Two-hinged arch
The two-hinged arch is a static structure , which consists of an arch that is guided on both sides in an immovable support .
static system
In each support two work support forces (horizontal and vertical). Thus there are four unknowns which cannot be solved with the three equilibrium conditions ΣH = 0, ΣV = 0, ΣM = 0 of the rigid statics. So an elasticity equation has to be introduced in addition to the solution. The following approach is taken to solve this problem:
Two-hinged arch loaded
Deformed two-hinge arch
Two-hinged arch deformed back
The horizontal displacement is released for a support and the displacement is calculated from the load. Then the equivalent horizontal load is calculated, which is necessary to achieve the same displacement as was created under the original load. If you now add up both load cases, you get the desired internal forces and moments of the double-hinge arch.
Applications
The double-hinge arch is mainly used in structures that have to span large spans. This creates a large cavity under the arch. This is used in hall structures and bridges. Since the calculation is relatively simple, double-hinge arches were used early on in large bridges that span entire valleys.
Nösslachbrücke near the Brenner motorway
Lieserschlucht bridge in Carinthia
Further applications can be found in numerous bridge representations.
literature
- Fritz Chemelka, Ernst Melan : Introduction to strength theory. 5th edition 1972, Springer-Verlag, ISBN 978-3-7091-8305-2 .
- Walter Wagner, Gerhard Erbhof: practical structural analysis 3rd 6th edition 1977, BGTeubner Stuttgart.
- Karl-Eugen Kurrer : History of Structural Analysis. In search of balance , Ernst and Son, Berlin 2016, pp. 76–80, pp. 97ff. and pp. 483f., ISBN 978-3-433-03134-6 .