COMPOUND STRAINS AND STRESSES 147 
forces to the right of C, the forces R, and Q, produce a bending moment 
= 3120 x 15-6000 x 7=4800 inch-lbs., and the forces Q and Q, 
produce a twisting moment = 6000 x 6 = 36,000 inch-lbs. The equivalent 
twisting moment at C due to these is 
’ 4800+ ,/4800? + 36000? = 41,119 inch-Ibs. 
_ If fis the maximum stress in the shaft at C, then gent 41,119, from 
which f= 4884 lbs. per square inch. 
Consider lastly the straining actions on the crank pin B. Taking the 
forces to the right of B, the forces Q, and R, produce a bending moment 
= 6000 x 14 —3120 x 22 = 15,360 inch-lbs., and the forces Q, Q,, Q,, and 
eee a twisting moment = 6000 x 12 — 3120 x 6 = 53,280 inch-lbs. 
equivalent twisting moment at B due to these is 
15360+ ,/15360? + 53280? = 70,810 inch-lbs. 
 Iff is the maximum stress in the pin B, then 1g 32 = 70,810, from 
which f= 8411 Ibs. per square inch. 
) 147. Ellipse of Stress.—ABCD (Fig. 199) is an indefinitely small 
eube, edges of length 7. On the faces AD and BC there is pure normal 
stress of inten- 
sity p, and on q 
a faces AB and Ac | B 
CD there is pure sa rer 
normal stress of = SEP. 
intensity g. It is Pp Pp 
required to find ) fees Paap 
the direction and __]M NI, 
intensity of the D Cc 
‘Stress on any a x | \a| | 
interface LN - 
clined at an an 
> Ge Draw ; thy 1 
parallel to ae ae 
AB. Consider add Y Tow 
_ the equilibrium M N 
¢ an pion A 
; ‘ @ re- 
i sultant of the Fia. 199. 
_ Stress, and ¢ its inclination to LM. R=r/?/cos@. Then, since R must ~ 
_ balance P and Q, 
+ 
R sin =P, or av sin @=pl? tan 0, therefore sin 6=" sin ¢. 
cos 0 p 
if ad rl? «4 Zz 
a Reos p=Q, or oe = ql’, therefore cos er cos ¢. 
ee Hens sin pr? aan? 6 + cos? = 1. 
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