# Steps to solve moment of force about an axis 12 1

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Steps to Solve Moment of Force about an Axis 12 1. Identify knows and unknowns. 2. Select the X-Y-Z coordinates system (use the problem default system). 3. Identify three vectors in terms of rectangular components: force vector F , position vector r , and unit direction vector λ for the axis. 4. Calculate the moment.
Sample Problem x y z C(0,0.9,-0.4) D(0,0.7,0) B(1.2,0.35,0) T CF =33N The triangular plate ABC is supported by ball- and-socket joints at B and D and is held in the position shown by cables AE and CF . If the force exerted by cable CF at C is 33 N, determine the moment of that force about the line joining Points D and B . F(0.6,0,-0.6) r
Sample Problem The triangular plate ABC is supported by ball- and-socket joints at B and D and is held in the position shown by cables AE and CF . If the force exerted by cable CF at C is 33 N, determine the moment of that force about the line joining Points D and B . x y z C(0,0.9,-0.4) D(0,0.7,0) B(1.2,0.35,0) T CF =33N F(0.6,0,-0.6) r
Fundamental Concepts A Couple 15 A couple is an interaction involving multiple forces that produce no translation, but only rotation; in other words, the couple produces net moment, but zero force.
Fundamental Concepts A Couple 16 The net moment of a couple formed by two equal and opposite forces is the same about all points. ∑M| O =F(0)+F(d)=Fd ∑M| P =F(d)+F(0)=Fd ∑M| Q =F(d Q )−F(d Q −d)=F(d Q )−F(d Q )+Fd=Fd Fd rF M F r M sin r
Fundamental Concepts Equivalent Forces system 17 To preserve static equivalency when changing the point of application of a force to a new line of action, one must also apply a couple. The couple restores the original tendency to rotate, the moment, without altering the sum of forces. The additional couple must be equal to the moment of the original force about the point to which the force has been moved.
Fundamental Concepts Equivalent Forces System 18 A system of forces may be replaced by a collection of force-couple systems acting at a given point O. The force and couple vectors may be combined into a resultant force vector and a resultant couple vector, R O R F M r F
Sample Problem