{"id":731,"date":"2022-03-24T11:50:22","date_gmt":"2022-03-24T11:50:22","guid":{"rendered":"https:\/\/www.mub.eps.manchester.ac.uk\/structural-concepts\/?page_id=731"},"modified":"2022-03-24T11:52:32","modified_gmt":"2022-03-24T11:52:32","slug":"contents","status":"publish","type":"page","link":"https:\/\/www.mub.eps.manchester.ac.uk\/structural-concepts\/contents\/","title":{"rendered":"Contents"},"content":{"rendered":"\n

Contents<\/h1>\n\n\n\n

Preface
Acknowledgement<\/p>\n\n\n\n

1.Overview of structural concepts<\/strong>
    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<\/p>\n\n\n\n

PART I Statics<\/strong><\/p>\n\n\n\n

2. Equilibrium<\/strong>
    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 \u2018float\u2019 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<\/p>\n\n\n\n

3 Centre of Mass<\/strong>
    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<\/p>\n\n\n\n

4 Effect of Different Cross Sections<\/strong>
    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<\/p>\n\n\n\n

5 Stress Distribution<\/strong>
    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<\/p>\n\n\n\n

6 Bending<\/strong>
    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<\/p>\n\n\n\n

7 Shear and Torsion<\/strong>
    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<\/p>\n\n\n\n

8 Span and Deflection<\/strong>
    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<\/p>\n\n\n\n

9 Direct Force Paths<\/strong>
    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<\/p>\n\n\n\n

10 Smaller Internal Forces<\/strong>
    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<\/p>\n\n\n\n

11 Buckling<\/strong>
    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<\/p>\n\n\n\n

12 Prestress<\/strong>
    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\u2019s web
            12.4.4 A cable-net roof
    Problems<\/p>\n\n\n\n

13 Horizontal Movements of Frame Structures Induced by Vertical Loads<\/strong>
    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<\/p>\n\n\n\n

PART II Dynamics<\/strong><\/p>\n\n\n\n

14 Energy Exchange<\/strong>
    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<\/p>\n\n\n\n

15 Pendulums<\/strong>
    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
            15.3.2 Effect of added masses
            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<\/p>\n\n\n\n

16 Free Vibration<\/strong>
    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<\/p>\n\n\n\n

17 Resonance<\/strong>
    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 \u2013 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<\/p>\n\n\n\n

18 Damping in Structures<\/strong>
    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<\/p>\n\n\n\n

19 Vibration Reduction<\/strong>
    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<\/p>\n\n\n\n

20 Human Body Models in Structural Vibration<\/strong>
    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<\/p>\n\n\n\n

PART III Synthesis<\/strong><\/p>\n\n\n\n

21 Static and modal stiffnesses<\/strong>
    21.1 General comments on stiffness
    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<\/p>\n\n\n\n

22 Static and dynamic problems<\/strong>
    22.1 Preliminary comments
    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 Periodic dynamic loads and corresponding static loads
            22.4.1 Relationship equation
            22.4.2 Human jumping loads
    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<\/p>\n\n\n\n

23 Experimental and theoretical studies<\/strong>
    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<\/p>\n\n\n\n

24 Theory and practice<\/strong>
    24.1 Preliminary comments
    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<\/p>\n","protected":false},"excerpt":{"rendered":"

Contents PrefaceAcknowledgement 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 […]<\/p>\n","protected":false},"author":116,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-book.php","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"class_list":{"0":"post-731","1":"page","2":"type-page","3":"status-publish","5":"entry"},"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.mub.eps.manchester.ac.uk\/structural-concepts\/wp-json\/wp\/v2\/pages\/731","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mub.eps.manchester.ac.uk\/structural-concepts\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mub.eps.manchester.ac.uk\/structural-concepts\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mub.eps.manchester.ac.uk\/structural-concepts\/wp-json\/wp\/v2\/users\/116"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mub.eps.manchester.ac.uk\/structural-concepts\/wp-json\/wp\/v2\/comments?post=731"}],"version-history":[{"count":2,"href":"https:\/\/www.mub.eps.manchester.ac.uk\/structural-concepts\/wp-json\/wp\/v2\/pages\/731\/revisions"}],"predecessor-version":[{"id":735,"href":"https:\/\/www.mub.eps.manchester.ac.uk\/structural-concepts\/wp-json\/wp\/v2\/pages\/731\/revisions\/735"}],"wp:attachment":[{"href":"https:\/\/www.mub.eps.manchester.ac.uk\/structural-concepts\/wp-json\/wp\/v2\/media?parent=731"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}