Issue 29

D. Addessi et al., Frattura ed Integrità Strutturale, 29 (2014) 178-195; DOI: 10.3221/IGF-ESIS.29.16 185 , , , =1 w l w n x yz w w n w w n n N N x              q C d C C u (30) 0   dx L T     D b d (31) , , , 0 , , , , , , , , , =1 0 dx                                        p C C d C C C u w L w i x yz w i w w i w L l w i w n w i w n x xy yz ww w n w i ww w i w n ww w n n N N  dx x N N N N N N N N x x x x (32) Eq. (30) represents the generalized section constitutive law and contains two contributions. The first term takes into account the standard deformation d associated to the cross-section rigid motion, depending on the section stiffness matrix, defined as: T A dA   C c   (33) The second term is related to the section deformations associated to the warping. The section warping stiffness matrices are defined as follows: = = x x T x w w r w r A dA          C C P cM P  = =          C C P cM P yz yz T yz w w r w r A dA    = = T x T x x T x ww r w w r β r ww r β A dA            C P M cM P k P C P k   = = T yz T yz yz T yz ww r w w r β r ww r β A dA            C P M cM P k P C P k   = = T xy T x yz T xy ww r w w r β r ww r β A dA            C P M cM P k P C P k where: ( )            and           T r w β m β    P I R V k V V I ( ) w m is a w w m m  identity matrix and R a 3 w m  matrix that represents the rigid body motions of the element section, i.e. a matrix containing the coordinates of the w m warping points as follows: 1 1 2 2 1 1 1 w w m m y z y z y z                R  Finally, V is a matrix containing the average value and the first moments of the shape functions over the cross section: