Question

A steel rod of 4m long and 30mm diameter is connected to two grips and the rod is maintained at a temperature of 70° C. find out the force exerted by the rod after it has been cooled to 25°C, if a) the ends do not yield, and b) the ends yield by 1.5mm. Take
E=2.1X105N/mm2. Coefficient of linear expansion as 12x10-6/ °C.​

Answer 1

$answer$

b part is correct

Coefficient is 2.1×105N

as 12×10-6 °C

I hope it helps you ...

Answer 2

in given :

L = 4×10^3mm

D= 30mm

T = 70 -25

= 45 °c

E = 2.1×10^5

coefficient of linear expansion ( denoted by alfa)

( alfa ) = 12 × 10^-6

now,

Area = π(D) ^2/4

=706.5

i) The ends do not yield ∆ = 0

then,

p = ( afla ) × T × E ×A

=80117.5 N/mm^2

ii) The ends yeild by 1.5mm

therefore,

∆ = 1.5mm

p = E [{(alfa) ×T×L - ∆ } / L] × A

= 8060.58 N/mm^2