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slide1

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

slide2

2. Determine the force in AB, BE and DE and indicate whether the members are in tension or compression.

400 N

800 N

E

D

C

3 m

B

A

3 m

3 m

400 N

CD

26.565°

CB

800 N

DE = 800 N T

DB = 800 N C

DE

CD = 800 N

DB

DB = 800 N

CB = 894.4 N

BE

26.565°

26.565°

26.565°

AB

slide3

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

4.5 ft

9 ft

430 lb

920 lb

V

(lb)

430

0

M

5.079

-920

x

V

M

(ft lb)

430

1456

0

-180

slide4

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 = -4.849 kN

slide5

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 = 0.4. The wheel is pin-connected at its center, B.

Ay

By

Bx

Ax

500 Nm

T1

T2

T2

P

slide6

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

slide7

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

By

Bx

w = 706.3 kN/m

Ay

slide8

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.

Maximum Principal Axis

8.7°

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