Free rigging calculators: what they do well, and where the answer stops

Governing utilisation is computed from these checks only.

Independent utilisations from the other methodology families, shown for comparison. Not included in the governing result.

Lifting load $F$ at angle $\theta$ (in-plane) is decomposed at the weld centroid into a normal component $N=F\cos \theta$, a transverse shear $V=F\sin \theta$, and an in-plane bending moment $M=V\cdot h$, where $h$ is the pin-to-weld centroid distance. Topology: parallel side welds (two line welds along the lug sides).

• Geometry is a single-plate lug / padeye without cheek plates. Cheek-plate configurations are out of scope for v1 and require detailed analysis.
• The pin-region checks (net section, shear-out, bearing, pin) take the full load resultant, which is conservative for the membrane load path. When an out-of-plane load direction is declared, the out-of-plane component is checked separately at the base section and weld group; without it, the load is assumed in the plane of the lug.
• Behaviour assumed linear-elastic, isotropic, homogeneous. No plastic redistribution, residual stresses, or fatigue effects are considered.
• Load line passes through the hole centre. Eccentricities between sling and lug centreline are not explicitly evaluated.
• Allowable stresses are supplied by the user. The app does NOT apply any code-specific allowable factor (ASME BTH-1 $0.45F_y$, Eurocode ${\gamma }_M$, DNV DAF, etc.) until the corresponding source clause has been supplied and validated.
• Pin-to-hole fit is assumed reasonable (pin diameter slightly less than hole diameter). Extreme clearances or wear are not modelled.
• Bearing stress is taken as the projected nominal value ${\sigma }_b=\frac{F}{d_{p}t}$; actual contact stress peaks are not resolved.
• Fillet welds are symmetric about the load line. The weld group is analysed with $N=F_{ip}\cos \theta$, $V=F_{ip}\sin \theta$, $M=V\cdot h$ (in-plane), plus - when an out-of-plane load direction is declared - $V_{oop}=F\sin {\theta }_{oop}$ and $M_{oop}=V_{oop}\cdot h$ resisted by the line method about the weld group's longitudinal axis. Root components combine vectorially before the $45°$ throat decomposition (${\sigma }_{\perp }={\tau }_{\perp }=f_t/\sqrt{2}$, ${\tau }_{\parallel }=f_v$). Asymmetric weld runs remain out of scope.

• MECH_NET_SECTIONMechanics of Materials - net-section tension
  Average tensile stress on the net cross-section through the pin hole: $\sigma =\frac{F}{(w-d)t}$. Classical identity; no code-specific allowable applied.
• MECH_DOUBLE_SHEAR_OUTMechanics of Materials - double-plane shear-out
  Average shear stress on two tear-out planes between hole and free edge: $\tau =\frac{F}{2L_{s}t}$, where $L_s=a-\frac{d}{2}$. Classical identity; no code-specific allowable applied.
• MECH_BEARINGMechanics of Materials - bearing stress
  Nominal bearing stress on the projected pin-on-plate area: ${\sigma }_b=\frac{F}{d_{p}t}$. Classical identity; no code-specific allowable applied.
• MECH_PIN_SHEARMechanics of Materials - pin double shear
  Average shear stress on two pin cross-sections (single-lug in clevis): $\tau =\frac{F}{2A_{\text{pin}}}$. Classical identity; no code-specific allowable applied.
• MECH_FILLET_WELD_THROATMechanics of Materials - fillet weld throat resultant
  Resultant throat stress on a fillet weld group with angle-aware demand decomposition $N=F\cos \theta$, $V=F\sin \theta$, $M=V\cdot h$. Root components $f_z=\frac{N}{A_w}+\frac{M}{S_w}$ and $f_v=\frac{V}{A_w}$ give throat components ${\sigma }_{\perp }={\tau }_{\perp }=f_z/\sqrt{2}$ and ${\tau }_{\parallel }=f_v$; $|R|=\sqrt{f_z^2+f_v^2}$ is compared to the user-supplied shear allowable. No ${\gamma }_M$ or electrode-specific factor applied.
• MECH_FILLET_WELD_VMMechanics of Materials - von Mises throat stress
  Combined throat stress for a fillet weld group using the von Mises equivalent ${\sigma }_{\mathrm{eq}}=\sqrt{{\sigma }_{\perp }^2+3({\tau }_{\perp }^2+{\tau }_{\parallel }^2)}$, compared to the user-supplied tensile allowable (falls back to ${\tau }_{\text{allow}}\sqrt{3}$).
• AISC_WELD_J24AISC 360-22 §J2.4 · 2022 · §J2.4, Eq. J2-5 (directional strength increase)
  Nominal fillet-weld strength per unit throat area $F_{nw}=0.60F_{EXX}(1.0+0.5{\sin }^{1.5}\theta )$, where $\theta$ is the angle between the line of action of the force resultant and the weld longitudinal axis. ASD safety factor $\Omega =2.0$ per §B3.2.
• MECH_BASE_SECTIONMechanics of Materials - cantilever base section
  The lug is a rectangular cantilever plate fixed at the base section, loaded at the pin a lever arm $h$ above it. Load decomposition $F_{ip}=F\cos {\theta }_{oop}$, $F_{oop}=F\sin {\theta }_{oop}$; base actions $N=F_{ip}\cos \theta$, $V_{ip}=F_{ip}\sin \theta$, $M_{ip}=V_{ip}h$, $V_{oop}=F_{oop}$, $M_{oop}=F_{oop}h$; section $A=wt$, $S_{maj}=t{w}^2/6$, $S_{min}=w{t}^2/6$. Classical identities; the mechanics check compares the combined von Mises stress against the user-supplied allowable.
• BTH1_NET_TENSIONASME BTH-1-2020 §3-3.3.1 · 2020 · §3-3.3.1 (eqs 3-45 through 3-48)
  Static strength of pin-connected plate - tension on the effective net area either side of the pin hole, with $C_r$ reduction for pin/hole clearance and $b_{\mathrm{eff}}=\min \left(4t,0.6b_e\sqrt{\frac{F_u{D}_h}{F_y{b}_e}}\right)$. Allowable includes design factor $N_d$ per §3-1.3.
• BTH1_DESIGN_FACTORASME BTH-1-2020 §3-1.3 · 2020 · §3-1.3
  Design factor $N_d$: $2.00$ for Design Category A, $3.00$ for Design Category B. Applied to all §3-3 allowables.
• BTH1_FRACTUREASME BTH-1-2020 §3-3.3.1 · 2020 · §3-3.3.1 (eq 3-49)
  Single-plane fracture strength beyond the pin hole: $P_b=C_r\frac{F_u}{1.20N_d}\left[1.13\right(R-\frac{D_h}{2})+\frac{0.92b_e}{1+b_e/D_h}]t$, with $R$ measured from the hole centre to the plate edge in the direction of the applied load.
• BTH1_SHEAR_OUTASME BTH-1-2020 §3-3.3.1 · 2020 · §3-3.3.1 (eqs 3-50 through 3-52)
  Double-plane shear-out strength: $A_v=2t[a+\frac{D_p}{2}(1-\cos \phi )]$, with $\phi =55^{\circ }\frac{D_p}{D_h}$ and allowable $P_v=\frac{0.70F_u{A}_v}{1.20N_d}$.
• BTH1_BEARINGASME BTH-1-2020 §3-3.3.4 · 2020 · §3-3.3.4 (eqs 3-53 / 3-54)
  Pin bearing strength on the lug plate. Static bearing allowable $\frac{1.25F_y}{N_d}$; rotating (Service Class $\ge 1$) reduced to $\frac{0.63F_y}{N_d}$.
• BTH1_WELDASME BTH-1-2020 §3-3.4.3 · 2020 · §3-3.4.3 (eq 3-55)
  Allowable fillet-weld shear on the effective throat $F_v=\frac{0.60F_{EXX}}{1.20N_d}$. Extended to combined in-plane loading by comparing the resultant throat stress $f_{\mathrm{res}}=\sqrt{f_z^2+f_v^2}$ against the clause allowable.
• BTH1_TENSION_BENDINGASME BTH-1-2020 §3-2.4(c) · 2020 · §3-2.4(c) (eq 3-35), with §3-2.1 (eq 3-1) for $F_t$
  Combined axial tension and biaxial bending: $f_t/F_t+f_{bx}/F_{bx}+f_{by}/F_{by}\le 1.0$, with $F_t=F_y/N_d$ on the gross section. Reduces to the §3-2.3.5 biaxial criterion (eq 3-26) when $f_t=0$.
• BTH1_RECT_MAJORASME BTH-1-2020 §3-2.3.3 · 2020 · §3-2.3.3 (eqs 3-19 through 3-24)
  Major-axis bending of solid rectangular bars, banded by $\lambda =L_{b}d/t^2$: $\lambda \le 0.08E/F_y$ → $F_b=1.25F_y/N_d$; $0.08E/F_y<\lambda \le 1.9E/F_y$ → $F_b=C_{LTB}{C}_b[1.52-0.274\lambda F_y/E]F_y/N_d\le 1.25F_y/N_d$; $\lambda >1.9E/F_y$ → $F_b=C_{LTB}1.9E{C}_b/(N_d\lambda )\le 1.25F_y/N_d$. $C_{LTB}=1.00$ braced, else $3.00\sqrt{E{I}_x/(GJ)}/(L_b/t)\le 1.00$. Page-verified 2026-08-12.
• BTH1_RECT_MINORASME BTH-1-2020 §3-2.3.4 · 2020 · §3-2.3.4 (eq 3-25)
  Minor-axis bending of solid rectangular sections: $F_b=1.25F_y/N_d$.
• BTH1_MATERIAL_CONSTANTSASME BTH-1-2020 §1-6.1 · 2020 · §1-6.1
  Material constants used by the standard's member equations: $E=200000$ MPa, $G=77200$ MPa.
• BTH1_CRITICAL_STRESSASME BTH-1-2020 §3-2.5 · 2020 · §3-2.5 (eq 3-37)
  Combined normal and shear stresses at a point: $f_{cr}=\sqrt{f_x^2-f_x{f}_y+f_y^2+3f_v^2}\le F_y/N_d$. At the lug base corner $f_y=0$ (free surface).
• BTH1_PLATE_SHEARASME BTH-1-2020 §3-2.3.6 · 2020 · §3-2.3.6 (eq 3-28)
  Average shear stress on bars, pins, and plates: $F_v=F_y/(N_d\sqrt{3})$, valid for $h/t\le 2.45\sqrt{E/F_y}$ where $h$ is the clear plate depth parallel to the applied shear. Beyond that limit the clause requires a buckling method with the §3-1.3 design factor - the check reports indeterminate rather than a number.
• EC3_PIN_GEOMETRYEN 1993-1-8:2005 §3.13.1 · 2005 · §3.13.1, Table 3.9 (Type A - given thickness)
  Geometric requirements for pin-connected plates, Type A (given thickness $t$): $a\ge \frac{F_{\mathrm{Ed}}{\gamma }_{M0}}{2t{f}_y}+\frac{2d_0}{3}$ and $c\ge \frac{F_{\mathrm{Ed}}{\gamma }_{M0}}{2t{f}_y}+\frac{d_0}{3}$, where $a$ and $c$ are measured from the edge of the hole to the plate end / side edge. The Type B (given geometry) alternative $t\ge 0.7\sqrt{F_{\mathrm{Ed}}{\gamma }_{M0}/f_y}$, $d_0\le 2.5t$ applies only to the specific lug shape drawn in Table 3.9 and is reported informatively.
• EC3_PIN_SHEAREN 1993-1-8:2005 §3.13.2 · 2005 · §3.13.2, Table 3.10 (shear)
  Pin shear resistance per plane: $F_{v,\mathrm{Rd}}=\frac{0.6A{f}_{up}}{{\gamma }_{M2}}$. A single-lug / clevis assembly presents two shear planes.
• EC3_PLATE_BEARINGEN 1993-1-8:2005 §3.13.2 · 2005 · §3.13.2, Table 3.10 (bearing)
  Pin/plate bearing resistance: $F_{b,\mathrm{Rd}}=\frac{1.5td{f}_y}{{\gamma }_{M0}}$.
• EC3_PIN_BENDINGEN 1993-1-8:2005 §3.13.2 · 2005 · §3.13.2, Table 3.10 & Figure 3.11 (bending)
  Pin bending resistance: $M_{\mathrm{Rd}}=\frac{1.5W_{\mathrm{el}}{f}_{yp}}{{\gamma }_{M0}}$ with $W_{\mathrm{el}}=\frac{\pi d^3}{32}$. The demand $M_{\mathrm{Ed}}$ follows Figure 3.11: $M_{\mathrm{Ed}}=\frac{F_{\mathrm{Ed}}}{8}(b+4c+2a)$; evaluated when the user supplies the shackle fork geometry (jaw thickness $a$ and either inside-jaw width $W$ or clearance $c$).
• EC3_PIN_COMBINEDEN 1993-1-8:2005 §3.13.2 · 2005 · §3.13.2, Table 3.10 & Figure 3.11 (combined)
  Combined shear + bending interaction on the pin: ${\left(\frac{M_{\mathrm{Ed}}}{M_{\mathrm{Rd}}}\right)}^2+{\left(\frac{V_{\mathrm{Ed}}}{F_{v,\mathrm{Rd}}}\right)}^2\le 1$. Gated on the same shackle fork geometry as the pin-bending check.
• EC3_WELD_DIRECTIONALEN 1993-1-8:2005 §4.5.3.2 · 2005 · §4.5.3.2 (directional method)
  Directional check for a fillet weld throat. Two criteria: $\sqrt{{\sigma }_{\perp }^2+3({\tau }_{\perp }^2+{\tau }_{\parallel }^2)}\le \frac{f_u}{{\beta }_w{\gamma }_{M2}}$ and ${\sigma }_{\perp }\le \frac{0.9f_u}{{\gamma }_{M2}}$. Correlation factor ${\beta }_w$ taken from Table 4.1 based on the weaker joined steel grade.
• EC3_WELD_SIMPLIFIEDEN 1993-1-8:2005 §4.5.3.3 · 2005 · §4.5.3.3 (simplified method)
  Simplified check on the weld throat as a vector shear: $F_{w,Ed}\le F_{w,Rd}=f_{vw,d}a$ with $f_{vw,d}=\frac{f_u/\sqrt{3}}{{\beta }_w{\gamma }_{M2}}$. Conservative relative to the directional method; shown as a cross-check.
• EC3_BASE_YIELDEN 1993-1-1:2005 §6.2.1(5) · 2005 · §6.2.1(5), eq (6.1)
  Elastic yield criterion at a critical point; with ${\sigma }_z=0$: ${\left(\frac{{\sigma }_x{\gamma }_{M0}}{f_y}\right)}^2+3{\left(\frac{\tau {\gamma }_{M0}}{f_y}\right)}^2\le 1$. Applied at the lug base section extreme fibre.
• DNV_N001_DAFDNV-ST-N001 §16.2.5 · 2018, amended 2020-01 · §16.2.5, Table 16-1 (DAF in air, excluding elevated jackups)
  Dynamic amplification factor from Table 16-1 by environment column and static hook load. For $3<\mathrm{SHL}\le 100$ t: onshore $1.10$, inshore $1.07+0.05\sqrt{100/\mathrm{SHL}}$, offshore $1+0.25\sqrt{100/\mathrm{SHL}}$; banded constants above 100 t. Items lighter than 3 t are taken as 3 t (note 1). SHL includes rigging weight - the app approximates SHL with the design load; user-overridable.
• DNV_N001_SKEWDNV-ST-N001 §16.2.6 · 2018, amended 2020-01 · §16.2.6 (skew load factor)
  Skew-load factor for rigging tolerance / force-distribution effects. §16.2.6.9 permits $\mathrm{SKL}=1.00$ for statically determinate lifts; the default 1.10 is retained as a conservative baseline for a single-lug padeye. Multi-sling redistribution is out of scope for v1.
• DNV_N001_CONSEQUENCEDNV-ST-N001 §16.8.3 · 2018, amended 2020-01 · §16.8.3, Table 16-5 (consequence factors)
  Consequence factor ${\gamma }_c$ applied to lift points including their attachments to the structure: $1.30$ per Table 16-5, applied together with all relevant §16.2 factors per §16.8.4.1. Members directly supporting or framing into the lift points use $1.15$ (out of scope for this single-lug check set).