Vibration Problems in Structures

1 Vibrations induced by people.- 1.1 Pedestrian bridges.- 1.1.1 Problem description.- 1.1.2 Dynamic actions.- 1.1.3 Structural criteria.- a) Natural frequencies.- b) Damping.- c) Stiffness.- 1.1.4 Effects.- 1.1.5 Tolerable values.- 1.1.6 Simple design rules.- a) Tuning method.- b) Code method.- c) Calculation of upper bound response for one pedestrian.- d) Effects of several pedestrians.- 1.1.7 More advanced design rules.- 1.1.8 Remedial measures.- a) Stiffening.- b) Increased damping.- c) Vibration absorbers.- 1.2 Floors with walking people.- 1.2.1 Problem description.- 1.2.2 Dynamic actions.- 1.2.3 Structural criteria.- a) Natural frequencies.- b) Damping.- 1.2.4 Effects.- 1.2.5 Tolerable values.- 1.2.6 Simple design rules.- a) High tuning method.- b) Heel impact method.- 1.2.7 More advanced design rules.- 1.2.8 Remedial measures.- a) Shift of the natural frequency.- b) Non-structural elements.- 1.3 Floors for sport or dance activities.- 1.3.1 Problem description.- 1.3.2 Dynamic actions.- 1.3.3 Structural criteria.- a) Natural frequencies.- b) Damping.- 1.3.4 Effects.- 1.3.5 Tolerable values.- 1.3.6 Simple design rules.- 1.3.7 More advanced design rules.- 1.3.8 Remedial measures.- a) Raising the natural frequency by means of added stiffness.- b) Increasing structural damping.- c) Use of vibration absorbers.- 1.4 Floors with fixed seating and spectator galleries.- 1.4.1 Problem description.- 1.4.2 Dynamic actions.- 1.4.3 Structural criteria.- a) Natural frequencies.- b) Damping.- 1.4.4 Effects.- 1.4.5 Tolerable values.- 1.4.6 Simple design rules.- 1.4.7 More advanced design rules.- 1.4.8 Remedial measures.- 1.5 High-diving platforms.- 1.5.1 Problem description.- 1.5.2 Dynamic actions.- 1.5.3 Structural criteria.- a) Natural frequencies.- b) Damping.- 1.5.4 Effects.- 1.5.5 Tolerable values.- 1.5.6 Simple design rules.- a) Stiffness criteria.- b) Frequency criteria.- 1.5.7 More advanced design rules.- 1.5.8 Remedial measures.- References to Chapter 1.- 2 Machinery-induced vibrations.- 2.1 Machine foundations and supports.- 2.1.1 Problem description.- 2.1.2 Dynamic actions.- a) Causes.- b) Periodic excitation.- c) Transient excitation.- d) Stochastic excitation.- 2.1.3 Structural criteria.- a) Natural frequencies.- b) Damping.- 2.1.4 Effects.- a) Effects on structures.- b) Effects on people.- c) Effects on machinery and installations.- d) Effects due to structure-borne sound.- 2.1.5 Tolerable values.- a) General Aspects.- b) Structural criteria.- c) Physiological criteria.- d) Production-quality criteria.- e) Tolerable values relative to structure-borne sound.- 2.1.6 Simple design rules.- a) General.- b) Data desirable for the design of machine supports.- c) Measures for rotating or oscillating machines.- d) Measures for machines with impacting parts.- e) Rules for detailing and construction.- 2.1.7 More advanced design rules.- 2.1.8 Remedial measures.- 2.2 Bell towers.- 2.2.1 Problem description.- 2.2.2 Dynamic actions.- 2.2.3 Structural criteria.- a) Natural frequencies.- b) Damping.- 2.2.4 Effects.- 2.2.5 Tolerable values.- 2.2.6 Simple design rules.- 2.2.7 More advanced design rules.- 2.2.8 Remedial measures.- 2.3 Structure-borne sound.- 2.3.1 Problem description.- 2.3.2 Dynamic actions.- 2.3.3 Structural criteria.- 2.3.4 Effects.- 2.3.5 Tolerable values.- 2.3.6 Simple design rules.- a) Influencing the initiation.- b) Influencing the transmission.- 2.3.7 More advanced design rules.- 2.3.8 Remedial measures.- 2.4 Ground-transmitted vibrations.- 2.4.1 Problem description.- 2.4.2 Dynamic actions.- 2.4.3 Structural criteria.- a) Natural frequencies.- b) Damping.- 2.4.4 Effects.- 2.4.5 Tolerable values.- 2.4.6 Simple design rules.- a) Emission.- b) Transmission.- c) Immission.- 2.4.7 More advanced design rules.- 2.4.8 Remedial measures.- References to Chapter 2.- 3 Wind-induced vibrations.- 3.1 Buildings.- 3.1.1 Problem description.- 3.1.2 Dynamic actions.- 3.1.3 Structural criteria.- a) Natural frequencies.- b) Damping.- c) Stiffness.- 3.1.4 Effects.- 3.1.5 Tolerable values.- 3.1.6 Simple design rules.- 3.1.7 More advanced design rules.- 3.1.8 Remedial measures.- a) Installation of damping elements.- b) Vibration absorbers.- 3.2 Towers.- 3.2.1 Problem description.- 3.2.2 Dynamic actions.- 3.2.3 Structural criteria.- a) Natural frequencies.- b) Damping.- c) Stiffness.- 3.2.4 Effects.- 3.2.5 Tolerable values.- 3.2.6 Simple design rules.- 3.2.7 More advanced design rules.- 3.2.8 Remedial measures.- 3.3 Chimneys and Masts.- 3.3.1 Problem description.- 3.3.2 Dynamic actions.- 3.3.3 Structural criteria.- a) Natural frequencies.- b) Damping.- 3.3.4 Effects.- 3.3.5 Tolerable values.- 3.3.6 Simple design rules.- 3.3.7 More advanced design rules.- 3.3.8 Remedial measures.- 3.4 Guyed Masts.- 3.4.1 Problem description.- 3.4.2 Dynamic actions.- 3.4.3 Structural criteria.- a) Natural frequencies.- b) Damping.- 3.4.4 Effects.- 3.4.5 Tolerable values.- 3.4.6 Simple design rules.- 3.4.7 More advanced design rules.- 3.4.8 Remedial measures.- 3.5 Pylons.- 3.5.1 Problem description.- 3.5.2 Dynamic actions.- 3.5.3 Structural criteria.- a) Natural frequencies.- b) Damping.- 3.5.4 Effects.- 3.5.5 Tolerable values.- 3.5.6 Simple design rules.- 3.5.7 More advanced design rules.- 3.5.8 Remedial measures.- 3.6 Suspension and Cable-Stayed Bridges.- 3.6.1 Problem description.- 3.6.2 Dynamic actions.- 3.6.3 Structural criteria.- a) Natural frequencies.- b) Damping.- 3.6.4 Effects.- 3.6.5 Tolerable values.- 3.6.6 Simple design rules.- 3.6.7 More advanced design rules.- 3.6.8 Remedial measures.- 3.7 Cantilevered Roofs.- 3.7.1 Problem description.- 3.7.2 Dynamic actions.- 3.7.3 Structural criteria.- a) Natural frequencies.- b) Damping.- 3.7.4 Effects.- 3.7.5 Tolerable values.- 3.7.6 Simple design rules.- 3.7.7 More advanced design rules.- 3.7.8 Remedial measures.- References to Chapter 3.- 4 Vibrations induced by traffic and construction activity.- 4.1 Roads.- 4.1.1 Problem description.- 4.1.2 Dynamic actions.- 4.1.3 Structural criteria.- 4.1.4 Effects.- 4.1.5 Tolerable values.- 4.1.6 Simple design rules.- 4.1.7 More advanced design rules.- 4.1.8 Remedial measures.- 4.2 Railways.- 4.2.1 Problem description.- 4.2.2 Dynamic actions.- 4.2.3 Structural criteria.- 4.2.4 Effects.- 4.2.5 Tolerable values.- 4.2.6 Simple design rules.- a) General aspects.- b) Measures against increased vibration level.- 4.2.7 More advanced design rules.- 4.2.8 Remedial measures.- 4.3 Bridges.- 4.3.1 Problem description.- 4.3.2 Dynamic actions.- 4.3.3 Structural criteria.- 4.3.4 Effects.- 4.3.5 Tolerable values.- 4.3.6 Simple design rules.- 4.3.7 More advanced design rules.- 4.3.8 Remedial measures.- 4.4 Construction Work.- 4.4.1 Problem description.- 4.4.2 Dynamic actions.- 4.4.3 Structural criteria.- 4.4.4 Effects.- 4.4.5 Tolerable values.- 4.4.6 Simple rules.- a) Vehicles on construction sites.- b) Piling, sheet piling.- c) Vibratory compaction.- d) Dynamic consolidation.- e) Excavation.- f) Blasting.- 4.4.7 More advanced measures.- 4.4.8 Remedial measures.- References to Chapter 4.- A Basic vibration theory and its application to beams and plates.- A.1 Free vibration.- A.2 Forced vibration.- A.3 Harmonic excitation.- A.4 Periodic excitation.- A.4.1 Fourier analysis of the forcing function.- A.4.2 How the Fourier decomposition works.- A.4.3 The Fourier Transform.- A.5 Tuning of a structure.- A.6 Impedance.- A.7 Vibration Isolation (Transmissibility).- A.8 Continuous systems and their equivalent SDOF systems.- B Decibel Scales.- B.1 Sound pressure level.- B.2 Weighting of the sound pressure level.- C Damping.- C.1 Introduction.- C.2 Damping Quantities (Definitions, Interpretations).- C.3 Measurement of damping properties of structures.- C.3.1 Decay curve method.- C.3.2 Bandwidth method.- C.3.3 Conclusions.- C.4 Damping mechanisms in reinforced concrete.- C.5 Overall damping of a structure.- C.5.1 Damping of the bare structure.- C.5.2 Damping by non-structural elements.- C.5.3 Damping by energy radiation to the soil.- C.5.4 Overall damping.- D Tuned vibration absorbers.- D.1 Definition.- D.2 Modelling and differential equations of motion.- D.3 Optimum tuning and optimum damping of the absorber.- D.4 Practical hints.- E Wave Propagation.- E.1 Introduction.- E.2 Wave types and propagation velocities.- E.3 Attenuation laws.- F Behaviour of concrete and steel under dynamic actions.- F.1 Introduction.- F.2 Behaviour of concrete.- F.2.1 Modulus of elasticity.- F.2.2 Compressive strength.- F.2.3 Ultimate strain in compression.- F.2.4 Tensile strength.- F.2.5 Ultimate strain in tension.- F.2.6 Bond between reinforcing steel and concrete.- F.3 Behaviour of reinforcing steel.- F.3.1 Modulus of Elasticity.- F.3.2 Strength in Tension.- F.3.3 Strain in tension.- G Dynamic forces from rhythmical human body motions.- G.1 Rhythmical human body motions.- G.2 Representative types of activity.- G.3 Normalised dynamic forces.- H Dynamic effects from wind.- H.1 Basic theory.- H.l.1 Wind speed and pressure.- H.l.2 Statistical characteristics.- a) Gust spectrum.- b) Aerodynamic admittance function.- c) Spectral density of the wind force.- H.1.3 Dynamic effects.- H.2 Vibrations in along-wind direction induced by gusts.- H.2.1 Spectral methods.- a) Mechanical amplification function.- b) Spectral density of the system response.- H.2.2 Static equivalent force method based on stochastic loading.- H.2.3 Static equivalent force method based on deterministic loading.- H.2.4 Remedial measures.- H.3 Vibrations in along-wind direction induced by buffeting.- H.4 Vibrations in across-wind direction induced by vortex-shedding.- H.4.1 Single structures.- H.4.2 Several structures one behind another.- H.4.3 Conical structures.- H.4.4 Vibrations of shells.- H.5 Vibrations in across-wind direction: Galloping.- H.6 Vibrations in across-wind direction: flutter.- H.7 Damping of high and slender RC structures subjected to wind.- I Human response to vibrations.- I.1 Introduction.- I.2 Codes of practice.- I.2.1 ISO 2631.- I.2.2 DIN 4150/2.- J Building response to vibrations.- J.1 General.- J.2 Examples of recommended limit values.- References to the Appendices.- List of Codes and Standards.