Cable stay bridges, summary of a lecture delivered as part of MSc course at University of Surrey UK. Outlines key issues for sizing major bridges. The work draws on Manual of bridge Enginnering, the authors book Steel Concrete composite bridges - which has a chapter on cable stay bridges, and recent research on cable stay and extradosed bridges.
Cable stay bridges, summary of a lecture delivered at Uni of Surrey, UK
1. 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.
2. 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.
3.
4. Chapter 10
Cable stay bridges
“..have a system of forces that are
resolved within the deck-stay-tower
system..”
10. 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
11. 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.
12. 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.
13. 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.
14.
15. 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
20. Wind, vortex shedding and flutter. Picture is an extract from
Collings, Steel-Concrete Composite Bridges.
21. The susceptibility of a bridge to dynamic wind
effects can be determined by a factor P
P = (ρ b2
/m) (44 vmo
2
/ 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.
34. 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.