6 RESISTANCE OF MATERIALS 



and indicates that in determining the resistance of any material the 

 elastic limit is much more important than the ultimate strength. 



Overstrain of any kind results in a gradual hardening of the 

 material. Where this has already occurred, the elastic properties of 

 the material can be partially or wholly restored by annealing ; that 

 is, by heating the metal to a cherry redness and allowing it to 

 cool slowly. 



6. Working stress. The stress which can be carried by any 

 material without losing its elastic properties is called the allowable 

 stress or working stress, and must always lie below the elastic 

 limit. The ratio of the assumed working stress to the ultimate 

 strength of the material is called the factor of safety ; that is, 



ultimate strength 



(5) Working stress = 



factor of safety 



Average values of the ultimate strength, factors of safety, and other 

 elastic constants for the various materials used in construction are 

 given in Table I. 



Since for wrought iron and steel the elastic limit can be definitely 

 located, the working stresses for these materials is usually assumed 

 as a certain fraction, say 1 to |, of the elastic limit. 



Materials like cast iron, stone, and concrete have no definite 

 elastic limits ; that is, they do not conform perfectly to Hooke's 

 law. For such materials, therefore, the working stress is usually 

 assumed as a small fraction, say from i to ^, of the ultimate 

 strength. 



Under repeated loads, where the stress varies an indefinite num- 

 ber of times between zero and some large value, the working stress 

 may be assumed as J of its value for a static load. 



If the stress alternates between large positive and negative 

 values, that is, between tension and compression, the working stress 

 may be assumed as ^ of its value for a static load. 



For example, if the elastic limit for mild steel is 35,000 lb./in. 2 , 

 the working stress for a static load may be taken as 18,000 lb./in. 2 ; 

 for repeated loads, either tensile or compressive, as 12,000 lb./in. 2 ; 

 and for loads alternating between tension and compression, as 

 6000 lb./in. 2 



