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at all points of the cross section and the condition ,1 dy J TsWe prove now that (4) at all points of the boundary curve, c is a constant of integration, ds is an element of the boundary curve. F is the load assumed to act vertically on a horizontal cantilever beam. The natural requirement of bending by transversal vertical force is that the resultant moment due to horizontal shear stresses is zero. In this case the resultant of the shear stresses over the cross section is equal to the transversal force which is the actual load applied at the end of the beam. Analytically expressed, this requirement isWe make use now of the condition (5) and proceed to determine the position of the center of flexure. Since we have already ffr yz dxdy = 0 (6) the resultant shear stresses are in the vertical plane only and satisfy the condition of bending by the vertical transverse load. If for any value of the arbitrary constant c the condition (5) is not fulfilled, we introduce torsional stresses = +Gr ; ,. --Or* (7) where the stress function } • --+**>** where ^2 is defined by (17). ConclusionAs we see from Eqs. (20) and (17), the center of flexure is independent from Poisson's ratio.

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