Thermal Stress

Q.

When a rod is heated but prevented from expanding, the stress developed is independent of

1. Material of the rod

2. Rise in temperature

3. Length of rod

4. None of above

Q. Two rods of lengths $L_1$ and $L_2$ are made of materials whose coefficients of linear expansion are ${\alpha }_1$ and ${\alpha }_2$ respectively. If the difference between the two lengths is independent of temperature, then choose the correct option.

1. $\left(L_1/L_2\right)=\left({\alpha }_1/{\alpha }_2\right)$
2. $\left(L_1/L_2\right)=\left({\alpha }_2/{\alpha }_1\right)$
3. $L_1^2{\alpha }_1=L_2^2{\alpha }_2$
4. ${\alpha }_1^2{L}_1={\alpha }_2^2{L}_2$

Q.

A steel wire of cross-sectional area $0.5m{m}^2$ is held between two fixed supports. If the wire is just taut at ${20}^{\circ }C$, determine the tension when the temperature falls to $0^{\circ }C$. Coefficient of linear expansion of steel is $1.2\times {10}^{-5}{}^{\circ }{C}^{-1}$ and its Young's modulus is $2.0\times {10}^{11}N{m}^{-2}$

Q. The value of tension in a long, thin metal wire has been changed from $T_1$ to $T_2$. The lengths of the metal wire at two different values of tension $T_1$ and $T_2$ are $l_1$ and $l_2$ respectively. The actual length of the metal wire is :

1. $\frac{T_1{l}_2-T_2{l}_1}{T_1-T_2}$
2. $\frac{T_1{l}_1-T_2{l}_2}{T_1-T_2}$
3. $\frac{l_1+l_2}{2}$
4. $\sqrt{T_1{T}_2{l}_1{l}_2}$

Q. There is some change in length when a $33,000\text{N}$ tensile force is applied on a steel rod of area of cross-section ${10}^{-3}{\text{m}}^2$. The change of temperature required to produce the same elongation, if the steel rod is heated, is -
[Take modulus of elasticity $Y=3\times {10}^{11}{\text{N/m}}^2$ and the coefficient of linear expansion of steel is $\alpha =1.1\times {10}^{-5}{/}^{\circ }\text{C}$]

1. ${20}^{\circ }\text{C}$
2. ${15}^{\circ }\text{C}$
3. ${10}^{\circ }\text{C}$
4. $0^{\circ }\text{C}$

Q.

A steel rod is clamped at its two ends and rests on a fixed horizontal base. The rod is unstrained at ${20}^{\circ }C$. Find the longitudinal strain developed in the rod if the temperature rises to ${50}^{\circ }C$. Coefficient of linear expansion of steel $=1.2\times {10}^{-5}{}^{\circ }{C}^{-1}$.

Q. A steel rod of length $1\text{m}$ is fixed between two walls. If the rod is heated from ${25}^o\text{C}$ to ${35}^o\text{C}$, the stress developed in the rod is expressed as $x\times {10}^7{\text{N/m}}^2$. Find the value of $x$.
(coefficient of expansion for steel is $2\times {10}^{-5}{/}^{\circ }C$, Young's modulus of steel is $2\times {10}^{11}{\text{N/m}}^2$)

1. $2$
2. $4$
3. $7$
4. $8$

Q. If the temperature of a wire of length $2\text{m}$ and area of cross-section $1{\text{cm}}^2$ is increased from $0^{\circ }\text{C}$ to ${80}^{\circ }\text{C}$, then force required so that the wire is not allowed to increase in length is: (Given $Y={10}^{10}{\text{N/m}}^2,\alpha ={10}^{-6}{}^{\circ }\text{C}$)

1. $160\text{N}$
2. $80\text{N}$
3. $400\text{N}$
4. $120\text{N}$

Q. A spring balance shows wrong readings after using for a long time . Why ?

Q.

A wire of cross-sectional area A at temperature t is held taut with a negligible tension between two rigid supports. If the wire is cooled to a temperature $(t-\Delta t)$, what tension is developed in the wire? The coefficient of linear expansion is $\alpha$ and Young's modulus of the wire is Y.

1. $YA\alpha \Delta t$

2. $\frac{YA}{\alpha \Delta T}$

3. $\frac{Y\alpha \Delta t}{A}$

4. $\frac{A\alpha \Delta t}{Y}$

Q. The temperature of a wire of length 1 m and area of cross section
$1c{m}^2$ is increased from $0^{\circ }C$ to ${100}^{\circ }C$. If the length of rod is not allowed to increase, then force developed will be $(\alpha ={10}^{-5}/CandY={10}^{11}\frac{N}{m^2})$

1. 10³ N
2. 10⁴ N
3. 10⁵ N
4. 10⁹ N

Q. Diameter of steel rod fixed between two rigid supports is $20\text{mm}$. Find the stress in the rod when the temperature increases by ${80}^{\circ }\text{C}$.
$($Take Young's modulus, $Y=2\times {10}^{11}{\text{N/m}}^2$ and thermal expansion coefficient , $\alpha =12\times {10}^{-6}/{}^{\circ }\text{C})$

1. $150\text{MPa}$
2. $192\text{MPa}$
3. $250\text{MPa}$
4. $100\text{MPa}$

Q. An iron rod of length $1\text{m}$ is fixed between two walls as shown in figure. Find thermal stress and thermal strain developed in the rod if it is heated by $\Delta T={20}^{\circ }C$
(Given: Coefficient of linear expansion of iron is $1.2\times {10}^{-5}{}^{\circ }{C}^{-1}$; Young's modulus of iron is $2\times {10}^{11}{\text{N/m}}^2$).

1. $48\times {10}^6{\text{N/m}}^2,32\times {10}^{-4}$
2. $24\times {10}^7{\text{N/m}}^2,48\times {10}^{-5}$
3. $48\times {10}^6{\text{N/m}}^2,24\times {10}^{-5}$
4. $32\times {10}^7{\text{N/m}}^2,48\times {10}^{-4}$

Q.

A steel rod is rigidly clamped at its two ends. The rod is under zero tension at ${20}^{\circ }C$. If the temperature rises to ${100}^{\circ }C$, what force will the rod exert on one of the clamps? Area of cross section of the rod = $2.0m{m}^2$. Coefficient of linear expansion of steel $=12.0\times {10}^{-6}{}^{\circ }{C}^{-1}$ and Young's modulus of steel = $2.00\times {10}^{11}N{m}^{-2}$.

Q. A steel rod of length $5\text{m}$ and diameter $30\text{mm}$ is fixed between two rigid supports. Determine the thermal stress and change in diameter of the rod, when the temperature increases by $50{}^{\circ }\text{C}$. Take Young's modulus of elasticity $\left(Y\right)=2.0\times {10}^6{\text{kg/cm}}^2$, coefficient of thermal expansion $\left(\alpha \right)=12\times {10}^{-6}{/}^{\circ }\text{C}$ and Poisson's ratio $\left(\nu \right)=0.3$.

1. $120{\text{kg/cm}}^2,0.0234\text{mm}$
2. $1200{\text{kg/cm}}^2,0.018\text{mm}$
3. $12000{\text{kg/cm}}^2,0.0054\text{mm}$
4. $1200{\text{kg/cm}}^2,0.0234\text{mm}$

Q. Two plates are connected by fillet welds of size $8mm$ and subjected to a tensile force of $350kN$. The thickness of each plate is $12mm$. The yield stress and ultimate stress of steel are $250MPa$ and $410MPa$ respectively. As per IS 800 : 2007, the length $\left(l\right)$ required to transmit the load is ____mm. (The welding is done at site).

1. 145

Q. A metal bar of length $1\text{m}$ and area of cross-section $1{\text{mm}}^2$ is clamped between two rigid supports. For the material of rod, its Young's modulus is $Y={10}^{11}{\text{N/m}}^2$ and coefficient of linear expansion is $\alpha =1.8\times {10}^{-5}{}^{\circ }{C}^{-1}$. If the temperature of the rod is decreased by $\Delta T={10}^{\circ }C$, the force exerted by the rod on the supports is

1. $9\text{N}$
2. $6\text{N}$
3. $16\text{N}$
4. $18\text{N}$

Q. A steel bar $2.5\text{cm}$ in diameter is rigidly attached to two parallel supports which are $5\text{m}$ apart. Find the stress and the change in the diameter of the bar when the temperature is increased by ${100}^{\circ }C$.
Take $\alpha =12\times {10}^{-6}/{}^{\circ }C,Y=210\text{GPa}$.

1. $252\text{MPa}$, $0.03\text{mm}$
2. $212\text{MPa}$, $0.13\text{mm}$
3. $150\text{MPa}$, $0.13\text{mm}$
4. $59\text{MPa}$, $0.33\text{mm}$

Q.

In a fillet weld, the direct shear stress and bending tensile stress are 60 MPa and 140 MPa, respectively. As per IS 800 : 2007 the equivalent stress will be MPa.

1. 174.36

Q. An iron ring measuring 15.00 cm in diameter is to be shrunk on a pulley which is 15.05 cm in diameter. All measurements refer to the room temperature ${20}^{\circ }$C. To what minimum temperature should the ring be heated to make the job possible? Calculate the strain developed in the ring when it comes to room temperature. $\alpha$ for iron = $12\times {10}^{-6}{/}^{\circ }$C.

1. 288
2. 278
3. 268
4. 298

Q. A metal bar of length $1\text{m}$ and area of cross-section $1{\text{mm}}^2$ is clamped between two rigid supports. For the material of rod, its Young's modulus is $Y={10}^{11}{\text{N/m}}^2$ and coefficient of linear expansion is $\alpha =1.8\times {10}^{-5}{}^{\circ }{C}^{-1}$. If the temperature of the rod is decreased by $\Delta T={10}^{\circ }C$, the force exerted by the rod on the supports is

1. $9\text{N}$
2. $6\text{N}$
3. $16\text{N}$
4. $18\text{N}$

Q. For a plane stress condition, the major principal stress is 140 MPa and minor principal stress is $\sigma$. The shear stress on a plane inclined at ${45}^{\circ }$ to the principal plane is 60 MPa, the value of $\sigma$ (in MPa, correct upto nearest integer )is_____.

1. 20

Q. A steel rod of length $1\text{m}$ is fixed between two walls. If the rod is heated from ${25}^o\text{C}$ to ${35}^o\text{C}$, the stress developed in the rod is expressed as $x\times {10}^7{\text{N/m}}^2$. Find the value of $x$.
(coefficient of expansion for steel is $2\times {10}^{-5}{/}^{\circ }C$, Young's modulus of steel is $2\times {10}^{11}{\text{N/m}}^2$)

1. $2$
2. $4$
3. $7$
4. $8$

Q. There is some change in length when a $33000\text{N}$ tensile force is applied on a steel rod of area of cross section ${10}^{-3}{\text{m}}^2$. The change of temperature required to produce the same elongation, if steel rod is heated, is: (The modulus of elasticity is $3\times {10}^{11}{\text{N/m}}^2$ and the coefficient of linear expansion of steel is $1.1\times {{10}^{-5}}^{\circ }{C}^{-1}$)

1. $1^{\circ }C$
2. ${10}^{\circ }C$
3. ${20}^{\circ }C$
4. ${30}^{\circ }C$

Q. A metal rod is fixed rigidly at two ends so as to prevent its thermal expansion. If $L,\alpha$ and $Y$ respectively denote the length of the rod, coefficient of linear thermal expansion and Young's modulus of its material, then for an increase in temperature of the rod by $\Delta T$, the longitudinal stress developed in the rod is:

1. inversely proportional to $\alpha$
2. directly proportional to $\Delta T/Y$
3. inversely proportional to $Y$
4. independent of $L$

Q. For a perfect rigid body the value of Young's modulus will be.

1. Infinity
2. Zero
3. Unity
4. Finite non-zero value

Q. The critical stress for elastic plate buckling depends upon.
1. Support conditions.

2. Width to thickness ratio.

3. Elastic properties of plate material

4. length to width ratio.

1. 1, 2 and 3
2. 2 and 4 only
3. 2, 3 and 4
4. 1, 2, 3 and 4

Q.

In the given figure, a rod is free at one end and other and is fixed. When we change the temperature of rod by $\Delta$T, then strain produced in the rod will be

1. zero
2. information incomplete

3. $\alpha \Delta T$

4. $\frac{1}{2}\alpha \Delta T$

Q. A hot wire of copper is stretched at a temperature of ${150}^{\circ }C$ between two fixed walls. At what temperature will the wire break when it is cooled? The breaking stress of copper is $2.45\times {10}^{8}N/m^2$. Young's modulus of copper $=11.8\times {10}^{10}N/m^2$, coefficient of linear expansion of copper $=1.6\times {10}^{-5}{/}^{\circ }C$.

1. ${43.2}^{\circ }C$
2. ${64.9}^{\circ }C$
3. ${70.2}^{\circ }C$
4. ${20.2}^{\circ }C$

Q. The length of a metal wire is $3.75\text{m}$ when the tension in it is $100\text{N}$ and is $3.50\text{m}$ when the tension is $80\text{N}$. The natural length of the wire $\left(\text{in cm}\right)$ is