ME221Lecture 121 ME 221 Statics LECTURE # 12 Sections 3.8 – 3.9

ME221Lecture 122 Homework #4 Chapter 3 problems: –1, 4, 8, 11, 17, 25, 26, 28, 35 & 40 –Due Today Homework #5 Chapter 3 problems: –48, 51, 55, 57, 61, 62, 65, 71, 72 & 75 –You may use MathCAD, etc. on any of the problems –Due Friday, October 3

ME221Lecture 123 Equivalent Force Systems Learn how to replace a given set of forces with an equivalent force-moment system

ME221Lecture 124 Equivalent Force Systems The action of a force tends to translate the body along the direction of the force and rotate it about an axis not located along the line of action of the force. The External Effects remain the same if the force is moved from one point to another (from A to B ) if:

ME221Lecture 125 A force can be replaced by an equal magnitude force provided it has the same line of action and does not disturb equilibrium B A 1- Point B is on the line of action of the force

ME221Lecture Point B is not on the line of action of the force Start with a rigid body having force F applied to it. A B F Replace this force with a force and couple at A. Add “zero” to the body in the form of adding +F and -F +F+F -F-F

ME221Lecture 127 Next, group two forces to create couple C A B +F+F C +F+F -F-F F r B/A Let r B/A be the relative position of B with respect to A. Define couple with cross product C = r B/A x F In essence, the force F has been moved from point B to A with the addition of couple C.

ME221Lecture 128 For More Than One Force A similar procedure is used when there are many forces on the body: R =  F i C =  c i =  r i x F i

ME221Lecture 129 A parallel force system has the lines of action of all forces acting parallel to a common line. A concurrent force system has the lines of action of all forces passing through a single point. More on these later (Monday).

ME221Lecture 1210 Example Problem