The Kellogg method converts external piping mechanical loads (bending moment M and axial force F) into an equivalent internal fluid pressure: P_eq = P_design + (16*M)/(pi*G^3) + (4*F)/(pi*G^2), where G is the effective gasket contact diameter. If P_eq exceeds the flange ASME B16.5 rating at design temperature, the flange is at severe risk of joint leakage.

The classic Kellogg formula uses a conservative 16*M / (pi*G^3) multiplier based on linear elastic beam-bending stress across the gasket circle. ASME Section III NC-3658.3 applies a 16*M / (pi*G^3) derivation with higher allowable factors for welded-neck flanges with high-strength bolts, recognizing that bolted joints have greater plastic reserve than simple elastic beams.

Under severe piping bending moments, the outer flange face tilts, compressing the gasket on the compression side while relieving bolt clamp pre-load on the tension side. If the tensile stress exceeds the residual gasket seating stress (m * P), the gasket relaxes below its leak-tight threshold, allowing fluid escape.

Flange material yield and tensile allowable stresses drop substantially at elevated temperatures per ASME B16.5 Table 2 rating tables. For example, a Class 300 A105 carbon steel flange rated at 740 psig at 100°F is derated to 570 psig at 500°F (260°C) and 410 psig at 750°F (400°C), drastically reducing the permissible external piping load.

Slip-on flanges lack the tapered hub transition of weld-neck flanges, causing severe stress concentration at the fillet weld neck and greater flange ring rotation (warping) under external bending moments, which unloads the gasket significantly faster.