Documentation · rigging

Lifting Lug Calculator - methodology & sources

The Lifting Lug Calculator verifies single-plate lifting lugs / padeyes with checks organised into four methodology families. The selected route becomes the primary utilisation basis; every other family is still computed and shown as an independent cross-check. Mechanics-of-materials identities compute raw stresses against user-supplied allowables; code-route checks are active only where the underlying clause and a worked validation example have been verified. Xarpis never invents formulas.

Mechanics of Materials

Check	Description	Status
Net-section tension (mechanics)	Average tensile stress across the plate's net cross-section through the pin hole.	Implemented
Double-plane shear-out (mechanics)	Average shear stress on the two tear-out planes between hole and free edge.	Implemented
Pin bearing on lug (mechanics)	Nominal projected bearing stress between pin and lug plate.	Implemented
Pin double shear (mechanics)	Average shear stress on two pin cross-sections (single lug in clevis).	Implemented
Fillet weld throat resultant (mechanics)	Angle-aware throat-resultant stress on the fillet weld group: $∣ R ∣ = f_{z}^{2} + f_{v}^{2}$ compared to the user-supplied shear allowable.	Implemented
Fillet weld von Mises throat stress (mechanics)	von Mises equivalent stress on the fillet weld throat, $σ_{eq} = σ_{⊥}^{2} + 3 (τ_{⊥}^{2} + τ_{∥}^{2})$ .	Implemented
Fillet weld strength - AISC 360-22 §J2.4	AISC 360-22 §J2.4 nominal fillet-weld throat strength with the directional strength increase $(1 + 0.5 sin^{1.5} θ)$ ; ASD $Ω = 2.0$ .	Implemented
Base section combined stress (mechanics)	Combined axial + biaxial bending + shear at the lug base section (cantilever model), von Mises vs the user tensile allowable.	Implemented

ASME BTH-1-2020

Check	Description	Status
Net-section tension - BTH-1 §3-3.3.1	Static allowable tensile strength of the pin-connected plate per BTH-1-2020 §3-3.3.1 (eqs 3-45 through 3-48).	Implemented
Single-plane fracture - BTH-1 §3-3.3.1	Single-plane tension fracture on the ligament beyond the pin hole (eq 3-49).	Implemented
Double-plane shear-out - BTH-1 §3-3.3.1	Tear-out (double-plane shear) strength of the pin-connected plate (eqs 3-50 to 3-52).	Implemented
Pin bearing - BTH-1 §3-3.3.4	Static or rotating pin-bearing allowable; switches formula based on BTH-1 Service Class.	Implemented
Fillet weld allowable - BTH-1 §3-3.4.3	BTH-1 allowable fillet-weld stress: resultant throat stress $f_{res}$ vs $F_{v} = 0.60 F_{E X X} / (1.20 N_{d})$ .	Implemented
Base section interaction - BTH-1 eq (3-35)	Tension + biaxial bending interaction at the lug base per BTH-1 eq (3-35), with §3-2.3.3/§3-2.3.4 rectangular-bar bending allowables.	Implemented
Base section critical stress - BTH-1 eq (3-37)	Combined normal + shear critical stress at the lug base per BTH-1 §3-2.5 (eq 3-37).	Implemented
Base section shear - BTH-1 eq (3-28)	Average shear at the lug base per BTH-1 §3-2.3.6 (eq 3-28), with the clause's h/t validity gate.	Implemented

EN 1993-1-8:2005 §3.13

Check	Description	Status
Pin-plate geometry - EC3 §3.13.1	Minimum end/edge distances for pin-connected plates per Table 3.9 Type A (given thickness); $a$ and $c$ measured from the hole edge.	Implemented
Pin shear - EC3 §3.13.2	Shear resistance of the pin at two planes: $F_{v, Rd} = 0.6 A f_{u p} / γ_{M 2}$ .	Implemented
Plate bearing - EC3 §3.13.2	Plate/pin bearing resistance $F_{b, Rd} = 1.5 t d f_{y} / γ_{M 0}$ from Table 3.10.	Implemented
Pin bending - EC3 §3.13.2	Pin bending resistance $M_{Rd} = 1.5 W_{el} f_{y p} / γ_{M 0}$ against $M_{Ed}$ from Figure 3.11 ( $F_{Ed} /8 (b + 4 c + 2 a)$ ).	Implemented
Pin combined shear + bending - EC3 §3.13.2	Interaction on the pin: $(M_{Ed} / M_{Rd})^{2} + (V_{Ed} / F_{v, Rd})^{2} \leq 1$ per Table 3.10.	Implemented
Fillet weld - EN 1993-1-8 §4.5.3.2 directional method	Directional check on the throat: $σ_{⊥}^{2} + 3 (τ_{⊥}^{2} + τ_{∥}^{2}) \leq f_{u} / (β_{w} γ_{M 2})$ and $σ_{⊥} \leq 0.9 f_{u} / γ_{M 2}$ .	Implemented
Fillet weld - EN 1993-1-8 §4.5.3.3 simplified method	Simplified check: $F_{w, E d} \leq F_{w, R d} = f_{v w, d} a$ with $f_{v w, d} = (f_{u} / 3) / (β_{w} γ_{M 2})$ .	Implemented
Base section yield criterion - EN 1993-1-1 eq (6.1)	Elastic yield criterion at the lug base section per EN 1993-1-1 §6.2.1(5) eq (6.1).	Implemented

DNV-ST-N001 §16

Check	Description	Status
Dynamic amplification factor - DNV-ST-N001 §16	$DAF$ from DNV-ST-N001 Table 16-1: environment column (onshore / inshore / offshore) + $SHL$ weight band, with the $\leq 100$ t formula cells (user-overridable).	Implemented
Skew-load factor - DNV-ST-N001 §16	Skew multiplier applied to the rigging load for a single-lug padeye (user-overridable).	Implemented
Lift-point consequence factor - DNV-ST-N001 §16.8.3	$γ_{c}$ multiplier from Table 16-5 (1.30 for lift points and attachments), applied to the DNV design load (user-overridable).	Implemented

Source registry

Metadata only - no copyrighted standard text is reproduced. Every implemented check cites at least one traceable source below.

Mechanics of Materials - net-section tension
Average tensile stress on the net cross-section through the pin hole: $σ = \frac{F}{( w - d ) t}$ . Classical identity; no code-specific allowable applied.
Mechanics of Materials - double-plane shear-out
Average shear stress on two tear-out planes between hole and free edge: $τ = \frac{F}{2 L _{s} t}$ , where $L_{s} = a - \frac{d}{2}$ . Classical identity; no code-specific allowable applied.
Mechanics of Materials - bearing stress
Nominal bearing stress on the projected pin-on-plate area: $σ_{b} = \frac{F}{d _{p} t}$ . Classical identity; no code-specific allowable applied.
Mechanics of Materials - pin double shear
Average shear stress on two pin cross-sections (single-lug in clevis): $τ = \frac{F}{2 A _{pin}}$ . Classical identity; no code-specific allowable applied.
Mechanics of Materials - fillet weld throat resultant
Resultant throat stress on a fillet weld group with angle-aware demand decomposition $N = F cos θ$ , $V = F sin θ$ , $M = V \cdot h$ . Root components $f_{z} = \frac{N}{A _{w}} + \frac{M}{S _{w}}$ and $f_{v} = \frac{V}{A _{w}}$ give throat components $σ_{⊥} = τ_{⊥} = f_{z} / 2$ and $τ_{∥} = f_{v}$ ; $∣ R ∣ = f_{z}^{2} + f_{v}^{2}$ is compared to the user-supplied shear allowable. No $γ_{M}$ or electrode-specific factor applied.
Mechanics of Materials - von Mises throat stress
Combined throat stress for a fillet weld group using the von Mises equivalent $σ_{eq} = σ_{⊥}^{2} + 3 (τ_{⊥}^{2} + τ_{∥}^{2})$ , compared to the user-supplied tensile allowable (falls back to $τ_{allow} 3$ ).
AISC 360-22 §J2.4 (2022) · §J2.4, Eq. J2-5 (directional strength increase)
Nominal fillet-weld strength per unit throat area $F_{n w} = 0.60 F_{E X X} (1.0 + 0.5 sin^{1.5} θ)$ , where $θ$ is the angle between the line of action of the force resultant and the weld longitudinal axis. ASD safety factor $Ω = 2.0$ per §B3.2.
AWS A2.4 - Standard Symbols for Welding, Brazing, and Nondestructive Examination
Weld-symbol conventions used in the schematic: triangular fillet-weld reference marker on the side of the joint to be welded, with the weld-all-around circle on the reference line when the perimeter is closed.
ASME 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 $b_{eff} = min (4 t, 0.6 b_{e} \frac{F _{u} D _{h}}{F _{y} b _{e}})$ . Allowable includes design factor $N_{d}$ per §3-1.3.
ASME BTH-1-2020 §3-3.3.1 (2020) · §3-3.3.1 (eq 3-49)
Single-plane fracture strength beyond the pin hole: $P_{b} = C_{r} \frac{F _{u}}{1.20 N _{d}} [1.13 (R - \frac{D _{h}}{2}) + \frac{0.92 b _{e}}{1 + b _{e} / D _{h}}] t$ , with $R$ measured from the hole centre to the plate edge in the direction of the applied load.
ASME BTH-1-2020 §3-3.3.1 (2020) · §3-3.3.1 (eqs 3-50 through 3-52)
Double-plane shear-out strength: $A_{v} = 2 t [a + \frac{D _{p}}{2} (1 - cos φ)]$ , with $φ = 5 5^{\circ} \frac{D _{p}}{D _{h}}$ and allowable $P_{v} = \frac{0.70 F _{u} A _{v}}{1.20 N _{d}}$ .
ASME 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 $\frac{1.25 F _{y}}{N _{d}}$ ; rotating (Service Class $\geq 1$ ) reduced to $\frac{0.63 F _{y}}{N _{d}}$ .
ASME BTH-1-2020 §3-3.4.3 (2020) · §3-3.4.3 (eq 3-55)
Allowable fillet-weld shear on the effective throat $F_{v} = \frac{0.60 F _{E X X}}{1.20 N _{d}}$ . Extended to combined in-plane loading by comparing the resultant throat stress $f_{res} = f_{z}^{2} + f_{v}^{2}$ against the clause allowable.
EN 1993-1-8:2005 §4.5.3.2 (2005) · §4.5.3.2 (directional method)
Directional check for a fillet weld throat. Two criteria: $σ_{⊥}^{2} + 3 (τ_{⊥}^{2} + τ_{∥}^{2}) \leq \frac{f _{u}}{β _{w} γ _{M 2}}$ and $σ_{⊥} \leq \frac{0.9 f _{u}}{γ _{M 2}}$ . Correlation factor $β_{w}$ taken from Table 4.1 based on the weaker joined steel grade.
EN 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: $F_{w, E d} \leq F_{w, R d} = f_{v w, d} a$ with $f_{v w, d} = \frac{f _{u} / 3}{β _{w} γ _{M 2}}$ . Conservative relative to the directional method; shown as a cross-check.
ASME 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.
EN 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 $t$ ): $a \geq \frac{F _{Ed} γ _{M 0}}{2 t f _{y}} + \frac{2 d _{0}}{3}$ and $c \geq \frac{F _{Ed} γ _{M 0}}{2 t f _{y}} + \frac{d _{0}}{3}$ , where $a$ and $c$ are measured from the edge of the hole to the plate end / side edge. The Type B (given geometry) alternative $t \geq 0.7 F_{Ed} γ_{M 0} / f_{y}$ , $d_{0} \leq 2.5 t$ applies only to the specific lug shape drawn in Table 3.9 and is reported informatively.
EN 1993-1-8:2005 §3.13.2 (2005) · §3.13.2, Table 3.10 (shear)
Pin shear resistance per plane: $F_{v, Rd} = \frac{0.6 A f _{u p}}{γ _{M 2}}$ . A single-lug / clevis assembly presents two shear planes.
EN 1993-1-8:2005 §3.13.2 (2005) · §3.13.2, Table 3.10 (bearing)
Pin/plate bearing resistance: $F_{b, Rd} = \frac{1.5 t d f _{y}}{γ _{M 0}}$ .
EN 1993-1-8:2005 §3.13.2 (2005) · §3.13.2, Table 3.10 & Figure 3.11 (bending)
Pin bending resistance: $M_{Rd} = \frac{1.5 W _{el} f _{y p}}{γ _{M 0}}$ with $W_{el} = \frac{π d ^{3}}{32}$ . The demand $M_{Ed}$ follows Figure 3.11: $M_{Ed} = \frac{F _{Ed}}{8} (b + 4 c + 2 a)$ ; evaluated when the user supplies the shackle fork geometry (jaw thickness $a$ and either inside-jaw width $W$ or clearance $c$ ).
EN 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: $(\frac{M _{Ed}}{M _{Rd}})^{2} + (\frac{V _{Ed}}{F _{v, Rd}})^{2} \leq 1$ . Gated on the same shackle fork geometry as the pin-bending check.
Mechanics 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 $F_{i p} = F cos θ_{oo p}$ , $F_{oo p} = F sin θ_{oo p}$ ; base actions $N = F_{i p} cos θ$ , $V_{i p} = F_{i p} sin θ$ , $M_{i p} = V_{i p} h$ , $V_{oo p} = F_{oo p}$ , $M_{oo p} = F_{oo p} h$ ; section $A = w t$ , $S_{maj} = t w^{2} /6$ , $S_{min} = w t^{2} /6$ . Classical identities; the mechanics check compares the combined von Mises stress against the user-supplied allowable.
ASME 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.
ASME 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 $λ = L_{b} d / t^{2}$ : $λ \leq 0.08 E / F_{y}$ → $F_{b} = 1.25 F_{y} / N_{d}$ ; $0.08 E / F_{y} < λ \leq 1.9 E / F_{y}$ → $F_{b} = C_{L T B} C_{b} [1.52 - 0.274 λ F_{y} / E] F_{y} / N_{d} \leq 1.25 F_{y} / N_{d}$ ; $λ > 1.9 E / F_{y}$ → $F_{b} = C_{L T B} 1.9 E C_{b} / (N_{d} λ) \leq 1.25 F_{y} / N_{d}$ . $C_{L T B} = 1.00$ braced, else $3.00 E I_{x} / (G J) / (L_{b} / t) \leq 1.00$ . Page-verified 2026-08-12.
ASME BTH-1-2020 §3-2.3.4 (2020) · §3-2.3.4 (eq 3-25)
Minor-axis bending of solid rectangular sections: $F_{b} = 1.25 F_{y} / N_{d}$ .
ASME 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: $f_{t} / F_{t} + f_{b x} / F_{b x} + f_{b y} / F_{b y} \leq 1.0$ , with $F_{t} = F_{y} / N_{d}$ on the gross section. Reduces to the §3-2.3.5 biaxial criterion (eq 3-26) when $f_{t} = 0$ .
ASME BTH-1-2020 §3-2.5 (2020) · §3-2.5 (eq 3-37)
Combined normal and shear stresses at a point: $f_{cr} = f_{x}^{2} - f_{x} f_{y} + f_{y}^{2} + 3 f_{v}^{2} \leq F_{y} / N_{d}$ . At the lug base corner $f_{y} = 0$ (free surface).
ASME BTH-1-2020 §3-2.3.6 (2020) · §3-2.3.6 (eq 3-28)
Average shear stress on bars, pins, and plates: $F_{v} = F_{y} / (N_{d} 3)$ , valid for $h / t \leq 2.45 E / F_{y}$ 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.
EN 1993-1-1:2005 §6.2.1(5) (2005) · §6.2.1(5), eq (6.1)
Elastic yield criterion at a critical point; with $σ_{z} = 0$ : $(\frac{σ _{x} γ _{M 0}}{f _{y}})^{2} + 3 (\frac{τ γ _{M 0}}{f _{y}})^{2} \leq 1$ . Applied at the lug base section extreme fibre.
DNV-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 $3 < SHL \leq 100$ t: onshore $1.10$ , inshore $1.07 + 0.05 100/ SHL$ , offshore $1 + 0.25 100/ SHL$ ; 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-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 $SKL = 1.00$ 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-ST-N001 §16.8.3 (2018, amended 2020-01) · §16.8.3, Table 16-5 (consequence factors)
Consequence factor $γ_{c}$ 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).

Units

All internal calculation is in canonical SI (N, mm, MPa). Inputs and results display in SI or US customary via the calculator's unit toggle; the engine result is identical in both systems.

Scope

This calculator covers single-plate lugs under in-plane loading. Out-of-plane loading, fatigue beyond the BTH-1 service-class derating, multi-plate cheek-plate lugs, and geometries that trigger the built-in scope flags are outside v1. The calculator surfaces these as warnings in the UI and on the report, and recommends FEA where appropriate.

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