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MSU ME 221 - Lecture 12 sect 3.8

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PowerPoint PresentationHomework #4Slide 3Equivalent Force SystemsSlide 52- Point B is not on the line of action of the forceSlide 7For More Than One ForceSlide 9Example ProblemME221 Lecture 12 1ME 221 StaticsLECTURE # 12Sections 3.8 – 3.9ME221 Lecture 12 2Homework #4•Chapter 3 problems:–1, 4, 8, 11, 17, 25, 26, 28, 35 & 40–Due TodayHomework #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 3ME221 Lecture 12 3Equivalent Force Systems•Learn how to replace a given set of forces with an equivalent force-moment systemME221 Lecture 12 4Equivalent 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:ME221 Lecture 12 5A force can be replaced by an equal magnitude force provided it has the same line of action and does not disturb equilibriumBA1- Point B is on the line of action of the forceME221 Lecture 12 62- Point B is not on the line of action of the forceStart with a rigid body having force F applied to it.ABFReplace this force witha force and couple at A.Add “zero” to the bodyin the form of adding+F and -F+F-FME221 Lecture 12 7Next, group two forces to create couple CAB+FC+F-FFrB/ALet rB/A be the relative position of B with respect to A.Define couple with cross productC = rB/A x FIn essence, the force F hasbeen moved from point B toA with the addition of couple C.ME221 Lecture 12 8For More Than One ForceA similar procedure is used when there are many forces on the body:R =  FiC =  ci =  ri x FiME221 Lecture 12 9A 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).ME221 Lecture 12 10Example


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