Determine the stresses within the rod, Civil Engineering

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

Posted Date: 1/30/2013 5:55:13 AM | Location : United States







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