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Arch Formulas

Simply select the picture which most resembles the arch configuration and loading condition you are interested in for a detailed summary of all the structural properties. Equations for Resultant Forces, Shear Forces and Bending Moments can be found for each arch case shown.

Additional information regarding engineering arch theory and the assumptions that have been made can be found Here.

Additional information regarding engineering beam theory can be found Here.

Three Hinged Arches (Any Shape)

Three Hinged Arch on Pin Supports with Uniformly Distributed Load

Three Hinged Arch - UDL

Three Hinged Arch on Pin Supports with Uniformly Distributed Load over Half of Span

Three Hinged Arch - Half UDL

Three Hinged Arch on Pin Supports with Uniformly Distributed Load Acting on Side

Three Hinged Arch - Side UDL

Three Hinged Arch on Pin Supports with Point Load at Any Point

Three Hinged Arch - PL

Three Hinged Arch on Pin Supports with Uniformly Increasing Loads towards supports

Three Hinged Arch - UIL

Three Hinged Arch on Pin Supports with Uniformly Increasing Load on Half of Span

Three Hinged Arch - Half UIL

Three Hinged Arch on Pin Supports with Uniformly Increasing Load on Side of Span

Three Hinged Arch - Side UIL

Three Hinged Arch on Pin Supports with Bending Moments at Centre Hinge

Three Hinged Arch - BM

Two Hinged Parabolic Arches

Two Hinged Parabolic Arch on Pin Supports with Uniformly Distributed Load

Two Hinged Arch - UDL

Two Hinged Parabolic Arch on Pin Supports with Uniformly Distributed Load over Half of Span

Two Hinged Arch - Half UDL

Two Hinged Parabolic Arch on Pin Supports with Uniformly Distributed Load over Side of Span

Two Hinged Arch - Side UDL

Two Hinged Parabolic Arch on Pin Supports with Point Load at Any Point

Two Hinged Arch - PL

Two Hinged Parabolic Arch on Pin Supports with Uniformly Increasing Load over Half of Span

Two Hinged Arch - Half UIL

Two Hinged Parabolic Arch on Pin Supports with Uniformly Increasing Load on Side of Span

Two Hinged Arch - Side UIL

Two Hinged Parabolic Arch on Pin Supports after Support Has Moved

Two Hinged Arch - Support Moved

Fixed Parabolic Arches

Fixed Parabolic Arch with Uniformly Distributed Load

Fixed Arch - UDL

Fixed Parabolic Arch with Uniformly Distributed Load over Half of Span

Fixed Arch - Half UDL

Fixed Parabolic Arch with Uniformly Distributed Load on Side of Span

Fixed Arch - Side UDL

Fixed Parabolic Arch with Point Load at Any Point

Fixed Arch - PL

Fixed Parabolic Arch with Central Point Load

Fixed Arch - Central PL

Fixed Parabolic Arch with Uniformly Increasing Loads towards Supports

Fixed Arch - UIL

Fixed Parabolic Arch on Fixed Supports after Support Has Moved

Fixed Arch - Support Moved

Tied Parabolic Arch - Two Hinge

Two Hinged Tied Parabolic Arch on Pinned Supports with Uniformly Distributed Load

Tied Arch - UDL

Two Hinged Tied Parabolic Arch on Pinned Supports with Uniformly Distributed Load over Half of Span

Tied Arch - Half UDL

Two Hinged Tied Parabolic Arch on Pinned Supports with Side Uniformly Distributed Load

Tied Arch - Side UDL

Two Hinged Tied Parabolic Arch on Pinned Supports with Point Load

Tied Arch - PL

Two Hinged Tied Parabolic Arch on Pinned Supports with Side Uniformly Increasing Load

Tied Arch - Side UIL

Two Hinged Tied Parabolic Arch on Pinned Supports with Uniformly Increasing Load over Half of Span

Tied Arch - Half UIL