Processes 97

9.1.1 Soil/Rock Exploration 97

9.1.2 Soil/Rock Sampling 98

9.1.3 Field Testing 99

9.2 Soil Description 100

9.2.1 Color 100

9.2.2 Basic Soil Type 100

9.2.3 Modifying Terms 1019.2.4 Special Soil Types 101

9.3 Field and Laboratory Tests for Soil Identification 103

9.3.1 Field Tests for Soil Identification 103

9.3.2 Laboratory Testing for Soil Identification 105

9.4 Soil Classification Systems 106

9.4.1 Textural Classification 106

9.4.2 Engineering Classification 1069.5 Excel Workbooks and VBA Programs 108

Related Workbooks on DVD 109

9.6 Soil Mechanics Symbol Nomenclature 109References 113

List of Workbooks available in the DVD

Soil ClassRl

Soil Class-VBAr2

SoilClassUsingVBA

10 Soil Strength Properties 11510.1 Discrete and Elastic Finite Element Models 115

10.2 General Elasticity Equations Relating Stress and Strain 11510.2.1 Alternative Constitutive Equation Formulation 11610.2.2 Two-Dimensional Plane-Stress and Plane-Strain Constitutive

Equations 11710.3 Modulus of Elasticity and Poisson's Ratio 118

10.3.1 The Stress-Strain Curve 118

10.3.2 Failure Strength Related to Confining Pressure Dependency 12010.3.3 Elastic Modulus - Relation to Pore Water Pressure and Water

Content 121

10.3.4 Elastic Modulus for Repeated Loading 12310.3.5 Elastic Modulus for Dynamic Loading 12410.3.6 Analytical Expressions for Elastic Modulus 124

Contents xiii

10.3.7 Secant and Tangent Modulus Values for Iterative and Incremental Analysis 132

10.3.8 General and Local Failure Conditions 134

10.3.9 The Relation between v, 4>, and KD 134

10.3.10 Analytical Representation of Poisson's Ratio 13510.3.11 Typical E and v Values 135

10.4 Coefficient of Subgrade Reaction 13510.4.1 Terzaghi Relation for kv and kh 13610.4.2 Bowles Relation for kh 136

10.4.3 E and kh Developed from Lateral Wall Movement 13710.4.4 Relation between kv and E 138

10.5 Mathematical Descriptions of Curves Using Program Curve Fit 138References 139

List of Workbooks and Examples available in the DVDCrvFitRelations

CurveFitl4

Soil Material Property Table

Example 10.1 phi-denExample 10.1 phi-denout

11 Stresses in an Elastic Half-Space 14111.1 Closed-Form Elasticity Solutions 14111.2 Lateral Stresses against a Wall Restrained from Movement

due to Point, Line, and Strip Loading 14111.3 Boussinesq Equation 141

11.3.1 Assumptions 142

11.4 Westergaard Equation 142

11.5 Mindlin Equation 142

11.6 Chart Solutions 142

11.7 Excel Workbook - Lat&VertStress 143

11.8 VBA Pro