# Quiz 3A - Your Section Your Name ENGRD 202 — MECHANICS OF...

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Unformatted text preview: Your Section #: . . . .. Your Name: ENGRD 202 — MECHANICS OF SOLIDS Quiz #3 / A — Lecture #1 Monday, November 13, 2006 12 Points 1. Statics and Axial Loading. The 6ft long, (a) h 2 steel pipe AB is loaded with a horizontal force P (8 ' g p P as shown in the ﬁgure. The pipe is held in the F3 (:1) 2 vertical position with a very strong, rod-like + ,_ ‘2':- ﬂ - . . ' ML? ”' ’g‘ :31: cable (1.5—inch diameter) attached as shown. a _ The pipe has an outer diameter of 6inches and (P: 9'1“" a wall thickness of 0.25 inches. The Young’s Bah/l W: 03575 modulus, of the steel used in the pipe is ' E m 30 X 106 [psi] and its yield stress cryield m 55 [ksi] and the maximmn allowable stress for the cable, (73,110“, = 150 [ksi]. End A of is— the pipe is pin—connected as is the connection 2'5 ﬁ—al between cable and pipe at end B. A horizontally loaded vertical pipe. (a) For a given applied force P what will be the corresponding force Pcable in the cable? (13) For a given applied force P What will be the corresponding axial force Paxial in the pipe? (0) What is the value of the maximum lateral force P = me the pipe and cable system can support if yield and failure are to be avoided? (d) What will be the axial strain in the pipe at maximum load me. 7 @ fit/m: 0 =7 -P L+ (FggflMlP)L—’ =10 “'9 Egg; Jmlesﬁgw “Pipe l Pane. :— '2..é'>o?l SF, =0 ==> rﬁcC—DNPJFAV Av = PM“, .. @Wu 1 (260:?)(0‘429) BM: ‘3“ Q—‘HOP © CDWFlPLe/LFNIQMVQ ﬁ’b “Ml a Q0M§£MV Mﬂlﬁm a": MLIQI GYMaL 3‘5 m == Pﬂgilm Emma: 2 Use rsx ~= leklm 1. Li ”WV-1: ”filigbm Q) 3313A? ACALW I: ﬂ 0:251 1: ‘5‘“qu F141 ‘t i .; mm ;a sea—W m» mm: 0% rim—+1») , ”w aura-v a '- s s S 28“ KW PM“ 7—“ #27? ¢‘- Iii) )f) "‘ 7>W2 2639} __ IDZJD Hiya, \ ‘ (:29 MM. Wearable ane . {02 a know ‘ 70"" ' ”Pi/I Mm, Lc'l ® PW ¢ 102.0(6)?) "Barre - 2W3? K? m r-D me [Dyan/4W”? igﬂwo /: 10 Points 2. A circular shaft half—hollow along its (3 pt / ea) length is mounted to ﬁxed supports at its ends. A torque of 120 N—m is applied at its midpoint as shown in the ﬁgure at right. The shaft is 250 mm long and 20 mm in diameter, with the hollowed-out portion 125 mm long and the hole 16 mm in diameter. Recall that the maximum shear stress 7' 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. T c i . 7- : 7 where c E outer radius _ _ _ TL and the angle of tunst qt for a shaft of length L is glven by qt = _J G (a) Write down the equation of compatibility for the shaft shown. (13) What Will be the reaction torques at the ends of the circular shaft, i. e. ill/IA and IVIB ? You may express these reactions in terms of the quantities: Shear modulus G ; polar moment of inertia J; magnitude of the applied torque T; shaft radius 0; and shaft section length L. A 5 X2 c C 5: X5: 8 (c) What will be the angle of twist at O ? 17:4 * .5, A E!" ‘2,” en «H20 ”we _ 335% (#1.?! TH IZDN‘IM TH no +72: 0 ...
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