NORTH CAROLINA STATE UNIVERSITY
Mat E 455/555: Exam 3
Prof. Martin Thuo
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Student Number \( \qquad \)
1. Given a graphite/epoxy laminate with the following structure [+45/-45/-45/+45], calculate its stiffness matrix given that the lamina are all \( 0.25 \mathrm{~mm} \) and \( \mathrm{E}_{1}=138 \mathrm{GPa}, \mathrm{E}_{2}=9 \) \( \mathrm{GPa}, \mathrm{G}_{12}=6.9 \mathrm{GPa}, v_{12}=0.3, v_{21}=0.0196 \mathrm{GPa} \).
a. The composite above is subjected to a single uniaxial force per unit length \( N_{x}=50 \) \( \mathrm{MPa}-\mathrm{mm} \). Calculate the stresses in the \( \mathrm{x} \) and \( \mathrm{y} \) axes in each lamina.
b. Calculate the effective Young's moduli, in-plane shear modulus, longitudinal Poisson's ratio, and shear coupling ratio associated with \( \mathrm{x} \) and \( \mathrm{y} \) directions.
2. How does the stiffness matrix of the composite above compare to its anti-symmetric analog, \( [-45 /+45 /-45 /+45] \) laminate.
3. The anti-symmetric composite in (2) isheated from \( 293 \mathrm{k} \) to \( 373 \mathrm{k} \). Assuming that lamina properties do not change, determine the hygrothermal stress. What are the stresses on top and bottom of each lamina?
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