1. 1. For a publicity stunt to promote a popular children’s TV show, an entertainment company’s engineers must design a static hoist to suspend Bernard the Boisterous Elephant 20-ft in the air. Determine the tension that cables AO, BO, and CO must be able to withstand to keep 250-lb Bernard from falling down onto his adoring crowd. (0,-4,3) (4.5,6,10) (-2,0,0) 250 lb CO BO AO

2. 2. Determine the force in AB, BE and DE and indicate whether the members are in tension or compression. 3 m 800 N 400 N A B C D E 26.565° CD CB 400 N 800 N CD = 800 NDE DB DE = 800 N T DB = 800 N C DB = 800 N CB = 894.4 N BE AB 26.565°

3. 3. Draw the shear and moment diagrams for the beam. Please notice that the support reactions are given. w = 300 lb/ft 4.5 ft 9 ft 180 ft lb V (lb) 0 0 M (ft lb) 920 lb 430 lb x 430 M V -920 -180 5.079 1456

4. 4. Given that the tension in cables BC and BD are 5 kN each, find the applied load P at the end of the pipe. P (-2,0,3) (2,0,3) (0,1,1) Ax Az Ay 5 kN Ax = 0 Ay = 3.33 kN Az = -4.849 kN

5. 5. Determine the smallest lever force P needed to prevent the wheel from rotating if it is subjected to a torque M = 500 Nm. The coefficient of static friction between the belt and the wheel is µ s = 0.4. The wheel is pin-connected at its center, B. P T2T2 Ax Ay By Bx T1T1 T2T2 500 Nm

6. 6. Determine the x and y coordinates of the centroid of the shaded area shown below. Dimensions are in mm. [Hint: It is necessary to determine the point where the line and parabola intersect.] 20 mm

7. 7. The gate shown is 8 m wide. Determine the reaction at the smooth support at A and the reactions at the pin at B. Water has density of 1.0 Mg/m3. w = 392.4 kN/m w = 706.3 kN/m Ay Bx By

8. 8. Given that Ixy = -12.96 X 106 mm4 determine the principal moments of inertia of the shaded area with respect to the centroidal x-y axes. Also specify the angle from the x-axis to the maximum principal moment of inertia. 8.7° Maximum Principal Axis