Fillet Weld Strength Calculator

The elastic weld-line method uses uniform, equal-leg fillets at a 90° joint. Effective throat $a=0.707w$ and area $A_w=aL_w$. Integrate each straight segment exactly to obtain centroid coordinates, line second moments $I_{xu}=\int y^2\,dl$, $I_{yu}=\int x^2\,dl$, product $I_{xyu}=\int xy\,dl$ and $J_u=I_{xu}+I_{yu}$. Coordinates are relative to the centroid; line properties have units of mm³. Throat properties are the line properties multiplied by $a$.

Resolve $F_x=P\cos\alpha$, $F_y=P\sin\alpha$ and $F_z=N_z$. Include eccentricity once:

The force demand per unit length is

For bending use $q_z=F_z/L_w+k_xx+k_yy$. Obtain the two gradients from equilibrium:

A single straight line uses only its supported bending direction. The resultant is $q_r=\sqrt{q_x^2+q_y^2+q_z^2}$ and throat stress is $q_r/a$. Demand is affine along each segment, so its norm is convex: checking both endpoints finds the exact maximum for this model. For the stress colors, sample each segment at 65 positions, interpolate its three force components and then take their resultant magnitude. The endpoint table may repeat a shared corner; length and area count each segment only once.

Use $F_{nw}=0.60F_{EXX}$ with $k_{ds}=1$: LRFD available stress $F_{av}=0.75F_{nw}$ or ASD $F_{av}=F_{nw}/2$. Utilization is $q_{max}/(aF_{av})$, and the unrounded strength leg is $q_{max}/(0.707F_{av})$.

Minimum leg follows AISC 360-22 Table J2.4, based on the thinner connected part. Maximum leg follows J2.2b(b) for ordinary welded edges without a specified full-throat exception. Choose the SI or US dimensional set separately from display units. The rounded required leg also respects the supported segment-length range; a result above the upper size limit requires a revised joint. See attached AISC pp. 194–196 and 198–200 (printed pp. 126–128 and 130–132). Force-distribution examples are checked against Structural Central and RoyMech; their different design-code strength factors are not substituted.

• Static loading, small deformation, rigid connected parts, uniform stiffness per unit weld length and identical filler strength on every segment.
• Equal legs meeting at 90°; no penetration credit or weld reinforcement included in the effective throat.
• Weld roots lie in the x–y plane. Loads are applied at the entered x and y offsets with no z offset. Additional moments use the right-hand sign convention. The schematic stress arrows show in-plane endpoint demand; the endpoint table also gives out-of-plane demand.
• The elastic equilibrium equations are derived here from line integrals. Product-of-inertia coupling is retained for asymmetric L groups.
• The maximum-leg screen assumes ordinary edge fillets. Use the smallest applicable edge thickness. Base material and the rest of the connection have been or will be checked separately.
• No directional strength increase: longitudinal and transverse segments are assessed with the same base weld-metal stress.
• SI and US detailing use the specification's respective rounded dimensional provisions; the viewer unit switch is only a conversion.

Scope: ANSI/AISC 360-22 (August 1, 2022), Sections J2.2 and J2.4; this calculator implements the weld-metal strength and listed size screens, not complete code compliance. Check against the standard in force, including applicable errata and project requirements.

Each segment must have full-size effective length from $4w$ to $100w$. For longer end-loaded welds, use the J2.2b(d) effective-length reduction in a separate analysis; do not treat the unmodified result here as adequate. Intermittent welds and their minimum segment lengths are excluded. A single vertical line cannot resist $M_y$ and a single horizontal line cannot resist $M_x$ in this line model.

The passing assessment covers only the entered static weld-metal load combination and leg limits. It does not verify base metal rupture, block shear, plate flexibility, effective attachment width, local bending, prying, buckling, load combinations, weldability, procedure qualification or inspection. No HSS effective-width check is included.

Fatigue needs a separate stress-range/detail-category assessment (AISC Appendix 3); a static utilization below one does not establish fatigue life. Seismic, impact, elevated-temperature and unequal-leg/skewed joints are outside this model. A qualified designer must verify the complete connection and its fabrication details.