12.3 Fillet and Groove Weld Sizing under Direct Stress in ASD and LRFD

12.2 Static Sizing of Fillet, Groove & Plug Welds under Direct Stress

Quick Answer: Under AISC 360 and AWS D1.1, fillet welds are designed assuming failure occurs by pure shear across the effective throat ($t_e = 0.7071 w$ for $90^\circ$ equal-leg fillets). In Load and Resistance Factor Design (LRFD), the design shear strength is $\phi R_n = \phi (0.60 F_{EXX}) t_e L$ with $\phi = 0.75$. In Allowable Stress Design (ASD), the allowable strength is $R_n / \Omega = (0.60 F_{EXX} / 2.00) t_e L = 0.30 F_{EXX} t_e L$ (which equals $21.0\text{ ksi}$ or $144.8\text{ MPa}$ for an E70 electrode). When a fillet weld is loaded transversely ($\theta = 90^\circ$), an empirical directional multiplier $[1.0 + 0.50 \sin^{1.5}(\theta)]$ boosts capacity by $50%$. CJP groove welds share the allowable stress of the parent metal, while PJP groove welds require a $3\text{ mm}$ ($1/8\text{ in}$) throat deduction when welded at $45^\circ$ with SMAW.

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Fillet Weld Mechanics and Geometric Throat Definitions

A fillet weld joins two intersecting surfaces at approximately $90^\circ$ (or skewed dihedral angles) by depositing a bead of triangular cross-section. Sizing is governed by the geometry of the largest inscribed right triangle.

                              |\
                              | \  Convexity (C)
                              |  \---_
                              |   \   `\
                              |    \    \
                    Leg (w)   | t_e \    | Actual Face
                              |      \  /
                              |       \/
                              +--------+-----------------
                                  w
                              |<----->| Leg Length (w)

Mathematical Throat Definitions

• Leg Length ($w$): The distance from the joint root to the toe of the fillet weld along the fusion face.
• Theoretical Throat ($t_t$): The perpendicular distance from the joint root to the hypotenuse of the largest right triangle that can be inscribed inside the fillet weld cross-section. For an orthogonal $90^\circ$ joint with equal legs ($w_1 = w_2 = w$): $t_t = w \cdot \cos(45^\circ) = w \cdot \sin(45^\circ) = \frac{w}{\sqrt{2}} \approx 0.7071 w$ For an unequal-leg fillet weld ($w_1 \ne w_2$): $t_t = \frac{w_1 \cdot w_2}{\sqrt{w_1^2 + w_2^2}}$
• Effective Throat ($t_e$): The minimum distance from the joint root to the weld face, minus any convexity. Under standard processes (SMAW, GMAW, FCAW), $t_e = t_t = 0.7071 w$.
• Deep Penetration Credit (Submerged Arc Welding): Because Submerged Arc Welding (SAW) utilizes high current densities with deep plasma gouging, AWS D1.1 Clause 4.4.2 permits deep penetration credit:
  • For leg size $w \le 9.5\text{ mm}$ ($3/8\text{ in}$): $t_e = w$.
  • For leg size $w > 9.5\text{ mm}$: $t_e = 0.7071 w + 2.8\text{ mm}$ ($0.11\text{ in}$).
• Actual Throat ($t_a$): The shortest distance from the joint root to the actual exterior face of the weld: $t_a = t_t + C$, where $C$ is surface convexity.

Convexity Limits (AWS D1.1 Table 7.8, Weld Profiles)

Excessive convexity creates a sharp notch at the weld toes, producing stress concentrations that cause premature fatigue cracking. AWS D1.1 Table 5.8 restricts convexity ($C$) based on measured face width ($W$):

Governing Mechanical Principle: Regardless of whether the applied external force is tension, compression, or shear, structural codes assume that all fillet welds fail in pure shear on the effective throat plane. The shear area is defined as $A_w = t_e \cdot L = 0.7071 w \cdot L$.

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Longitudinal vs. Transverse Fillet Welds & The Directional Strength Factor

When a fillet weld group is loaded at an angle $\theta$ relative to its longitudinal axis, its ultimate shear capacity and deformation behavior vary dramatically.

       LONGITUDINAL FILLET (θ = 0°)              TRANSVERSE FILLET (θ = 90°)
              Load: P                                    Load: P
                 ^                                          ^
                 |                                          |
        +--------+--------+                        +--------+--------+
        |  [ WELD BEAD ]  |                        |=================| [WELD BEAD]
        |                 |                        |                 |
        +-----------------+                        +-----------------+
         Shear Parallel to Weld                     Shear & Tension Normal to Throat

AISC 360-16 Directional Factor Formulation

Under AISC 360-16 Specification Section J2.4, the nominal shear stress of a fillet weld ($F_{nw}$) is modified by the load angle $\theta$ (where $\theta = 0^\circ$ for longitudinal shear and $\theta = 90^\circ$ for transverse shear):

$F_{nw} = 0.60 F_{EXX} \left[ 1.0 + 0.50 \sin^{1.5}(\theta) \right]$

• Longitudinal Welds ($\theta = 0^\circ$): $\sin(0^\circ) = 0 \implies F_{nw} = 0.60 F_{EXX} [1.0] = 0.60 F_{EXX}$
• Transverse Welds ($\theta = 90^\circ$): $\sin(90^\circ) = 1.0 \implies F_{nw} = 0.60 F_{EXX} [1.0 + 0.50(1.0)^{1.5}] = 1.50 \times (0.60 F_{EXX}) = 0.90 F_{EXX}$

A pure transverse fillet weld exhibits $50%$ greater nominal strength than an identical longitudinal fillet weld. This strength enhancement arises from the complex triaxial stress state across the inclined throat plane, which combines normal tensile stresses with shear stresses.

The Strength-Ductility Trade-off

While transverse welds are 50% stronger, they exhibit significantly lower deformation capacity (ductility) than longitudinal welds:

• Longitudinal fillet weld fracture strain: $\Delta_u \approx 0.17 w$ to $0.30 w$ (high ductility, extensive plastic yield plateau).
• Transverse fillet weld fracture strain: $\Delta_u \approx 0.05 w$ to $0.10 w$ (brittle-like rupture with minimal plastic deformation).

    Stress (F_nw)
      ^
      |             /--- Transverse (θ = 90°): Peak = 1.50 F_0, Brittle Fracture at Δu ≈ 0.05 w
 1.50 |            / \
      |           /   \
 1.00 |          /     \___________ Longitudinal (θ = 0°): Peak = 1.0 F_0, Ductile Plateau to Δu ≈ 0.20 w
      |         /                  \
      |        /                    \
      +-------+----------------------+---------------------> Deformation (Δ)
              Δ_u(90°)               Δ_u(0°)

Combining Longitudinal and Transverse Fillets (AISC J2.4)

Because transverse welds fail at small deformations before longitudinal welds reach their peak plastic strength, directly adding unreduced peak capacities ($R_n = 1.0 R_{nw-\text{long}} + 1.5 R_{nw-\text{trans}}$) is physically non-conservative. AISC 360 Section J2.4 mandates that the nominal strength of a combined weld group be taken as the greater of:

$R_n = R_{nwl} + R_{nwt} \quad \text{(Equation J2-10a, using basic unamplified } 0.60 F_{EXX} \text{ for both)}$ $R_n=0.85 R_{nwl} + 1.5 R_{nwt} \quad \text{(Equation J2-10b, pairing amplified transverse with 85\% longitudinal)}$

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Allowable Stress Design (ASD) vs. Load & Resistance Factor Design (LRFD)

Structural sizing must adhere strictly to either ASD or LRFD design methodologies per AISC 360 and AWS D1.1 Clause 4.

Sizing Matrix for Fillet Welds

Base Metal Strength Limits (AISC J2.4)

The strength of the connection is the minimum of the weld metal strength and the adjacent base metal strength evaluated along the fusion boundary:

1. Base Metal Shear Yielding (gross area $A_{gv}$):
   • LRFD: $\phi R_n = 1.00 \times (0.60 F_y A_{gv})$
   • ASD: $R_n / \Omega = \frac{0.60 F_y A_{gv}}{1.50} = 0.40 F_y A_{gv}$
2. Base Metal Shear Rupture (net area $A_{nv}$):
   • LRFD: $\phi R_n = 0.75 \times (0.60 F_u A_{nv}) = 0.45 F_u A_{nv}$
   • ASD: $R_n / \Omega = \frac{0.60 F_u A_{nv}}{2.00} = 0.30 F_u A_{nv}$

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Filler Metal Matching Relationships (AWS D1.1 Table 5.4)

Selecting filler metal strength relative to the base metal yield and tensile strength governs failure modes, preheat requirements, and cracking susceptibility.

Matching Categories

     UNDERMATCHED                 MATCHED                     OVERMATCHED
  [F_EXX < F_u,base]        [F_EXX ≈ F_u,base]             [F_EXX > F_u,base]
   Plastic strain in          Uniform plastic               Plastic strain forced
   weld; high ductility;      deformation across            into base metal HAZ;
   prevents HAZ cracks.       joint assembly.               brittle cleavage risk.

• Matching Filler Metal (Standard): The electrode tensile strength matches the specified minimum tensile strength of the base metal (e.g., AWS A5.1 E7018 with ASTM A36, A572 Gr 50, or A992 steel). Mandated for Complete Joint Penetration (CJP) groove welds transferring full tension.
• Undermatching Filler Metal: The electrode tensile strength is intentionally lower than that of the base metal (e.g., using E7018 filler metal on ASTM A514 $100\text{ ksi}$ quenched and tempered plate). Highly recommended for fillet welds and PJP groove welds in high-strength steels. The softer weld metal yields plastically to relieve severe thermal shrinkage strains, preventing hydrogen-induced cold cracking in the high-hardenability heat-affected zone (HAZ).
• Overmatching Filler Metal: The electrode strength exceeds that of the base metal (e.g., depositing E9018 on ASTM A36). Overmatching is generally discouraged in structural engineering. Under severe overload, the ultra-strong weld deposit refuses to yield, forcing plastic strain localization into the narrow, notch-sensitive HAZ coarse-grained region, which dramatically increases the risk of catastrophic brittle fracture.

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Groove Welds: CJP vs. PJP Sizing Rules

1. Complete Joint Penetration (CJP) Groove Welds

Under AWS D1.1 Clause 4.4 and AISC 360 Section J2.1:

• Effective Area ($A_e$): Equal to the plate thickness multiplied by the weld length: $A_e = t \cdot L$.
• Tensile or Compressive Stress Normal to Effective Area: The design/allowable stress of a CJP weld using matching filler metal equals the base metal design/allowable stress: $\text{LRFD: } \phi R_n = \phi F_y A_e \quad (\phi = 0.90) \quad \text{or} \quad \phi F_u A_e \quad (\phi = 0.75)$ $\text{ASD: } F_{\text{allow}} = 0.60 F_y \quad \text{or} \quad 0.50 F_u$
• Engineering Rule: CJP groove welds with matching electrodes are $100%$ efficient; calculations of weld metal throat stress under direct tension or compression are unnecessary because the base metal will yield before the weld fails.

2. Partial Joint Penetration (PJP) Groove Welds

PJP welds do not penetrate the entire joint thickness. The effective throat ($E$) is a function of joint preparation angle and process.

AWS D1.1 Clause 5.4 / Table 5.5 Effective Throat Deduction Rules

         60° GROOVE ANGLE                          45° GROOVE ANGLE (SMAW)
           (Full Credit)                            (3 mm / 1/8-in Deduction)
               \ 60° /                                    \ 45° /
                \   /                                      \   /
                 \ /                                        \ /   <-- S
     =============+=============                =============+=============    |
     E = S                                      E = S - 3 mm                  V E
     (Depth of bevel equals                     (Arc cannot reach root apex;
      effective throat)                          unfused gap forms)

• Groove Angle $\ge 60^\circ$: Effective throat equals the depth of bevel preparation ($E = S$) for all processes (SMAW, GMAW, FCAW, SAW).
• Groove Angle $= 45^\circ$: When manual Shielded Metal Arc Welding (SMAW) or self-shielded flux-cored arc welding (FCAW-S) is used without backing, the manual rod diameter prevents full penetration to the root apex. AWS D1.1 mandates a $3\text{ mm}$ ($1/8\text{ in}$) deduction: $E = S - 3\text{ mm} \quad (E = S - 1/8\text{ in})$
• For Gas Metal Arc Welding (GMAW) or Gas-Shielded Flux Cored (FCAW-G) in $45^\circ$ grooves, full credit ($E = S$) is permitted provided the process is qualified in the flat or horizontal position.

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