# Lecture 29
Elements of Cable-Stayed Bridges
cables
pylon
girder
abutment
adjacent pier
pier
foundation
pylon
cables
girder
pier
adjacent pier
foundation
The Tampa Skyway Bridge in 1984. The main span is 400 m.
Dr. Santiago Calatravas Alamillo Bridge in Sevilla. Note the 13 pairs of harp cables.
The equilibrium of the forces does not
develop bending moments at the bottom
of the pylon.
The moment at the base of the pylon for the Alamillo Bridge.
The Cables
Two-span
radial
fan
harp
star
Cable arrangements for multi-spans
a = inclination angle (0.4 = tan a = 0.50)
cable tension
G cable weight
The cables are inclined, and therefore the actual (effective) stiffness EA is a function of their nominal
stiffness EA, through a relation proposed by Tang (1),
EA
EA(effective) =
G 2 EAcos 2 a
1 +
12T 2
Most cables are stresses to about 40% of their ultimate strengths under permanent load conditions. Cables
under normal loading conditions have their effective stiffness approach the actual stiffness. A factor of
safety of 2.2 is common for cables, which results in an allowable stress of 45% of the guaranteed ultimate
tensile stress (GUTS) under dead and live loads.
Note that the weakest point of a cable is its anchorage with respect to capacity and fatigue.
The minimum modulii of elasticity E for strand and rope are:
strand
0.5 to 2.56 diameter
strand
2.625 diameter and larger
rope
0.375 to 4 diameter
E=24,000 ksi
E=23,000 ksi
E=20,000 ksi
Tensile strength of an ASTM A421 type BA, 0.25 diameter wire provides a minimum tensile strength of
240 ksi.
The Towers
Towers, commonly referred to as pylons, may be hinged or fixed to the pier. It can also be a portal frame
as shown above. When the base is fixed, it induces large bending moments into the pylon, but it is
compensated by having an increased rigidity, costs less than a pinned bearing and is easier to erect.
Live Loads.
The level of live loads is determined by evaluation of influence lines, and the stress s at any point of the
bottom flange of the girder is a combination of several force components,
1
= P
A
y
+ M + cK
I
where A is the girder cross-section, I is the moment of inertia, y is the distance from the neutral axis, c is
the stress influence coefficient due to the cable force K anchored close by, P is the axial force and M is
the bending moment. This equation is commonly rewritten as,
= a1P + a2 M + a3 K
where the constants a1, a2 and a3 depend on the effective width, location of the point, and other
geometric parameters. Under live loads, the terms P, M and K are individual influence lines, which a makes
s combination influence line. An alternative method is to find the maximum and minimum values of P,
M and K and use the worst condition. This method however, is considered too conservative, and does not
give an accurate picture of the state of stress in the girder.
The magnitude of the compressive force in the deck is represented by this step graph,
which shows how the girder forces increase as it reaches the pylon.
Pylon anchorage detail.
Pylon plate thickness ranges from
1.6 thick from the base to the 1st
cable junction, 1.2 between the first
and ninth cable junctions, and 0.5
above the top cable.
The pylon experiences compressive
axial forces from the cables aligned
with the pylon, and bending from
variable cable forces and the wind,
thereby requiring it be designed as
a beam/column.
GT STRUDL was used to analyze
the frame.
Section of the Alamillo Bridge pylon.
Crisscrossing the cables at the pylon is a good technical solution: safe, simple and economical, but it poses
great geometrical difficulties. To avoid torsional moments in the pylon, the cables coming from the main
span and going to the side span should be anchored in the pylon in the same plane. In order to avoid crossing
some designers use double cables, or like Bostons Bunker Hill bridge, the two planes of the cables are
arranged in a symmetrical pattern. If the pylon is a box (figure at right) the cables are anchored in front and
back, and the walls are post-tensioned; tendons can be wrapped around three walls at a time.
The cable anchor cradle within the pylon (Figg Engineering).
The Deck and Span Arrangement
Beginning the cantilever of a double fan cable system.
Erecting one of the 48 long main span girders. The rigid box section is to provide torsional rigidity, since the box girders
are supported along its centerline by the main stay cables, and by the west abutment steel frame. Otherwise it would
teeter about these supports. The five-sided shape is only 2 deep, with a 1.9 high parapet on each side.
For two-span asymmetrical bridges, the longer span ranges from 0.60 to 0.70 of the total length.
However, if the backstay is a single cable (for example, Rotterdam) the ratio of the long span to the total
length can reach 0.80. In a three-span bridge, the center span is about 0.55 of the total length. In multispans, the spans are roughly of equal length, except the spans connecting to the abutments.
fixed cable
fixed cable
fixed cable
fixed cable
minimum angle
pinned pylon
Moment diagram
no connection btw girders and pylons
connected
Example #1:
Example #2:
Example #3:
Example #4:
References