Issue 1 V1.08
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Three Hinge Arch - Any Shape - Central BMs

More Arches

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

Notation and Units

Metric and Imperial Units

The above arch formulas may be used with both imperial and metric units. As with all calculations care must be taken to keep consistent units throughout with examples of units which should be adopted listed below:


  • FBD = free body diagram
  • BMD = bending moment diagram

  • A, B & C = points of interest on arch
  • f = height of arch from supports, in or mm
  • H = horizontal reaction load at bearing point, lbf or N
  • L = span length under consideration, in or mm
  • M = maximum bending moment, or Nmm
  • R = vertical reaction load at bearing point, lbf or N
  • y = vertical distance from reaction point, in or mm