4 STRENGTH OF MATERIALS 



6. Unit deformation. If a bar of length / is subjected to tension 

 or compression, its length is increased or diminished by a certain 

 amount, say AZ. The ratio of this change in length to the original 

 length of the bar is called the unit deformation, and will be denoted 

 by s. Thus A ^ 



s = y 



In other words, the unit deformation is the elongation or contraction 

 per unit of length, or the percentage of deformation, and s is there- 

 fore an abstract number. 



Problem 3. 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. 



Problem 4. If the wire in Problem 3 was 250 ft. long, how much would it 

 lengthen under the same pull ? 



Problem 5. 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? 



7. Strain diagrams. As mentioned in Article 1, experiment has 

 shown that the effect of the action of external forces upon a body is 

 to produce a change in its shape. If the body returns to its original 

 shape when these external forces are removed it is said to be elastic, 

 whereas if it remains deformed it is said to be plastic. 



For instance, the steel hairspring of a watch is an example of an 

 elastic body, for although it is compressed thousands of times daily 

 it returns each time to its original shape when the compressive force 

 is removed. Wood, iron, glass, and ivory are other examples of elastic 

 substances. 



As examples of plastic bodies may be taken such substances as 

 putty, lead, and wet clay, for such materials retain any shape into 

 which they may be pressed. 



It has been found by experiment that most of the materials used 

 in engineering are almost perfectly elastic, if the forces acting on 

 them are not too large. That is to say, if the external forces do not 

 surpass a certain limit, the permanent deformation, although not 

 zero, is so small as to be negligible. If, however, the external forces 

 gradually increase, there comes a tune when the body no longer 

 regains its original form completely upon removal of the stress, but 

 takes a permauent "set" due to plastic deformation. If the exter- 

 nal forces increase beyond this point, the permanent (or plastic) 



