The Melan system embeds curved steel ribs within a concrete arch. Explore that construction arrangement and, in a separate statics exercise, calculate support reactions for an ideal three-hinged parabolic arch.
Ideal Three-Hinged Parabolic-Arch Reactions
Enter span, rise and a full-span uniform vertical line load. Results apply only to a symmetric three-hinged parabolic idealization and do not allocate force between concrete and steel.
Equation Used
- The comparison arch is symmetric, three-hinged and parabolic with level supports.
- Uniform vertical load acts over the complete horizontal span.
- Only support reactions are computed; section forces, stiffness, material sharing and construction stages are excluded.
- The worksheet is not a model of any particular historic Melan bridge.
Span, rise and uniform line load determine the reactions in the stated three-hinged idealization. These reactions do not establish how a real Melan bridge shares load between its concrete and steel.
Curved steel ribs embedded in concrete
Official historic-bridge records describe Josef Melan's system as curved parallel steel beams embedded in concrete. The Rock Rapids bridge used five 4-inch I-beams within its concrete arch.
The drawing illustrates that documented topology. It does not assign a universal percentage of load to either material.
Historical context and a separate statics exercise
Use the calculator only to inspect support reactions for the stated ideal arch. It cannot assess a historic bridge, design a new bridge, size reinforcement, stage a pour or establish capacity.
Symmetric three-hinged idealization
These are equilibrium reactions for a separate symmetric parabolic arch with three hinges and full-span uniform load. A real Melan bridge may have different geometry, continuity, loading and material interaction.
Reaction example
For L=30 m, f=3.75 m and w=100 kN/m, the ideal worksheet gives H=3.00 MN, V=1.50 MN, R=3.35 MN and f/L=0.125.
Material interaction and structural limits
Force sharing between concrete and embedded steel depends on section properties, material stiffness, compatibility and structural continuity. It is not calculated by these support-reaction equations. Real bridge analysis requires drawings, materials, boundary conditions, load combinations, deterioration data and applicable standards.
Melan-arch worksheet questions
Does this calculate force in the embedded steel?
No.
Does it model the Rock Rapids bridge?
No. The equations are a separate ideal statics exercise.
Can it rate an existing bridge?
No.
Official history and structural reference
- Iowa DOT, Melan Arch Bridge: embedded parallel steel beams and historic bridge details.
- Library of Congress HAER IA-15: Rock Rapids span, rise and five embedded I-beams.
- Washington DAHP, Historic Bridge Types: Melan patent and curved rolled I-beams embedded in concrete.
- Fundamentals of Structural Engineering, three-hinged arches: ideal reaction derivation.
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