PURE BENDING OF BEAMS OF VARIABLE RECTANGULAR SECTION

A method is presented for the calculation of stresses and deflections of thin rectangular beams of arbitrary variable depth according to the theory of plane stress. The solution is obtained in the form of a series, the first term of which is identical with the strengthof-materials solution and the others represent the necessary correction to that theory. This correction is found to be small for thin beams and when certain conditions are satisfied by the ordinates and their span-wise derivatives of the upper and lower edges of the beam. The proper choice of the axis of non-uniform beam is discussed. Author