Standards strategy.

Classical identities — no code-specific partial factors or allowables. Used as cross-checks and for the demo / preview mode.

• Mechanics 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.
  id: MECH_NET_SECTION
• Mechanics 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.
  id: MECH_DOUBLE_SHEAR_OUT
• Mechanics 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.
  id: MECH_BEARING
• Mechanics 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.
  id: MECH_PIN_SHEAR
• Mechanics 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.
  id: MECH_FILLET_WELD_THROAT
• Mechanics 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 ${\tau }_{\text{allow}}\sqrt{3}$).
  id: MECH_FILLET_WELD_VM

Pinned-connection static strength (§3-3.3) and fillet-weld allowable (§3-3.4.3) extended to a combined-stress interpretation, with design factor Nd (§3-1.3) and service-class bearing reduction (§3-1.4). The weld check consumes the angle-aware root components f_z = N/A_w + M/S_w and f_v = V/A_w.

• 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 $b_{\mathrm{eff}}=\min \left(4t,0.6b_e\sqrt{\frac{F_u{D}_h}{F_y{b}_e}}\right)$. Allowable includes design factor $N_d$ per §3-1.3.
  id: BTH1_NET_TENSION
• ASME BTH-1-2020 §3-3.3.2
  2020 · §3-3.3.2 (eq 3-49)
  Single-plane fracture strength of the plate beyond the pin hole.
  id: BTH1_FRACTURE
• ASME BTH-1-2020 §3-3.3.3
  2020 · §3-3.3.3 (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 $P_v=\frac{0.70F_u{A}_v}{1.20N_d}$.
  id: BTH1_SHEAR_OUT
• 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 $\frac{1.25F_y}{N_d}$; rotating (Service Class $\ge 1$) reduced to $\frac{0.63F_y}{N_d}$.
  id: BTH1_BEARING
• ASME BTH-1-2020 §3-3.4.3
  2020 · §3-3.4.3 (eq 3-55)
  Allowable fillet-weld shear on the effective throat $F_v=\frac{0.60F_{EXX}}{1.20N_d}$. 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.
  id: BTH1_WELD
• 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.
  id: BTH1_DESIGN_FACTOR

Pin connection geometry (Table 3.9) and resistances (Table 3.10): pin shear, plate/pin bearing, and — when the shackle fork geometry (inside jaw width W and jaw thickness a) is entered — pin bending plus the combined shear+bending interaction per Figure 3.11. Weld group analysis: §4.5.3.2 directional method and §4.5.3.3 simplified method, with β_w taken from Table 4.1 and γ_M2 from §2.2.

• 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: $\sqrt{{\sigma }_{\perp }^2+3({\tau }_{\perp }^2+{\tau }_{\parallel }^2)}\le \frac{f_u}{{\beta }_w{\gamma }_{M2}}$ 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.
  id: EC3_WELD_DIRECTIONAL
• 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: $F_{w,Ed}\le F_{w,Rd}=f_{vw,d}a$ with $f_{vw,d}=\frac{f_u/\sqrt{3}}{{\beta }_w{\gamma }_{M2}}$. Conservative relative to the directional method; shown as a cross-check.
  id: EC3_WELD_SIMPLIFIED
• EN 1993-1-8:2005 §3.13.1
  2005 · §3.13.1, Table 3.9
  Geometric requirements for pin-connected plates: minimum plate thickness, minimum distances $a$ and $c$ from hole centre to plate edges as functions of $F_y$, ${\gamma }_{M0}$, and $d_0$.
  id: EC3_PIN_GEOMETRY
• EN 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.
  id: EC3_PIN_SHEAR
• EN 1993-1-8:2005 §3.13.2
  2005 · §3.13.2, Table 3.10 (bearing)
  Pin/plate bearing resistance: $F_{b,\mathrm{Rd}}=\frac{1.5td{f}_y}{{\gamma }_{M0}}$.
  id: EC3_PLATE_BEARING
• EN 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 $c$).
  id: EC3_PIN_BENDING
• 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: ${\left(\frac{M_{\mathrm{Ed}}}{M_{\mathrm{Rd}}}\right)}^2+{\left(\frac{V_{\mathrm{Ed}}}{F_{v,\mathrm{Rd}}}\right)}^2\le 1$. Gated on the same shackle fork geometry as the pin-bending check.
  id: EC3_PIN_COMBINED

Lifting operations: dynamic amplification factor (DAF) and skew-load factor (SKL) from Section 16. Applied with the user dynamic factor on the demand side of every resistance check — pin, plate and weld — when the DNV methodology is selected.

• DNV-ST-N001 §16
  2020-01 · Section 16 (lifting)
  Dynamic amplification factor applied to the static rigging load. Values depend on lift weight and environment category (onshore light / standard / heavy; offshore sheltered / open sea). Defaults below are starting values — user must confirm against the project-specific clause.
  id: DNV_N001_DAF
• DNV-ST-N001 §16
  2020-01 · Section 16 (lifting)
  Skew-load factor for multi-sling lifts. Single-lug padeyes receive only the SKL multiplier on the sling force; governing SKL redistribution applies to multi-point rigging.
  id: DNV_N001_SKEW

Fillet-weld nominal strength per §J2.4 with the directional strength increase $(1+0.5{\sin }^{1.5}\theta )$ and ASD safety factor $\Omega =2.0$. Shares the electrode classification $F_{EXX}$ with the BTH-1 weld check.

• AISC 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.
  id: AISC_WELD_J24

AWS A2.4 weld symbols used on the schematic: fillet leg $s$ on the symbol arrow, weld-all-around circle for closed-perimeter groups, and throat $a=0.707s$ shown on the side view.

• 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.
  id: AWS_A24_SYMBOLS