You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Other

Strength of Materials

Thermal Stresses in Composite Bars

A brass bar o...

Question

A brass bar of solid section is encased in a steel tube as shown in the diagram below

The coefficient of expansion of steel is $11.2 \times 10^{- 6} p e r ° C$ and the coefficient of expansion of brass is $16.5 \times 10^{- 6} p e r ° C$ . The composite bar is heated through 60°C.
Now consider the following statements:
1. The stress in the brass will be tensile.
2. The stress in the steel will be tensile.
3. The stress in the steel will be compressive.
4. The stress in the brass will be compressive.
Which of these statements are correct?

1

and

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1

and

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2

and

4

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

2

and

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $2$ and $4$
As both brass and steel should move together by same amount and coefficient of expansion of brass is more than that of steel. So brass will have compressive stress and steel will be under tension.

Suggest Corrections

Similar questions

Q. Two steel rods and a copper rod of equal length

l_{0}

and equal cross-sectional area are joined rigidly as shown in figure. All the rods are in a state of zero tension at

0^{\circ} C

. The temperature of the system is increased to

30^{\circ} C

. Then:
[coefficient of linear expansion of copper is more than that of steel]

Q. The length of a steel rod is

5 c m

greater than that of a brass rod. If this difference in their lengths is to remain the same at all temperatures, then the length of brass rod will be:

[Coefficient of linear expansion for steel and brass are

12 \times 10^{- 6} /^{\circ} C

and

18 \times 10^{- 6} /^{\circ} C

respectively]

Q. A steel rod of cross-sectional area

16 c m

^{2}

and two brass rods each of cross-sectional area

10 c m

^{2}

together support a load of

5000 k g

as shown in figure. Find the stress in the brass and steel rod (in kg/cm

^{2}

). Take

Y

for steel

=

2.0

\times

^{6}

kg / cm

^{2}

and for brass

=

1.0

\times

^{6}

kg / cm

^{2}

A steel bolt of cross-sectional area

A_{b} = 5 \times 10^{- 5} m^{2}

is passed through a cylindrical tube made of aluminium. Cross-sectional area of the tube material is

A_{t} = 10^{- 4} m^{2}

and its length is l = 50 cm. The bolt is just taut so that there is no stress in the bolt and temperature of the assembly increases through

Δ θ = 10^{\circ} C

. Given, coefficient of linear thermal expansion of steel,

α_{b} = 10^{- 5} /^{\circ} C .

Young's modulus of steel

Y_{b} = 2 \times 10^{11} N / m^{2} .

Young's modulus of Al,

Y_{t} = 10^{11} N / m^{2},

coefficient of

linear thermal expansion of Al

α_{t} = 2 \times 10^{- 5} /^{\circ} C .

The tensile stress in bolt is:

Q. A steel scale is correct at

0^{o} C

, the length of a brass tube measured by it at

40^{o} C

5 m

. The correct length of the tube at

0^{o} C

is (Coefficients of linear expansion of steel and brass are

11 \times 10^{- 6 /^{o} C}

and

19 \times 10^{- 6 /^{o} C}

respectively).

Join BYJU'S Learning Program

The correct option is C 2 and 4As both brass and steel should move together by same amount and coefficient of expansion of brass is more than that of steel. So brass will have compressive stress and steel will be under tension.

The correct option is C $2$ and $4$
As both brass and steel should move together by same amount and coefficient of expansion of brass is more than that of steel. So brass will have compressive stress and steel will be under tension.