A rod is 3m long at a temperature of 15 0 C. Find the expansion of the rod, when the temperature is raised to 95 0 C. If this expansion is prevented, find the stress induced in the material of the rod. Take E= 1x10 5 N/mm 2 and α= 0.000012 per degree centigrade.
Answers
Answer:
Free expansion of the rod =αLΔθ
=15×10−60C×2m×(50−20)0C
=9×10−4m=0.9mm
If the expansion is fully prevented, then
Strain=29×10−4=4.5×10−4
Temperature Stress = Strain ×Y
=4.5×10−4×2×1011=9×107N/m2
If 0.4 mm expansion is allowed, then length restricted to expand
=0.9−0.4=0.5mm
Strain=25×10−4=2.5×10−4
Temperature stress = Strain ×Y=2.5×10−4×2×1011=5×107N/m2
Given info : A rod is 3m long at a temperature of 15°C. Find the expansion of the rod, when the temperature is raised to 95°C. coefficient of expansion, α = 1.2 × 10¯⁵/°C and elasticity, E = 10⁵ N/mm² = 10¹¹ N/m²
To find : if this expansion is prevented, find the stress induced in the material of the rod.
solution : first find change in length of rod, ∆l
using formula, ∆l = lα∆T
= 3m × 1.2 × 10¯⁵/°C × (95°C - 15°C)
= 3.6 × 10¯⁵ × 80
= 2.88 × 10¯³ m
now using formula, stress = elasticity × strain
= E × ∆l/l
= 10¹¹ N/m² × 2.88 × 10¯³ m/3m
= 2.88/3 × 10^8 N/m²
= 0.96 × 10^8 N/m²
= 9.6 × 10^7 N/m²
Therefore the stress induced in the material of the rod is 9.6 × 10^7 N/m²