final_samples - 1 See figure below When a couple M is...

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Unformatted text preview: 1. See figure below. When a couple M is applied at A, the frame is in equilibrium, While the crank AB is vertical, the beam CD is horizontal, and the cable makes a 20° angle with the horizontal line. Neglect the friction between the cable and the pulley. (a) Draw free-body diagrams for members AB, BD, CDE and the pulley at E. (10) (b) Determine the force in the member BD. (5) (c) Determine the moment M applied at A. (5) La) E BOA”! = .‘I - 7224/ ~loI7A/ a“ an. E] : "‘ T(/+3M20°) From/L : ZMG 3 O: 50(959‘ (l) +Ex (o~6)+Ei(3)=0i => F59 == 473+A/ LC) From 3 ZMA=0 ; M —~ (33035.49 (my) :1 0 § M21567/V‘W" mmwrm.“WWV...”.WMWVFW”mw.w.m~w.m~«mi.m‘mflw.fwwfiw, 2. See figure below. The bracket is loaded by two cables and supported at O by the nut and bolt. (a) Express the forces exerted by the cables as vectors. (5) (b) Determine the reaction force and moments at O to maintain equilibrium. Calculate their magnitudes, and specify their directions in unit vectors. (20) La) E :a‘bkw)(C0$S‘ong - SLi/lfoo : L029}; - (.2262 (EU) T : (2»? (cu) (60550:? ~s¢vt§°°é€> 22,07?j -12}; c WU) “(5'0 J; (WU/M) o W H Ti/st MR 3 {(7}; + 3602 Jrz‘kf'vl: ( mm) 1 Lb) ' 00M Id: _K£d Readoth- 7am! 53" R+f+l =0 3 {32*(Ff7‘): —{‘o;gi—w‘5§2j+[5zlvf (tr/U) [51:1‘775'16/1/ .53.. M V\: 2-037 3 } ~ M753 mggflf 3. See figure below. A beam AB is subjected to a concentrated force and a distributed load. Neglect the weight of the beam. (21) Find the reactions at the fixed support A. (5) (b) Find the internal shear force and bending moment at a section 2 m to the right of A. (5) (c) Draw the shear force and bending moment diagrams for the beam. (10) La) A] I 4 +UX2 MA L41 m-‘FL’i HEAL“. 2::‘11———+§g MA: 4xl+ I‘S'XLX(3> 34+? ;: /3((c/l/vm) CL) [W‘fCVM( Shear force“ 4. Determine the range of cylinder mass m for which the 50-kg block is in equilibrium. Neglect the mass of the pulley. (a) Assume frictionless contact between the belt and the pulley. (10) (b) Re—do your calculation with the coefficient of friction between the belt and pulley ,u = 0.1. (5) (a) [V0 (frivfx'm ECWQW aww‘ Pix—((27. 7 Tl :: mgfiiww” MW/lidiwszo" 22:7A/ ,uze 77,1716 zgggM I I TNMW._MWW7_.MFW-M_ (E) W 3% W; <14. whim 7; #72 am 561% QM [Maggy F2 r {he Lav er LOW 0% Mu; m 3} ~ T S; 69 Le Ni T T;‘('~ (M S /;:rr\g_ 30‘! I (9 0W“ m- ~: ’7“ (WW; ((+evue 4, 7; ) z ,4“ (0 4/ as .7ZCGOL 1% ca >3 5. (a) Determine the x- and y—coordinates of the centroid of the shaded area. (10) (b) Calculate the moment of inertia of the shaded area about the x-axis. (10) La) 7omt (Area; A = “A? 4 2. == 4x/z+g’/<ft- King) "1 : 7w, 2 ((34.2) 3 2.” = 2’ Km” == I7w-7u'nt> N \l %-(L2§)Lr+ ZC/‘zrf' x31 2‘ gt“ (if) It? may)" + K cmnzxzz = 1145*”) Toe”; : Zx :: 230¢+l70.7’SM-/—'2/-é 3 Zl§7(tl/\(P) H K .4: N ...
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