Theoretical analysis of moment-shear interaction in knee braced frames

In this paper the similarities between knee elements of knee braced (KB) frames and intermediate links of eccentrically braced frames are pointed out. In fact, as it is easy to recognize, for an assigned collapse mechanism of a KB-frame, due to the action of the diagonal, the knee element is divided into two parts, each one subjected at its ends to plastic deformations of different values, where moment-shear interaction mechanism is not always negligible. With reference to intermediate knees , where moment-shear interaction is significant, a procedure for calculating the ultimate resistances and the corresponding plastic deformations has been developed. In particular, two approaches have been followed. The first approach is based on the kinematic theorem of plastic collapse which suggests to impose, for each part of the knee and at both its ends, the yielding condition, the flow rule, the kinematic compatibility condition and the minimization of the internal work. Conversely, the second approach is based on the static theorem of plastic collapse, requiring the fulfilment of the yielding condition at each end and of the equilibrium equations. The resulting solutions are obviously coincident, validating the goodness of the theoretical analysis. Therefore, by means of the proposed procedure, the ultimate resistances and the plastic deformations of intermediate knees can be calculated. This allows to determine the knee internal work within a design methodology for KBFs proposed by the Authors in a companion paper.