Tham khảo tài liệu 'aircraft structures 1 2011 part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 426 Stress analysis of aircraft components corresponding to CT is given by q y and ƠỴ Eị ị where El is the modulus of elasticity of the lamina in the direction of the filament. Also using the suffixes f and m to designate filament and matrix parameters we have Of f i om Further if A is the total area of cross-section of the lamina in Fig. is the cross-sectional area of the filament and the cross-sectional area of the matrix then for equilibrium in the direction of the filament V A ơịAị ơm 4m or substituting for 71 ƠỊ and 7m from Eqs and iei EịEịAị so that Xi Writing Vị and Amf A vm Eq. becomes El vịEị vmEm Equation is generally referred to as the law of mixtures. A similar approach may be used to determine the modulus of elasticity in the transverse direction t . In Fig. the total extension in the transverse direction is produced by 7t and is given by Fig. Determination of Et. Laminated composite structures 427 or which gives Et Em Rearranging this we obtain E_Ec Et - .-Ỉ7- 10-49 vmEf V Em The major Poisson s ratio i ll may be found by referring to the stress system of Fig. and the dimensions given in Fig. . The total displacement in the transverse direction produced by 71 is given by At ỉ t t . At ỉ ltEi t iWf from which i it W m w The minor Poisson s ratio Pti is found by referring to Fig. . The strain in the longitudinal direction produced by the transverse stress crt is given by 1 From the last two of Eqs __Eĩ ĩ Em Substituting in Eq. I vĩ p VrnEra V Ef or from Eq. A lt Now substituting for ỉ m in the first two of Eqs t Et or tl I fr m m w El El 428 Stress analysis of aircraft components Matrix Filament Finally the shear modulus G t Gti is determined by assuming that the constituent materials are subjected to the same shear stress Tit as shown in Fig. . The displacement As produced by shear is A Tlt 7 _ Tlt 7 Ot 7 As TT
