Issue 41

R. M. De Salvo, Frattura ed Integrità Strutturale, 41 (2017) 350-355; DOI: 10.3221/IGF-ESIS.41.46 354 For the concordance on verses, each one of these sums must have a verse concordant to the corresponding plastic moment and this implies that, for each plastic hinge, their product must be always not negative. This condition implies that the following inequalities must be satisfied: Each one of these conditions furnishes a lower limit for the parameter  . By selecting, among these, the greatest value, that is  =0.0938*M p l/EI, all the inequalities associated to the seven plastic hinges characterizing the collapse kinematics are simultaneously satisfied. Therefore, by substitution into the expressions of the above sums of rotations, the complete picture of all rotations is obtained. These are depicted in fig. 5 together with the diagram of bending moments at collapse. Remind is made that rotations are expressed less than the factor M p l/EI. The analysis of the result, as obvious, highlights everywhere the concordance in verses between plastic moments and rotations at correspondent hinges. It is also to be noted that, in the case under study, the last hinges are two, namely at the middle section E of the left beam and at the head section 3 of the central pillar. For a better understanding these have been individualized through a white circle. The procedure ends here, once the two plastic hinges have been found together with the rotations of other hinges and displacements, at an instant just before the collapse. Regarding, it has been considered appropriate to perform some checks. In particular, the structure has been separately solved by applying the rotation method under three hypotheses: last hinge at section E, last hinge at the head section 3 of the central pillar; last hinges simultaneously at the two positions. In all the three cases the result coincided with that one above reported. Figure 5 : Collapse kinematic mechanism.