contestada

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

Respuesta :

Answer:[tex]\Delta L=0.0101\ m[/tex]

Explanation:

Given

Length of track [tex]L_o=28\ m[/tex] when

[tex]T_o=2^{\circ}C[/tex]

Coefficient of linear expansion [tex]\alpha =11\times 10^{-6}\ ^{\circ}C^{-1}[/tex]

When Temperature rises to [tex]T=35^{\circ}C[/tex]

[tex]\Delta T=35-2=33^{\circ}C[/tex]

and we know length expand on increasing temperature

[tex]L=L_o[1+\alpha \Delta T][/tex]

[tex]L-L_o=L_o\alpha \Delta T[/tex]

[tex]\Delta L=28\times 11\times 10^{-6}\times (33)[/tex]

[tex]\Delta L=0.0101=10.164\ mm[/tex]

(b)When rails are clamped thermal stress induced

we know [tex]E=\frac{stress}{strain}[/tex]

[tex]Stress=E\times strain[/tex]

[tex]Stress=20\times 10^{10}\times \frac{\Delta L}{L_o}[/tex]

[tex]Stress=20\times 10^{10}\times \frac{0.0101}{28}[/tex]

[tex]Stress=72.14\ MPa[/tex]

[tex]Stress=72.14\times 10^{6}\ N/m^2[/tex]