ch04 - Chapter4 :Statics ChapterObjectives...

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Engineering Mechanics: Statics Chapter 4:  Force System Resultants
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Chapter Objectives To discuss the concept of the moment of a force and  show how to calculate it in two and three dimensions. To provide a method for finding the moment of a force  about a specified axis. To define the moment of a couple. To present methods for determining the resultants of  non-concurrent force systems. To indicate how to reduce a simple distributed loading  to a resultant force having a specified location.
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Chapter Outline Moment of a Force – Scalar Formation Cross Product Moment of Force – Vector Formulation Principle of Moments Moment of a Force about a Specified Axis
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Chapter Outline Moment of a Couple Equivalent System Resultants of a Force and Couple System Further Reduction of a Force and Couple  System Reduction of a Simple Distributed Loading
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Moment  of a force about a point or axis – a  measure of the tendency of the force to  cause a body to rotate about the point or axis Case 1 Consider horizontal force  F x which acts perpendicular to  the handle of the wrench and  is located  d y  from the point O 4.1  Moment of a Force  – Scalar Formation
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F x  tends to turn the pipe about the z axis The larger the force or the distance  d y , the  greater the turning effect Torque  – tendency of  rotation caused by  F x   or simple moment ( M o z   4.1  Moment of a Force  – Scalar Formation
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Moment axis (z)  is perpendicular  to shaded  plane (x-y) F x  and  d lies on the shaded plane (x-y) Moment axis (z) intersects  the plane at point O 4.1  Moment of a Force  – Scalar Formation
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Case 2 Apply force  F z  to the wrench Pipe does not rotate about z axis Tendency to rotate about x axis The pipe may not actually  rotate  F z  creates tendency  for rotation so moment  ( M o x  is produced 4.1  Moment of a Force  – Scalar Formation
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Case 2 Moment axis (x)  is perpendicular  to shaded  plane (y-z) F z  and  d lies on the shaded plane (y-z) 4.1  Moment of a Force  – Scalar Formation
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4.1  Moment of a Force  – Scalar Formation Case 3 Apply force  F y  to the wrench No moment is produced about point O Lack of tendency to rotate  as line of action passes  through O
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4.1  Moment of a Force  – Scalar Formation In General Consider the force  F  and the point O which lies in the  shaded plane The moment  M O  about point O,  or about an axis passing through O and perpendicular to the plane, is a  vector  quantity Moment  M O  has its specified  magnitude and direction  
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4.1 
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