arch 3423 Building Technology II: Building Structures Term

arch 3423 Building Technology II: Building Structures Term 1 2018-2019

Lecture 6 Arches Form Active: Funicular Structures

Lion s Gate, Mycenae mid-13th century B.C. Pont du Gard Bridge, France 1st century A.D. Example of stone post and beam with corbeled arch above Example of a true arch (Roman)

Pont du Gard Roman Aqueduct Near Nimes, France. 1st century AD Exchange House Office Building Docklands, London 1996

View of Ancient Rome ca. 2nd century A.D. Contemporary model at the E.U.R.

The Pantheon Rome, Italy Apollodorus of Damascus ca. A.D. 114-128 The dome of the Pantheon is the world s largest unreinforced concrete dome. The diameter of the inner circle and height to the oculus is 43.3m.

The Pantheon A slice thru the hemispherical dome reveals the profile and the direction of compressive forces in the structure. Although not an arch, the section of the Pantheon has arch-like compressive forces in the longitudinal direction that are transferred to the ground through the walls. In order to redirect these forces more downward, it has been suggested by some researchers that the thickening of the dome structure above the outside walls acts as a weight to help turn the compressive forces more downward, keeping it within the thickness of the wall section.

Illustration from a work by Giovanni Poleni, Padua, 1748 describing how a masonry arch carries load. Note the parallelogram of vector forces in Fig. X, the resultant of which represents the thrust line of the arch. In Fig.XII is the hanging chain analogy used in finding the funicular shape of an arch. The trajectory of the resultants of each successive pair of spheres forms the thrust line of the arch.

As hangs the flexible line, so inverted will stand the rigid arch Robert Hooke 17 th century

From P. Block, M. DeJong and J. Ochsendorf. As Hangs the Flexible Line: Equilibrium of Masonry Arches in Nexus Network Journal, Oct. 2006, Vol. 8 Issue 2, pp.13-24.

Thrust line superimposed on a rigid frame The lines of action of the weights is identical to the lines of action in the stone arch, therefore the natural thrust line or stress trajectory will be the same. In this case the stress trajectory is mostly outside the frame structure. The amount of divergence from the centerline of the frame structure is an indication of the amount of bending force present in the frame.

Typical funicular structures

Graphical statics construction for finding the thrust line in a three hinged arch with variable concentrated loads. Concept of the kern area (fig. 469) If the thrust line stays within the kern area there will be no tension present in the section. This principle was important for masonry arch construction that is unable to resist tensile forces.

Salginatobel Bridge Robert Maillart Switzerland 1932

Orly Airfield Dirigible Hangars Eugene Freyssinet Paris, France 1912

Engr: Eugene Freyssinet Train repair sheds Arch: Le Corbusier Palace of the Soviets, 1930

Aircraft Hangars Pier Luigi Nervi Orbetello, Italy 1942

Expo Hall Pier Luigi Nervi Turin, Italy 1957

Gallerie of Machines Arch: Dutert Paris 1889 Centennial Expo 1889

Arches: characteristics number of hinges: 3 hinge, 2 hinge,1 hinge, none (fixed) advantages / disadvantages relative to i) rigidity ii) support settlements iii) temperature expansion / contraction statically determinate versus indeterminate Lateral bracing requirements of arches i) Lateral stability ii) Lateral buckling

Case Studies Ludwig Erhard Haus. Berlin, Germany 1998. Nicolas Grimshaw & Partners Linz Convention Center. Linz, Germany, 2001. Thomas Herzog Waterloo Rail Terminal. London, England, 1993. Nicolas Grimshaw & Partners

Ludwig Erhard Haus Nicolas Grimshaw & Partners Berlin, Germany 1998

Linz Convention Center Arch: Thomas Herzog Linz, Germany 2001

Elevation of purlin Section of purlin

Waterloo Rail Terminal Nicolas Grimshaw & Partners London, England 1993

Reference Structures 6th ed. D. Schodek and M. Bechthold. Pearson-Prentice Hall, 2008. See Ch. 5: Cables and Arches. Shaping Structures: Statics. Waclaw Zalewski and Edward Allen. John Wiley, 1998. See Ch. 12 Shaping a Three-Hinged Truss Arch Equilibrium: The Work of Nicholas Grimshaw & Partners. Hugh Pearman. Phaidon, 2000. (Ludwig Erhard House) Design Center, Linz. Thomas Herzog. NA 1088 H42 A63 1994. Structure Space and Skin: The Work of Nicholas Grimshaw & Partners. Kenneth Powell and Rowan Moore. Phaidon, 1993. (Waterloo Station)