Modulus of Elasticity

#580 / Mechanics of Materials Easy

Consider a 5 m long extrusion with a square shaped cross sectional area of 0.25 m^2 is made from an unknown grade of Aluminum. What is the modulus of elasticity in GPa if the Poisson’s Ratio is 0.4 and the bulk modulus is 80 GPa?

Expand Hint
A substance’s bulk modulus describes how resistant the material is to compression.
Hint 2
Bulk (Volume) Modulus of Elasticity:
$$$K=\frac{E}{3(1-2\nu )}$$$
where $$K$$ is the bulk modulus, $$E$$ is the modulus of elasticity, and $$\nu$$ is Poisson’s ratio.
A substance’s bulk modulus describes how resistant the material is to compression. Bulk (Volume) Modulus of Elasticity:
$$$K=\frac{E}{3(1-2\nu )}$$$
where $$K$$ is the bulk modulus, $$E$$ is the modulus of elasticity, and $$\nu$$ is Poisson’s ratio.
$$$80GPa=\frac{E}{3(1-2(0.4))}$$$
$$$E=80GPa\times 3(1-0.8)$$$
$$$=80GPa\times 0.6=48\:GPa$$$
48 GPa


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