CV2101 Chapt 3 - Force System Resultants

CV2101 Chapt 3 - Force System Resultants - Chapter 3 h...

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Chapter 3 orce System Resultants Force System Resultants 3-1
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bjectives Objectives ± To discuss the concept of the moment of a force and show how to calculate it in two and three dimensions. ± To determine the moment of a force about an axis. o determine the moment of a couple ± To determine the moment of a couple. ± To find an equivalent force-couple system for a stem of non ncurrent forces and couples system of non-concurrent forces and couples. 3-2
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1Moment 3.1 Moment The moment of a force indicates the tendency of a body to turn about an axis passing through a point O. In 2-D analysis, the moment of F about a point O is represented by a vector M O normal to the plane containing F and of magnitude M O = F d, where d is the ٣ distance from point O to the line of action of the force. 3-3 Direction of rotation: (+) for CCW, (-) for CW moments.
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1Moment 3.1 Moment cont. The right-hand rule: the moment vector is pointing in the direction of e thumb with the fingers curled in the thumb, with the fingers curled in the direction of rotational tendency. Moment of a system of forces The resultant moment produced byasystem of forces about any point O is equal to the sum of the moments of the individual forces about that point. 3-4 M Ro = Σ F d
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xample 3 3 Example 3.3 Determine the resultant moment of the four forces cting on the rod about acting on the rod about point O. Solution: Assume that CCW moment is positive M Ro = Σ Fd = -50×2 + 60×0 + 20×(3 sin30 ° ) - 40×(4 + 3 cos30 ° ) = -334 N ڄ m = 334 N ڄ m The negative sign indicates that the rotation is CW. 3-5
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2CrossProduct 3.2 Cross Product 1. C = A × B = A B sin θ ڄ u C u C is a unit vector normal to e plane formed by A & B. the plane formed by A & B. 2. B × A = - A × B . Cross product of unit vectors: 3 C oss p oduct o u t ecto s i × i =0 j × j = 0 k × k = 0 i × j = k j × k = ik × i = j i × k = -j j × i = - k k × j = - i 3-6
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2CrossProduct 3.2 Cross Product cont. 4. A×B in determinant form (Pg 83) where component component 3-7
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ractice problem Practice problem 1. A force of magnitude F is applied to the wrench in four directions (P, Q, R, & S). Select the cases resulting in the maximum and minimum moment on the nut. (Max, Min). (a) (Q, P) (b) (R, S) (c) (P, R) (d) (Q, S) 3-8
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3 Moment in 3- 3.3 Moment in 3 D Moment in 2-D can be calculated using a scalar approach. For 3-D problems, it is sometimes easier to use vector cross product for calculation. M O = r × F r is a position vector from point O to any point on the line of action of F. The magnitude of this moment is rFs in θ F(rs θ )F d M O = r F sin = F (r sin ) = Fd The direction and sense of rotation of M O follow the ght and Rule 3-9 right-hand Rule.
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3 Moment in 3- 3.3 Moment in 3 D cont. The physical meaning of each element becomes evident if we consider the force components separately, using a 2-D approach.
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CV2101 Chapt 3 - Force System Resultants - Chapter 3 h...

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