Chapter -4- Force System Resultant

Size: px

Start display at page:

Download "Chapter -4- Force System Resultant"

Chad Gardner
6 years ago
Views:

Ishik University / Sulaimani Civil Engineering Department Chapter -4- Force System Resultant 1 4.3 MOMENT OF A COUPLE Couple - two parallel forces. - same magnitude but opposite direction.

1 Ishik University / Sulaimani Civil Engineering Department Chapter -4- Force System Resultant MOMENT OF A COUPLE Couple - two parallel forces. - same magnitude but opposite direction. - separated by perpendicular distance d. Resultant force = 0 Tendency to rotate in specified direction. Couple moment = sum of moments of both couple forces about any arbitrary point. Example; Position vectors r A and r B are directed from O to A and B, lying on the line of action of F and F. Couple moment about O M = r A X (-F) + r B X (F) Couple moment about A M = r X F since moment of F about A = 0 2 1

4.3 MOMENT OF A COUPLE A couple moment is a free vector - It can act at any point since M depends only on the position vector r directed between forces and not position vectors r A and r B, directed

In all cases, M acts perpendicular to plane containing the forces. 3 4.

2 4.3 MOMENT OF A COUPLE A couple moment is a free vector - It can act at any point since M depends only on the position vector r directed between forces and not position vectors r A and r B, directed from O to the forces. - Unlike moment of force, it do not require a definite point or axis. Scalar Formulation Magnitude of couple moment M = Fd Direction and sense are determined by right hand rule. In all cases, M acts perpendicular to plane containing the forces MOMENT OF A COUPLE Vector Formulation For couple moment, M = r X F If moments are taken about point A, moment of F is zero about this point. r is crossed with the force to which it is directed. Resultant Couple Moment Couple moments are free vectors and may be applied to any point P and added vectorially. For resultant moment of two couples at point P, M R = M 1 + M 2 For more than 2 moments, M R = (r X F) 4 2

Equivalent Couples Two couples are equivalent if

forces, forces of equal couples either lie on

3 Equivalent Couples Two couples are equivalent if they produce the same moment. Since moment produced by the couple is always perpendicular to the plane containing the forces, forces of equal couples either lie on the same plane or plane parallel to one another. 5 Example 4.6 : Force Couple 6 3

4 Example 4.7 : Force Couple 7 8 4

5 Example 4.8 Determine tile resultant couple moment acting on the beam. Ans: 9 Example 4.9 Determine the resultant couple moment acting on the triangular plate. Ans: 10 5

6 Example 4.10 If F=200 Ib, determine the resultant couple moment. 11 Solution; 12 6

7 13 Example 4.11 Determine the required magnitude of force F if the resultant couple moment on the frame is 200 Ib.ft, clockwise. 14 7

8 Solution; Equivalent System A force has the effect of both translating and rotating a body. The extent of the effect depends on how and where the force is applied. We can simplify a system of forces and moments into a single resultant and moment acting at a specified point O. A system of forces and moments is then equivalent to the single resultant force and moment acting at a specified point O. 16 8

9 4.4 Equivalent System Point O is on the Line of Action Consider body subjected to force F applied to point A. Apply force to point O without altering external effects on body. - Apply equal but opposite forces F and F at O Equivalent System Point O is on the Line of Action - Two forces indicated by the slash across them can be cancelled, leaving force at point O. - An equivalent system has be maintained between each of the diagrams, shown by the equal signs. 18 9

4.4 Equivalent System Point O is on the Line of Action - Force has been simply

- External effects remain unchanged after force is moved.

4 Simplification of a Force and Couple System Simplifying any force and couple

10 4.4 Equivalent System Point O is on the Line of Action - Force has been simply transmitted along its line of action from point A to point O. - External effects remain unchanged after force is moved. - Internal effects depend on location of F Simplification of a Force and Couple System Simplifying any force and couple system, F R = F M R = M C + M O If the force system lies on the x-y plane and any couple moments are perpendicular to this plane, F Rx = F x F Ry = F y M Ro = M C + M O 20 10

11 4.4 Simplification of a Force and Couple System MOVING A FORCE OFF OF ITS LINE OF ACTION 21 Example

13 Example

14 27 Example 4.14 Replace the force system acting on the beam by an equivalent force and couple moment at point A

15 solution: 29 Example 4.15 Replace the force system acting on the beam by an equivalent force and couple moment at point A

16 solution: 31 16

Ishik University / Sulaimani Architecture Department Structure ARCH 214 Chapter -4- Force System Resultant

Ishik University / Sulaimani Architecture Department 1 Structure ARCH 214 Chapter -4- Force System Resultant 2 1 CHAPTER OBJECTIVES To discuss the concept of the moment of a force and show how to calculate