Saved Bookmarks
| 1. |
A rod of steel is 5 m long and 3 cm diameter at a temperature of 20^(@)C. Find the free expansion of the rod when the temperature is raised to 65^(@)C. Determine the stress and pull exerted if (i) the ends do not yield and (ii) the ends yield by 0.12 cm. Take Y=2xx10^(5" MN")//m^(2) and alpha=12xx10^(-6)" per "^(@)C |
|
Answer» SOLUTION :GIVEN DATA : Diameter of the rod, d = 3 CM = 30 mm Area of the rod, `A=(pi)/(4)xx30^(2)=706.86"mm"^(2)` , Length of the rod, L=5m=5000 mm Initial temperature, `T_(1)=20^(2)C` , Final temperature `T_(2)=65^(@)C` `therefore ` Rise in temperature, `(T)=65-20=45^(@)C , Y=2xx10^(5 N)//mm^(2)` Coefficient of linear expansion `alpha=12xx10^(-6)//""^(@)C` (i) When the ends do not yield The stress is `=alpha. T.Y=12xx10^(-6) xx 45xx2xx10^(5)=108 N//mm^(2)` (tensile) Pull in the rod = Stress `xx` Area `=108xx706.86=76340.88N=76.34kN.` (II) When the ends yield by 0.12cm, `delta=0.12cm=1.2mm` The stress when the ends yield is Stress `=((alpha TL-delta))/(L)xxY=((12xx10^(-6)xx45xx5000-1.2))/(5000)xx2xx10^(5)=60N//mm^(2)` Pull in the rod = Stress `xx` Area `=60xx706.86=42411.6=42.41`kN |
|