238 APPLIED SCIENCE 



If a bar of 4 sq. in. cross-section is under a total pull of 36,000 

 Ibs., the unit stress is then one-fourth of 36,000 Ibs., or 9000 Ibs. 

 per square inch. 



When a piece is stressed beyond the elastic limit and 

 consequently breaks, we say that it has been stressed to its 

 ultimate strength. The ultimate strength or breaking stress 

 is a unit stress and is always given in pounds per square inch. 

 The ultimate strength is that unit stress which is found just 

 before rupture and is the greatest unit stress the piece will bear. 



Suppose we find, by testing, that a bar of wrought iron 2 in. square 

 breaks under a tension of 240,000 Ibs. What is its ultimate strength? 

 Since the sectional area is 4 sq. in. and the total stress which it took 

 to break the bar was 240,000 Ibs., the stress per unit of area will 

 be 240,000 * 4, or 6000 Ibs., the ultimate strength. 



286. The Stress of Elongation. Ultimate strength and 

 the unit of ultimate elongation are closely related. The ulti- 

 mate elongation is a strain produced in a unit of length by a 

 stress equal to the ultimate strength of the material. In other 

 words, the elongation of a test piece 1 in. long just at 

 the point of rupture is its ultimate elongation. A rule for 

 finding the ultimate elongation is: Divide the total elongation 

 of the piece at rupture by the original length. 



In making tests of materials, it is often well to record 

 the percentage of elongation. This is nothing more than 

 the ultimate elongation expressed in per cent. 



Suppose we find that a 50-in. rod elongates Yi in. under a certain 

 load. The unit of ultimate elongation will then be }/% + 50 or 

 -j-^ in. The per cent of elongation will be T -J- T in. expressed 

 in per cent. If the ultimate elongation is expressed as a decimal 

 the same rule will hold; that is, simply multiply the decimal by 100 

 and call the answer per cent. For example, if an ultimate elonga- 

 tion figures .025 in., multiplying this by 100 will give us 2.5%. 



