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Virtual Displacements

# Virtual Displacements - In other words the vertical...

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QUICK METHOD FOR DETERMINATION OF VIRTUAL DISPLACEMENTS Consider the shaded object above, which pivots around point O. If the entire object experiences a small virtual rotation δθ , then lines OA, OB and OC each rotate δθ . For very small angles, the virtual displacement δ Α is exactly equal to L δθ ( and is perpendicular to OA). Similarly, δ y B = Lcos θ δθ and δ x C = Lsin θ δθ . When analyzing displacements at point A, it’s convenient to recognize that δ y A = δ y B and δ x A = δ x C
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Unformatted text preview: . In other words, the vertical displacement at A depends on the horizontal distance times δθ and the horizontal displacement at A depends on the vertical distance times δθ . This method gives results identical with the differential calculus method, albeit without the minus signs that sometimes appear. Your active force diagram should clearly show the proper directions, however, and allow you to use the proper sign for the virtual work term....
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