Thermal Stresses in Composite Bars

Q. Two bars one of material A and the other of material B of same length are tightly secured between two unyielding walls. Coefficient of thermal expansion of bar A is more than that of B. When temperature rises the stresses induced are

1. tension in both the materials
2. tension in material A and compression in material B
3. compression in material A and tension in material B
4. compression in both the materials

Q. A steel bar is held by two fixed supports as shown in the figure and is subjected to an increase of temperature $\Delta T={100}^{o}C$. If the coefficient of thermal expansion and Young's modulus of elasticity of steel are $11\times {10}^{-6}{/}^{o}C$ and 200 GPa, respectively. the magnitude of thermal stress (in MPa) induced in the bar is

1. 220

Q. A metal bar of length $100mm$ is inserted between two rigid supports and its temperature is increased by ${10}^{\circ }C$. If the coefficient of thermal expansion is $12\times {10}^{-6}\text{per}{}^{\circ }C$ and the Young's modulus is $2\times {10}^{5}MPa$, the stress in the bar is

1. Zero
2. $12MPa$
3. $24MPa$
4. $2400MPa$

Q. 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 $11.2\times {10}^{-6}per°C$ and the coefficient of expansion of brass is $16.5\times {10}^{-6}per°C$. 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. $1$ and $2$
2. $1$ and $3$
3. $2$ and $4$
4. $2$ and $3$

Q. A solid steel cube constrained on all six faces is heated so that the temperature rises uniformly by $\Delta T$. If the thermal coefficient of the materials is $\alpha$, Young's modulus is E and the Poisson's ratio is $v$, the thermal stress developed in the cube due to heating is

1. $-\frac{\alpha \left(\Delta T\right)E}{(1-2v)}$
   
2. $-\frac{2\alpha \left(\Delta T\right)E}{(1-2v)}$
   
3. $-\frac{3\alpha \left(\Delta T\right)E}{(1-2v)}$
   
4. $-\frac{\alpha \left(\Delta T\right)E}{3(1-2v)}$
   

Q. A 200 mm long, stress free rod at room temperature is held between two immovable rigid walls. The temperature of the rod is uniformly raised by ${250}^{o}C$. If the Young's modulus and coefficient of thermal expansion are 200 GPa and 1 x ${10}^{-5}{/}^{o}C$, respectively, the magnitude of the longitudinal stress (in MPa) developed in the rod is

1. 500

Q. A circular metallic rod of length 250 mm is placed between two rigid immovable walls as shown in the figure. The rod is perfect contact with the wall on the left side and there is a gap of 0.2 mm between the rod and the wall on the right side. If the temperature of the rod is increased by ${200}^{o}C$, the axial stress developed in the rod is _____ MPa.
Young's modulus of the material of the rod is 200 GPa and the coefficient of thermal expansion is ${10}^{-5}pe{r}^{o}C$

1. 240

Q. A free bar of length $l$ is uniformly heated from $0^{\circ }$ to a temperature $t^{\circ }C$, $\alpha$ is the coefficient of linear expansion and E is the modulus of elasticity. The stress in the bar is

1. $\alpha tE$
   
2. $\alpha tE/2$
   
3. Zero
4. None of these

Q. A steel cube, with all faces free to deform, has Young's modulus E, Poisson's ratio $\nu$, and coefficient of thermal expansion $\alpha$. The pressure (hydrostatic stress) developed within the cube, when it is subjected to a uniform increase in temperature, $\Delta T$, is given by

1. 0
2. $\frac{\alpha \left(\Delta T\right)E}{1-2v}$
   
3. $-\frac{\alpha \left(\Delta T\right)E}{1-2v}$
   
4. $-\frac{\alpha \left(\Delta T\right)E}{3(1-2v)}$
   

Q. Two similar bars of Steel and Aluminium are heated to a same temperature. Forces are applied at the ends of the bars to maintain their lengths unaltered. If the ratio of Young's modulii of Steel and Aluminium is 3, and the ratio of the coefficients of thermal expansion of Steel to that of Aluminium is 0.5, what is the stress on the Aluminium bar if the stress on the Steel bar is 100 MPa?

1. 16.7 MPa
2. 66.7 MPa
3. 136.7 MPa
4. 1500 MPa

Q.

Why is the cement floor made in small slabs, rather than in a single block? Explain.

Q. An elastic bar of length $L$, uniform cross sectional area $A$, coefficient of thermal expansion $\alpha$ and Young's modulus $E$ is fixed at the two ends. The temperature of the bar is increased by $T$, resulting in an axial stress $\sigma$. Keeping all other parameters unchanged, if the length of the bar is doubled, the axial stress would be

1. $\sigma$
2. $2\sigma$
3. $0.5\sigma$
4. $0.25\alpha \sigma$