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Unformatted text preview: 1 Engineering Mechanics: Statics Engineering Mechanics: Statics Chapter 3: Force System Resultants Chapter 3: Force System Resultants Chapter Three Outline Chapter Three Outline 3. Force System Resultants 3.1 Moment of a Force – Scalar Formation 3.2 Cross Product 3.3 Moment of Force – Vector Formulation 3.4 Principle of Moments 3.5 Moment of a Force about a Specified Axis 3.6 Moment of a Couple 3.7 Equivalent System 3.8 Resultants of a Force and Couple System 3.9 Further Reduction of a Force and Couple System 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. 3.1 Moment of a Force – Scalar Formation 3.1 Moment of a Force – Scalar Formation Case 1: Horizontal force F x , which acts perpendicular to the handle of the wrench and is located d y from point O z F x tends to turn the pipe about the z axis z The larger the force or the distance d y , the greater the turning effect 3.1 Moment of a Force – Scalar Formation 3.1 Moment of a Force – Scalar Formation Case 1 continued z Moment axis (z) is perpendicular to shaded plane (xy to shaded plane (x y) z F x and d y both lie on the shaded plane (xy) z Moment axis (z) intersects the plane at point O Case 2 Apply force F z to the wrench z Pipe does not rotate about z axis 3.1 Moment of a Force – Scalar Formation 3.1 Moment of a Force – Scalar Formation z Tendency to rotate about x axis So moment ( M o ) x is produced. z Moment axis (x) is perpendicular to shaded plane (yz) z F z and d y lies on the shaded plane (yz) 3.1 Moment of a Force – Scalar Formation 3.1 Moment of a Force – Scalar Formation Case 3 Apply force F y to the wrench z No moment is produced about z No moment is produced about point O z Lack of tendency to rotate as line of action passes through O 2 3.1 Moment of a Force – Scalar Formation 3.1 Moment of a Force – Scalar Formation In General z Consider the force F and the point O which lies in the shaded plane shaded plane z The moment M O about point O, or about an axis passing through O and perpendicular to the plane, is a vector quantity z Moment M O has its specified magnitude and direction 3.1 Moment of a Force – Scalar Formation 3.1 Moment of a Force – Scalar Formation Magnitude z For magnitude of M O , M O = Fd where d = moment arm or perpendicular distance from the axis at point O to its line of action of the force. Units for moment is N.m Direction z Direction of M O is specified by using “right hand rule” z Fingers of the right hand are curled to follow the sense of rotation when force rotates about point O z Thumb points along the moment axis to give the direction and sense of the moment vector z Moment vector is upwards and perpendicular to the shaded plane 3.1 Moment of a Force – Scalar Formation 3.1 Moment of a Force – Scalar Formation Direction continued M O is shown by a vector arrow with a curl to distinguish it from a force vector z Arrowhead shows the sense of rotation...
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This note was uploaded on 09/29/2010 for the course MECHANICS 445896 taught by Professor Lauren during the Three '10 term at Swinburne.
 Three '10
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 Force

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