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(a)  3
(b) — 6
(c) — 4 Your Section #: Your Name: ENGRD 202— MECHANICS OF SOLIDS
Quiz #3/B — Lecture #1 Monday, November 13, 2006 l. A circular shaft that is hollowed—out for a portion
along its length is attached to ﬁxed supports at its
ends. A torque of 180 N—m is applied at the
location C along the shaft as shown in the ﬁgure
at right. The entire shaft is 0.6111 long and 25 mm in
diameter, with the hollowedout portion 0.4m long
and and 18 mm in ID (inside diameter). Recall that the maximum shear stress T Of a shaft
of shear modulus G , polar moment of inertia J
and subjected to torque T is given by A circular shaft with ﬁxed ends
undergoing torsion. Tc . I 7r (:4 . . '
T = 7 where c E outer radius; and J = “*2” for a sohd Circular shaft
' TL
Further, the angle of twist q’) for a shaft of length L is given by gt = 36 (a) Write down the equation which describes the net deformation of the shaft in terms of
its material properties, geometry and loading(s). m (b) What will be the reaction torques at the ends of thecircular shaft, i. e. M A and M B ? (c) What will be the angle of twist of the shaft at C' ‘? Specify the direction (clockwise or
counterclockwise), as viewed from B. 94L C. 5’ x 5 g M: T,» + [3’0 U‘m +Tg, :0 an =4». 13. "in. We ﬂew El... 12 Points
(a) —'.2
(b)  3
(C)  5
(d)  2 @ 2. Statics and Axial Loading. The 6ft long1 steel
pipe AB is loaded with a verticaldownward force
P as shown in the ﬁgure. The pipe is held in the
horizontal position with a very strong, rod~1ike
cable (1.5—inch diameter) attached as shown. The
pipe has an outer diameter of 6inches and a wall
thickness of 0.25 inches. The. Young’s modulus, of the steel used ' the pipe is E = 30 X 106 [psi] and
its Whmit 0'ng 55 [ksi] and the allowable stress for the cable, Hallow = 150 [ksi].
End A of the pipe is pinconnected as is the . A vertically loaded horizontal pipe.
connection between cable and pipe at end B . (a) For a given applied force P what will be the corresponding force, Pcabie in the cable? (b) For a given applied force P what will be the corresponding axial force Pam in the pipe? You may neglect the weight pf this p1 e.
61" ‘gﬁ
(c )_ What is the value of the maximum 1 force P = Pmx the pipe and cable system can support if yield and failure are to be avoided? (d) What will be the social strain in the pipe at maximum load Pmax ? 2} Ma“? ""9 ”PL “'1' (FBCW§)L 7‘0 ”‘9'" FEE—Elana '' 33' R‘Y’h (Page: 2‘60? 3‘12an 7 vFgcceJQ—sAx:0 Ax  Pmm :— 0 £122 Fm, 2(a) 612902150?) :21 ZLFDPJZ.”
© CoﬂﬁolQ/x. \ﬁ‘ﬂﬂ d“) WW1 67W :— 31?” —= PWHQ 7537M
APane :TT(3"'._ 2,711") ; kf S‘lfvm quiz3hi06: 1132.06 ...
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 Fall '06
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