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