CIVE 210 Exam, Spring 2008

American University of Beirut Department of Civil and Environmental Engineering Spring 2008-2009 Instructor: Professor Fouad Kasti NAME: Mr. Solution_________ ID: CIVE210 Exam I____________ ExISpring0809 1/1 CIVE 210 Statics Exam I 1 ½ Hour Exam Sat Apr 4, 09 Closed Books 1/1 Problem #1: (50%) The crane ABC consists of 3 rigid, weightless and straight bars AB, BC and AC. The crane is lifting a mass M with a weightless cable connected to C. A spring having K = 30Kg/cm tie point B back to a rigid support at point D. Assume: 1- Bar AC and AB make angles 30º and 60º respectively with the horizontal 2- BD is perpendicular to AB 3- Hinge support at A 4- Length AB = 2m, BC = 4m 5- Drawing is not to scale. Answer the following: a- Draw the Free Body Diagram and indicate clearly all necessary information (10%) b- Determine the tension force in spring DB in terms of M (15%) �M@A = 0 � Ts*AB = M*AC*cos(30) � Ts = 1.5*M c- Assuming the tension force capacity in the cable holding M at C is 10Kg and the tension force capacity of the spring BD is 12Kg, determine the maximum mass M that can be carried (10%) M = T cable = 10Kg � Ts = 15Kg > 12Kg capacity � Ts = 12Kg & M= 8Kg d- In part C, determine the corresponding spring force and corresponding deformation. Indicate magnitudes, tension or compression, shortening or elongation (5%) Ts = 12Kg (Tension) � � = 12/30 = 0.4cm (Elongation) e- In part C, determine the corresponding reactions at A. Indicate magnitudes and directions. (15%) �Fx = 0 � Ha = Ts*cos(30) = 10.4Kg � = Ha, �Fy = 0 � Ha = Ts*sin(30)+8 = 14Kg � = Va Problem #2: (50%) The rigid, weightless and straight bar ABC is roller supported at A and B over a circular path of radius R = 24m and subjected to a pair of forces P and F. P is acting at a point G located in the middle of segment AB oriented perpendicular to AB, F is acting at tip C oriented at an angle � to the direction of bar ABC as shown. Assume: 1- The magnitude of P = 60N 2- Frictionless and dimensionless roller supports A and B 3- Length AB = 12m, BC = 6m 4- Drawing is not to scale. Answer the following: a- Draw the Free Body Diagram and indicate clearly all necessary information (10%) OP = sqrt (24^2 – 6^2) = 23.24, angle OAP = cos-1(6/24) = 75.52º b- Determine the minimum force F required for equilibrium and the corresponding angle � and reactions at A and B. Indicate magnitudes and directions (25%) Na, Nb and P passes through center of circle. �M@O = 0 � F*dF = 0 � Minimum F = 0, � = any Na = Nb = 60/(2*sin 75.52) = 30.98 = Na = Nb c- Determine the minimum force F required to cause roller at B to barely touch the ground (reaction at B = 0) and the corresponding reaction at A. Indicate magnitudes and directions (15%) �M@O = 0 � F passes thru O � � = tan-1(OP/PC) = tan-1(23.24/12) = 62.69º = � �Fx = 0 � F*cos � = Na * cos 75.52 � Na = 1.84*F �Fy = 0 � F*sin � + Na * sin 75.52 = 60 � F = 22.5N, Na = 41.4N Nb Na O 10º Va 30º Ha Ts 60º F P R R �º B C B A C G M