THE STRENGTH AND DUCTILITY OF FLAT STEEL BARS. 205 
section, and {2’ the final area of cross-section of the bar. Then, if the volume of the 
metal remains constant, a condition which is nearly fulfilled,— 
0 = Oren) eo’ 
or the extension is, 
dA _O-0’ 
ug 
This gives approximately the maximum limiting extension. The mean values are 
70 
L=linch 
60 
® i | L=3inches 
z 
ira} 
> = i e 
a 
Bee L=5inches 
. > L=7 inches 
o ; 
oO L=-9 inches 
en L=Ilinches 
iE l=|3 inches 
a L L=!5inches 
oO I 2 4 6 8 10 12 14 16 
WIOTH 
THICKNESS 
Fic. 7.—Variation of extension of flat steel test-pieces with change in the ratio of width to thickness from 2 to 16, a 
constant thickness of + inch, and gauge-lengths of 1 inch to 15 inches. 
the bars wider ham 1 inch the values are ne constant. 
Fig. 7 shows the data of Table IV. plotted, not for each bar separately, but for each 
fixed length of bar, and it illustrates the manner in which the extension of a fixed 
length varies as the width of the bar is increased. The curves, excluding that for a 
‘l-inch length, are all of the same type; the extension rises at first as the width of the 
bar is increased, then remains almost constant, and finally rises again at about the 
Same rate as at first. In fig. 8 is drawn separately, with a more open vertical scale, the 
curve of extension for a length of 8 inches, the standard fixed length for flat test-pieces 
im this country. ‘he vertical distance between the two curves of fig. 8 represents the 
