Question

A1.50 m long rectangular bar elongates 1.22 mm under an axial load of35.0 kN. If the cross-sectional dimensions are 6 by 50-mm. The proportional limit of this alloy is 300 MPa.
Determine:
a. The axial stress in the bar.
b. The modulus of elasticity of the material.
c. The change in the two lateral dimensions if Poisson's ratio for the material is 0.32.

Answer 1

Answer:

a) 116.67 MPa

b) 368.85 GPa

c) -1.0122 *10^{-4}

Explanation:

Given data:

length of bar is 1.50 m

total elongation in bar = 1.22 mm

axial load = 35.0 kN

cross section dimension = 6 by 50 mm

proportional limit = 300 MPa

a) AXIAL STRESS

Stress =force/area

$stress = \frac{35 \times 10^3}{6\times 50} = 116.67 MPa$

b) modulus of elasticity

$\sigma_y = \epsilon_y \times E$

where E = modulus of elasticity

$\epsilon = \frac{\delta L}{l_o}$

$\epsilon = \frac{1.22}{1.5 \times 10^3} = 0.8133 \times 10^{-3}$

$E= \frac{300}{0.8133 \times 10^{-3}}$

E = 36.8.85 GPa

c) $\epsilon_y = \frac{-\mu \sigma}{E}$

where $\mu$ is  poisson's ration= 0.32

$\epsilon_y = -0.32 \times \frac{116.67}{368.85 \times 10^{-3}}$

$\epsilon_y = - 1.0122 \times 10^{-4}$