Probabilistic analysis of the Stussi-Kollbrunner paradox

Probabilistic analysis of the Stussi-Kollbrunner paradox

Waarts, P.
Vrouwenvelder, A.

Civil Engineering and Geosciences

1997-01-01

In most text books on Plasticity Theory a reference is made to the famous tests performed by Stiissi and Kollbrunner in 1935. The test object was a continuous beam on four supports, loaded by a concentrated point load halfway the central span. According to a straight forward application of the theory of plasticity the load carrying capacity of this beam is independent of the length of the outer spans. However, if the length of the outer span approaches infinity, the stiffness of the outer beam parts goes to zero. The centre span is then to be considered as a simply supported beam, having only half the load carrying capacity of the continuous beam. As usual, such a paradox can only be solved by using a more advanced theory, including both elastic and plastic deformations, as well as the real stress strain relationship. This of course has been done in the past successfully and the theoretical results were confirmed by tests. The present paper intends to reconsider this problem, however including also the random nature of the material properties. This wayan adequate approach to the reliability aspects of the problem can be achieved. Such an approach is considered especially useful for high strength steel and concrete materials that are used nowadays. For these materials aspects of deformation capacity become more and more important. Apart from some simplified calculations, the numerical results in this paper have been attained using a special purpose computer program that combines the standard Finite Element Method and First Order Reliability Methods. Some attendance will be given to the possibilities and limitations of the present program and the techniques that are used to reduce the computation time.

reliability
rotation capacity
plasticity
steel structure

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Delft University of Technology

0046-7316

HERON, 42 (3), 1977

Institutional Repository

journal article

(c) 1997 The Authors