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Glossary of Terms - Engineering Arch Theory Explained

What is engineering arch theory?

Engineering Arch Theory

Arches employ the principal that when weight is uniformly applied to them the forces resolve into axial compressive stresses and thrust at the base or bearing points instead of into bending moments. The fundamental feature of arched structures is that horizontal reactions appear even if the structure is subjected to vertical loads only. This phenomenon is known as arch action. As the height or rise of the arch decreases, the outward thrust increases and as a result, maintaining the arch action and preventing the arch from collapsing, internal ties or external bracing must be employed. The efficiency of an arch can be demonstrated by comparing it with a beam of the same span under the same loading conditions.

Fixed arch: statically indeterminate structures to the third degree, the end points require solid restraints. These types of arches are the most ridged but are sensitive to relative settlement at the supports as well as any additional forces created by changes in temperature.

Two-hinged arch: statically indeterminate to the first degree and although are not as rigid as fixed arches, they are somewhat insensitive to relative settlement at the supports.

Three-hinged arch: statically determinate and are not affected by settlement or the additional forces created by temperature changes.

Tied-arch: provides an internal member or tie to resist the outward thrust caused by arch action. A strong tension member connected between the arch springing points reduces the amount of any external bracing requirements.

Parabolic arch: because both the shape of the arch and the shape of the bending moment diagram are parabolic, when the arch is subjected to a uniform load, the bending moment at every section of the arch is theoretically zero. The arch will be under pure axial compression.


Assumptions and Limitations

  • The cross-section of the arch is considered small compared to its length (beam is long and thin)
  • Loads act transverse to the longitudinal axis and pass through the shear centre (any torsion/twist is eliminated).
  • Self weight of the arch has been ignored (this may have to be added).
  • The material of the arch is homogenous and isotropic and has a constant Young's modulus in all directions.
  • The young's modulus is considered to be constant in both compression and tension.
  • The resultant moment of the bending stress is equal to the external moment along the entire length of the beam.
  • The centroidal plane (Neutral surface) is subjected to zero axial stress and does not undergo any change in length.
  • Deflections are assumed to be very small compared to the overall length of the arch.
  • The cross-section remains planar and perpendicular to the longitudinal axis during bending.
  • Any deflection of the arch follows a circular arc with the radius of curvature considered to remain large compared to the dimension of the cross section.

A selection of arch equations along with relevant engineering calculators can be found Here.

Additional information regarding engineering beam theory can be found Here.