Cable-Stayed Bridges; Introduction and Analysis.

Making the complex simple.

Summary Presentation of a lecture by David Collings BSc CEng FICE

at University of Surrey, UK; March 2014.

Introduction

Start by looking at bridges others have designed and built. See books such as Collings, Steel Concrete Composite Bridges and ICE Manual of Bridge Engineering, as well as papers in Proceedings of ICE, Bridge Engineering.

Chapter 10Cable stay bridges

“..have a system of forces that are resolved within the deck-stay-tower

system..”

From MOBE by ICE publishing

Left, Stonecutters bridge during construction, picture from VSL. Below, cantilevering of Rusky Bridge, picture from NCE.

Scan of BE cover

Ahkai Sha Bridge a stiff decked cable-stayed form

Ah Kai Sha bridge; a cable-stay form with a stiff double deck, the deck stiffness of such bridges is often larger than that of an extradosed bridge, for some layouts of stay there may be some overlap in behaviour (see figure 6).

Image from RBA archives

Analysis

The basic stay system is basically a series of superimposed triangular trusses. A good approximation of the behaviour can be obtained relatively simply, however, in detail the bending, shear and axial load interaction together with non linear behaviour of the stays make detailed analysis relatively complex.

Analysis

Consider an isolated deck-stay-tower system shown in the figure. Element 1 of the main span has a weight W1 and is located a distance L1 from the tower, it is attached to a tower of height h1. A tension T1 in the stay and compression C1 in the deck is required for stability.

C1 = W1 L1 /h C2 = W2 L2 / h T1 = (W12 + C12)½ T2 = (W22+ C22)½ To avoid out of balance forces at the tower top and in the deck, C1 = C2, and W2 = W1 L1/ L2. Which also gives equilibrium about point o.

The natural frequency (fn) of a structure is a function of its mass (m) and stiffness (K):

fn = 1 (K / m )½ 2π

The frequency of various bridge structures are shown in figure (see full presentation).

Dynamics

Analysis of Second Severn Bridge, see Collings, Steel-concrete composite bridges.

From MOBE by ICE publishing

Loads

Key loads to consider:• Construction; • Traffic, Rail, People; • Wind; • Ship Impact.

Loads

Viana Bridge, see Proceedings of ICE, Bridge Engineering, Dec 2013

Wind, vortex shedding and flutter. Picture is an extract from

Collings, Steel-Concrete Composite Bridges.

The susceptibility of a bridge to dynamic wind effects can be determined by a factor P

P = (ρ b2/m) (44 vmo2/ b L fb

2) Where ρ is the density of air, b is the bridge width, L is the span, m is the mass per unit length of the bridge and fb the first bending frequency of the structure. For P < 0.04 the structure is unlikely to be susceptible to aerodynamic excitation. For P < 1 the structure should be checked against some simplified criteria to check for any aerodynamic instability. If P > 1 the structure is likely to be susceptible to aerodynamic excitation and some changes to the mass, stiffness or structure layout may be required, wind tunnel testing will be required to verify the structures behaviour.

Ship Impact

Design stays to limit stress at working loads to 0.4Pu, or limit live load variation to 200 Mpa.

Deck- Stay ConnectionFrom SCCD by D COLLINGS,ICE publishing

Towers

The main visual element, they can use many differing shapes.

Example 1

Taney Bridge, Ireland, see ICE Proceedings paper by Collings and Brown.

Summary

Cable-Stayed Bridges; Introduction and Analysis.

Making the complex simple.

Summary Presentation of a lecture by David Collings BSc CEng FICE

at University of Surrey, UK; March 2014.

Presentation by CRD and Wolf productions.