Concrete 99 Sydney May 1999

Concrete 99Concrete 99Sydney May 1999Sydney May 1999

Arch Structures - Spanning Past Present and Future

Doug Jenkins

Reinforced Earth

Engineering Manager

The Sydney Opera House The Sydney Opera House and Harbour Bridgeand Harbour Bridge

Gladesville BridgeGladesville Bridge

Why Arches?Why Arches?

Arches are efficient in use of Arches are efficient in use of materialsmaterials

Arch behaviour is now well understoodArch behaviour is now well understood

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Actual

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Non-Lin

Elastic SS

Non Lin SS

Kouchi ExpresswayRelative Crown Displacement; DY

Arches are now economical to constructArches are now economical to construct

Early Arch BridgesEarly Arch Bridges

The Landscape Arch, UtahThe Landscape Arch, Utah

The Industrial RevolutionThe Industrial Revolution

Telfords Proposal for London BridgeTelfords Proposal for London Bridge

Theories of Arch DesignTheories of Arch Design

Robert Hooke, 1676:Robert Hooke, 1676:

"The true mathematical and mechanical form of all manner of arches for building, with the true butment necessary to each of them. A problem which no architectonick writer hath ever yet attemted, much less performed”

"As hangs the flexible line, so but inverted will stand the rigid arch."

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David Gregory:David Gregory:

"When an arch of any other figure is supported, it is because in its thickness some catenaria is included"

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Parabolic arch enclosing a catenaryParabolic arch enclosing a catenary

An old photograph of Pontypridd BridgeAn old photograph of Pontypridd Bridge

An-Ji BridgeAn-Ji Bridge

The Blackfriars CommitteeThe Blackfriars Committee

Eight “gentlemen of the most approved knowledge in building geometry and mechanics”– A clergyman– The Astronomer Royal– A Teacher of medicine– A lawyer– Two professors

Samuel JohnsonSamuel Johnson "If the elliptical arch be equally strong

with the semicircular, that is, if an arch, by approaching to a straight line, looses none of its stability, it will follow that all arcuation is useless…

But if a straight line will bear no weight, which is evident to the first view, it is plain like wise that an ellipsis will bear very little, and that as an arch is more curved its strength is increased."

““Publicus” (believed to be Robert Publicus” (believed to be Robert Mylne himself)Mylne himself)

"…so that, if I understand it right, all from the haunches of the arch downward becomes a pier or abutment, to support a small part of the arch in the middle as a segment of a circle.

This middle part, if built like other arches would make a lateral pressure against these abutments, but to take that away he has placed cubical stones, which he calls joggles, in the joints of the arch; so that every stone tends to fall perpendicularly by its being carried along with the one above it, and nor shoved aside as in other arches, which is the cause of the lateral pressure."

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Funicular

Circular

Parabolic

Funicular CurveComparison with circular and parabolic

Fill Height Over Crown = 1000.0m

K =0.00

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Funicular

Circular

Parabolic

Funicular CurveComparison with circular and parabolic

Fill Height Over Crown = 1.0m

K =0.00

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Funicular

Circular

Parabolic

Funicular CurveComparison with circular and parabolic

Fill Height Over Crown = 1000.0m

K =1.00

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Funicular

Circular

Parabolic

Funicular CurveComparison with circular and parabolic

Fill Height Over Crown = 1.0m

K =1.00

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Funicular

Circular

Parabolic

Funicular CurveComparison with circular and parabolic

Fill Height Over Crown = 1000.0m

K =0.50

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Funicular

Circular

Parabolic

Funicular CurveComparison with circular and parabolic

Fill Height Over Crown = 1.5m

K =0.50

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Distance From Crow n, m

Mom

ent,

kNm

Circular - Final Circular - Max Circular - Min

Funicular - Final Funicular - Max Funicular - Min

Moments on Buried ArchCircular and Funicular Curves

The Twentieth CenturyThe Twentieth Century

A Monier Arch BridgeA Monier Arch Bridge

Grafton Road Bridge, AucklandGrafton Road Bridge, Auckland

Salginatobel BridgeSalginatobel Bridge

Floating Formwork for Plougastel BridgeFloating Formwork for Plougastel Bridge

Today and the FutureToday and the Future

Shin Hamadera Bridge, JapanShin Hamadera Bridge, Japan

Properties of the ideal arch materialProperties of the ideal arch material

High compressive strength at comparatively low cost.

The ability to form any desired shape cheaply and accurately.

Erection without elaborate formwork. Low maintenance and excellent durability,

particularly under compression.