Oszacowanie Krzywej Nośności Granicznej przy Jednoczesnym Skręcaniu z Rozciąganiem

Making use of the variational theorems of plasticity a general method is given for the determination of the upper and lower bound of the limit curve in the (Ms, N)– plane of external loads where Ms is the torque and N- the longitudinal force (tensile or compressive). The method de- scribed can be used for investigating the limit load (Ms, N) of bars of any cross section.
The first part of the paper is devoted to the determination of a certain scheme of statically admissible stresses σij approaching the real stress distribution as well as possible. For this purpose the Nádai roof analogy is made use of [12]. Similarly, the system of inematically admissible dis- placements described in the second part of the paper is valid for any form of the cross-section and enables us to find the upper bound of the limit curve f(Ms, N) = 0. In the two particular cases 1) of pure torsion and 2) of pure tension the upper and lower bound thus found coincide with the accurate values. For any load combination (Ms, N) they enable us to obtain an estimate of the correctness of the known approximations, [18], to the accurate solution (the accurate solution of the problem of limit load of a bar subject to combined tension and torsion has not yet been found).
To illustrate the methods described based on the variational theorems, the case of a square bar is solved effectively thus finding by means of Hermitian interpolation the full equation of the lower and the upper bound of the limit curve in the (Ms, N)-plane. Finally (cf. Fig. 7) the results of the present paper are used to estimate the accuracy of the solution of the problem given in [18].