Figure P3.15 shows a thin cantilever beam of unit thickness carrying a uniform load of intensity p per unit length. Assume that the stress function is expressed by

In which a, ? e are constant. Determine (a) the requirements on a, ?, e so that ? is biharmonic; (b) the stresses ? _x , ? _y , and ? _xy .

Figure p3.15

$ = ax + bxy + cy + dy + exy YA h ht k - - X