1. The bricks on top of the beam and the supports at the bottom create the distributed loading shown in the second figure. Determine the required intensity w and dimension d of the right support so that the resultant force and couple moment about point A of the system are both zero.
2. Determine the magnitude and direction of the moment of the force of the movement if the force at A about point P.
3. The boys A, B and C stand near the edges of a raft as shown. Determine the location (x, y) of boy D so that all four boys create a single resultant force acting through the raft's center O. Provided the raft itself is symmetric, this would keep the raft afloat in a horizontal plane. the mass of each boy is indicated in the diagram.
4. Replace the loading by an equivalent force and couple moment acting at point O.
5. Replace the force and couple system by an equivalent single force and couple acting at point P.
6. Determine the moment of force F3 about point A on the beam.
7. Replace the force at A by an equivalent force and couple moment at P. Express the results on Cartesian vector form.
8. A force and couple act on the pipe assembly. Replace this system by an equivalent single resultant force. Specify the location of the resultant force along the y axis, measured from A. The pipe lies in the x-y plane.
9. Determine the couple moment. Use a vector analysis and express the result as a Cartesian vector.
10. Replace the loading system acting on the post by an equivalent force and couple system at point O.
11. Determine the moment of the force at A about point P. Use a vector analysis and express the result in Cartesian vector form.
12. Determine the magnitude and direction of the couple shown.
13. Determine the magnitude and direction of the moment of the force at A about point P.
14. Three parallel forces act on the rim of the tube. If it is required that the resultant force FR of the system have a line of action that coincides with the central z axis, determine the magnitude of FC and its location on the rim. What is the magnitude of the resultant force FR?
15. A force of 50 N is applied to the handle of the door as shown. Determine the projection of the moment of this force about the hinged axis z. Neglect the size of the doorknob. Suggestion: Use a scaler analysis.
16. The wind has blown sand over a platform such that the intensity of load can be approximated by the function . Simplify this distributed loading to a single concentrated force and specify the magnitude and location of the force measured from A.
17. The pole supports a 22-lb traffic light. Using Cartesian vectors, determine the moment of the weight of the traffic light about the base of the pole at A.
18. Determine the magnitude and direction of the couple moment.
19. A twist of 4 N-m is applied to the handle of the screwdriver. Resolve this couple moment into a pair of couple forces F exerted on the handle.
20. Replace the force F, having a magnitude of F = 40 lb and acting at B, by an equivalent force and couple moment at A.
21. The resultant force of a wind loading acts perpendicular to the face of the sign as shown. Replace this force by an equivalent force and couple moment acting at point O.
22. The man at B exerts a force of 140N on the rope attached to the end of beam AC as shown. Determine the moment of this force about the base of the beam at A.
23. The three forces acting on the water tank represent the effect of the wind. Replace this system by a single resultant force and specify its vertical location from point O.
24. This structural connection is subjected to the 8,000-lb force. Replace this force by an equivalent force and couple acting at the center of the bolt group, O.
25. Express the moment of the couple acting on the pipe on Cartesian vector form. What is the magnitude of the couple moment?