24(i WORK DONE ON BARS, 



of the tests of a mild steel bar (see Fig. 68, p. 148). This 

 may be taken as a typical load-strain curve. It may also be 

 supposed to be either plotted from individual results, or to 

 have been produced by means of an automatic apparatus. 



The whole life of the test bar, from the time when the 

 load upon it is first applied, may be divided into four stages. 

 Referring to the diagram, from A to D the bar is elastic, 

 and its strains are relatively small, and not permanent ; 

 this is the elastic stage. At D the limit is approached, 

 and the strains are greatly increased. From D to E is the 

 second stage, during which the bar is in a state of unstable 

 equilibrium, the stress alternately increasing and decreasing 

 with the strain, and producing an uneven and serrated 

 curve, if the diagram is automatically drawn ; this may 

 be due to a succession of sudden local yieldings of the 

 material. When the point E is reached, the uniform semi- 

 plastic stage begins ; here the strains and stresses 

 increase together in a uniformly varying ratio. At F the 

 maximum load is reached, and the third stage is complete. 

 From F to G represents the fourth and last stage, during 

 which the strain is chiefly that due to local extension. The 

 fourth stage is complete at G, which marks the point of 

 fracture of the bar. 



Mechanical work is the product of a force into the 

 linear distance through which it is exerted. The force or 

 load on a test bar is represented on the diagram by 

 horizontal measurements parallel to the base line A B, ar.d 

 from the zero line A H. Strains are measured vertically 

 upwards from the zero line A B. The total strain is 

 the distance through which the varying load has done its 

 work. The area A H G F E D of the diagram is the pro- 

 duct of horizontal and vertical linear measurements. 

 Therefore the area represents, to some scale, the total 

 work done upon the bar in breaking it. 



Thus, if m is the number of tons represented by one 

 inch, horizontally, n is the number of inches of strain 

 represented by one inch vertically, and a is the measured 

 area of the diagram in square inches. 



Then m. n. a. will be the work done on the bar in inch- 

 tons. 



The area of the diagram may be ascertained by means 

 of a planimeter. In the present instance the area, a, is 

 found to be 17 '48 square inches. 



m = 5, and 

 2 



