Calculation of Stress Trajectories Using Fracture Mechanics

In structures composed of plates and plate-like elements subjected to in-plane stresses, the stress flow around discontinuities is an important design consideration. Stress dispersion angles are used extensively in gusset plate design and calculations for web local yielding of wide flange members. The current design values are empirical, and the variables affecting the dispersion angles are not well understood. Due to the wide range of angles published in the literature, an analytical model that accounts for all variables is necessary for full understanding of the behavior of these elements. Using fracture mechanics principles, this paper shows that the dispersion angle is dependent on geometry, constraint and inelastic deformation capacity. A versatile design procedure, which explicitly accounts for all variables affecting the stress dispersion angle, is presented.