Ductile Materials wider Combined Stress. 103 



strains was 0*000002022 for a l£-inch diameter tube. Ex- 

 amples of the results of this extensometer will be found plotted 

 in some of the stress-strain curves (figs. 21, 23, & 24). 



The values of P, W, p , the axial and the twist readings 

 for the yield-point in the various tests are tabulated in Tables 

 VI., VII., and VIII. under the head of observations. 



41. Determination of the Sectional Area and Thickness of 

 the Tubes. — The external diameter of the specimens was 

 determined by the use of a micrometer-caliper ; they were 

 all practically uniform. The thickness was determined in 

 every case by calipering, and also indirectly from the area of 

 cross-section. The cross-section was determined in cases 

 I., III., X., XL, XII., and XIII. by weighing the tubes in 

 air and in water, the tubes being well boiled in the water, 

 and the specific . gravity of the water at the temperature 

 checked. The density as well as the cross-section was thus 

 determined. The other tubes were weighed and the thickness 

 deduced from the result : as it always closely agreed with the 

 makers' statement and with the result of direct measure- 

 ment, the values may be regarded as fairly close. It should 

 be noticed that errors in the thickness will only very slightly 

 affect the relative results of the tests upon a tube, as the 

 change in the mean diameter is the only way by which the 

 relative results would be affected. 



42. Calculation of the Stresses. — The effect of an axial force 

 P is to produce a stress p, equal to the force divided by the 

 area of the specimen : the values of these stresses for the 

 various experiments are tabulated in the column headed^. 



Owing to the smallness of the friction at the bearings, it 

 has not been thought necessary to allow for it in the value 

 of W; the cases which it affects most are those in which P is 

 large and W comparatively small, the friction being practically 

 proportional to P. The effect of a torque 15 W is to produce 

 a shearing-stress q in the material of the tube varying from 

 the inner surface to the outer proportionally to the distance 

 from the axis. As the thickness of the tube is only from 0*04 

 to 0'06 of the radius, the variation of the shearing-stress from 

 its mean value is only 2 or 3 per cent. The value of q is 

 taken as equal to the torque divided by the product of the 

 area of section and the mean radius. A simple shearing- 

 stress q is equivalent to two principal stresses + q and — q. 

 It is to be noticed that neither tension, torsion, nor their 

 combination produces a third principal stress. 



The effect of. the fluid pressure is to produce an axial 

 stress pi and a circumferential stress whose mean value is 2/> 1; 



