Bridges’ Dynamics

This introductory chapter presents a brief historical review of bridge structures. From ancient times up to present days, bridge engineering is a continuously developing field of science although various construction materials have been used. From stone and wood in the past to concrete and structural steel at the present, various types of bridges have been designed and constructed. The most representative types of bridges are given schematically of in photographs.

This chapter deals with all load types imposed to bridge structures. Typical permanent and live loads such as self-weight, traffic loads, snow and wind loads and thermal loads are presented with reference to international codes for structural loadings. Special loads such as seismic loads, accidental loads, blast loads, support settlement, centrifugal forces etc. are also given. The designer must take into account all loads specified by the codes as well as special load cases due to structural type of the bridge.

In this chapter, the most important aspects related to dynamic analysis of structures are presented. Calculus of variations and energy principles such as d’Alembert principle, Lagrange equations of motion and Hamilton principle are given in brief form. The general form of equations of motion is presented along with the most common solution methods such as integral transformation or Ritz and Galerkin methods. The equations for free vibration in axial, bending and torsional mode are solved for various boundary conditions. The problem of forced vibrations is also presented for the above cases.

This chapter presents the special cases of loads with or without mass moving over a bridge structure. More specifically, the cases of concentrated loads and uniform loads are treated taken into account the effect of damping. Dynamic influence lines are presented for each case taking into account the effect of load mass as well. The influence of deck irregularities is also presented in brief form.

In this chapter, the special problem of support settlement is exclusively treated. The corresponding shape functions for settlement of one or more supports of simple beams with up to three spans with various boundary conditions are derived and presented in detail. Among the examined cases are supports vibrating along the longitudinal and the transverse of the bridge or the vertical direction as well.

This chapter deals with the bridge as structural element. Single span bridges, two-span and three-span bridges, arched bridges, cable-stayed and suspension bridges are analyzed in detail regarding their bending and torsional vibration. The most important relations for studying single cable vibration, harp and fan type cable systems with dense or not arrangement of cables as well as the curved in plane bridges are presented. The determination of modal shapes for some characteristic cases of bridges is also given in detail.

This chapter deals with the basic principles of aeroelasticity theory (Theodorsen theory) and how these can be applied to bridge structures with sensitive deck shapes. The most common aerodynamical models with two or three forces as well as buffeting forces are briefly presented. Special effects such as galloping instability, torsional divergence and flutter are also presented. The technique of experimental design employing test results from scaled models is also described.

This chapter deals with dynamic instability aspects of cable-stayed and suspension bridges. The technique for determining the instability regions of frequencies as well as the boundaries of critical frequencies based on the solution of Mathieu-Hill equations is presented in detail. In the cases examined, instability phenomena in pylons, bridge decks and cables are analytically presented.

In this chapter, the most characteristic cases of damping systems in bridges are presented. Damping systems are categorized into external damping systems (such as special bearings) and internal damping systems (such as masses and dampers in the bridge) and their modeling aspects are presented in detail.