The Book

CONTENTS

Preface
Acknowledgement

STATICS

1. Equilibrium
    1.1 Definitions and Concepts
    1.2 Theoretical Background
    1.3 Model Demonstrations
            1.3.1 Action and reaction forces
            1.3.2 Stable and unstable equilibrium
            1.3.3 A plate-bottle system
            1.3.4 A magnetic ‘float’ model
    1.4 Practical Examples
            1.4.1 A barrier
            1.4.2 A footbridge
            1.4.3 An equilibrium kitchen scale
            1.4.4 Stage performance
            1.4.5 Magnetic float strain
            1.4.6 A dust tray

2 Centre of Mass
    2.1 Definitions and Concepts
    2.2 Theoretical Background
    2.3 Model Demonstrations
            2.3.1 Centre of mass of a piece of cardboard of arbitrary shape
            2.3.2 Centre of mass and centroid of a body
            2.3.3 Centre of mass of a body in a horizontal plane
            2.3.4 Centre of mass of a body in a vertical plane
            2.3.5 Centre of mass and stability
            2.3.6 Centre of mass and motion
    2.4 Practical Examples
            2.4.1 Cranes on construction sites
            2.4.2 The Eiffel Tower
            2.4.3 A display unit
            2.4.4 The Kio Towers

3 Effect of Different Cross Sections
    3.1 Definitions and Concepts
    3.2 Theoretical Background
    3.3 Model Demonstrations
            3.3.1 Two rectangular sectioned beams and an I-sectioned beam
            3.3.2 Lifting a book using a bookmark
    3.4 Practical Examples
            3.4.1 A steel framed building
            3.4.2 A rail bridge
            3.4.3 I section members with holes (cellular beams and columns)

4 Bending
    4.1 Definitions and Concepts
    4.2 Theoretical Background
    4.3 Model Demonstration
            4.3.1 Assumptions in beam bending
    4.4 Practical Examples
            4.4.1 Profiles of girders
            4.4.2 Reducing bending moment using overhangs
            4.4.3 Failure due to bending
            4.4.4 Deformation of a staple due to bending

5 Shear and Torsion
    5.1 Definitions and Concepts
    5.2 Theoretical Background
            5.2.1 Shear stresses due to bending
            5.2.2 Shear stresses due to torsion
    5.3 Model Demonstrations
            5.3.1 Effect of torsion
            5.3.2 Effect of shear stress
            5.3.3 Effect of shear force
            5.3.4 Open and closed sections subject to torsion with warping
            5.3.5 Open and closed sections subject to torsion without warping
    5.4 Practical Examples
            5.4.1 Composite section of a beam
            5.4.2 Shear walls in a building
            5.4.3 Opening of a drinks bottle

6 Stress Distribution
    6.1 Concepts
    6.2 Theoretical Background
    6.3 Model Demonstrations
            6.3.1 Balloons on nails
            6.3.2 Uniform and non-uniform stress distributions
    6.4 Practical Examples
            6.4.1 Flat shoes vs high-heel shoes
            6.4.2 The Leaning Tower of Pisa

7 Span and Deflection
    7.1 Concepts
    7.2 Theoretical Background
    7.3 Model Demonstrations
            7.3.1 A rule with a weight at its free end
            7.3.2 Effect of boundary conditions
            7.3.3 Measurement of the bending moment at one fixed end of a beam
    7.4 Practical Examples
            7.4.1 Column supports
            7.4.2 Phenomenon of Prop roots
            7.4.3 Metal props used in structures

8 Direct Force Paths
    8.1 Definitions and Concepts
    8.2 Theoretical background
            8.2.1 Introduction
            8.2.2 Concepts for achieving a stiffer structure
                    8.2.2.1 Definition of stiffness
                    8.2.2.2 Pin-jointed structures
                    8.2.2.3 Beam types of structure
                    8.2.2.4 Expression of the concepts
            8.2.3 Implementation
                    8.2.3.1 Five criteria
                    8.2.3.2 Numerical verification
    8.2.4 Discussion
            8.2.4.1 Safety, economy and elegance
            8.2.4.2 Optimum design and conceptual design
    8.3 Model Demonstrations
            8.3.1 Experimental verification
            8.3.2 Direct and zigzag force paths
    8.4 Practical Examples
            8.4.1 Bracing systems of tall buildings
            8.4.2 Bracing systems of scaffolding structures
                    8.4.2.1 The collapse of a scaffolding structure
                    8.4.2.2 Some bracing systems used for scaffolding structures

9 Smaller Internal Forces
    9.1 Concepts
    9.2 Theoretical Background
            9.2.1 Introduction
            9.2.2 A ring and a tied ring
    9.3 Model Demonstrations
            9.3.1 A pair of rubber rings
            9.3.2 Post-tensioned plastic beam
    9.4 Practical Examples
            9.4.1 Raleigh Arena
            9.4.2 Zhejiang Dragon Sports Centre
            9.4.3 A cable-stayed bridge
            9.4.4 A floor structure experiencing excessive vibration

10 Buckling
    10.1 Definitions and Concepts
    10.2 Theoretical Background
            10.2.1 Buckling of a column with different boundary conditions
            10.2.2 Lateral torsional buckling of beams
    10.3 Model Demonstrations
            10.3.1 Buckling shapes of plastic columns
            10.3.2 Buckling loads and boundary conditions
            10.3.3 Lateral buckling of beams
            10.3.4 Buckling of an empty aluminium can
    10.4 Practical Examples
            10.4.1 Buckling of a bracing members
            10.4.2 Buckling of a box girder
            10.4.3 Prevention of lateral buckling of beams

11 Prestress
    11.1 Definitions and Concepts
    11.2 Theoretical Background
    11.3 Model Demonstrations
            11.3.1 Prestressed wooden blocks forming a beam and a column
            11.3.2 A toy using prestressing
    11.4 Practical Examples
            11.4.1 A centrally post-tensioned column
            11.4.2 An eccentrically post-tensioned beam
            11.4.3 Spider’s web
            11.4.4 A cable-net roof

12 Horizontal Movements of Frame Structures Induced by Vertical Loads
    12.1 Concepts
    12.2 Theoretical Background
            12.2.1 Static response
                    12.2.1.1 A symmetric system
                    12.2.1.2 An anti-symmetric system
                    12.2.1.3 An asymmetric system
                    12.2.1.4 Further comparison
            12.2.2 Dynamic response
    12.3 Model Demonstrations
            12.3.1 A symmetric frame
            12.3.2 An anti-symmetric frame
            12.3.3 An asymmetric frame
    12.4 Practical Examples
            12.4.1 A grandstand
            12.4.2 A building floor
            12.4.3 Rail bridges

DYNAMICS

13 Energy Exchange
    13.1 Definitions and Concepts
    13.2 Theoretical Background
    13.3 Model Demonstrations
            13.3.1 A moving wheel
            13.3.2 Collision balls
            13.3.3 Dropping a series of balls
    13.4 Practical Examples
            13.4.1 Roller coasters
        13.4.2 A torch without a battery

14 Pendulums
    14.1 Definitions and Concepts
    14.2 Theoretical Background
            14.2.1 A simple pendulum
            14.2.2 A generalised suspended system
                    14.2.2.1 Symmetrical (vertical) vibration
                    14.2.2.2 Antisymmetical (lateral and rotational) vibration
            14.2.3 Translational and rotational systems
    14.3 Model Demonstrations
            14.3.1 Natural frequency of suspended systems
            14.3.2 Effect of added masses
            14.3.3 Static behaviour of an outward inclined suspended system
    14.4 Practical Examples
            14.4.1 An inclined suspended wooden bridge in a playground
            14.4.2 Seismic isolation of a floor
            14.4.3 The Foucault pendulum

15 Free Vibration
    15.1 Definitions and Concepts
    15.2 Theoretical Background
            15.2.1 A single degree-of-freedom system
            15.2.2 A generalised single degree-of-freedom system
            15.2.3 A multi-degrees-of-freedom system
            15.2.4 Relationship between the fundamental natural frequency and the maximum displacement of a beam
            15.2.5 Relationship between the fundamental natural frequency and the tension force in a straight string
    15.3 Model Demonstrations
            15.3.1 Free vibration of a pendulum system
            15.3.2 Vibration decay and natural frequency
            15.3.3 An overcritically-damped system
            15.3.4 Mode shapes of a discrete system
            15.3.5 Mode shapes of a continuous system
            15.3.6 Tension force and fundamental natural frequency of a straight tension bar
    15.4 Practical Examples
            15.4.1 A musical box
            15.4.2 Measurement of the fundamental natural frequency of a building through free vibration generated by vibrators
            15.4.3 Measurement of the natural frequency of a multi-flare stack through vibration generated by the environment
            15.4.4 The tension forces in the cables of the London Eye

16 Resonance
    16.1 Definitions and Concepts
    16.2 Theoretical Background
            16.2.1 A SDOF system subjected to a harmonic load
                    16.2.1.1 Equation of motion and its solution
                    16.2.1.2 Dynamic magnification factor
                    16.2.1.3 The phase lag
            16.2.2 A SDOF subject to harmonic support movements
            16.2.3 Resonance frequency
    16.3 Model Demonstrations
            16.3.1 Dynamic response of a SDOF system subject to harmonic support movements
            16.3.2 Effect of resonance
    16.4 Practical Examples
            16.4.1 The London Millennium Footbridge
            16.4.2 Avoidance of resonance – design of structures used for pop concerts
            16.4.3 Measurement of the resonance frequency of a building
            16.4.4 An entertaining resonance phenomenon

17 Damping in Structures
    17.1 Concepts
    17.2 Theoretical Background
            17.2.1 Evaluation of viscous damping ratio from free vibration tests
            17.2.2 Evaluation of viscous damping ratio from forced vibration tests
    17.3 Model Demonstrations
            17.3.1 Observing the effect of damping in free vibration
            17.3.2 Hearing the effect of damping in free vibration
    17.4 Practical Examples
            17.4.1 Damping ratio obtained from free vibration tests
            17.4.2 Damping ratio obtained from forced vibration tests
            17.4.3 Reducing footbridge vibration induced by walking
            17.4.4 Reducing floor vibration induced by walking

18 Vibration Reduction
    18.1 Definitions and Concepts
    18.2 Theoretical Background
            18.2.1 Change of dynamic properties of systems
            18.2.2 Tuned mass dampers
    18.3 Model Demonstrations
            18.3.1 A tuned mass damper
            18.3.2 A tuned-liquid damper
        18.3.3 Vibration isolation
    18.4 Practical Examples
            18.4.1 Tyres used for vibration isolation
            18.4.2 The London Eye
            18.4.3 The London Millennium Footbridge

19 Human Body Models in Structural Vibration
    19.1 Concepts
    19.2 Theoretical Background
            19.2.1 Introduction
            19.2.2 Identification of human body models in structural vibration
    19.3 Demonstration Tests
            19.3.1 The body model of a standing person in the vertical direction
            19.3.2 The body model of a standing person in the lateral direction
    19.4 Practical Examples
            19.4.1 The effect of stationary spectators on a grandstand
            19.4.2 Calculation of the natural frequencies of a grandstand
            19.4.3 Dynamic response of a structure used at pop concert
            19.4.4 Indirect measurement of the fundamental natural frequency of a standing body
            19.4.5 Indirect measurement of the fundamental natural frequency of a chicken