It is a pleasure to reply to someone who asks clear questions and provides sufficient detail in the post including geometry images.
Evaluation of the stress in a structure to determine a Safety Factor on Yield or Fatigue is rarely done on a beam model because the idealization of the geometry hides the true peak stress. Even a shell model can have an inaccurate peak stress. Take your example of the Tee-intersection. The vertical part would be welded to the horizontal part. A full penetration weld can bond the full wall thickness and provide a weld bead on the outside edge that is not in the shell model. In that case, a solid model can include the material added by the weld bead which may be further shaped by grinding.
If you need to calculate the Equivalent Stress in a Beam model, you must do some hand calculations using beam equations to get the six components of stress at a point of interest. The beam tool will only give you axial stress and bending stress, which add together in the Combined Stress output, and that gives you one component of normal stress along the beam. You can request Beam Results and get one component of the shear stress.
Look at the horizontal beam in your beam model. That has a significant torsion load that creates a significant shear stress, but the shear stress from Beam Results does not capture this shear stress because it is on a different plane. You have to obtain the Reaction Moment on the Fixed Support, and use that along with the equation for shear stress in a beam under torsion to hand calculate that shear stress component.
Once you have all six components of stress (3 normal and 3 shear) use the Von Mises equation to get Equivalent Stress.
You can see why the initial evaluation of yield and fatigue safety factors would be done in a shell model which can calculate the Equivalent Stress and Safety Factor for you with no hand calculation. Depending on the location of the peak stress, a detailed solid model may be required.