Journal of Optimization Theory and Applications

, Volume 23, Issue 1, pp 111–117 | Cite as

Optimal layout of cantilever trusses

  • W. Prager
Contributed Papers


For given allowable stress, Michell (Ref. 1) has investigated the optimal design of a cantilever truss that is to transmit a given load to two given fixed points of support. Disregarding the weight of the connections between the bars, he found that the truss of minimum weight is a truss-like continuum with an infinity of joints, and with bars that are mostly of infinitesimal length. In the present paper, a finite number of joints is enforced by including in the structural weight, which is to be minimized, not only the weight of the bars but also the weight of their connections, which is assumed to be proportional to the number of joints. The concept of two adjoint trusses is introduced, each of which coincides with the Maxwell diagram of the other truss. Two adjoint trusses have the same weight, and an optimal truss is therefore self-adjoint. The optimal configurations of 6-joint and 11-joint cantilever trusses are discussed, and the range of the weight of the typical joint is determined for which the 6-joint truss is optimal.

Key Words

Cantilever truss self-adjoint truss optimal configuration optimal number of joints 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Michell, A. G. M.,The Limits of Economy in Frame-Structures, Philosophical Magazine, Series 6, Vol. 8, pp. 589–597, 1904.Google Scholar
  2. 2.
    Prager, W.,A Note on Discretized Michell Structures, Computer Methods in Applied Mechanics and Engineering, Vol. 3, pp. 349–355, 1974.Google Scholar
  3. 3.
    Parkes, E. W.,Joints in Optimum Frameworks, International Journal of Solids and Structures, Vol. 11, pp. 1017–1022, 1975.Google Scholar

Copyright information

© Plenum Publishing Corporation 1977

Authors and Affiliations

  • W. Prager
    • 1
  1. 1.Brown UniversityProvidence

Personalised recommendations