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Welding expert Duane Miller wrote an excellent pair of articles for the February and March 2024 issues of STRUCTURE Magazine. The articles described 10 conditions where welds can experience uneven loading. These conditions can be problematic if not avoided or given special attention in design. The common assumption that applied loads cause uniform stresses in a weld does not apply for these conditions. However, what if you are using a design approach that never makes such an assumption? Connection design by inelastic analysis, for example using the component-based finite element method (CBFEM) such as implemented in IDEA StatiCa Connection, makes no broad assumptions about the distribution of stress in welds, or any other components. Stresses arise naturally in the analysis based on the stiffness of the various components of the connection. This article walks through each of Miller’s 10 conditions to identify what special attention they require when designing by inelastic analysis.
In his 2024 STRUCTURE two-part series on unevenly loaded welds (February and March issues), author Duane Miller summarized the following common conditions encountered.
Condition 1: Unevenly Loaded Because of Bending About the Root of Fillet or PJP Groove Welds
Condition 2: Unevenly Loaded Because of a Single Transverse Weld in an End-Loaded Lap Joint
Condition 3: Unevenly Loaded Because of Short Spacing Between Transverse Welds in End-Loaded Connections
Condition 4: Unevenly Loaded Because of Shear Lag
Condition 5: Unevenly Loaded Because of a Long Weld in an End-Loaded Connection
Condition 6: Unevenly Loaded Because the Weld Group Is Unevenly Loaded
Condition 7: Unevenly Loaded Because the Weld Attaches a Rigid Member to a Flexible Member
Condition 8: Unevenly Loaded Because Transverse Welds Are Combined with Longitudinal Welds
Condition 9: Unevenly Loaded Because the Weld Is Part of a Tubular Connection
Condition 10: Unevenly Loaded Because Welds Are Combined With Bolts or Rivets
The first condition is uneven loading because of bending about the root of a fillet or PJP groove weld. The second condition is a single transverse weld in an end-loaded lap joint, where there is potential for uneven loading because of bending about the root if the deflection of the lapped parts is not sufficiently restrained. Modeling of welds varies in inelastic analysis approaches, but in the CBFEM, fillet welds and PJP groove welds are modeled using multi-point constraints and an equivalent weld shell element that approximates the elastoplastic behavior of the weld. An important aspect of this modeling approach is that it results in zero bending stiffness about the root of the weld. As a result, no bending stresses can develop and, for the details shown in Miller’s article, the analysis will not run because the lack of bending stiffness makes the model unstable. However, in some cases, the connection may not rely on the bending stiffness of the weld to be stable, and bending deformations about the root of a weld can develop. Bending deformations should be avoided by inspection of the deflected shape from the analysis model and proper detailing of the connection.
In the third condition, the uneven loading is due to short spacing between transverse welds in end-loaded connections. Using the CBFEM, the spacing has minimal effect on the strength of the welds. Consider the connection shown in Figure 1. Without geometric nonlinearity, the boundary conditions and eccentricity result in significant bending in the plates. Bending is reduced with geometric nonlinearity due to membrane effects, yet the short spacing has no effect on the welds. For very short spacing (e.g., overlap of 1/2 inch), the plates yield, limiting strength, but again the evaluation of the welds is not affected. Ealuating strength by inelastic analysis eliminates the need to check certain limit states captured by the model, but it does not eliminate the need to satisfy detailing requirements such as the requirement in AISC Specification Section J2.2b(f) which prescribes a minimum overlap distance.
Shear lag is the concern in the fourth condition. While shear lag exists in connections such as the end-loaded lap joint shown in Figure 2, whether shear lag affects the strength of the connection is unclear. CBFEM analyses do not detect any reduction in weld strength due to shear lag for this connection, but neither did a recent series of physical experiments conducted by the author. Nonetheless, just like for the third condition, American Welding Society (AWS) detailing requirements must be satisfied even when assessing strength using inelastic analysis. Specifically, AWS D1.1 Clause 4.9.2 specifies that the length of each fillet weld shall be no less than the perpendicular distance between them if longitudinal fillet welds are used alone in lap joints of end connections of flat bar or plate members.
Long welds in end-loaded connections experience uneven loading due to strain compatibility between the connected parts. The stress near the ends of the welds is greater than near the middle with the difference depending on the relative stiffness between the welds and the connected parts. In traditional design, this fifth condition of unevenly loaded weld is addressed by using a reduced effective length for long welds. In design by inelastic analysis, the stiffnesses of the welds and connected parts are modeled explicitly, and strain compatibility is enforced. Thus, the results more accurately capture the effect of uneven loading than the approximate equation. A comparison between the results from CBFEM analyses and traditional design is shown in Figure 3 based on a larger study.
The sixth condition is when the weld group is unevenly, or eccentrically, loaded. In traditional design, this condition is often addressed using the instantaneous center of rotation method via tables in Part 8 of the AISC Manual. The instantaneous center of rotation method is itself a nonlinear analysis method that ensures equilibrium and strain compatibility are satisfied while also incorporating the beneficial effect of the directional strength increase factor. Comparisons between the instantaneous center of rotation method and the CBFEM for bracket plate connections have shown that the CBFEM conservatively captures the uneven loading.
Conditions 7 through 10 feature multiple possible load paths, with uneven loading arising because some paths are stiffer or stronger than others. Design by inelastic analysis is well suited to properly evaluate these conditions because the stiffness of all components is modeled explicitly and strain compatibility and equilibrium are enforced.
Welding a rigid member to a flexible member is the seventh condition. A plate under tension welded across the flange of an I-shaped section such as shown in Figure 4 is a classic example of Condition 7. The weld between the plate and the flange is unevenly loaded because a greater portion of the load is attracted to the stiffer path directly through the flange and into the web. When modeled using the CBFEM, the weld stresses are highest at the web of the I-shaped member. These welds reach their full utilization first, signaling that the strength of the connection has been reached, even when the portions of the weld near the flange tips are not at their full capacity. The ninth condition, welds that are part of a tubular connection, is another example of welding a rigid member to a flexible member. Again, the CBFEM is able to pick up the uneven loading and compute the utilization of the welds accordingly.
In the eighth condition, transverse welds are combined with longitudinal welds and uneven loading occurs because welded connection with transverse welds are stronger but less ductile than similar connections made with longitudinal welds. The AISC Specification provides Equation J2-6 for concentrically loaded weld groups such as this. Even without implementation of this equation, the CBFEM captures the effect well since the underlying behavior is modeled and incorporated in the strength checks (Fig. 5).
The tenth and final condition of uneven loading occurs when welds are combined with bolts or rivets. AISC Specification Section J1.8 allows bolts and welds to be considered as sharing load only in the design of shear connections on a common faying surface where strain compatibility between the bolts and welds is considered. Strength checks for bolts and welds are independent in the CBFEM with no special handling of when bolts and welds share load. Given the explicit modeling of the stiffness of bolts, welds, members, and connecting elements, strain compatibility is always considered in the CBFEM. When bolts and welds share load, the required strength of each is based on their relative stiffness. The result is overall strengths that are similar to those obtained using the approximate method also presented in AISC Specification Section J1.8. However, the CBFEM generally does not prohibit sharing of loads between bolts and welds in tension connections. The user must avoid cases such as this by modeling either bolts or welds in tension connections, even if both are present in the physical connection.
Unevenly loaded welds such as evaluated in Miller’s original articles and revisited here deserve special attention because they can be less efficient than evenly loaded welds and because they violate common assumptions in traditional design approaches. Design by inelastic analysis provides a path forward for these welds because well-defined analysis models never assume that welds are evenly loaded. Furthermore, inelastic analysis can be used to identify if action is needed to mitigate the effects of uneven loading, and, where necessary, help determine the best mitigation strategy. ■
About the Author
Mark Denavit is an associate professor in the Department of Civil and Environmental Engineering at the University of Tennessee, Knoxville.
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