Annex P: Reference Stress

BS 7910:2019 Annex P — Net-section plastic collapse reference stress for 33 crack geometries

BS 7910 Annex P — Reference Stress (\sigma_{ref})

Based on BS 7910:2019+A1:2020 Annex P, this calculator finds the reference stress \sigma_{ref} that measures how close a flawed section is to plastic collapse (net-section yielding). It supports 33 crack geometries — flat plates, thin and thick cylinders (axial and circumferential), spheres, round bars and bolts — and routes each crack type to its matching closed-form solution from Annex P (P.4 through P.12).

From \sigma_{ref} it returns the load ratio L_r = \sigma_{ref}/\sigma_Y and the plastic-collapse cut-off L_{r,max}, which together set the horizontal axis of the Failure Assessment Diagram (FAD). The inputs are the flaw size, the section geometry, the primary membrane and bending stresses P_m / P_b, and the material yield \sigma_Y and tensile \sigma_U strengths (the latter sets L_{r,max}, after R6 Revision 6:2023). Some solutions take extra inputs: pressurised thick-wall cylinders use an applied internal pressure p', and thin axial through-cracks in a cylinder include the Folias bulging factor.

Some solutions offer a choice of boundary condition or stress state:

• for plate edge bending, choose fixed-grip / restrained (Eq. P.9) or pin-jointed / free-rotation (Eq. P.10), which gives a higher \sigma_{ref};
• for the double-edge cracked plate, choose a plane-stress or plane-strain limit load (plane strain gives a higher limit load, so a lower \sigma_{ref}).

\sigma_{ref} is normally one of the building blocks called by the Clause 7 fracture assessment, but it is useful on its own to see how near a section is to plastic collapse.

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