8 RESISTANCE OF MATERIALS 



In actual practice the unit working stresses are usually specified, 

 and the designer simply follows his specifications without reference 

 to the factor of safety. Where a large number of men are employed, 

 this method eliminates the personal equation and insures uniformity 

 of results. The student should become familiar with both methods, 

 however, as it is no small part of an engineer's training to know 

 what relation his working stress should bear to the elastic limit 

 and ultimate strength of the material. 



7. Resilience. The work done in straining a bar up to the elastic 

 limit of the material is called the resilience of the bar. The area 

 under the strain diagram from the origin up to the elastic limit 

 evidently represents the work done on a unit volume of the material, 

 say one cubic inch, in straining it up to the elastic limit. This area 

 therefore represents the resilience per unit volume, and is called the 

 modulus of elastic resilience of the material. 



Thus, if p denotes the unit stress and s the unit deformation at 

 the elastic limit, then, since the strain diagram up to this point is a 

 straight line, the area subtended by it, or modulus of elastic resili- 

 ence, is ljt?. Since - = E, the expression for the modulus may 

 s 



therefore be written 



(6) Modulus of elastic resilience = f 



O 77T 



Hence, if V denotes the volume of the test piece, its total resilience is 



(7) Total resilience = 



The resilience of a bar is a measure of its ability to resist a blow 

 or shock without receiving a permanent set. If a load W is applied 

 gradually, as in a testing machine, the maximum stress when the 



load is all on is p = , where A denotes the area of the cross 



A 



section of the bar. If, however, the load W is applied suddenly, 

 as in falling from a height ^, it produces a certain deformation of 

 the bar, say A/, and consequently the total external work done 

 on the bar is 



External work = (h + AZ) W. 



