A steel bar (shown in Fig. 1) has a cross-sectional area of 10−3 m2, Young’s modulusof 2 × 1011 Pa and Poisson’s ratio of 0.4. If the bar is subjected to a compressive forceof 105 N, find the corresponding longitudinal and transverse strains
Question
A steel bar (shown in Fig. 1) has a cross-sectional area of 10−3 m2, Young’s modulusof 2 × 1011 Pa and Poisson’s ratio of 0.4. If the bar is subjected to a compressive forceof 105 N, find the corresponding longitudinal and transverse strains
Solution
To find the longitudinal and transverse strains, we need to use the definitions of stress, strain, and Poisson's ratio.
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First, we calculate the stress (σ) on the bar using the formula:
σ = F/A
where F is the force applied and A is the cross-sectional area of the bar.
Substituting the given values:
σ = 105 N / 10^-3 m^2 = 1 x 10^8 Pa
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Next, we calculate the longitudinal strain (ε) using the formula:
ε = σ/E
where E is Young's modulus.
Substituting the given values:
ε = 1 x 10^8 Pa / 2 x 10^11 Pa = 0.5 x 10^-3
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Finally, we calculate the transverse strain (ε_t) using the formula:
ε_t = -ν * ε
where ν is Poisson's ratio.
Substituting the given values:
ε_t = -0.4 * 0.5 x 10^-3 = -0.2 x 10^-3
So, the longitudinal strain is 0.5 x 10^-3 and the transverse strain is -0.2 x 10^-3.
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