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The Quarterly Journal of Mechanics and Applied Mathematics 1959 12(3):314-324; doi:10.1093/qjmam/12.3.314
© 1959 by Oxford University Press
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ON THE ABSOLUTE MINIMUM WEIGHT DESIGN OF FRAMED STRUCTURES{dagger}

JACQUES HEYMAN{ddagger}

( (Engineering Laboratories, Cambridge University)
{ddagger} Fellow of Peterhouse, Lecturer in Engineering, University of Cambridge. Visiting Professor, Brown University, 1957–8. )

If the cross-section of the members of a frame is varied continuously so that the ‘strength’ of the frame follows the bending moment diagram, then, provided the design is carried out in a certain way, the frame will have absolute minimum material consumption. This theorem is proved separately here, although for plastic design the theorem is a special case of the general principles given by Drucker and Shield (1, 2). However, this special theorem applies equally well to certain completely elastic structures.

The theorem is applied to determine the minimum weight of some simple continuous beam systems, and a trial and error ‘relaxation’ technique is developed. These designs are compared with more practical designs in which the cross-section of the members varies discontinuously.


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