Criteria for design of reinforced concrete arches
1967 Edition

IS 4090 (1967) specifies design criteria for reinforced concrete arches with spans up to 120 meters and a rise-to-span ratio ranging from 1/8 to 1/3. It encompasses all reinforced concrete arch types within these geometric boundaries, including circular, parabolic, and segmental arches, provided that the design is executed by qualified engineers. The standard works in conjunction with IS 456 and permits other design approaches if validated by analysis or testing, assuming competent supervision during construction.

Seismic loads are determined according to IS 1893 and are applied longitudinally or transversely at the centroid of each mass and live load. Longitudinal seismic forces acting on live loads and decks behave as tractive forces on the arch; forces on arch and spandrel supports act at their centers of gravity. Forces on suspenders are distributed equally between the arch and decking, while forces on arch ribs are considered at their segmental centroids. For filled spandrel arches, seismic forces may be disregarded in the arch itself but must be accounted for in supporting substructures.

For economical arch design, IS 4090 recommends a rise-to-span ratio between one-third and one-sixth of the span. Shorter spans typically use a rise equal to one-third of the span, resulting in steeper arches with lower bending moments, while longer spans favor a rise of one-sixth, producing flatter arches that have higher bending moments due to temperature and shrinkage effects. This balance optimizes structural efficiency and construction costs.

Temperature variations must be considered by providing minimum transverse reinforcement equal to 0.2% of the sectional area on each face, as per IS 456 guidelines, especially for tied arches free to move at the ends where temperature effects are minimal. Shrinkage strain, approximately 0.00015, is treated as equivalent to a 15°C temperature drop and about 60% of shrinkage stress is relieved by creep. Shrinkage influences are included in design calculations only if they increase stresses or deflections adversely. Proper anchorage and expansion joints are also recommended to mitigate restraint stresses.

IS 4090 suggests several analytical methods: Exact analysis involves adjusting the arch axis to the thrust line under dead load and calculating moments at critical points; elastic analysis estimates maximum bending moments and thrusts for preliminary design, with ultimate load checks following; and deflection moment methods analyze loads separately to obtain moments and thrusts, then combine them to find maximum moments, considering the properties of the undeformed arch. These methods ensure accurate and reliable arch design.