THE STRENGTH AND DUCTILITY OF FLAT STEEL BARS. 213 
in Table IX., both at the fracture and at a point originally distant therefrom a length 
equal to the width of the bar. From fig. 14, in which these values are plotted, it is 
seen that the change in the ratio increases fairly continuously with the ratio itself as 
regards the measurements at fracture, while in the sensibly straight portion of the bar 
the increase of the ratio is almost constant at about 34 per cent. 
TABLE IX. 
IniviaL aND Fina Ratios or Wipta to THICKNEss. 
Width/Thickness, 
Final ratio / Initial ratio. 
Per cent. 
Nominal Width. Final. 
Inches. is 
Initial. 
Outside of Outside of 
At Fracture. Constriction. po raeume. Constriction. 
4 1:76 2:07 1:82 1176 103°4 
1 3°81 4°85 3°95 ITS) 103°7 
1} 5:64 7°30 5°85 129°4 103-7 
2 (oy 9°91 7°86 130°9 103°8 
2 9°57 13°53 9°88 141°4 103°2 
3 11:14 15:01 11°50 134°8 103°2 
34 13°32 19°50 13°85 146°4 104:0 
4 15°39 21:60 15°92 140°4 103-4 
SUMMARY. 
In a series of flat test-bars of mild steel, of constant thickness and variable width, 
the effect of the ratio of width to thickness upon the apparent strength and ductility 
of the metal has been determined. 
(1) The strength, both elastic and ultimate, is sensibly unaffected. 
(2) The extension, measured on a fixed gauge-leneth of 8 inches, increases as the 
ratio width/thickness is increased from 2 to 7, remains sensibly constant from 7 to 12, 
and rises again as the ratio passes from 12 to 16. The extreme difference of extension 
is 10 per cent. on 8 inches, that is, nearly one-half of the extension of the narrowest bar. 
The extension on other fixed gauge-lengths varies in a manner closely similar to 
- the above. 
(3) The extension, measured on a variable gauge-length equal to some definite 
Proportion of the ratio width/thickness expressed in inches, decreases somewhat irregu- 
larly as the ratio itself increases. 
7 (4) The extension, measured on a variable gauge-length equal to 11:3 area, 
increases as the ratio width/thickness is increased from 2 to about 7, then decreases 
from 7 to about 12, and then increases as the ratio passes from 12 to 16. The extreme 
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