COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 401 
to the fracture range, the range of real stress will never attain the higher real value 
reached when the full bending moment is put on the (mild) steel in its primitive 
elastic condition. 
The author does not, of course, put forward initial ‘ overstressing’ in bending 
tests as an explanation of ‘ understressing,’ which is a phenomenon observed also 
in alternating direct loading. Initial overstressing of the above kind would cause 
overestimation of the effect of ‘ understressing ’ in torsion and bending tests. 
The author is indebted to Mr. N. P. Inglis, B.Eng., for making the torsion tests 
of the A.R.C. steel. 
APPENDIX I. 
CALCULATION OF THE RusistING MOMENT OF THE SECTION OF A Sorry Rounp BAR 
ON WHICH THE SHEAR STRESS DUE TO TORSION HAS A DISTRIBUTION LIKE THAT 
SHOWN IN F ia. 5. 
Referring to fig. 18— 
Let C be the elastic modulus corresponding to the line OP ; 
C’ be the modulus corresponding to RS— 
Pa ny A (stress) 
A (strain)’ between R and 8. 
N 
Resisting moment of the section = | 2. ft. Qt 
0 
where q is the stress at radius r. 
With linearity of strain throughout body, and distxibution of stress as in fig. 18— 
Between O and R, stress = Ce : A A z : : sh (09) 
== irs 
: : ; e 
where ¢ is the strain at radius r and k =-. 
t 
Between R, and §, stress = C.k.r, + C.k.(r — r®) 
=(C—Ckire+C. kur. f P eh a(2) 
where? is the radius at which the modulus changes from C to C’. 
The above expression for the resisting moment may now be written as : 
Ve  - i) 
2n.C. | dr + 24 (C—C’). kore rir +24. 0'.8. | dr 
0 Te Ye 
» 4 " . 
= 2m. O.bE + 2m. (CC) deere M58 4 De. Of, b, tet 
where r, is the outside radius. 
The resisting moment, calculated on the usual assumption of linear distribution of 
stress from axis to skin 
| 
ins 
9 + Wes 
where q, is the stress at the skin calculated in this manner. 
EE 2 
