ABSTRACT

This paper presents the theoretical fundaments, as well as the practical procedure to evaluate the complementary modes of Generalized Beam Theory (GBT) concerning the shear and transversal elongation energies of membrane’s behaviour in pipes and thin-walled hollow circular cross-sections. This study outgrows the classical assumptions of GBT, which impose no participation of shear and transversal elongation to membrane’s strain energy. Although recent developments already address this problem for both open and close segmented cross-sections, the solution for the case of thin-walled circular cross-section was still unsolved. As results, these complementary modes reach the following highlights: i) the complementary membrane shear deformations in GBT not only lead to Timoshenko Beam Theory for the lower bending modes, but also can express high order shear deformation in the respective GBT’s high modes; ii) the transversal elongation and the shear energies of membrane’s behaviour are coupled in each mode and also coupled with the other strain energies, such as plate’s bending and membrane’s longitudinal elongation, only by Poisson’s effect; iii) the introduction of these complementary modes in non-linear GBT analysis leads to the initial shear and transversal stress matrices. To illustrate the present procedure, an example applied in a gas pipeline system is carried out and its final results are compared with a full shell element model.