Determine the stresses within the rod:
Two parallel walls are stayed together through a steel rod of 5 cm diameter passing through metal plates and nuts at both ends. The nuts are tightened, while the rod is at 150ºC, to remain the walls 10 m apart. Determine the stresses within the rod while the temperature falls down to 50ºC, if
(a) The ends do not yield, and
(b) The ends yield by 1 cm.
Take E = 2 × 105 N/mm2 and α = 12 × 10-6 K-1.
Solution
Given Length of the rod, L = 10 m =104 mm
Diameter of the rod, d = 5 cm = 50 mm
Change in temperature, ΔT = 150 - 50 = 100ºC
E = 2 × 105 N/mm2
α = 12 × 10-6 K-1
(a) When the ends do not yield (let the stress be σ1)
Thermal stress, σ1, in the rod = E α ΔT
= 2 ×105 × 12 × 10- 6 × 100 = 240 N/mm2
(b) When the ends yield by 1 cm (let the stress be σ2)
Thermal Stress, σ2 = ( α ΔT -ΔL′ /L) × E
= (12 × 10 -6 × 100 -10/104) × 2 × 105
= (0.0012 - 0.001) × 2 × 105 = 40 N/mm2