What will be the stress at - 20 ° C , if a steel rod with a cross-sectional area of 150 mm 2 is stretched between two fixed points? The tensile load at 20 ° C is 5000 N . (Assume α = 11.7 × 10 - 6 ° C - 1 and Y = 200 × 10 11 N m - 2 )

Step-by-step solution

Let L = free length at 0   ° C L 0 = final stretched length in each case. L 1 and L 2 are free length at + 20   ° C and -   20   ° C respectively. We know s 2 = s 1 + 2 α L Δ T Here, s 1 and s 2 are load deformation. F 2 L A Y = F 1 L A Y + 2 α L Δ T σ 2 = F 2 A = F 1 A + 2 α Δ T Y = 5000 150   × 10 - 6 + 2   11.7   × 10 - 6   20   2   × 10 11 = 127   × 10 6   N   m - 2