Free Body Diagrams and Equilibrium Problems of Rigid Bodies, Exams of Engineering

Download Free Body Diagrams and Equilibrium Problems of Rigid Bodies and more Exams Engineering in PDF only on Docsity! Soli on PROBLEM 1 (15 points) Consider the boom structure that is supporting 2 1800/b load as shown below. ‘The members BC and BD are cables and the rod member AB is pinned at both ends. (Neglect the weight of the members). <TD secl ii) Suv the Unit yecrovs y @ [¢00 1lete free body diagram at point B. (5 pt) mplete vector equilibrium equation at point B. (5 pd) ystem of equations needed to solve for the member forces (you do not have to solve the system)? (5 pt) wu S550 = “Vee ce = 265-3 Toa =Ten (34-61-38) =Ton (7 i aN es Vee et See 28g +2 ge = Es eC Bx Ip * Toc totaal (34 ze 34 -6)+ “CHE HB J os 5 ZF o- = (Fea <3 Tee, “3 i ele Ss lec 28 Liv) 4-4 \ Ten” 0 (2/ ae oe $ Be f= 0 SE)  PROBLEM 2 (20 points) In the following problem we consider two men trying to slide a 6m long plank over an overhead rack. The plank has a mass of 100kg and the coefficient of kinetic friction between the plank and each support is 0.5. (i) Draw a clear free body diagram of the plank while it is sliding on the rack.. The complete free body diagram should include all relevant forces and couples, coordinate axis, and proper dimensions. (8 pt) (ii) Compute the minimum force ‘P’ that must be applied to the rope to begin moving the rack. (8 pt) (iii) Assuming that the force applied to the rope does not change, the chance that plank may lift off the support at A (4 pt) (a) Does not exist (b) increases when the angle between the rope and the plank is greater than 30 o (c) increases when the angle between the rope and the plank is less than 30o (d) The information provided is not sufficient to answer the question. (i) (ii) The forces in Cartesian form are ( ) ( ) ( ) ( ) ( ) 200 ( ) Summing the moments about point A yields From geometry 2 2 1 0.5 2 Hence 0.5 200 2 2 Expanding and rearrangin A x y z E E D D A AC AB E D AB AC AB E D A A A T T N T T = + + = = = − = × + × + = = + − = = + − + − × − + + − × + = ∑ F i j k T i T j F k M r F r T T 0 r i j k r r i j k i j k k i j k i j 0 ( ) ( ) g the terms gives 2 200 2 100 ( 2 )D E D ET T T T− + − + + − =i j k 0 Hence (iii) 50 ( )ET N= 100 ( )DT N= NOTE: The same answers will be obtained (without any vector analysis) by computing the scalar components of the moments about the x- and y-axes. Coordinates of A (0,0,0) Coordinates of B (1,2,-2) NOTE: The absolute values of the coordinates will depend on the coordinate system chosen but the position vector rAB will not. rAB rAC PROBLEM 4 (15 points) Consider the frame structure shown below. Neglect the weight of the members and frictionless pulleys. 3m— To alll mm 7 mm i @ Draw the complete free-body diagrams of the two pulleys. (2 pt}' Gi) Determine the values of ail the forces on the pulleys (3 pt) = . Gii) | Draw the complete free-body diagram of member a-d. (2 pt) (iv) Draw the complete free-body diagram of member c-f. (2 pt) 8 (vy) Solve for all the unknown forces on the free-body diagrams form parts @.6r) fw) The free body diagrams should include all relevant forces and moments, coordinate axis, and proper dimensions. Be sure the forces and moments are drawn consistently with respect to the relationship of forces of one owe to the other. ( t ) 500 ’ (Riad Paley > ane RS S00 Soo sy y 500 f RS 1 dy= 800 _e Or, GO vc. gue 1 Fee OS ow oO One. Same ar ok For tember Cf Unlenowns aye Ca, Cy ) Fay Fy Hower guar, wrdetewminal G=t360 Gem memote ad Gre Mp=0 = 560 nee = (300 (5) + Gv (3) 3 LF =O = Ax 7 WE Fys0 = S) +500 -1300 [Ky> Boo A] Work Paese values vetuen to SE on all Ax e-Cx = -16G15 [Rez loons <| OE ers | Gearing Comments: fe tater omy Seer? | Cun (i) >, point Lov eat missing Lovee no Geometric dimensions needed Sov () -_ i, Point Lov euth Soret wrong: So(tee) They shodd ae She WY onlerowns shoud 4 nouns Shon Grd \inewe dimensions — douwndo ~Yy ow eat € Do not take off iF the Lov get @ dimenslon ovr Used he eight dimension tn (YY) Loe GV) = Same Comments af vii) (W) TF toere is an eavly Orvor mate try dy Lollow ular 15 done to not malic them pay Move Than Once, They netd to ve 3 equections on euch FeO, wich gis ~4,Sov euth wot Used. less oft if thney Aid om ber made a mistake. PROBLEM 6 (20 points) Two weightless members (AB and BC) are loaded and supported as shown in the figure. The supports at A, B, and C are a fixed support, a smooth pin, and a roller, respectively. 1) Determine the resultant R of the distributed load and locate its line of action with respect to the left most support for the beam (point A). (2 pt) 2) Draw a free body diagram that will assist you to solve the external support reaction at C (only at C). The complete free body diagram should include all relevant forces and couples, coordinate axis, and proper dimensions. (4 pt) 3) For this free body diagram the sufficient and necessary equilibrium equations required to solve the external support reaction at C (please circle the most accurate answer): (2 pt) a. ΣFx=0, ΣFy=0 b. ΣMB=0 c. ΣMC=0 d. ΣMC=0,ΣFx=0 e. ΣMA=0 f. ΣFx=0, ΣFy=0, ΣMB=0 g. ΣFx=0, ΣFy=0, ΣMA=0, ΣMB=0 4) Find the support reaction at C. (3 pt) 5) Draw a free body diagram that will assist you to solve the external support reaction at A. The complete free body diagram should include all relevant forces and couples, coordinate axis, and proper dimensions. (4 pt) 6) For this free body diagram the sufficient and necessary equilibrium equations required to solve the external support reactions at A (please circle the most accurate answer): (2 pt) a) ΣFx=0, ΣFy=0 b) ΣMB=0 c) ΣMC=0 d) ΣMC=0,ΣFx=0 e) ΣMA=0 f) ΣFx=0, ΣFy=0, ΣMA=0 g) ΣFx=0, ΣMB=0 h) ΣFx=0, ΣFy=0, ΣMA=0, ΣMB=0 7) The support at C is moved to mid point of beam BC. How would that affect the reaction at A? (3 pt) (please circle only one answer) a. Ax and Ay will not change. MA will decrease. b. Ax will not change. Ay will decrease and MA will decrease. c. Ax will not change. Ay and MA will increase. d. Ax and Ay will increase, and MA=0. e. Ax and Ay will decrease, and MA=0. f. The information provided is not sufficient to answer the question. Probhen 6 1) 1000¥9= 2000W d= 4m ‘t ROOUN fe—22-s » x 6 Ny 3} 6 4) QZ Maro & H- R090% R= deg vooew Af + Ay t Ay 4 = loeov