SE 
erie 
SIMPLE STRAINS AND STRESSES 69 
the stress is sensibly proportional to the load, but ductile materials, such 
as wrought-iron and mild steel, alter considerably in 
cross section when loaded in tension or compression 
beyond the elastic limit, and the stresses are there- 
fore no longer proportional to the load. For 
example, if a bar in tension has an area of cross 
section at the fracture equal to half its original 
area, the actual stress at fracture will be twice 
the nominal stress, the nominal stress being equal 
to load + original area. If, therefore, the diagram . 
(Fig. 79) is a true stress-strain diagram, it will 
not be a true load-strain diagram. In practice it 
is the load-strain diagram which is actually drawn 
by the autographic apparatus on a testing machine. The diagrams are, 
however, often spoken of as stress-strain diagrams when they should be 
called load-strain diagrams. 
The actual form of the stress-strain diagram or load-strain diagram 
varies greatly for different materials. Different forms of the diagram are 
considered in Chapter XI. 
87. Work.done in Producing Strain——The load-strain diagram is 
also a diagram representing the work done in producing the strain, In 
previous Articles of this chapter strain has been 
denoted by x//. Hence referring to Fig. 80, it fol- 
lows that if OX represents a particular amount of 
strain it will by altering the scale also represent 
the quantity z. Lengths along ON then represent 
distances through which the load acts, and the 
heights of the line OAB above ON represent the 
variation in the load as the bar is deformed. It 
follows that the work done in deforming the bar, ~~ STRAIN 
say by the amount OX, is represented by the area Fra. 80 
of the figure OAYX, where XY is perpendicular <u 
toON. (See Art. 41, p. 25.) 
88. Resilience and Shock.—The work done in straining a bar up to 
the elastic limit is called the resilience of the bar. Referring to Fig. 80, 
the area of the triangle OAM represents the work done in straining the 
bar up to the elastic limit. If the bar is in tension or compression, 
OM =z, the amount of extension or compression, and AM is the load W 
at the elastic limit. Hence the resilience=4Wx=4afx, where a is 
the area of the cross section of the bar, and / the stress at the elastic 
limit. But it has been shown (Art. 83) that za, therefore 
STRAIN 
Fia. 79. 
B 
resilience = aa , but al is the volume of the bar, therefore, putting V = al, 
resilience = hag 
If the bar is strained to some point below the elastic limit the 
expression for the work done will still be oe but the stress f will not’ 
now be the stress at the elastic limit, but will correspond to the strain 
produced, 
