CIVE 210 Exam, Spring 2002

American University of Beirut Department of Civil and Environmental Engineering Spring 2002-2003 Instructor: Professor Fouad Kasti CIVE 210| Statics | Exam#1 Sat Mar 22,03 | 1/1 « " Problem #1: (50%) A 50 Kg mass Mis attached at B to a single weightless cable AB, length = 10cm and hinged at A. The cable is in equilibrium at the position shown (angle o with the vertical) when subjected to a force F making an angle B with the horizontal. a- What is the minimum possible force in cable AB? Determine a, 8 and the magnitude of the force F. b- Ifa = 30° and B = 0, determine the magnitude of the force F and cable tension. c- If a =.30°, determine the minimum magnitude of force F. What is the corresponding cable AB tension and angle B. . Problem #2: (50%) A 20cm, 10 Kg homogeneous uniform bar is roller supported at A and B. The inclined plane makes 60° with the horizontal while bar AB makes a 30° angle with the horizontal. Spring BD has stiffness K=10 Kg/cm. Bar AB is supported at A and B by cables AC and BC hinged at C. Bar AB is in equilibrium and barely touching the horizontal and inclined planes. Bar AC is vertical. Bar BC makes a 60° angle with AC. Assume frictionless surfaces. a- Find tension in cable AC. Arch. Lipeaty b- Find force in spring BD. Specify tension or compression. Eng, & c- Compute deformation in spring BD. Specify shortening or elongation. Cc fo¥y T Find tension in cable BC. ExlSpr0203 Vi American University of Beirut Department of Civil and Environmental Engineering Fall 2000-2001 Instructor: Professor Fouad Kasti Problem #1: (30%) Concerr Ennon =- 10, Carcomnon Entel a. 5. Note dove QO 1v , A cable is wound around pulleys at A, B, and C. Another cable winds around pulleys C and D as shown. The pulleys are frictionless and dimensionless. Cables tensile capacity (maximum allowed tension force) is 1OON. Points A and B are hinged: ~ ; l- For d=20cm, compute the maximum weight W that the system can carry. (15%) 2- Determine the optimum value of d to maximize the carried weight W (that is what is the value of d that will allow the cable system to carry the highest possible weight W ?). For this optimum d, compute the weight W. (15% , . _ - iv WOO) tase TROD @eesei FPL 0 . == io —— Aas + : WE TT dow - é Tv T “ay a) 32) y t tw i wl _ : P wA= 0 is TT = WON ‘ja ETIL] wovt= i414 (4/2) (4/2) a N ? ¢ ° j\4j4,4 CONT | ——— 10cm lOcm tang, & Arch. Libraiy Weight W C:AFouad\Personal\CE0t \\Ex12000 2A \ -American University of Beirut Department of Civil and Environmental Engineering Fall 2000-2001 Instructor: Professor Fouad Kasti Problem #1: (30%) Eng, & Arch Li The uniform bar with end rollers weighs 500 N and is held in equilibrium in the position shown by the horizontal cable CD. Determine the reactions at A&B & the tension in the cable. 0) A =W-= 20’: cy ve —~» _—, ZM,<0 We 225 + Teo 2253 — Q. a0 ~O Z so. (2 tn) 2B <0 Tepe =) Ay = 500"} C:\Fouad\Personal\CEO! 1\Upi2000 2/4 American University of Beirut Department of Civil and Environmental Engineering Fall 1999-2000 Instructor: Professor Fouad Kasti Problem #1: (30%) The rigid loading/unloading equipment (ABC) shown is uséd to pickup objects from an inclined frictionless loading dock making an angle with the horizontal surface. The equipment rolls on wheels at B and C. The object is rectangular in shape, 0.50 m long and 0.25 m high and weighs 50 kg. Member AB is 2.0m long perpendicular to member BC. Member BC is 0.5m long. : : (8%) 1- Compute the vertical force F (in kg) acting at A needed to pickup the object (object loaded) and roll the equipment on wheel B only. Assume angle @ is 30°. 4 2- For F = 0, compute maximum angle ® (in degrees) before the equipment overtums with the object - picked up (object loaded). . . . a ) oo ~~ DIAGONAL = Votes. ossat Sidewalk po . : 7 . . e: oe | 7 FED Eng. & Arch. LiDfaly ESowiSaomM ABour forst ©: AMO : aaa RRR een O81, ve Seses', F = [Sososts cose foeu8) => F- T10%¢ Fs So, oist/) 9 — ©) FeO: —e cose 0, y= 96, 8. 9. 65S =t> O-cae C2\Fouad\PersonaliCEO1 1 *Exam_[ So /-- “\ecrore | Ay | Y - 7 fo. American University of Beirut . va Department of Civil and Environmental Engineering J! Fall 1999-2000 Instructor: Professor Fouad Kasti cn. & asvin, LADY ayy: Problem #2: (30%) Cee . .. .. ...+ The cable system shown is used to support a pedestrian bridge. The pedestrian bridge applies 80KN and 50. KN concentrated loads at points B and C respectively. Determine the tension forces in cables AB, BC and CD in KN and the difference i in elevation between points A and D in m. +t 20m + D Co A _ x 10m + . sm —> v , a Bo 80kN x i. So it 30m —- 40m.. : Ere FOp@ 2&0; Mg 229 ey igs oder: — . 4021 BCL < | ELE «0 5 Ee 1D. = ~- b= 17 es KO ‘Se; * ? 40. ect Sl us -& iS 34 yee 164. (i ISZ, Fap@C; ERO, 40 E.=& cosy — 4031 Gc™ CD 50 i _( Tee" Loans CR =0 »—=_E Rp Sw - SO 40 & fou & Fou wt Xx 22.37 4 Gy- 1680 Crk = comme) = 823" Av), » 823% S"_id*. 373"= ADY ‘neem Cy Fouad\Personal-CE0t 1:Exam_{ Be Eng. & Arch. Library \Fouad\e any >. 2 hee BP 2001-2002 Problem #1: (30% American University of Beirut AC makes 30° with the vertical. Pulley A carries a [00 Kg mass. Neglect pulley dimensions a- Find the force T and t horizontal)required to b- Determine the cable force in segment BC. c- Compute the reaction he angle « (with the - carry the 100 Kg mass. h hile segment Department of Civil and Environmental Engineering Instructor: Professor Fouad Kasti tng & Arch. Library at Pulley B assuming B -hinge supports at B and C. i ax ——e- ersonal\CEOt I\Upt2a0g 24 Lag: OC ARCH. LADEATY . American University of Beirut {Department of Civil and Environmental Engineering 2001- 2002 Instructor: Professor Fouad Kasti Problem #2: (35%) A plane is subjected to two forces F, and F, as shown in the figure below (hinge at D, roller-at C). a- (fF, =450N, a = 30° and F, = 0: determine the thoment of F, about point D. , b- [€F, =0: what is the smallest force F, and angle B (with the horizontal) that will produce the same moment computed in a- about point D. c- (fF, =0: what is F, and a (with the vertical) so that the reaction at C:is zero. wots ——_——__. Los a; . F, 450 Cof3O}c0 TK ~ 450 SinO)e0.15 | . | i | CAFouadPersonahCEGt \Upt2000 Ja, — . . Eng-ar-Arch-cibeary American University of Beirut Department of Civil and Environmental Engineering Fall 2004-2005 - Instructor: Professor Fouad Kasti Problem #1: (50%) A uniform, homogeneous bar AB is 10cm long and weighs 100 kg. AB is hinge supported at A, makes. an angle o with the vertical and is subjected to a force F at end B making an angle f with the horizontal. + 1- What is the minimum force F and the corresponding angles a and B (10%) ? | F=0 &=0 B=Any 2- Assuming «#0, B 4 0 and F 4 0, what is the minimum horizontal reaction at A and the corresponding force F 8 and angles and (20%) frye 0, F=90', X= Any| EMO FW ©----1---------- B z 3- Assuming a # 0, BF OandF #0, what is the value of Fy ao 7 the angle B for the force F to be minimum ? For a= a7, what is Ine and the corresponding minimum force F ? (20%) =e <0 — (A nel eh Siiq — ea Wows = olf [35.44 - af | Problem: #2: (50%) 4 Springs J and II have 100N/cm spring stiffness.each and are parallel to edges AB and BC respectively. Spring I is attached to a mass M; while spring I is attached to mass Mg. The contact at both masses My and Mr is frictionless with edges AB and BC respectively. Springs I and II are attached to a cable that winds around a pulley at B. Edges AB and BC make angle o and B with the horizontal respectively, y is the angle between edges AB and BC, M; = 50 kg: 1- Assuming angle a = 30° and angle y = 90°: (25%) a- Find the elongations in springs I and II respectively b- Find the corresponding mass My carried at the end of spring 2- Assuming My = 100 kg: (25%) a- Find the maximum possible cable tension force for the cable joining springs Land b- Find angles a, B and y c- Find elongations in springs I and II i Eph Wy sue eT, = 505430 =|25°S ‘J }p a juss A . A, sO T Xa ea American University of Beirut Department of Civil and Environmental Engineering Fall 2005-2006 Instructor: Professor Fouad Kasti CIVE 210| Statics Exam #1 Sat Nov 12,05 | 1/1 1% Hour Exam, Closed Books Problem #1: (45%) The rigid bar AC shown has 10Kg mass. AC is parallel to the sloping plane which makes an angle of 30° with the horizontal. A single cable connects at A, winds around pulley at B and ties to C. Bar AC is roller supported at ends A and C with dimensionless and frictionless pulleys / surfaces. Assume the length of AC = 20cm and point B hinge supported. Vertical spring CC’ and horizontal spring AA’ have a spring constant = 100 Kg/cm each. Assume A’ and C’ fully fixed. Assume cable segment 'A Pulleys at A and C are barely touching the horizontal and vertical planes. a- Draw the Free Body Diagramland aye & T. 0.866 necessary information (6% 0.13 28 ey b- Determine/fe terion foffe in cab ati <0 s = - —~T(AG Ep=0 The ®)- wécl3) —T (4g) = c- Determine the forces in springs AA’ & CC’. Indicate tension o: Pompression: % A= = Vs W685 ©) d- etermin et = +0183 W) 1.88 (©) if Problem #2: (30%) The rigid weightless & dimensionless bar ABC is fully fixed at A and connects to a dimensionless & frictionless pulley at C. A single cable connects at D (hinged supported) and winds around C with a force F applied at its free end at an angle a with the horizontal. Assume force F = 10N, length of AB = 20cm, length of BC = Scmy—. c- Determine the angle « and the reactions at A when the moment reaction at A is maximum (12%) Me Eld-\ Tf - Mi” > d= Maye he F(%e) wate des AC LE ExiSpr0305 R= Toi) w )e j 4, pu 4O- TR=0 Yas Pr steve 14] 41 oN Tht Ks lo coc 256 lic Dar Eng, & Arch. Library American University of Beirut Department of Civil and Environmental Engineering . Spring 2005-2006 Instructor: Professor Fouad Kasti CIVE 210] Statics Exam #1 Sat Mar 25,06 | 1/1 1 1/2 Hour Exam, Closed Books P44 Lig Problem I (40%): A The rigid weightless bar BC is roller supported at B, attached to a weightless cable AC at C, and is connected to spring BD at B as shown. A horizontal F = 100N force is applied at C with a spring constant K of 100N/cm. Cable AC is hinge supported at A. Spring BD is fully fixed at D. Assume frictionless roller at B. The system is in equilibrium. 5m 1- Draw a free body diagram (5%) 2- Find the spring force and corresponding deformation. Indicate. © : =,100N ve te aN or, akan ha ee (15%) 5m ra A AG sok SATION) 3- Fin =O Tice im ey oS ° =a = 4- Find the reactice. at roller’ B Bit = tae. SO direction) (10%) B N Fl a ar SHO MOLE, = = D| eS XG Problem H (35%): Bo Rs The rigid bar AB is roller supported at A & B along two inclined planes making 45° as shown. A force F is applied at ~ B along the slope. Assume frictionless rollers at A & B, 2m tL length of bar AB and 50N weight of bar AB. The system is in equilibrium. l- Draw a free body diagram (5%) ee 4 2- -For an angle @ = 30, find the following: (15%) _& Cos 4 a- The force F (magnitude and direction) M20 F(C) W a W. Weep 9) FL ae b- The reaction at A (magnitude and direction c c- The reaction at B (magnitude and direction) F= 5040 Jaane ‘ 3- Find the minimum possible force F (magnitude and omg 20 — Ke direction) and the corresponding angle @ as well as ees) ~ w{ CE the magnitude and directions of the reactions at A and B. (15%) Fayy=O qs = 240\-6 Cw 7&a _ - chk ZERO Ry- wes ; ir » Rex sod sans