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) CO BO
(-2,0,0) AO
250 lb

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

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

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.
(-2,0,3)
5 kN
(2,0,3)
5 kN
(0,1,1) Az P Ay Ax
Ax = 0
Ay = 3.33 kN
Az = 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 µs = The wheel is pin-connected at its center, B. Ay By Bx Ax
500 Nm T1 T2 T2 P

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 = kN/m By Bx
w = kN/m Ay

8. 8. Given that Ixy = 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.
Maximum Principal Axis
8.7°