laminated laminated unidirectional honey comb laminated foam foam blade box beam spar laminated steel aluminum foam unidirectional wood ski leaf spring transmission shaft Figure 15.1 Composite Beams S Figure 15.2 Composite Beam,with Plane of Symmetry 15.1.1 Degrees of Freedom 15.1.1.1 Equivalent Stiffness One writes in condensed form the following integrals taken over the total cross section: (E=Eds or=∑EBS number of phases (）=∫Esor=∑ (15.1) number of phases (G=∫Gids or=∑G number of phases is the quadratic moment of the Phase i with respect with z axis. 2003 by CRC Press LLC15.1.1 Degrees of Freedom 15.1.1.1 Equivalent Stiffness One writes in condensed form the following integrals taken over the total cross section2 : (15.1) Figure 15.1 Composite Beams Figure 15.2 Composite Beam, with Plane of Symmetry 2 Izi is the quadratic moment of the Phase i with respect with z axis. · Ò ES EidS or EiSi i = ÚD = Â number of phases EIz · Ò Ei y 2 dS or EiIzi i = ÚD = Â number of phases · Ò GS GidS or GiSi i = ÚD = Â number of phases TX846_Frame_C15 Page 284 Monday, November 18, 2002 12:30 PM © 2003 by CRC Press LLC