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Engineering · Statics & Structural Analysis

Three-Hinged Arch Analysis Calculator

Calculate vertical reactions, crown horizontal thrust and bending moment at a selected section of a symmetric parabolic three-hinged arch.

Engineering · Statics & Structural Analysis

Enter the engineering model

Explicit properties, geometry, units and assumptions
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
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Visual modelSchematic · not to scale
Statics & Structural Analysis: udl visual explanationA simplified diagram showing the relationship represented by the selected calculator mode. It is explanatory and not a fabrication, safety or scale drawing.crown hinge condition determines horizontal thrustequivalent beam moment − H·y
The diagram explains the selected relationship only. Dimensions, symbols and proportions are illustrative; use the entered values and stated assumptions for the calculation.

Keep every unit basis, sign convention, property source and idealization consistent. Values stay in this browser.

Engineering calculation result

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Understand the structural model

How arch shape converts bending into thrust

A three-hinged arch carries part of the equivalent beam moment through horizontal thrust. At the crown hinge, zero bending moment provides the equation used to find that thrust.

Relationship used

Vertical reactions match the equivalent simple beam; crown hinge equilibrium gives H=Mbeam,crown/f; March(x)=Mbeam(x)−H·y(x), y=4fx(L−x)/L².

Worked scenario: A 20 m span, 5 m rise arch under 10 kN/m full-span load has 100 kN vertical reactions and 100 kN horizontal thrust.

Keep the boundary visible: Only a symmetric parabolic three-hinged arch is represented; stability and member capacity remain outside scope.

Quick guide

How to use this calculator

  1. Choose the analysis mode that matches the physical model before entering values.
  2. Enter properties, geometry, loads, states and coefficients from one consistent unit and sign convention.
  3. Use the intermediate outputs to audit the relationship, then retain the stated idealization before applying it.

Calculation method

Transparent engineering model

Vertical reactions match the equivalent simple beam; crown hinge equilibrium gives H=Mbeam,crown/f; March(x)=Mbeam(x)−H·y(x), y=4fx(L−x)/L².

The calculator evaluates only the declared relationship and preserves visitor-entered assumptions rather than selecting materials, factors, components or standards.

Worked example

Worked example

A 20 m span, 5 m rise arch under 10 kN/m full-span load has 100 kN vertical reactions and 100 kN horizontal thrust.

Vertical reactions match the equivalent simple beam; crown hinge equilibrium gives H=Mbeam,crown/f; March(x)=Mbeam(x)−H·y(x), y=4fx(L−x)/L².

Supported inputs

Precision and limits

Analysis, not approval

Symmetric parabolic geometry with a crown hinge only. The result does not check axial force, shear, stability, second-order effects, foundations, connections or code capacity.

Standards and properties

Material properties, allowable values, load combinations, safety factors, correlations, manufacturer data, codes and jurisdictional requirements are not supplied automatically.

Units and precision

Use one consistent unit basis. Results retain working precision but cannot be more accurate than the entered measurements and properties.

Privacy

Entered engineering values and results stay in this browser and are not sent to analytics or third parties.