Question

1- The reduced stiffness matrix [Q] is given for a unidirectional lamina as follows: 5.681 0.3164 0 ] [Q]=0.3164 1.217 0 Msi I 0 0 0.6006 Calculate the four engineering constants E1, E2, V12, G12 of the lamina. 2- Calculate the transformed reduced stiffness [Q] for the above problem for 0 = 30°. Glass 3- A glass/epoxy lamina consists of 70% fiber volume fraction. Use properties of glass and epoxy from the tables below to determine: a) Density of the lamina b) Mass fraction of the glass and epoxy c) Volume of composite lamina if the mass of the lamina is 4 kg d) Volume and mass of glass and epoxy in (c) above Typical Properties of Fibers (SI System of Units) Property Units Axial modulus Transverse modulus Axial Poisson's ratio 0.20 Transverse Poisson's ratio 0.20 Axial shear modulus GPa 35.42 Axial coefficient of thermal expansion um/m/C Transverse coefficient of thermal expansion m/m/°C Axial tensile strength MPa 1550 Axial compressive strength MPa 1550 Transverse tensile strength MPa Transverse compressive strength MPa 1550 Shear strength MPa Specific gravity 1550 2.5 030 Typical Properties of Matrices (SI System of Units) Property Units Epoxy Axial modulus Cra Transverse modulus GPS Axial Poisson's ratio Transverse Poisson's ratio Axial shear medulus 1305 Coefficient of thermal expansion umm/ Coefficient of moisture expansion m/m/kg/kg 23 Axial tensile strength MPa Axial compressive strength MP Transverse tensile strength MP Transverse compressive strength MPa Shear strength MPa Specific gravity 1.2 100 102

please solve 2 and 3

Answer 1

Answer, Given data, Reduced stiffness matrix 5.681 0-3164 1 0.3164 Hallo | Msi 0 0-6006 0 = 30 lamina consists of 70% fibre Mass of the lamina = 4 Kgs. We know that, Reduced stiffness matrix . Qui 012 a r [Q] - Qaa o constants lo 0.066 Their relation with engineering E, E2, Via. 72,18 Gia Here via = | 866 = 9 : 06006 Asi

- 6 5. 68 4ร Go : 12E Rio - ในป่วม Gas : 6. 316, Ms E3 |-9 งฆ - - 87 4ร Let, via = Val = 8 Qa = vea |- 0” = 0 - 316% Vea = 0.3164 (I-UP) 10. 316404 365 - 0.316 , - 6 - 8) => 3, 85 : 1.217 Cๆ : I-UY) CI-IT) 3 4) “, - = 5- 68 l-ur 65 i-VY) 5 - 681

Dividing ② with ② @ es (-um) (1-21) (l-urs (5.681) 1. Cl-ur) (1-210 E, - 4.67 €2. from ③ and ④ E2- C1-unj (1.017) 0. 3164 4 + Vea -0.3164 - 0 0. 3164 ur + V Cr-un cra10) -0.3164 - 0 - 1.214 03 + 0.3164 v2 + 1.217 v - 0.3164 - 0 1.217 03- 0.3164 v2 1.217 V+0.3164 - 0 => V-1,-1, 0.25998 Taking V - 0.25998 W ~ 0.26 E, - C1-02) (5-681) = (1-0.26%) (5.681) E, - 5.3 Msi] Ez 4.67 Ez = 1.13 Msi] = Via Vai = 0.26) Ει 4.67 1:13