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Roark & other formulas for stress and strain

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Roark's flat plate formulas don't have the following case; do you 
know of another reference that does?

A pipe is connected, via a bolted flange, to a square plate, centered 
on the pipe.  Pipe axis is normal to plane of plate.    Ratio 
of pipe diameter to side of square is 3/4.

Various axial, shear, bending, and torsional  loads applied to the 
cantilever, in various directions,  induce out-of-plane deformations 
in the plate.  The goal is to determine the  plate stresses and 
deflections (without FEA!)

Thanks in advance,

Dave Evans, P.E.