—————— ee CU 
COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 397 
Round Specimens under Alternating Bending. 
The distribution of stress under alternating bending is more difficult to treat, 
because, unlike hollow specimens in torsion, the stresses in hollow specimens cannot 
directly be even approximately estimated. The author has used some data obtained 
in tests! of hollow and solid specimens bent to and fro under ranges of alternating 
bending moment, and has calculated the ultimate ranges of stress at the skin and 
throughout the specimen on the same assumption as that made use of for torsion. 
, 
Mrernating Bending 
21 LA. . 
the curnges of Sfresses plofléd are Wt Solid 
Colewlaléd by The formuta , — 
Stress = (radu) x (¢naing momeat] AIG. holiow 
(M- of inerlia of section) A le. hallow 
ta he. linearity of Stress 1s assumed. 
inch 
» 
e 
Range oF Stress 
IS per 4 
* 
an 
Mal} = Range eh SCI A SIAL Shan DACs 
z & 6 6 19 2 1? a 
Hie. 21 
Briefly stated, the method has been: To assume a stress distribution (at ranges of 
bending moment continued long enough to give constancy of range of strain) like 
nl 
that of fig. 19; to calculate the ranges of stress at the skin for various values of E 
(’ and E being the moduli corresponding to the lines OP and RS (fig. 19); and, 
by equating the range of resisting moment to the applied bending moment, to ascer- 
tain which value or values of = give approximately the same ultimate skin stress for 
hollow specimens on the one hand and for solid specimens on the other. Then, 
finally, to see if the curves of ‘ true’ stress and strain for hollow and solid specimens 
coincide. 
Table VI. gives data concerning the specimens, two of which are hollow and two 
solid. In calculating the bending strains from the observed ranges of bending in 
ems. onscale, 30 x 10° per sq. in. has been taken as the elastic modulus. The curves 
of fig. 21 have been plotted from columns 2 and 5 of Table VI. It will be observea 
1 Proc. Inst. Mech. Eng., Feb. 1917. 
