If I understood your description correctly, the structure is something like this (ignore the dimensions and loads themselves, they're simply representative of the relative values. Also, I didn't apply the self-weight, which can be applied as a simple uniform load along all the members):
This being the case, your structure is going to present all of the classic forces (axial force on the column and diagonal, shear and bending on all elements other than the diagonal). In this purely fictitious example, here are the normal, shear and bending diagrams, as well as the deformed configuration:
Knowing the forces, one can easily obtain the stresses and strains (via linear elastic theory) and compare them to the beam strength and code requirements (also, make sure you have the correct code. Many times specific structures have specific codes, so a standard "steel" code may not be sufficient for a davit). Depending on the flexibility of the structure, a second-order analysis may be necessary. This may very well be the case for a davit.
All figures were created with Ftool, a free 2D frame analysis program.