Review Questions

REVIEW QUESTIONS

1. Derive total elongation expression for bars of varying cross section.

2. Derive total elongation expression for uniformly tapering rod.

3. Derive, E = 2G ( 1 + 1/ m)

4. Derive, E = 3 K (1 – 2/m)

5. Derive an expression for temperature stresses in composite bars.

PROBLEMS FOR PRACTICE

1. A rod 200 cm long and of diameter 3 cm is subjected to an axial pull of 30 kN. If the Young's modulus of the material of the rod is 2 × 105 N/mm2.

Determine (i) Stress, (ii) Strain, (iii) Elongation of the rod.

[Ans. (i) 47.44 N/mm2, (ii) 0.000212, (iii) 0.0424]

2. Find the Young's modulus of rod of diameter 30 mm and of length 300 mm which is subjected to a tensile load of 60 kN and the extension of the rod is equal to 0.4 mm. 

[Ans. 63.6 GN/m2]

3. A rod circular in section tapers from 20 mm diameter at one end to 10 mm diameter at the other end and is 200 mm long. On applying an axial pull of 6000 N, it was found to extend by 0.068 mm. Find the Young's modulus of the material of the rod. 

[Ans. 1.123 × 105 N/mm2]

4. A copper rod 5 mm in diameter when subjected to a pull of 750 N extends by 0.125 mm over a gauge length of 327 mm. Find the Young's modulus for copper. 

[Ans. 99923 N/mm2]

5. A straight bar of steel rectangular in section is 4 m long and is 18 mm thick. The width of the rod varies uniformly from 130 mm at one end to 50 mm at the other. If the rod is subjected to an axial tensile load of 50 kN, find the extension of the rod. Take, E = 2 × 105 N/mm2. 

[Ans. 0.662 mm] 

6. A reinforced concrete column is 400 mm × 400 mm and is provided with 8 bars of 22 mm diameter. Find the safe axial load on the column if the Ec maximum stress in concrete is limited to 4 N/mm2. Take, Es = 18 Ec.

[Ans. 846 kN]

7. A rod tapers uniformly from 40 mm diameter to 20 mm diameter in a length of 400 mm. If the rod is subjected to an axial load of 10000 N, find the extension of the rod. Take, E = 2 × 105 N/mm2. 

[Ans. 0.032 mm]