? ??? 1. Find the three stiffness matrices [A], [B], and [D] for a [0/90] glass/epoxy laminate.

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1. Find the three stiffness matrices [A], [B], and [D] for a [0/90] glass/epoxy laminate. Use the properties of glass/epoxy unidirectional lamina from Table 2.2 and assume the lamina thickness to be 0.1 mm. Also, find the mass of the laminate if the top surface area of the laminate is 6 cm x 7 cm. Use densities of glass and epoxy from Table 3.3 and Table 3.4, respectively. 2. (20 pts) A unidirectional glass/epoxy lamina with a fiber volume fraction of 70% is replaced by a graphite/epoxy lamina with the same longitudinal Young's modulus. Find the fiber volume fraction required in the graphite/epoxy lamina. Use properties of glass, graphite, and epoxy from Table 3.1 and Table 3.2. 3. (30 pts) A laminate of 0.015 in. thickness under a complex load gives the following midplane strains and curvatures: 2x10* 3x10* in./in. 4x10* 1.2x10 1.5x10 1/in. 2.6x10 Find the global strains at the top, middle and bottom surface of the laminate. 4. (10 pts) Condense the following expanded laminate codes: a. [0/45/-45/90] b. [0/45/-45/-45/45/0] c. [0/90/60/60/90/0] d. [0/45/60/45/0] e. [45/-45/45/-45/-45/45/-45/45] 5. (10 pts) Expand the following laminate codes: a. [45/-45]s b. [45/-45₂/90]s c. [45/0]s d. [45/+30]; TABLE 2.2 Typical Mechanical Properties of a Unidirectional Lamina (USCS System of Units) Graphite/ epoxy Property Fiber volume fraction Longitudinal elastic modulus Transverse elastic modulus Major Poisson's ratio Shear modulus Ultimate longitudinal tensile strength Ultimate longitudinal compressive strength Ultimate transverse tensile strength Ultimate transverse compressive strength Ultimate in-plane shear strength Longitudinal coefficient of thermal expansion Transverse coefficient of thermal expansion Longitudinal coeffi moisture expansion Transverse coefficient of moisture expansion of Symbol V₁ E₁ E₂ V12 G12 (61) ult (61) ult (62) ult (02) ult (T12) ult α 0₂ B₁ B₂ Msi Msi Msi ksi ksi ksi ksi Units ksi uin./in./°F uin./in./°F lb/lb in./in./lb/lb Glass/ epoxy 0.45 5.60 1.20 0.26 0.60 154.03 88.47 4.496 17.12 10.44 4.778 12.278 0.60 Boron/ epoxy 0.50 29.59 2.683 0.23 0.811 182.75 362.6 8.847 29.30 9.718 3.389 16.83 0.60 0.70 26.25 1.49 0.28 1.040 217.56 217.56 5.802 35.68 9.863 0.0111 12.5 0.0 0.60 TABLE 3.3 Typical Properties of Fibers (USCS System of Units) Property Units Msi Msi Axial modulus Transverse modulus Axial Poisson's ratio Transverse Poisson's ratio Axial shear modulus Axial coefficient of thermal expansion Transverse coefficient of thermal expansion Axial tensile strength Axial compressive strength Transverse tensile strength Transverse compressive strength Shear strength Specific gravity Msi uin./in./°F uin./in./°F ksi ksi ksi ksi ksi Graphite Glass Aramid 33.35 17.98 3.19 1.16 0.30 0.35 3.19 -0.7222 3.889 299.7 289.8 11.16 6.09 5.22 1.8 12.33 12.33 0.20 0.20 5.136 2.778 2.778 224.8 224.8 224.8 224.8 5.08 2.5 0.36 0.37 0.435 -2.778 2.278 200.0 40.02 1.015 1.015 3.045 1.4 TABLE 3.4 Typical Properties of Matrices (USCS System of Units) Property Units Epoxy Msi 0.493 Msi 0.493 0.30 0.30 0.1897 Axial modulus Transverse modulus Axial Poisson's ratio Transverse Poisson's ratio Axial shear modulus Coefficient of thermal expansion Coefficient of moisture expansion Axial tensile strength Axial compressive strength Transverse tensile strength Transverse compressive strength Shear strength Specific gravity Msi uin./in./°F in./in./lb/lb ksi ksi ksi ksi ksi 35 0.33 10.44 14.79 10.44 14.79 4.93 1.2 Aluminum 10.30 10.30 0.30 0.30 3.915 12.78 0.00 40.02 40.02 40.02 40.02 20.01 Polyamide 0.5075 0.5075 0.35 0.35 0.1885 50 0.33 7.83 15.66 7.83 15.66 7.83 1.2 1. Find the three stiffness matrices [A], [B], and [D] for a [0/90] glass/epoxy laminate. Use the properties of glass/epoxy unidirectional lamina from Table 2.2 and assume the lamina thickness to be 0.1 mm. Also, find the mass of the laminate if the top surface area of the laminate is 6 cm x 7 cm. Use densities of glass and epoxy from Table 3.3 and Table 3.4, respectively. 2. (20 pts) A unidirectional glass/epoxy lamina with a fiber volume fraction of 70% is replaced by a graphite/epoxy lamina with the same longitudinal Young's modulus. Find the fiber volume fraction required in the graphite/epoxy lamina. Use properties of glass, graphite, and epoxy from Table 3.1 and Table 3.2. 3. (30 pts) A laminate of 0.015 in. thickness under a complex load gives the following midplane strains and curvatures: 2x10* 3x10* in./in. 4x10* 1.2x10 1.5x10 1/in. 2.6x10 Find the global strains at the top, middle and bottom surface of the laminate. 4. (10 pts) Condense the following expanded laminate codes: a. [0/45/-45/90] b. [0/45/-45/-45/45/0] c. [0/90/60/60/90/0] d. [0/45/60/45/0] e. [45/-45/45/-45/-45/45/-45/45] 5. (10 pts) Expand the following laminate codes: a. [45/-45]s b. [45/-45₂/90]s c. [45/0]s d. [45/+30]; TABLE 2.2 Typical Mechanical Properties of a Unidirectional Lamina (USCS System of Units) Graphite/ epoxy Property Fiber volume fraction Longitudinal elastic modulus Transverse elastic modulus Major Poisson's ratio Shear modulus Ultimate longitudinal tensile strength Ultimate longitudinal compressive strength Ultimate transverse tensile strength Ultimate transverse compressive strength Ultimate in-plane shear strength Longitudinal coefficient of thermal expansion Transverse coefficient of thermal expansion Longitudinal coeffi moisture expansion Transverse coefficient of moisture expansion of Symbol V₁ E₁ E₂ V12 G12 (61) ult (61) ult (62) ult (02) ult (T12) ult α 0₂ B₁ B₂ Msi Msi Msi ksi ksi ksi ksi Units ksi uin./in./°F uin./in./°F lb/lb in./in./lb/lb Glass/ epoxy 0.45 5.60 1.20 0.26 0.60 154.03 88.47 4.496 17.12 10.44 4.778 12.278 0.60 Boron/ epoxy 0.50 29.59 2.683 0.23 0.811 182.75 362.6 8.847 29.30 9.718 3.389 16.83 0.60 0.70 26.25 1.49 0.28 1.040 217.56 217.56 5.802 35.68 9.863 0.0111 12.5 0.0 0.60 TABLE 3.3 Typical Properties of Fibers (USCS System of Units) Property Units Msi Msi Axial modulus Transverse modulus Axial Poisson's ratio Transverse Poisson's ratio Axial shear modulus Axial coefficient of thermal expansion Transverse coefficient of thermal expansion Axial tensile strength Axial compressive strength Transverse tensile strength Transverse compressive strength Shear strength Specific gravity Msi uin./in./°F uin./in./°F ksi ksi ksi ksi ksi Graphite Glass Aramid 33.35 17.98 3.19 1.16 0.30 0.35 3.19 -0.7222 3.889 299.7 289.8 11.16 6.09 5.22 1.8 12.33 12.33 0.20 0.20 5.136 2.778 2.778 224.8 224.8 224.8 224.8 5.08 2.5 0.36 0.37 0.435 -2.778 2.278 200.0 40.02 1.015 1.015 3.045 1.4 TABLE 3.4 Typical Properties of Matrices (USCS System of Units) Property Units Epoxy Msi 0.493 Msi 0.493 0.30 0.30 0.1897 Axial modulus Transverse modulus Axial Poisson's ratio Transverse Poisson's ratio Axial shear modulus Coefficient of thermal expansion Coefficient of moisture expansion Axial tensile strength Axial compressive strength Transverse tensile strength Transverse compressive strength Shear strength Specific gravity Msi uin./in./°F in./in./lb/lb ksi ksi ksi ksi ksi 35 0.33 10.44 14.79 10.44 14.79 4.93 1.2 Aluminum 10.30 10.30 0.30 0.30 3.915 12.78 0.00 40.02 40.02 40.02 40.02 20.01 Polyamide 0.5075 0.5075 0.35 0.35 0.1885 50 0.33 7.83 15.66 7.83 15.66 7.83 1.2

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