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Unformatted text preview: 1 Force Analysis Static Systems By plane truss we mean a truss that is in one plane, say y x − , and all forces applied to it are in the same plane. The following equations hold for each link in a static plane truss of rigid links F = ∑ k k ( 1 ) = ∑ k k M ( 2 ) where k F is the th k force and k M is its moment about a fixed point of convenience. Lemma 1. Truss link at static equilibrium with two forces only If two forces are applied to a link at static equilibrium then they must be equal , opposite and collinear Proof From Equation 1 we have 2 1 F F − = so the forces are equal and opposite. Suppose that the forces are not collinear as in Figure 1. Sun of moments about A gives 2 ≠ d F , in contradiction to Equation 2. Lemma 2. Truss link at static equilibrium with two forces and a moment If two forces and a moment are applied to a link at static equilibrium then the forces must be equal and opposite . Figure 2 shows such a scenario. It is clear that Equations 1 and 2 are both satisfied provided that d f T 2 = 2 F 1 F Rigid link A d B Figure 1 2 F 1 F Rigid link A d B Figure 1 2 F 1 F A d B Figure 2 T 2 F 1 F A d B Figure 2 T 2 Lemma 3. A Three-Force Link If three forces are applied to a link at static equilibrium then they must close a triangle and their lines of action must pass through a common point . Proof The graphical interpretation of Equation 1 is that the three forces close a triangle, as in Figure 3b....
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This note was uploaded on 12/02/2011 for the course ME 4133 taught by Professor Ram during the Fall '06 term at LSU.
- Fall '06