STRESS AND DEFORMATION 11 



3. A steel ring fits loosely over a cylindrical steel pin 3 in. in diameter. Hovr 

 much clearance, or space between them, should there be in order that, when the 

 pin is subjected to a compressive load of 60 tons, the ring shall fit tightly ? 

 Solution. Unit compressive stress in pin is 



= 17,000 lb./in. 



IT 



Unit longitudinal deformation s = = 17 ' 00 = .000566. Unit transverse def- 



E 30,000,000 



ormation = .295 x .000566 = .000167. Radial clearance = 1.5 x .000167= .00025 in. 



4. A post 1 ft. in diameter supports a load of 1 ton. Assuming that the stress is 

 uniformly distributed over any cross section, find the unit normal stress. 



5. A shearing force of 50 Ib. is uniformly distributed over an area 4 in. square. 

 Find the unit shear. 



6. A steel rod 500 ft. long and 1 in. in diameter is pulled by a force of 25 tons. 

 How much does it, stretch, and what is its unit elongation ? 



7. A copper wire 10 ft. long and .04 in. in diameter is tested and found to stretch 

 .289 in. under a pull of 50 Ib. What is the value of Young's modulus for copper 

 deduced from this experiment ? 



8. A round cast-iron pillar 18 ft. high and 10 in. in diameter supports a load of 

 12 tons. How much does it shorten, and what is its unit contraction ? 



9. A wrought-iron bar 20 ft. long and 1 in. square is stretched .266 in. What is 

 the force acting on it ? 



10. What is the lateral contraction of the bar in problem 9 ? 



11. A soft-steel cylinder 1 ft. high and 2 in. in diameter bears a weight of 

 40 tons. How much is its diameter increased ? 



12. A copper wire 100 ft. long and .025 in. in diameter stretches 2.16 in. when 

 pulled by a force of 15 Ib. Find the unit elongation. 



13. If the wire in problem 12 was 250 ft. long, how much would it lengthen 

 under the same pull ? 



14. A vertical wooden post 30 ft. long and 8 in. square shortens .00374 in. under 

 a load of half a ton. What is its unit contraction ? 



15. How great a pull can a copper wire .2 in. in diameter stand without breaking ? 



16. How large must a square wrought-iron bar be made to stand a pull of 

 3000 Ib.? 



17. A mild-steel plate is \ in. thick. How wide should it be to stand a pull of 

 10 tons ? 



18. A round wooden post is 6 in. in diameter. How great a load will it bear ? 



19. A wrought-iron bar is 20 ft. long at 32 F. How long will it be at 95 F. ? 



20. A cast-iron pipe 10 ft. long is placed between two heavy walls. What will 

 be the stress in the pipe if the temperature rises 25 ? 



21. Steel railroad rails, each 30 ft. long, are laid at a temperature of 40 F. What 

 space must be left between them in order that their ends shall just meet at 100 F. ? 



22. In the preceding problem, if the rails are laid with their ends in contact, 

 what will be the temperature stress in them at 100 F. ? 



23. A f-in. wrought-iron bolt failed in the testing machine under a pull of 

 15,000 Ib, Find its ultimate tensile strength, 



