BEHAVIOUR OF MATERIALS IN TESTING MACHINE 189 
ss 
| Gauge length (), inches! 4 6 8 10 12 4 
} Elongation (c), percent.| 378 | 31:8 | 285 | 2967 | 255 | 245 
; - Plot on squared paper ¢ and wa where a is the area of the cross section of 
_ the bar in square inches. Draw the straight line which most nearly contains all 
the points, and find the values of the constants ¢ and 6 in the equation to the 
line, which is enone 5, Apply the equation to find the probable elongation 
om. in 8 inches of a test piece of the same material 1 inch wide and } inch 
6, A bar of mild steel 10 inches long and 1} inches in diameter has a ve 
_ turned on it at the centre of its length, the groove being 4 inch wide and 4 inch 
deep. Another bar of the same material has the same length and a uniform 
eter of l inch. Compare the resilience of the second bar with that of the 
first for the same maximum stress, the bars being loaded in tension. 
_ 1%. The averages of the results. of numerous tests of the crushing strength of 
hard steel balls are given’in the following table :— 
}a@-. inches} ¢ | w-| t | w | @ | 4 | 8 
‘|W. . tons} 0-77 160 | 288 | 407 | 582 | 9:50 | 13-04 
where d is the diameter of the ball, and W the crushing load. The balls were 
tested between two hard steel plates. Calculate for each size of ball the stress 
fin the formula w=3ay. Plot f and d, also W and d. Scales.—For d, eight 
times full size; for f, 1 inch to 10 tons per square inch ; for W, 1 inch to 2 tons. 
Show that an expression of the form f=a-—bd gives approximately the relation 
between f and ej in the above results, where a and 6 are constants, and find 
the values of these constants. Hence the relation between W and d is 
W=Ta\a —bd). 
8. The following table gives the results of crashing tests on cast-iron rollers 
' tested between steel plates :— ‘ 
; d » . inches 
ja } a t i 1 1s | 1a 
_|l.. . inches } 1 14 1} 14 18 1g 
|W .. tons} 4:3 
2 6°90 9°95. 12-70 17-11 | 21°20 27°00 
a 
_ d=diameter of roller, /=length of roller, W=crushing load. Plot W and dxl, 
_and find the most approximate value of ¢ in the expression W=cdl for the above 
results. Scales.—For dx/J, 1 inch to } square inch ; for W, 1 inch to 5 tons. 
_ 9. A cylindrical piece of cast-iron 0°727 inch in diameter and 2 inches long 
Was tested in compression, the load being axial. The piece gave way by 
she ng in a plane inclined at 37° to the axis when the crushing load was 
22°91 tons. Neglecting the alteration in the diameter of the piece, calculate the 
ensity of the shear stress in the plane of fracture. What is the value in this 
e of the coefficient « used in Art. 166, p. 175? 
10. Same as Exercise 9, except that the angle was 33° instead of 37°, and the 
ashing load was 19-25 tons instead of 22°91 tons. 
11. The load on a certain steel tie-bar in a bridge truss varies from 14 tons to 
L tons (both tensions). If the tenacity of the material is 28 tons per square 
inch, and the coefficient n in the formula given on p. 178 is 1°56, what must be 
