188 APPLIED MECHANICS 
2. Ina tensile test of a mild steel bar, the following observations were made: 
W=load in tons, s=extension in a length of 8 inches in inches, d=smallest 
diameter of bar in 
inches. 10°64 was : ‘i é : 
the [sad at the yield WwW O |10°64 |13°81 |15:07 | 15°64 | 15°60 | 12°97 
point, 15°64 was the | « 0 0°24 0°60 1:02 157 2°12 2°79 
maximum load, and . ‘ ; : ; ; - 
1807 was the break- d |0°906 | 0°891 |} 0°871] 0°851] 0°825| 0°799) 0°588 
ing load. The second 
value of x (0:24) was at the end of the “‘ yield.” Plot « and the nominal stress, 
also « and the actual stress. Scales.—Stresses, 1 inch to 5 tons per square 
inch ; x, 24 times full size. 
3. In a tensile test of a mild steel bar, the following observations were 
made: Diameter of bar, unloaded, 0°748 inch, W=load in tons, «=extension, in 
inches, on a length of 8 inches. Load at elastic limit, 6 tons. Maximum load, 
12°54 tons. 
1 2 3 4 5 6 | 681 “yield” point, | 
0-0014 | 0:0027 | 0:0040] 0:0055 | 0:0068 | 0°0082 | 0-18 atend of “yield.”| 
. 3 
W 75 9:0 10°5 12°0 12°54 12°25 |10°25 Breaking load. 
x 0°19 | 0:27 0°55 1:05 1:75 2°10 | 2:42 Total extension. 
(a) Plot W and x up to W=6 and #=0'0082. Scales.—W, 1 inch to 1 ton; 
x, 1000 times full size. 
(b) Draw the straight line which most nearly contains the points in (a), and 
calculate from it the modulus of elasticity in lbs. per square inch, 
(c) Calculate the load, in tons, necessary to elongate the bar 0°006 inch. ae 
(d) How many ft.-lbs. of work have been done in stretching the bar 0°0082 
inch ? 
(e) Plot W and « from no load up to the breaking point. Scales.—W, 1 inch 
to 2 tons; x, 24 times full size. 
(f) Determine the total work done, in ft.-Ibs., in breaking the bar. : 
(g) Plot x and the nominal stress, also x and the actual stress. Scales.— 
Stresses, 1 inch to 5 tons per square inch; «, 24 times full size. Assume volume 
of bar constant in finding. cross section up to maximum load. Assume also that 
the contracted section at fracture is 0°43 of the original section. é 
4. A cylindrical piece of mild steel was tested in compression, The load W, 
in tons, acted on the ends of the piece. The mean diameters of the piece at the 
top, middle, and bottom of its length were d,, dz, and dz inches respectively, and 
its length was / inches. Values of these dimensions for various values of W are 
given in the following table :— 
W 0 5 10 15 20 25 30 35 40 
d, | 0°719 | 0°720 | 0°757 | 0°813 | 0°884 | 0°965 | 1°054 | 1:13 1:20 
d, | 0°719 | 0°723 | 0°763 | 0°832 | 0°922 | 1°045 | 17144 | 1°21 1:60 
dz | 0°720 | 0°721 | 0°760 | 0°815 | 0°886 }| 1°000 | 1°085 | 1:14 1°22 
l 1°624 | 1589 | 1°452 | 1:236 | 1-025 | 0 804 | 0°690 | 0°61 | 0°54 
Under the greatest load the piece was free from cracks. 
Calculate the nonfinal and actual compressive stresses on the smallest sections, 
and plot the results in the manner shown in Fig. 243, p. 171. Scales.—Linear, 
twice full size. Stresses, 1 inch to 20 tons per square inch. 
5. A test piece of steel boiler plate of rectangular section 14 inches wide and 
& inch thick, when tested» for elongation, gave, after fracture, the following 
results :— A AY, 
