PSI - Issue 44

Mauro Mezzina et al. / Procedia Structural Integrity 44 (2023) 566–573 Author name / Structural Integrity Procedia 00 (2022) 000–000

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Fig. 2. a) "Bredt-like" torsional equilibrium in a building with box-like behavior; b) Beam segment; (c) "Bredt-like" torsional equilibrium in a thin-walled closed section. To determine the average tangential stresses , it should be noted that [Nunziante et al. (2010); Sollazzo and Marzano (1988)]: = = (1) Eq. (1) gives the mean value of tangential stress at chord b in the tube section: ( ) = 2 Ω ( ) = 2 ( ) (2) Eq. (2) is known as Bredt's first formula . The torsion angle can be derived using the principle of Virtual Works, which gives: = 4 Ω 2 � 1 ( ) = 4 Ω 2 � (3) Eq. (3) is known as Bredt's second formula (the second expression is related to a rectangular section consisting of several sides of length c i and thickness b i ) 3. The building section as a multi-connected thin-walled section Even in the case of a building with a horizontal multiconnected box section, the stress state in the vertical walls can be determined according to Bredt's formulation [Nunziante and Gambarotta (2010)]. Let us refer to a multi connected box section with a degree of connection greater than 2 subject to a torque T i . In the following discussion, a node is said to be a point on the section at which at least three sections of length l i concur. Each segment will be denoted by t i and a curvilinear abscissa s i will be associated with them; they will have thickness b i . As an example, let us consider the section in Fig. 3, with a degree of connection equal to 3 (i.e., 3 cuts are needed to make it single-connected), characterized by 2 closed meshes m i ( i=1,2 ) in each of which a tangential stress flow ϕ can be identified.