The Book

CONTENTS

Preface
Acknowledgement

1.Overview of structural concepts
1.1 What are structural concepts?
1.2 Why study structural concepts?
1.3 Approaches to learning structural concepts
1.3.1 Theoretical contents
1.3.2 Physical models
1.3.3 Practical examples
1.3.4 Engaging students
1.4 Organisation of the text
1.5 How to use this book
1.5.1 For students
1.5.2 For lecturers
1.5.3 For engineers

PART I Statics

2. Equilibrium
2.1 Definitions and Concepts
2.2 Theoretical Background
2.3 Model Demonstrations
2.3.1 Action and reaction forces
2.3.2 Stable and unstable equilibrium
2.3.3 A plate-bottle system
2.3.4 A magnetic ‘float’ model
2.4 Practical Examples
2.4.1 A barrier
2.4.2 A footbridge
2.4.3 An equilibrium kitchen scale
2.4.4 Stage performance
2.4.5 Magnetic float strain
2.4.6 A dust tray
Problems

3 Centre of Mass
3.1 Definitions and Concepts
3.2 Theoretical Background
3.3 Model Demonstrations
3.3.1 Centre of mass of a piece of cardboard of arbitrary shape
3.3.2 Centre of mass and centroid of a body
3.3.3 Centre of mass of a body in a horizontal plane
3.3.4 Centre of mass of a body in a vertical plane
3.3.5 Centre of mass and stability
3.3.6 Centre of mass and motion
3.4 Practical Examples
3.4.1 Cranes on construction sites
3.4.2 The Eiffel Tower
3.4.3 A display unit
3.4.4 The Kio Towers
Problems

4 Effect of Different Cross Sections
4.1 Definitions and Concepts
4.2 Theoretical Background
4.3 Model Demonstrations
4.3.1 Two rectangular sectioned beams and an I-sectioned beam
4.3.2 Lifting a book using a bookmark
4.4 Practical Examples
4.4.1 A steel framed building
4.4.2 A rail bridge
4.4.3 I section members with holes (cellular beams and columns)
Problems

5 Stress Distribution
5.1 Concepts
5.2 Theoretical Background
5.3 Model Demonstrations
5.3.1 Balloons on nails
5.3.2 Uniform and non-uniform stress distributions
5.3.3 Stress concentration
5.3.4 The core of a section
5.4 Practical Examples
5.4.1 Flat shoes vs high-heel shoes
5.4.2 The Leaning Tower of Pisa
Problems

6 Bending
6.1 Definitions and Concepts
6.2 Theoretical Background
6.3 Model Demonstration
6.3.1 Assumptions in beam bending
6.3.2 A thin beam and a thick beam
6.4 Practical Examples
6.4.1 Profiles of girders
6.4.2 Reducing bending moment using overhangs
6.4.3 Failure due to bending
6.4.4 Deformation of a staple due to bending
Problems

7 Shear and Torsion
7.1 Definitions and Concepts
7.2 Theoretical Background
7.2.1 Shear stresses due to bending
7.2.2 Shear stresses due to torsion
7.2.3 Shear centre
7.3 Model Demonstrations
7.3.1 Effect of torsion
7.3.2 Effect of shear stress
7.3.3 Effect of shear force
7.3.4 Open and closed sections subject to torsion with warping
7.3.5 Open and closed sections subject to torsion without warping
7.3.6 Shear centre of thin-walled open sections
7.4 Practical Examples
7.4.1 Composite section of a beam
7.4.2 Shear walls in a building
7.4.3 Opening of a drinks bottle
7.4.4 A box girder highway bridge
Problems

8 Span and Deflection
8.1 Concepts
8.2 Theoretical Background
8.3 Model Demonstrations
8.3.1 Effect of span
8.3.2 Effect of boundary conditions
8.3.3 The bending moment at one fixed end of a beam
8.3.4 Lateral stiffness of vertical members
8.4 Practical Examples
8.4.1 Column supports
8.4.2 Phenomenon of Prop roots
8.4.3 Metal props used in structures
Problems

9 Direct Force Paths
9.1 Definitions and Concepts
9.2 Theoretical background
9.2.1 Introduction
9.2.2 Concepts for achieving a stiffer structure
9.2.2.1 Definition of stiffness
9.2.2.2 Pin-jointed structures
9.2.2.3 Beam types of structure
9.2.2.4 Expression of the concepts
9.2.3 Implementation
9.2.3.1 Five criteria
9.2.3.2 Numerical verification
9.2.4 Discussion
9.2.4.1 Safety, economy and elegance
9.2.4.2 Optimum design and conceptual design
9.3 Model Demonstrations
9.3.1 Experimental verification
9.3.2 Direct and zigzag force paths
9.4 Practical Examples
9.4.1 Bracing systems of tall buildings
9.4.2 Bracing systems of scaffolding structures
9.4.2.1 The collapse of a scaffolding structure
9.4.2.2 Some bracing systems used for scaffolding structures
Problems

10 Smaller Internal Forces
10.1 Concepts
10.2 Theoretical Background
10.2.1 Introduction
10.2.2 A ring and a tied ring
10.3 Model Demonstrations
10.3.1 A pair of rubber rings
10.3.2 Post-tensioned plastic beam
10.4 Practical Examples
10.4.1 Raleigh Arena
10.4.2 Zhejiang Dragon Sports Centre
10.4.3 A cable-stayed bridge
10.4.4 A floor structure experiencing excessive vibration
10.4.5 A pitched roof
Problems

11 Buckling
11.1 Definitions and Concepts
11.2 Theoretical Background
11.2.1 Basics of buckling
11.2.2 Buckling of a column with different boundary conditions
11.2.3 Lateral torsional buckling of beams
11.2.4 Relationship between the maximum displacement and the buckling load of a straight member
11.3 Model Demonstrations
11.3.1 Buckling shapes of plastic columns
11.3.2 Buckling loads and boundary conditions
11.3.3 Lateral buckling of beams
11.3.4 Buckling of an empty aluminium can
11.3.5 Buckling load of a straight member predicted through a bending test
11.4 Practical Examples
11.4.1 Buckling of a bracing members
11.4.2 Buckling of a box girder
11.4.3 Prevention of lateral buckling of beams
11.4.4 Bi-stability of a slap bracelet
Problems

12 Prestress
12.1 Definitions and Concepts
12.2 Theoretical Background
12.3 Model Demonstrations
12.3.1 Prestressed wooden blocks forming a beam and a column
12.3.2 A toy using prestressing
12.4 Practical Examples
12.4.1 A centrally post-tensioned column
12.4.2 An eccentrically post-tensioned beam
12.4.3 Spider’s web
12.4.4 A cable-net roof
Problems

13 Horizontal Movements of Frame Structures Induced by Vertical Loads
13.1 Concepts
13.2 Theoretical Background
13.2.1 Static response
13.2.1.1 A symmetric system
13.2.1.2 An anti-symmetric system
13.2.1.3 An asymmetric system
13.2.1.4 Further comparison
13.2.2 Dynamic response
13.3 Model Demonstrations
13.3.1 A symmetric frame
13.3.2 An anti-symmetric frame
13.3.3 An asymmetric frame
13.4 Practical Examples
13.4.1 A grandstand
13.4.2 A building floor
13.4.3 Rail bridges
Problems

PART II Dynamics

14 Energy Exchange
14.1 Definitions and Concepts
14.2 Theoretical Background
14.3 Model Demonstrations
14.3.1 A moving wheel
14.3.2 Collision balls
14.3.3 Dropping a series of balls
14.4 Practical Examples
14.4.1 Roller coasters
14.4.2 A torch without a battery
Problems

15 Pendulums
15.1 Definitions and Concepts
15.2 Theoretical Background
15.2.1 A simple pendulum
15.2.2 A generalised suspended system
15.2.2.1 Symmetrical (vertical) vibration
15.2.2.2 Antisymmetical (lateral and rotational) vibration
15.2.3 Translational and rotational systems
15.3 Model Demonstrations
15.3.1 Natural frequency of suspended systems
15.3.3 Static behaviour of an outward inclined suspended system
15.4 Practical Examples
15.4.1 An inclined suspended wooden bridge in a playground
15.4.2 Seismic isolation of a floor
15.4.3 The Foucault pendulum
Problems

16 Free Vibration
16.1 Definitions and Concepts
16.2 Theoretical Background
16.2.1 A single degree-of-freedom system
16.2.2 A generalised single degree-of-freedom system
16.2.3 A multi-degrees-of-freedom system
16.2.4 Relationship between the fundamental natural frequency and the maximum displacement of a beam
16.3 Model Demonstrations
16.3.1 Free vibration of a pendulum system
16.3.2 Vibration decay and natural frequency
16.3.3 An overcritically-damped system
16.3.4 Mode shapes of a discrete system
16.3.5 Mode shapes of a continuous system
16.4 Practical Examples
16.4.1 A musical box
16.4.2 Measurement of the fundamental natural frequency of a building through free vibration generated by vibrators
16.4.3 Measurement of the natural frequency of a multi-flare stack through vibration generated by the environment
Problems

17 Resonance
16.1 Definitions and Concepts
17.2 Theoretical Background
17.2.1 A SDOF system subjected to a harmonic load
17.2.1.1 Equation of motion and its solution
17.2.1.2 Dynamic magnification factor
17.2.1.3 The phase lag
17.2.2 A SDOF subject to harmonic support movements
17.2.3 Resonance frequency
17.3 Model Demonstrations
17.3.1 Dynamic response of a SDOF system subject to harmonic support movements
17.3.2 Effect of resonance
17.4 Practical Examples
17.4.1 The London Millennium Footbridge
17.4.2 Avoidance of resonance – design of structures used for pop concerts
17.4.3 Measurement of the resonance frequency of a building
17.4.4 An entertaining resonance phenomenon
Problems

18 Damping in Structures
18.1 Concepts
18.2 Theoretical Background
18.2.1 Evaluation of viscous damping ratio from free vibration tests
18.2.2 Evaluation of viscous damping ratio from forced vibration tests
18.3 Model Demonstrations
18.3.1 Observing the effect of damping in free vibration
18.3.2 Hearing the effect of damping in free vibration
18.4 Practical Examples
18.4.1 Damping ratio obtained from free vibration tests
18.4.2 Damping ratio obtained from forced vibration tests
18.4.3 Damping ratios for floor structures
18.4.4 Damping ratios for buildings
18.4.5 Reducing footbridge vibration induced by walking
18.4.6 Reducing floor vibration induced by walking
Problems

19 Vibration Reduction
19.1 Definitions and Concepts
19.2 Theoretical Background
19.2.1 Change of dynamic properties of systems
19.2.2 Tuned mass dampers
19.3 Model Demonstrations
19.3.1 A tuned mass damper
19.3.2 A tuned-liquid damper
19.3.3 Vibration isolation
19.3.4 A pendulum tuned-mass-damper
19.4 Practical Examples
19.4.1 Tyres used for vibration isolation
19.4.2 The London Eye
19.4.3 The London Millennium Footbridge
Problems

20 Human Body Models in Structural Vibration
20.1 Concepts
20.2 Theoretical Background
20.2.1 Introduction
20.2.2 Identification of human body models in structural vibration
20.3 Demonstration Tests
20.3.1 The body model of a standing person in the vertical direction
20.3.2 The body model of a standing person in the lateral direction
20.4 Practical Examples
20.4.1 The effect of stationary spectators on a grandstand
20.4.2 Calculation of the natural frequencies of a grandstand
20.4.3 Dynamic response of a structure used at pop concert
20.4.4 Indirect measurement of the fundamental natural frequency of a standing body
20.4.5 Indirect measurement of the fundamental natural frequency of a chicken
Problems

PART III Synthesis

21 Static and modal stiffnesses
21.2 Definitions of static and modal stiffnesses
21.2.1 Static stiffness
21.2.2 Modal stiffness
21.3 The relationship between static and modal stiffnesses of a structure
21.4 Verification
21.4.1 Analytical verification
21.4.1.1 A simply supported beam
21.4.1.2 A simply supported plate
21.4.2 Experimental verification
21.4.3 Numerical verification
21.5 Application
21.5.1 The use of stiffness measurement of a composite floor
21.5.2 Displacement of structures induced by rhythmic human loads
21.5.3 Measuring static stiffness and loads on structures
21.5.3.1 Determining the static stiffness of a footbridge
21.5.3.2 Checking the proof load of a bridge
21.6 Discussion
21.7 Summary

22 Static and dynamic problems
22.2 Maximum displacement and fundamental natural frequency
22.2.1 Relationship equations
22.2.2 Examples
22.3 Buckling load and fundamental natural frequency
22.3.1 Relationship equations
22.3.2 Example
22.3.3 Buckling-vibration tests of a strut
22.4.1 Relationship equation
22.5 Tension force and fundamental natural frequency
22.5.1 Relationship equation
22.5.2 Tension force and natural frequency of a straight tension bar
22.5.3 Tension forces in the cables in the London Eye
22.6 Summary

23 Experimental and theoretical studies
23.1 Characteristics of theoretical and experimental studies
23.1.1 Experimental studies
23.1.2 Theoretical studies
23.1.3 Basis for combining experimental and theoretical studies
23.2 Modelling the relationships between theoretical and experimental studies
23.3 Comparison model
23.3.1 The model and features
23.3.2 A steel framed building
23.3.3 An appropriate floor model
23.4 Integration model
23.4.1 The model and features
23.4.2 Dynamic response of a reinforced concrete beam
23.4.3 A floor in a Sports Centre
23.5 Verification model
23.5.1 The model and features
23.5.2 Ratification of the authenticity of an assumption
23.5.3 Improving the certainty of predictions
23.6 Explanation model
23.6.1 The model and features
23.6.2 Effects of stationary people in structural vibration
23.6.3 Lateral stiffness of temporary grandstands
23.7 Creation model
23.7.1 The model and features
23.7.2 Human body models in structure interaction
23.7.3 Effective bracing systemw for structures
23.8 Extension model
23.8.1 The model and features
23.8.2 Measurement of the natural frequency of a standing human body
23.8.3 Identification of possible cracks in the pinnacles at Westminster
23.9 Links between the relationship models

24 Theory and practice
24.2 Theoretical and practical sources for structural concepts
24.3 Relationship between theory and practice
24.3.1 Structural concepts and intuitive understanding
24.3.2 Structural concepts and practical measures
24.3.3 Theory and practice
24.4 Bridging the gaps between theory and practice
24.4.1 Downward approach: from theory to practice
24.4.2 Upward approach: from practice to theory
24.4.3 Interdisciplinary approach: combining practice, research and teaching
24.4.3.1 Designing for stiffer structures
24.4.3.2 Horizontal resonance of a frame structure due to vertical dynamic loading
24.5 Summary

Index