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Unformatted text preview: 13 Points
(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 hollowed-out 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
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 the-circular 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
(b) - 3
(C) - 5
(d) - 2 @ 2. Statics and Axial Loading. The 6ft long1 steel
pipe AB is loaded with a vertical-downward 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 pin-connected 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.
(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—s-Ax:0 Ax - Pmm :— 0 £122 Fm, 2(a) 612902150?) :21 ZLFDPJZ.”
© CoﬂﬁolQ/x. \ﬁ‘ﬂﬂ d“)- WW1 67W :— 31?” —= PWHQ 7537M
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- Fall '06