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Ch. 2: Force Systems 2.0 Outline 27 Overview of Forces 28 2-D Force Systems Rectangular Coordinate Systems 33 Force, Moment, and Couple 45 Resultants 61 3-D Force Systems Rectangular Coordinate Systems 85 Force, Moment, and Couple 95 Resultants 109 2.0 Outline 27
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Ch. 2: Force Systems 2.1 Overview of Forces Force The measure of the attempt to move a body . It is a fixed vector . For the rigid body problems or only the external effects of the external force onto the objects are of interested, force can be treated as a sliding vector . Hence, the complete description must include magnitude , direction , and line of action . And the problem makes use of the principle of transmissibility . Contact vs. Body Force Concentrated vs. Distributed Force 2.1 Overview of Forces 28
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Ch. 2: Force Systems 2.1 Overview of Forces Contact vs. Body Force Concentrated vs. Distributed Force 2.1 Overview of Forces A P P B 29
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Ch. 2: Force Systems 2.1 Overview of Forces Force Measurement by comparison or by deformation of an elastic element (force sensor) Action vs. Reaction Force Isolate the object and the force exerted on that body is represented FBD Combining Force by parallelogram law and principle of moment Force Components along the specified coordinate system to satisfy the parallelogram law (reverse step) 2.1 Overview of Forces 30
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Ch. 2: Force Systems 2.1 Overview of Forces Orthogonal Projection along the specified direction . The components of a vector are not the same as the orthogonal projections onto the same coord. system, except the coordinate system is the orthogonal (rectangular) coordinate system . 2.1 Overview of Forces R F 1 F 2 F a F b a b R F a’ F b’ a' b' 31
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Ch. 2: Force Systems 2.1 Overview of Forces Addition of Parallel Forces by graphic or algebraic (principle of moment) approach 2.1 Overview of Forces F 2 F 1 (1) F 2 F 1 F -F R 1 R 2 (2) R 1 R 2 R (3) 32
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Ch. 2: Force Systems 2.2 2-D Simple Rectangular Coordinate Systems 2.2 2-D Rectangular Coord. Systems y x F x F y F θ ( ) xy 22 yx ˆˆ FF F= F F F Fcos F Fsin arctan 2 F ,F θθ θ + + = = = F=F F F= i+ j Magnitude is always positive Scalar component includes sign information too! 33
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Ch. 2: Force Systems 2.2 2-D Rectangular Coord. Systems 2.2 2-D Arbitrary Rectangular Coordinate Systems by convenience, right-handed, geometry of the problem β x y F F x = Fsin β F y = Fcos β β x y F F x = Fsin (π−β) F y = -Fcos (π−β) x F x = Fcos (α−β) F y = Fsin (α−β) β y F α 34
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Ch. 2: Force Systems P. 2/1 If the two equal tension T in the pulley cable together produce a force of 5 kN on the pulley bearing, calculate T. 5 kN 35
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Ch. 2: Force Systems P. 2/1 60 T T 5 kN 5 kN By cosine law: 2 22 5 T T 2T Tcos60 =++⋅ ° T = 2.89 kN 36
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Ch. 2: Force Systems P. 2/2 While steadily pushing the machine up an incline, a person exerts a 180 N force P as shown. Determine the components of P which are parallel and perpendicular to the incline.
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online ppt - Ch. 2: Force Systems 2.0 Outline Overview of...

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