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Voussoir Analysis Overview

Failure Modes Considered:

  • Shear (vertical slippage at abutments)
  • Arch snap-thru (buckling due to gravity)
  • Localized crushing failure (compression failure)

Main Assumptions

  1. Roof cannot sustain tensile stresses, and supports itself primarily through formation of a parabolic compression arch, as it deflects.
  2. Deflection of the beam occurs before slippage at the abutments. Stability against slippage is determined after the compression arch develops.
  3. Initial lateral stress resulting from in-situ stress and/or excavation geometry is not considered in this analysis. The beam is assumed to be initially stress free.
  4. Cross-cutting structure is angled at significantly less than the minimum angle of friction assumed for the jointed surfaces.


  • Low confining stresses
  • Span / depth ratios < 3 not recommended
NOTE: Voussoir Analysis is restricted to Rectangular Pillars only since the Voussoir formulations assume a rectangular geometry.
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