Annex 9C: Reference Stress

API 579-1 (2021) Annex 9C — Reference stress $\sigma_{ref}$ / load ratio $L_r$ (plate, cylinder, sphere, nozzle, bar/bolt, heavy-wall)

API 579 Annex 9C — Reference Stress / Load Ratio

Computes the reference stress \sigma_{ref} and the FAD load ratio L_r=\sigma_{ref}/\sigma_{ys} for cracked plates, cylinders and spheres, per API 579-1/ASME FFS-1 (2021) Annex 9C (the collection of reference-stress solutions). The reference stress is a net-section limit-load measure of how close the cracked component is to plastic collapse, and L_r is the horizontal axis of the failure assessment diagram.

It covers the Annex 9C library:

• flat plate (through-wall, surface, embedded, plate-with-hole)
• cylinder (longitudinal and circumferential, surface or embedded)
• sphere
• nozzle corner crack
• round bar and bolt
• fillet weld
• heavy-wall (1\le t/R_i\le 3) table solutions

Stress can be entered in three ways:

• direct membrane plus bending;
• internal pressure (the tool derives membrane/bending from shell geometry);
• a 4th-order through-wall polynomial that is reduced to an equivalent membrane and bending.

Round-bar and bolt solutions take a force and moment; heavy-wall solutions take pressure and read a geometry factor from Tables 9C.1/9C.3.

The cut-off uses the API 579 flow stress \sigma_f=(\sigma_{ys}+\sigma_{uts})/2, so L_{r,max}=\sigma_f/\sigma_{ys}; assessment points beyond it are governed by plastic collapse. Pressurised shell solutions apply the Folias bulging factor (reused from the Annex 9C.2.3 calculator) and a surface-crack correction, and the semi-elliptical heavy-wall tables (9C.2/9C.4) are not yet included. Outputs are \sigma_{ref}, L_r and L_{r,max} together with the membrane and bending stresses actually used.

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