Simplifications in Minimal Design of Frames

A new method of minimum volume design of frames with continuously varying cross-sectional area is introduced. It relies exclusively on statical considerations and does not involve kinematical concepts like the only previously known method, developed by Heyman. Both methods are still highly idealized; they neglect the effect of the axial force and assume sandwich behavior of the cross section (namely that the required area is proportional to the bending moment, as is approximately the case in wide-flange thin-web I sections). The statical method permits an easier recognition of the possible configurations of the minimal stresses, requiring only combinations of location of a number of points along the axis of the structure and not the evolvement of possible patterns of deformation. It leads to a greater number of linear equations than its predecessor and makes possible the detection of the case of optimal determinancy, defined for the first time in this paper, in which the minimal stress is obtained more easily than in the general case.