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Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI 1313 Mechanics I Lecture 13:Force System Resultants

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ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 2 Chapter 4 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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ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 3 Lecture 13 Objectives to examine concepts of the moment of a force in scalar notation to examine concepts in vector algebra on the cross product with respect to the moment of a force

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ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 4 Moment of a Force Tendency of a force (F x ) applied to a body to cause that body to rotate Force (F x ) is applied at a distance (d y ) from the body The force line of action is perpendicular to a line passing through the point of rotation (O) Moment (M o ) z about z-axis

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ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 5 Moment of a Force (cont.) Tendency of a force (F z ) applied to a body to cause that body to rotate Force (F z ) is applied at a distance (d y ) from the body The force line of action is perpendicular to a line passing through the point of rotation (O) Moment (M o ) x about x-axis

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ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 6 Moment of a Force (cont.) The force line of action passes through the point of rotation (O) Therefore no tendency for rotation is possible. No moment about O

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ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 7 Moment of a Force Definition Scalar Magnitude Direction Right-hand rule Moment axis to plane of F and d Moment axis intersects Point O Sense Arrowhead curl Counter-clockwise is positive +

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ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 8 Moment Force Line of Action Find Line of Action or Force Components? Often easier to get components Line of Action Force Component

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ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 9 Moment Force Line of Action (cont.) Find Line of Action O x y F d -

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ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 10 Moment Force Line of Action (cont.) Find Components O x y F FyFy FxFx -

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ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 11 Comprehension Quiz If a force of magnitude F can be applied in four different 2-D configurations (P,Q,R, & S), select the cases resulting in the maximum and minimum (Max, Min) torque (moment) values on the wrench about Point A. A) (Q, P) B) (R, S) C) (P, R) D) (Q, S) Answer: D Q S P R A

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ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 12 Example For each case illustrated, determine the moment of the force about point O. -

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ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 13 Example (cont.) For each case illustrated, determine the moment of the force about point O. -

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ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 14 Example (cont.) For each case illustrated, determine the moment of the force about point O. +

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ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 15 Example (cont.) For each case illustrated, determine the moment of the force about point O. +

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ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 16 Moment of Coplanar Force System System of Forces Acting on a Single Plane +

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ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 17 Moment of Coplanar Force System System of Forces Acting on a Single Plane +

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ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 18 Classification of Textbook Problems

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ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 19 Classification of Textbook Problems

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ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 20 Classification of Textbook Problems

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ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 21 Classification of Textbook Problems

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ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 22 Classification of Textbook Problems

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ENGI 1313 Statics I – Lecture 13© 2007 S. Kenny, Ph.D., P.Eng. 23 References Hibbeler (2007) mech_1

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