Gusset plates are used to strengthen the joints in various structures by distributing the stresses between the connected members. Typically, their design varies depending on the application. For example, in seismic design, they connect diagonal bracing to a structural frame by fixing orthogonal edges into corners of a beam column joint. This results in a non-uniform cross-sectional area along the gusset plate length, making it difficult to predict the distribution of stress in the plates. Among the various methods used in the design of gusset plates, the Whitmore width method developed in 1952 has been widely used. This method assumes a uniform distribution of force over an effective area and is commonly used to approximate the yielding area of gusset plates subjected to tension-induced stresses as well as those that do not buckle under compression.
Considering all the scenarios involved in the design of gusset plates, the feasibility of the Whitmore width method to accurately predict the yielding area for all gusset plates is questionable. In additional, international design codes provide equations for calculating the compressive strength of gusset plates based on their yielding capacity and slenderness. However, as these equations are based on the column buckling effects, they are only suitable for particular sizes of gusset plates. Additionally, even though compact and stiffened the gusset plate designs used in seismic systems can potentially reduce the local and global instabilities, the idea has not been widely accepted internationally, leading to a variety of different gusset plates in the market.
On this account, New Zealand researchers: Dr. Dan Court-Patience and Professor Mark Garnich from the University of Canterbury studied the yielding and buckling behavior in gusset plates using finite element modeling. Simulated testing with an initial imperfection and a monotonic uniaxial load was carried out. They predicted the critical buckling load, the elastic buckling strength, and the initial yield area of 184 different gusset plates with bolted connections. Specifically, the authors investigated the effects of various design parameters like the shape and thickness of the gusset plates. FEA predictions were also compared to those obtained via current design methods.
Results showed that the initial yielding area predicted by the FEA, especially those with larger connections, was non-conservative with that obtained through the Whitmore width method. Moreover, the authors observed that the Whitmore width method could effectively eliminate non-conservative predictions when the load dispersion angle was changed from 30 to 15°. Maintaining an angle of 15° also enabled the accurate computation of the section capacity in tension. Consequently, the elastic buckling length predicted by the Thornton method, particularly those of stocky gusset plates, was also inconsistent with the FEA.
When designing a gusset plate in compression, in most cases both the Thornton and NZS3404 method were found to be conservative when compared to FEA results. However, the level of safety is inconsistent and varies from being un-conservative in a few cases to providing a factor of safety of 32+ in some cases. To improve upon these gusset plate design methods, modifications to the Thornton method, based on curve fitting FEA results are proposed. In addition, the modifications to the existing methods, including adjusting the buckling curve’s maximum yield and elastic section, accommodated the gusset plate behaviors, thus improving the design process. The original research article is now published in the Journal of Constructional Steel Research.
In summary, the study investigated the effects of various geometric features on the yielding and buckling behaviors of gusset plates using finite element analysis (FEA). The choice of the FEA was influenced by the complicated nature of the stress-strain behaviors of such plates. Results demonstrated the unique features of the gusset plates. Modifying the Thornton method based on the FEA resulted in a new prediction method with desirable compressive strength curves and yield area for gusset plates. According to the FEA predictions, the modifications improved the safety and accuracy in the gusset plates design without complicating the design process. In a statement to Advances in Engineering, Professor Garnich explained their study will advance the design of gusset plates for various applications.
Court-Patience, D., & Garnich, M. (2021). Buckling analysis of gusset plates with bolted connections using finite element modeling. Journal of Constructional Steel Research, 176, 106420.