Structure

A structure can be defined as a rigid body that resists external effects (e.g : loads, temperature changes and support settlements) without excessive deformation. Typical structures such as residential buildings, industrial buildings, halls, towers, bridges, dams, tanks, channels and pavements are of interest to civil engineers.

Structural Analysis

Structural analysis is the determination of the response of a structure to external effects (e.g. : loads, temperature changes and support settlements) using theory of structures.

Theory of Structures

Theory of structures may be classified from different points of view as follows: static or dynamic, and if static, statically determinate or statically indeterminate, planar or space, linear or non-linear. Only, linear static analysis will be discussed here.

Structural Design

Structural design is the selection of a suitable arrangement of members (elements), and a selection of materials and member sections, to withstand the stress resultants (internal forces) of a specified set of loads, and satisfy the specified displacement constraints and the other code requirements.

Cources

  1. Structural Analysis (1)
  2. Structural Analysis (2)
  3. Structure (1+2)
  4. Structural Analysis (3).
  5. Computer Applications in Civil Engineering.

Content

1- Structural Analysis (1)

This course introduces the basic concepts of structural analysis. The student will be able to analyze Beam, Frame, Truss and Arch structures. In addition, he/she can calculate the internal forces in structural members and draw the normal, shear and bending moment diagrams.

Chapter 1: Introduction to Structural Modeling

    1.1 Introduction

    5

    1.2 Free-body diagram

    9

Chapter 2: Loads

    2.1 Introduction

    13

    2.2 Types of loads

    14

      2.2.1 Point load

      16

      2.2.2 Uniform load

      17

      2.2.3 Non-uniformly distributed load

      17

      2.2.4 Moments

      20

    2.3 Load distribution in concrete structures

    22

Chapter 3: Supports and Reactions

    3.1 Introduction

    35

    3.2 Types of supports

    35

      3.2.1 Roller support

      37

      3.2.2 Hinged support

      39

      3.2.3 Fixed support

      41

      3.2.4 Link support

      43

      3.2.5 Intermediate hinge

      44

    3.3 Equilibrium

    46

    3.4 Calculation of reactions

    48

    3.5 Examples

    49

Chapter 4: Stability and Determinacy

    4.1 Introduction

    69

    4.2 Stability

    69

    4.3 Determinacy

    73

Chapter 5: Internal Forces for Beams

    5.1 Introduction

    83

    5.2 Determination of internal forces at a section

    86

      5.2.1 Normal force

      87

      5.2.2 Shear force

      91

      5.2.3 Bending moment

      96

    5.3 Relations between load, shear and moment

    100

    5.4 Internal force diagrams

    106

      5.4.1 Normal force diagram

      106

      5.4.2 Shear force diagram

      109

      5.4.3 Bending moment diagram

      118

    5.5 Maximum bending moment and its position

    129

    5.6 Common cases of loading

    131

    5.7 Principle of superposition

    139

    5.8 General Examples

    141

    5.9 Problems

    151

Chapter 6: Analysis of Statically Determinate Frames

    6.1 Introduction

    157

    6.2 Calculation of reactions

    157

    6.3 Determination of internal forces

    167

    6.4 Internal force diagrams

    167

    6.5 Problems

    188

Chapter 7: Analysis of Statically Determinate Arches

    7.1 Introduction

    193

    7.2 Calculation of reactions

    194

    7.3 Determination of internal forces at a section

    198

Chapter 8: Analysis of Statically Determinate Trusses

    8.1 Introduction

    201

    8.2 Classification of trusses

    205

    8.3 Stability and determinacy

    207

    8.4 Method of joints

    213

    8.5 Method of sections

    224

    8.6 Space trusses

    237

Chapter 9: Influence Lines

    9.1 Introduction

    243

    9.2 Methods used to plot influence lines

    247

    9.3 Basic Method

    247

      9.3.1 Influence lines for beams

      248

      9.3.2 Influence lines for trusses

      272

      9.3.3 Influence lines for frames

      276

    9.4 Kinematic Method

    283

    9.5 Calculation of maximum influence at a point

    289

      9.5.1 Maximum influence due to concentrated loads

      289

      9.5.2 Absolute maximum influence

      291

      9.5.3 Maximum influence due to uniform loads

      295

    9.6 Cases of loading and envelopes

    296

Chapter 10: Computer Applications

    10.1 Introduction

    315

    10.2 Selecting units

    316

    10.3 Editing the frame

    316

    10.4 Editing supports

    319

    10.5 Assigning member sections

    320

    10.6 Assigning static load cases

    321

    10.7 Defining material properties

    323

    10.8 Running analysis

    324

    10.9 Checking the results

    325
2. Structural Analysis (2)

This course introduces the basic concepts of structural analysis. The student will be able to calculate the properties of plane areas. In addition, he/she can calculate the normal, shear, combined and principle stresses at any section of structural element.

Chapter 1: Properties of Sections

  • 1.1 Introduction

    5

    1.2 Area

    5

    1.3 Centroid

    6

    1.4 Moments of inertia

    19

    1.5 Parallel axis theorem

    26

    1.6 Polar moment of inertia

    31

    1.7 Product of inertia

    33

    1.8 Radius of gyration

    38

    1.9 Moments of inertia about inclined axes

    40

    1.10 Principal axes of inertia

    42

    1.11 Graphical solution by Mohr’s circle

    46

    1.12 Centroids of general bodies

    ..

    1.13 Examples on general areas

    ..

Chapter 2: Straining Actions

  • 2.1 Introduction

    63

    2.2 Normal forces

    65

    2.3 Shear forces .

    66

    2.4 Bending moments

    67

    2.5 Relations between load, shear and moment

    68

    2.6 Internal forces diagrams

    69

Chapter 3: Normal Stresses

  • 3.1 Introduction

    73

    3.2 Normal stresses due to axial forces

    78

    3.3 Composite system

    91

    3.4 Normal stresses due to bending moments

    97

    3.5 Economic sections

    113

    3.6 Unsymmetrical beams

    118

    3.7 Superimposed (built-up) beams

    130

    3.8 Combined effects of axial forces and bending moments

    133

    3.9 The general bending equation

    145

Chapter 4: Shear Stresses

  • 4.1 Introduction

    151

    4.2 Direct shear in bolts and rivets

    152

    4.3 Shear stress due to bending

    162

    4.4 Shear stress due to twisting moment (Torsion)

    167

Chapter 5: Principal Stresses

  • 5.1 Introduction

    193

    5.2 Plane state of stress

    193

    5.3 Coordinate transformations

    194

    5.4 Principal directions and principal stresses

    195

    5.5 Maximum shear stress direction

    166

    5.6 Mohr’s circle

    167

Chapter 6: Deformations of Statically Determinate Structures

  • 6.1 Introduction

    207

    6.2 Double integration method

    208

    6.3 Moment-area method

    232

    6.4 Conjugate beam method

    255

    6.5 Castigiliano's theorems

    268

Chapter 7: Virtual work method

  • 7.1 Principle of superposition

    283

    7.2 Maxwell-Betti Theorem (Reciprocal Theorem)

    284

    7.3 Deformation of members

    285

    7.4 Principle of virtual work

    290

    7.5 Evaluation of integrals

    291

Chapter 8: Euler Theory in Buckling

  • 8.1 Introduction

    311

    8.2 Maxwell-Betti Theorem (Reciprocal Theorem)

    311

REFERENCES

333
3. Structure (1+2)

This course introduces the basic concepts of structural analysis. The student will be able to draw Influence lines for statically determinate structures (beams, frames, arches, trusses) due to moving loads. In addition, he/she can calculate the deformation of structures using different methods (double integration, conjugate beam, moment area, and virtual work methods).

Chapter 1: Influence Lines

  • 1.1 Introduction

    5

    1.2 Methods used to plot influence lines

    9

    1.3 Basic Method

    9

      1.3.1 Influence lines for beams

      10

      1.3.2 Influence lines for trusses

      34

      1.3.3 Influence lines for frames

      38

    1.4 Kinematic Method

    45

    1.5 Calculation of maximum influence at a point

    51

      1.5.1 Maximum influence due to concentrated loads

      51

      1.5.2 Absolute maximum influence

      53

      1.5.3 Maximum influence due to uniform loads

      57

    1.6 Cases of loading and envelopes

    58

Chapter 2: Deformations of Statically Determinate Structures

  • 2.1 Introduction

    77

    2.2 Double integration method

    2.3 Moment-area method

    102

    2.4 Conjugate beam method

    125

    2.5 Castigiliano’s theorems

    138
4. Structural Analysis (3)

Chapter 1: Statically Indeterminate Structures

  • 1.1 Introduction

    5

    1.2 Advantages and disadvantages of indeterminate structures

    6

      1.2.1 Response to settlement of support

      6

      1.2.2 Response to changes in temperature

      7

      1.2.3 Response to tolerance problems during construction

      7

      1.2.4 Construction aspects

      8

      1.2.5 Behavior aspects

      8

    1.3 Redundancy

    9

    1.4 Boundary conditions

    15

    1.5 Compatibility

    16

    1.6 Degrees of freedom

    16

    1.7 Principle of superposition

    17

    1.8 Maxwell-Betti Theorem (Reciprocal Theorem)

    18

    1.9 Deformation of structures

    19

    1.10 Principle of virtual work

    24

    1.11 Methods for the solution of statically indet. structures

    25

      1.11.1 The compatibility method (the force method)

      25

      1.11.2 The equilibrium method (the displacement method)

      26

Chapter 2: Three-Moment Equation

  • 2.1 Introduction

    31

    2.2 Derivation of three-moment equation

    31

    2.3 Sign conventions

    34

    2.4 Applications

    35

Chapter 3: Virtual Work Method

  • 3.1 Introduction

    51

    3.2 Solution procedure using the virtual work method

    51

    3.3 Evaluation of integrals

    54

    3.4 Applications to statically in determinate beams

    59

    3.5 Applications to statically in determinate frames

    71

Chapter 4: Slope Deflection Method

  • 4.1 Introduction

    95

    4.2 Sign conventions

    96

      4.2.1 Sign convention for deformation

      96

      4.2.2 Sign convention for end moment

      97

    4.3 Slope deflection equations of equilibrium

    97

      4.3.1 Member with two fixed ends

      98

      4.3.2 Member with a fixed end and a hinged end

      103

    4.4 Applications to statically indeterminate beams

    107

    4.5 Applications to statically indeterminate frames

    112

Chapter 5: Moment Distribution Method

  • 5.1 Introduction

    137

    5.2 Definition of terms

    138

      5.2.1 Fixed end moment

      138

      5.2.2 Stiffness (rotational stiffness factor)

      138

      5.2.3 Distribution Factors

      142

      5.2.4 Carry over factor

      143

    5.3 Sign Convention

    143

    5.4 Solution procedure using the moment distribution method

    144

    5.5 Applications

    145

    5.6 Structures having sway

    161

      5.6.1 Solution as if the structure is restrained structure

      161

      5.6.2 Sway correction

      162

      5.6.3 Structures with multiple degrees of freedom

      163

    5.7 Symmetrical and Anti-symmetrical structures

    170

      5.7.1 Symmetrical structures with symmetrical loads

      172

      5.7.2 Symmetrical structures with anti-symmetrical loads

      177

    5.8 Effect of temperature change

    178

      5.8.1 Uniform change of temperature

      178

      5.8.2 Non-uniform change of temperature

      179
5. Computer Applications in Civil Engineering

Chapter 1

  • 1.1 Introduction

    5

    1.2 Advantages and disadvantages of indeterminate structures

    6

    1.3 Redundancy

    9

    1.4 Boundary conditions

    10

    1.5 Compatibility

    11

    1.6 Degrees of freedom

    11

    1.7 Methods for the solution of indeterminate structures

    12

      1.7.1 The compatibility method (the force method)

      12

      1.7.2 The equilibrium method (the displacement method)

      13

Chapter 2: Stiffness Method

  • 2.1 Introduction

    19

    2.2 Assumptions

    20

    2.3 Sign convention

    21

      2.3.1 Sign convention for displacements

      21

      2.3.2 Sign convention for forces

      21

    2.4 Derivation of the element stiffness matrix

    22

      2.4.1 Plane frame element

      23

      2.4.2 Beam element

      27

      2.4.3 Truss (bar) element

      28

    2.5 Loads between nodes

    29

    2.6 Transformation matrix

    30

    2.7 Element stiffness matrix in global coordinates

    33

    2.8 Applications

    39

Chapter 3: Modeling

  • 3.1 Introduction

    99

    3.2 Structural modeling

    100

    3.3 Types of Elements

    101

    3.4 Types of Boundary Elements

    104

    3.5 Types of Materials

    104

      3.5.1 Material Modeling Guidelines

      105

    3.6 Types of Loads

    106

    3.7 Modeling Discretization

    107

    3.8 SAP2000

    108

    3.9 Examples

    109