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If no horizontal thrusting forces are generated, this becomes an arch-shaped truss which is essentially a bent beam – see moon bridge for an example. If horizontal thrust is generated but the apex of the arch is a pin joint, this is termed as a three-hinged arch. If no hinge exists at the apex, it will normally be a two-hinged arch.
A fixed arch bridge, that is one without hinges, exerts a bending moment at the abutments and stresses caused by change of temperature or shrinkage of concrete have to be taken up by the arch. A two-hinged arch has a hinge at the base of each arch (the springing point), while a three-hinged arch has a third hinge at the crown of the arch. [3]
Robert Maillart, c. 1925. Robert Maillart (16 February 1872 – 5 April 1940) was a Swiss civil engineer who revolutionized the use of structural reinforced concrete with such designs as the three-hinged arch and the deck-stiffened arch for bridges, and the beamless floor slab and mushroom ceiling for industrial buildings.
Lancia Stratos Zero concept car [2] Lincoln Futura (glass roof canopy hinged at the rear) Loremo (large bottom-hinged front canopy) Maserati Birdcage 75th – extended canopy door, front 2/3 of the top of the car lifts up and moves forward; Messerschmitt Kabinenroller (aircraft-style canopy, hinge on right side)
If the spandrel is solid, usually the case in a masonry or stone arch bridge, the bridge is called a closed-spandrel deck arch bridge. If the deck is supported by a number of vertical columns rising from the arch, the bridge is known as an open-spandrel deck arch bridge. The Alexander Hamilton Bridge is an example of an open-spandrel arch bridge.
While a parabolic arch may resemble a catenary arch, a parabola is a quadratic function while a catenary is the hyperbolic cosine, cosh(x), a sum of two exponential functions. One parabola is f(x) = x 2 + 3x − 1, and hyperbolic cosine is cosh(x) = e x + e −x / 2 . The curves are unrelated.
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