ON MICHELL TRUSSES

A modification of Michell's problem1 is formulated. This concerns the minimum-weight design of a truss T that transmits a given load to a given rigid foundation with the requirement that the axial stresses in the bars of the truss stay within an allowable range. It is then shown that the truss T cannot be less stiff in the elastic range or in stationary creep than any other truss that uses the same amount of material and respects the same allowable range of axial stress. Finally, it is shown that a truss of minimum weight that supports given point masses from the given rigid foundation and has a given fundamental natural frequency has the same layout as the truss T but, in general, different cross-sectional areas. © 1969.