ELASTIC PROPERTIES OF MATERIALS V 



Problem 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 ? 



Problem 8. A round cast-iron pillar 18 ft. high and 10 in. in diameter sup- 

 ports a load of 12 tons. How much does it shorten, and what is its unit con- 

 traction ? 



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

 What is the force acting on it ? 



9. Poisson's ratio. It has been found by experiment that when 

 a rod is subjected to tension or compression its transverse dimensions 

 are changed as well as its length. For instance, if a round rod is in 

 tension, it increases in length and decreases in diameter, whereas, if 

 the rod is compressed, it decreases in length and increases in diam- 

 eter. Experiment has also shown that this lateral contraction or 

 expansion is proportional to the change in length of the bar; that 

 is to say, the ratio between the two is a constant. This constant 



is denoted by , and is called Poisson's ratio, from the name of its 



. . m 



originator. 



Poisson's ratio varies somewhat for different materials, but ordi- 

 narily lies between J and J. Values of this ratio for a number of 

 materials are given in Article 22. 



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

 Problem 11. A soft steel cylinder 1 ft. high and 2 in. in diameter bears a 

 weight of 76 tons. How much is its diameter increased ? 



10. Ultimate strength. From the definition given in Article 7, 

 the ultimate strength of a body is the greatest unit stress it can stand 

 without breaking. In calculating the ultimate strength no account 

 is taken of the lateral contraction or expansion of the body, the ulti- 

 mate strength being defined as the breaking load divided by the 

 original area of a cross section of the piece before strain. The reason 

 for this arbitrary definition of the ultimate strength is that the actual 

 load on any member of an engineering structure usually lies within 

 the elastic limit of the material, and within this limit the change 

 in area of a cross section of the member is so small that it can be 

 neglected. 



Tabulated values of the ultimate strength of various materials in 

 tension, compression, and shear are given in Article 22. 



