Question

PART ONE

A steel railroad track has a length of 28 m

when the temperature is 2◦C.

What is the increase in the length of the

rail on a hot day when the temperature is

35 ◦C? The linear expansion coefficient of

steel is 11 × 10^−6(◦C)^−1

.

Answer in units of m

PART TWO
Suppose the ends of the rail are rigidly
clamped at 2◦C to prevent expansion.
Calculate the thermal stress in the rail if
its temperature is raised to 35 ◦C. Young’s
modulus for steel is 20 × 10^10 N/m^2
Answer in units of N/m^2

Answer 1

Answer:
`\Delta L=0.0101\ m`

Step-by-step explanation:

Given

Length of track
`L_o=28\ m` when

`T_o=2^(\circ)C`

Coefficient of linear expansion
`\alpha =11* 10^(-6)\ ^(\circ)C^(-1)`

When Temperature rises to
`T=35^(\circ)C`

`\Delta T=35-2=33^(\circ)C`

and we know length expand on increasing temperature

`L=L_o[1+\alpha \Delta T]`

`L-L_o=L_o\alpha \Delta T`

`\Delta L=28* 11* 10^(-6)* (33)`

`\Delta L=0.0101=10.164\ mm`

(b)When rails are clamped thermal stress induced

we know
`E=(stress)/(strain)`

`Stress=E* strain`

`Stress=20* 10^(10)* (\Delta L)/(L_o)`

`Stress=20* 10^(10)* (0.0101)/(28)`

`Stress=72.14\ MPa`

`Stress=72.14* 10^(6)\ N/m^2`