Dr Ana M. Ruiz-Teran

Longitudinal schemes for bridges.

Part 5: Cable-stayed bridges

Longitudinal schemes for bridges. Bridge types:

Beams

Trusses

Portal frames

Arch bridges

Cable-stayed bridges

Suspension bridges

Cable-stayed bridges and Suspension bridges are the most economic longitudinal schemes for long span bridges. This is a consequence of the structural behaviour of these bridge types, in which the axial behaviour is the main structural response rather than the flexural behaviour.

Advantages of Cable-stayed bridges against Suspension bridges:

• Cable-stayed bridges are stiffer than suspension bridges under non-symmetrical live loads and under wind load

• The amount of cables required for the stays of a cable-stayed bridge is smaller than that required for the bearing cables of a suspension bridge

Disadvantages of Cable-stayed bridges against Suspension bridges:

• The horizontal components of the axial forces in the stay cables introduce large axial compressions in the deck in the sections close to the piers. Additional flexural stiffness must be provided to the deck in order to avoid buckling. Due to this fact, for very long bridges, suspension bridges are cheaper than cable-stayed bridges.

STRUCTURAL BEHAVIOUR UNDER PERMANENT LOADS:

The vertical deflection at the anchorages of the stay cables in the main span due to dead load and superimposed dead load are counterweight with those due to the prestressing of the stay cables.

The bending moment diagram in the deck in the main span is similar to that in a continuous bridge with supports at the sections where the stay cables are anchored on the deck

The prestressing of the back stays is established in order to cancel the bending moments in the towers in permanent state

Modelling: The prestressing of the stay cables can be modelled through imposed shortening of the stays (or imposed temperature change).

STRUCTURAL BEHAVIOUR UNDER LIVE LOADS:

STRUCTURAL BEHAVIOUR UNDER LIVE LOADS:

The efficiency of the cable-staying system under live loads is achieved by limiting the horizontal displacement of the tower crown, which in turn is achieved by:

providing enough flexural stiffness to the towers (expensive unless continuous bridges)

providing enough axial stiffness to the back stays

anchoring the back stays in fix points or points that have relatively small displacements

In addition, once the horizontal displacement of the tower crowns is limited:

The larger the axial stiffness of the stay cables in the main span, the larger the efficiency of the cable-staying system

The smaller the flexural stiffness of the deck, the larger the efficiency of the cable-staying system

LONGITUDINAL STAY CABLE ARRANGEMENT:

There are three different longitudinal arrangements:

harp system

fan system

intermediate system

LONGITUDINAL STAY CABLE ARRANGEMENT:

HARP SYSTEM:

Better aesthetical appearance, specially when the cable-staying system is arranged in two different vertical planes

The tower crown is less restricted to displacements and, therefore, the efficiency of this cable-staying system is smaller than others

An appropriate efficiency of the cable-staying system is achieved by mean of both providing enough flexural stiffness to the towers and anchoring the back-stays to points in which the deflections are restricted.

LONGITUDINAL STAY CABLE ARRANGEMENT:

FAN SYSTEM:

Higher efficiency of the cable-staying system

Smaller slope with the vertical alignment → Higher efficiency → Smaller cross-sectional area → Smaller amount of stay cables → Smaller cost

Smaller slope with the vertical alignment → Smaller axial load in the deck → → Smaller amount of additional flexural stiffness in the deck to avoid buckling → Smaller cost

Disadvantages: Lack of space for anchoring the stay cables in the tower crown + Superposition of stay cables when they are arranged in two different vertical planes (aesthetics)

LONGITUDINAL STAY CABLE ARRANGEMENT:

INTERMEDIATE SYSTEM:

The stay cable anchorages are located in the top of the tower but in a larger area that in a fan system

Advantages of the fan arrangement, with a slightly smaller efficiency (significantly larger than the harp arrangement)

Enough space available for anchoring the stay cables in the top of the tower

Superposition of stay cables when they are arranged in two different vertical planes (aesthetics)

LONGITUDINAL STAY CABLE ARRANGEMENT:

LONGITUDINAL SPACING BETWEEN ANCHORAGES OF STAY CABLES:

The smaller the spacing → the smaller the bending moments in permanent stage → the smaller the design bending moments for the deck → the smaller the required depth of the deck → the smaller the cross sectional area of the stay cables → The smaller the cost

The smaller the spacing → the smaller the bending moments during construction

TRANSVERSE STAY CABLE ARRANGEMENT:

There are three different transverse arrangements:

single cable-staying plane

double cable-staying plane

double cable-staying plane converging at the top of the towers

SINGLE CABLE-STAYING PLANE:

The cable-staying system contribute to the shear and bending response

The cable-staying system does not contribute to the torsional response. All the torsional response is resisted by the deck → single/multiple box girders

Good appearance (aesthetics). The stay cables are not seen one over other ones

The anchorages are located in the middle-axis of the deck

TRANSVERSE STAY CABLE ARRANGEMENT:

DOUBLE CABLE-STAYING PLANE:

The cable-staying system contribute to the shear, the bending, and the torsional response

All the torsional response may be resisted by the cable staying system → thin transverse slab with two main eccentric longitudinal ribs where the anchorages are located

Superposition of stay cables (aesthetics).

TRANSVERSE STAY CABLE ARRANGEMENT:

DOUBLE CABLE-STAYING PLANE CONVERGING AT THE TOP OF THE TOWERS:

The cable-staying system contribute to the shear, the bending, and the torsional response

All the torsional response may be resisted by the cable staying system → thin transverse slab with two main eccentric longitudinal ribs where the anchorages are located

Superposition of stay cables (aesthetics).

The torsional stiffness of the entire structural system is enhanced

Additional axial response of the towers under transverse wind loading

TRANSVERSE STAY CABLE ARRANGEMENT:

TRANSVERSE STAY CABLE ARRANGEMENT:

TOWERS:

Single tower

H-shape tower

H-shape tower with an horizontal bracing (better resistance under transverse horizontal loads)

A-shape tower (D: clearance when 2 cable-staying planes)

Inverted-Y-shape tower (A: larger space for anchorages)

Diamond-shape tower (appropriate when the deck in very high over the ground)

ANCHORAGES:

SINGLE-, TWO-, THREE- AND MULTIPLE-SPAN CABLE-STAYED BRIDGES:

In single- and two-span bridges a larger tower high / span length ratio is required

In two-span bridges with similar span lengths a tower with a high flexural stiffness is required to guarantee the efficiency of the cable-staying system under live load

In multiple-spans, three effective systems can be used to guarantee the efficiency of the cable-staying system:

• Stay cable bracing the top of all of the towers

• Stay cable from the top of each tower to the bottom of the adjacent towers

• Towers with a high flexural stiffness

NON-LINEAR BEHAVIOUR OF STAY CABLES:

S

SSC

EL

EE

3

22

121

REFERENCES:

CHEN, W. F. AND DUAN L. 2003. Bridge Engineering. CRC Press LLC

HAMBLY, E.C. 1991. Bridge Deck Behaviour. Spon Press.

PARKE G, HEWSON N. 2008. ICE manual of bridge engineering. ICE.

MANTEROLA, J. BRIDGES. (6 Volumes, in Spanish). ETSICCP, Madrid