This set of Strength of Materials Multiple Choice Questions & Answers (MCQs) focuses on “Bars of varying sections”.

1. If a bar of two different length are in a line and P load is acting axially on them then what will be the change in length of the bar if the radius of both different lengths is same?

a) P/E x (L_{1} + L_{2})

b) PA/E x (L_{1} + L_{2})

c) P/EA x (L_{1} + L_{2})

d) E/PA x (L_{1} + L_{2})

View Answer

Explanation: Change in length of section 1 = PL

_{1}/EA

_{1}

Change in length of section 2 = PL

_{2}/EA

_{2}

Since diameter is same for both the sections, the respective area will be the same

Total change in length of bar = PL

_{1}/EA

_{1}+ PL

_{2}/EA

_{2}= P/EA x (L

_{1}+ L

_{2}).

2. If a bar of two sections of different diameters of same length are in a line and P load is acting axially on them then what will be the change in length of the bar?

a) PL/E x (1/A_{1} + 1/A_{2})

b) P/E x (1/A_{1} + 1/A_{2})

c) P/EL x (1/A_{1} + 1/A_{2})

d) PE/L x (1/A_{1} + 1/A_{2})

View Answer

Explanation: Change in length of section 1 = PL

_{1}/EA

_{1}

Change in length of section 2 = PL

_{2}/EA

_{2}

Since length is same for both the sections,

Total change length of bar = PL/E x (1/A

_{1}+ 1/A

_{2}).

3. An axial pull of 35000 N is acting on a bar consisting of two lengths as shown with their respective dimensions. What will be the stresses in the two sections respectively in N/mm^{2}?

a) 111.408 and 49.5146

b) 111.408 and 17.85

c) 97.465 and 49.5146

d) 97.465 and 34.263

View Answer

Explanation: The stress = P/A

Where P = 35000N and A is the respective cross section area of the sections.

4. An axial pull of 1kN is acting on a bar of consisting two equal lengths as shown but of dia 10cm and 20cm respectively. What will be the stresses in the two sections respectively in N/mm^{2}?

a) 0.127 and 0.0031

b) 0.034 and 0.0045

c) 0.153 and 0.003

d) 0.124 and 0.124

View Answer

Explanation: The stress = P/A

Where P = 1000N and A is the respective cross section area of the sections.

5. An axial pull of 35000 N on a bar consisting of two lengths as shown with their respective dimensions. What will be the total extension of the bar if the young’s modulus = 2.1 x 10^{5}?

a) 0.153mm

b) 0.183mm

c) 0.197mm

d) 0.188mm

View Answer

Explanation: The total extension in the bar = P/E x ( L

_{1}/A

_{1}+ L

_{1}/A

_{1})

Where P = 35000 N, E = 2.1 x 10

^{5}N/mm

^{2}, L

_{1}and L

_{2}are the 20cm and 25cm respectively and A

_{1}and A

_{2}are the area of both the sections respectively.

6. An axial pull of 20 kN on a bar of two equal lengths of 20cm as shown with their respective dimensions. What will be the total extension of the bar if the young’s modulus = 2×10^{5}?

a) 0.200mm

b) 0.345mm

c) 0.509mm

d) 0.486mm

View Answer

Explanation: The total extension in the bar = P/E x (L

_{1}/A

_{1}+ L

_{1}/A

_{1})

Where P = 2 kN, E = 2 x 10

^{5}N/mm

^{2}, L

_{1}and L

_{2}are same of 20cm and A

_{1}and A

_{2}are the area of both the sections respectively.

7. Does the value of stress in each section of a composite bar is constant or not?

a) It changes in a relationship with the other sections as well

b) It changes with the total average length

c) It is constant for every bar

d) It is different in every bar in relation with the load applied and the cross sectional area

View Answer

Explanation: The value of stress in every section of a composite bar is given by P/A which is it is dependent on the load applied and the cross sectional area of the section. The value of stress in a section does not depend on the dimensions of other sections in the bar.

8. A composite bar of two sections of equal length and equal diameter is under an axial pull of 10kN. What will be the stresses in the two sections?

a) 3.18 N/mm^{2}

b) 2.21 N/mm^{2}

c) 3.45 N/mm^{2}

d) 2.14 N/mm^{2}

View Answer

Explanation: The stress = P/A

Where P = 1000N and A is the respective cross section area of the sections. Here the stress will be equal in both the sections as the dimensions are the same.

9. A composite bar of two sections of unequal length and equal diameter is under an axial pull of 10kN. What will be the stresses in the two sections?

a) 2.145 N/mm^{2}

b) 3.18 N/mm^{2}

c) 1.245 N/mm^{2}

d) 2.145 N/mm^{2}

View Answer

Explanation: The stress = P/A

Where P = 1000N and A is the respective cross section area of the sections. Here the stress will be equal in both the sections as the diameter is the same for both the sections. Even if the length is the variable it will not alter the stress value as the length does not depend on the stress.

10. A composite bar of two sections of equal length and given diameter is under an axial pull of 15kN. What will be the stresses in the two sections in N/mm^{2}?

a) 190.9 and 84.88

b) 190.9 and 44.35

c) 153.45 and 84088

d) 153045 and 44.35

View Answer

Explanation: The stress = P/A

Where P = 15000N and A is the respective cross section area of the sections.

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