Lecture 2

Lecture 2 - LECTURE 2 CURRENT FORCE SYSTEMS Contents...

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1 LECTURE 2 CURRENT FORCE SYSTEMS Contents: Introduction Forces and their characteristics Resultant of two concurrent forces Resultant of three or more concurrent forces Resolution of a force into components Rectangular components of a force Resultants by rectangular components Introduction Two effects exist when a force is exerted on a body: 1. The external effect , i.e., the tendency to change the motion of the body or to develop resisting forces on the body; 2. The internal effect , which is the tendency to deform the body. In the applications when the body is assumed to be rigid, the external effect is significant while the internal effect is not. Conversely, the internal effect, e.g. the deformation, must be considered in the Mechanics of Materials.

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2 Two force systems are equivalent if they produce the same external effect when applied to a given body. The resultant force of the force system is the simplest form of equivalent system to which the original system will reduce. Reduction is the process of reducing a force system to a simpler force or force system. Resolution is to expand a force or a force system into a less simple equivalent system. Forces and their characteristics A force has three properties: Magnitude : size of the force (positive number). The unit of force is with e .g. lb (pound) or kip (1000 pounds) in US and N (Newton) and kN (1000 N) in SI Direction : orientation and the sense of the line segment used to represent the force For a force of 2D Fig. 2-1 A 2D force and its components x yx y Ff if jf f == + = + Fi j G G G (1) For a force of 3D θ cos cos x fF θθ = ⋅= F G sin sin y = F G x F y
3 Fig. 2-2 A 3D force and its components Fig. 2-3 An example of 3D force The orientation of the force can be specified by providing three dimensions for a 3D force. The sense of the force can be specified by placing an arrowhead on the appropriate end of the line segment used to present the force. Alternatively, a plus or minus sign can be used with the magnitude of a force to indicate the sense of the force. Point of application : point of contact between the two bodies. Line of action is a straight line extending through the point of application in the direction of the force. Fig. 2-4 An example of line of action x y z x θ y z cos cos cos cos cos cos xx x yy y zz z fF θθ = ⋅= = = F F F G G G x y z 7in. 4in. 5in. F 100 lb 30 ° Line of action

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4 In the applications when the body is assumed to be rigid , the external effect is significant while the internal effect is not . Conversely, the internal effect, e.g. the deformation, must be considered in the Mechanics of Materials. Scalar and vector quantities A scalar can be completely described with a magnitude, e.g., mass, density, length, area, column, speed, energy, time and temperature.
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Lecture 2 - LECTURE 2 CURRENT FORCE SYSTEMS Contents...

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