Three Hinged Arches

The arch is one of the oldest structures. The Romans developed the semi circular true masonry arch.which they used extensively in both bridges and aqueducts. 

An arch is a curved beam in elevation. The horizontal moment at the supports is wholly or partially prevented in arches. Hence a horizontal thrust induced at the supports.

The supports must effectively arrest displacements in the vertical and horizontal directions in the arch action.

Types of Arches

Based on their geometry, arches can be classified as semicircular, segmental, or pointed.

Based on the number of internal hinges, they can be further classified as two-hinged arches, three-hinged arches, or fixed arches. 

An arch with a hinge at each support and third hing at the high point / crown or any where in the rib of arch is known as Three Hinged Arch.

An arch with a hinge at each support and no hinge exists anywhere in the rib, it will called as a Two-hinged arch.

An arch without hinges at  supports and  anywhere in the rib, it will called as a Fixed arch.

The horizontal distance between the lower hinges is called Span of the arch.

Eddy’s theorem: 

Eddy’s theorem states that “ The bending moment at any section of an arch is proportional to the vertical intercept between the linear arch (or theoretical arch) and the centre line of the actual arch.” 

Parabolic arches are preferably to carry distributed loads. Because, both, the shape of the arch and the shape of the bending moment diagram are parabolic. Hence the intercept between the theoretical arch and actual arch is zero everywhere. Hence, the bending moment at every section of the arch will be zero. 

The arch will be under pure compression which will be economical.

Three Hinged Arch:

A three-hinged arch is a geometrically stable and statically determinate structure. It consists of two curved members connected by an internal hinge at the crown and is supported by two hinges at its base. Sometimes, a tie is provided at the support level or at an elevated position in the arch to increase the stability of the structure.

Analysis of three-hinged arch :

The total no of unknown reactions in Three hinged arch are Four (Two vertical and two Horizontal).

These reactions will be calculated by using three static equilibrium equations and the bending moment at middle hinge is zero. 

So the Three hinged arch is statically determinate structure.

Normal thrust and radial shear in an arch rib:

Let θ be the inclination of the tangent at X. If H is the horizontal thrust and V the vertical shear at X, the normal and radial components at the section X is given by, 

Normal thrust , N = H cosθ + V sinθ

Radial Shear ,   R = V cosθ - H sinθ