CSA S16:24 Fillet Weld Capacity — Verification Benchmark

Complete hand calculation of a fillet welded gusset plate connection to CSA S16:24, showing weld metal resistance with step-by-step derivation. Hand results compared against Steel Calculator WASM output.

PRELIMINARY — NOT FOR CONSTRUCTION. All results are for educational and reference use only. Must be independently verified by a licensed Professional Engineer (P.Eng.) before use in any project.

Problem Statement

Connection: Gusset plate welded to column flange with two longitudinal fillet welds Weld: 8mm fillet weld, E49XX electrode classification, 150mm length each side Base metal: 350W steel (Fy = 350 MPa, Fu = 450 MPa), 12mm gusset plate Loading: Purely longitudinal (theta = 0 degrees, i.e. load parallel to weld axis) Objective: Determine the factored weld resistance Vr per CSA S16:24 Clause 13.13.3

Weld and Material Properties

Property Value Source
Weld leg size, w 8 mm —
Weld throat, t_throat 0.707 * w = 5.656 mm Geometry
Electrode E49XX —
Electrode ultimate strength, Xu 490 MPa CSA S16 Table 7
Weld length per side, L 150 mm —
Number of weld lines 2 —
Total throat area, Aw 2 _ 5.656 _ 150 = 1,697 mm^2 —
Loading angle, theta 0 deg (longitudinal) —

Hand Calculation — CSA S16:24

Step 1: Weld Metal Resistance — Clause 13.13.3.1

The factored resistance of a fillet weld is:

Vr = 0.67 * phi_w * Aw * Xu * (1.00 + 0.50 * sin^1.5(theta))

where:

Step 2: Directional Strength Enhancement

For longitudinal loading (theta = 0 degrees):

sin(0 deg) = 0
sin^1.5(0) = 0
(1.00 + 0.50 * 0) = 1.00

No directional strength increase. For transverse loading (theta = 90 deg), the enhancement factor becomes (1.00 + 0.50 * 1) = 1.50, recognizing that fillet welds loaded perpendicularly to their axis are stronger (the weld throat is in combined shear + tension rather than pure shear).

Step 3: Factored Resistance

Vr = 0.67 * 0.67 * 1,697 * 490 * 1.00
   = 0.67 * 0.67 * 831,530
   = 0.67 * 557,125
   = 373,274 N
   = 373.3 kN

Step 4: Base Metal Check — Clause 13.13.2

The base metal adjacent to the weld must also be adequate. For a longitudinal fillet weld, the base metal shear resistance per unit length along the fusion face:

For gusset plate (Fu = 450 MPa):
Vr_base = 0.67 * phi * Am * Fu
where Am = fusion face area

Fusion length = 2 * 150 = 300 mm
Am per mm = t_gusset per unit length = 12 mm^2/mm
Fusion shear area = 2 lines * 150 * 12 = 3,600 mm^2

Vr_base = 0.67 * 0.67 * 3,600 * 450
        = 0.67 * 0.67 * 1,620,000
        = 0.67 * 1,085,400
        = 727,218 N
        = 727.2 kN

Weld metal (373.3 kN) governs over base metal (727.2 kN). The weld is the critical element.

Step 5: Unit Weld Strength Per mm

For design convenience, the factored resistance per mm of weld length is often used:

Vr_per_mm = Vr / (2 * L) = 373,300 / (2 * 150) = 1,244 N/mm = 1.244 kN/mm

For a required factored load Vf = 250 kN:

Required length L_req = Vf / (1.244 * 2) = 250 / 2.488 = 100.5 mm per side
Provided length = 150 mm > 100.5 mm  →  OK
Utilization = 250 / 373.3 = 0.670  →  PASS at 67.0%

WASM Output Comparison

The Steel Calculator WASM engine (CSA S16 region), run with identical inputs:

Quantity Hand Calculation WASM Output Difference
Weld throat (mm) 5.656 5.657 0.02%
Aw total (mm^2) 1,697 1,697 0.00%
Directional factor 1.00 1.00 0.00%
phi_w 0.67 0.67 Match
Vr weld (kN) 373.3 373.27 0.01%
Vr base metal (kN) 727.2 727.22 0.00%
Controlling mode Weld metal Weld metal Match
Vr per mm (kN/mm) 1.244 1.244 0.00%
Utilization 0.670 0.670 0.00%
Verdict PASS PASS Match

All 10 quantities match within 0.02%. The 0.02% throat difference is from rounding in the 0.707 factor (0.707106 multiply by 8 = 5.65685 vs 5.657 displayed).

Transverse Loading Sensitivity

For the same weld with purely transverse loading (theta = 90 deg):

Directional factor = 1.00 + 0.50 * sin^1.5(90) = 1.00 + 0.50 * 1.0 = 1.50
Vr_transverse = 0.67 * 0.67 * 1,697 * 490 * 1.50 = 559.9 kN

| Quantity | Hand Calc | WASM |
|----------|-----------|------|
| Directional factor | 1.50 | 1.50 |
| Vr (transverse, kN) | 559.9 | 559.90 |

The WASM engine correctly applies the 50% directional strength increase for transverse fillet welds per Clause 13.13.3.

Code References — CSA S16:24

Clause Title Application
13.13.2 Base metal adjacent to welds Base metal shear/tear resistance
13.13.3 Fillet weld metal Vr equation, phi_w = 0.67
13.13.3.1 Weld metal resistance formula Vr = 0.67phi_wAwXuk
13.13.3.2 Directional strength increase k = 1.00+0.50*sin^1.5(theta)
Table 7 Electrode strengths Xu = 490 MPa for E49XX
13.13.1 General welding requirements Scope, preheat, inspection
13.13.4 Minimum fillet weld size Based on thicker part joined

How to Reproduce

  1. Navigate to the Steel Calculator Welded Connection tool
  2. Select CSA S16:24 as the design code
  3. Configure: 8mm fillet weld, E49XX, 2 lines at 150mm each, longitudinal loading
  4. Enter applied load Vf = 250 kN
  5. Click Calculate — the WASM engine checks weld metal and base metal

The WASM engine also handles plug/slot welds (Clause 13.13.5), combined longitudinal-plus-transverse loading, and minimum weld sizing per Clause 13.13.4.

Why Verification Matters

Every calculation engine in Steel Calculator is verified against CISC (Canadian Institute of Steel Construction) handbook examples, the CISC Steel Design Guide series, and independent hand calculations. These public benchmark pages demonstrate algorithmic accuracy across all supported code frameworks.

See also: AISC Beam Verification, EN 1993 Column Verification, AS 4100 Bolt Verification, AISC Base Plate Verification.

Last verified: 2026-05-08. WASM version: core-wasm-v2 stage-5-connection-design. Tolerance standard: all quantities within 1.0% of hand calculation or published value. CSA S16:24 edition used for verification.

Disclaimer: This content is for educational purposes only. Results must be verified by a licensed professional engineer. Steel Calculator provides preliminary design tools — NOT a substitute for professional engineering judgment.