This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1896 Excerpt: ...0, therefore the virtual work of R = 0, thereQ. Again, choose a virtual dis Fig. 147. fore R is parallel to P and placement of rotation about 0 through an angle = co. The virtual work of P is then P. co OA, and that of Q is--Q. co OB, while that of R is zero. Hence Finally, to find the magnitude of R, take a virtual ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1896 Excerpt: ...0, therefore the virtual work of R = 0, thereQ. Again, choose a virtual dis Fig. 147. fore R is parallel to P and placement of rotation about 0 through an angle = co. The virtual work of P is then P. co OA, and that of Q is--Q. co OB, while that of R is zero. Hence Finally, to find the magnitude of R, take a virtual displacement of translation parallel to the forces. This evidently gives R = P+Q. (2) Therefore the resultant of two parallel forces acting in the same sense is a force parallel to them in the same sense, equal to their sum, and dividing the line joining their points of application in the inverse ratio of the forces. Equation (l) asserts that the moments of two parallel forces with respect to any point on their resultant are equal and opposite. If P and Q act in opposite senses (Fig. 148), the resultant is obtained in magnitude and direction by simply changing the sign of Q. Thus (l) becomes Qj Q _OB = P' (3) which shows that 0 is on the production of AB at the side of the greater force; and (2) gives E=P-Q. (4) Examples. 1. To solve example 9, p. 157, by the principle of Virtual "Work. Imagine a displacement in which the ends A and B remain in contact with the planes. Then the virtual works of R and S are zero, and if y is the height of G above the horizontal plane, the equation of virtual work is-Wdy-P.d(AC) = 0. (1) Now y--asind, AC = (a + 6)cos0;.'. dy = a cos ddd, and d(AC)=-(a + b)nin6d0; Wa.'. (1) gives Wa cos 0 = P (a + b) sin 0, or tsui0=---- a + 0) 2. To solve example 10, p. 157, by the principle of Virtual Work. Choosing a virtual displacement which keeps A and B in contact with the planes, the equation of work is-Wdy-T.d(AC) = 0. (1) Now FC = BF cos 20 + AP2 sin 26, and this equation also holds in the displaced position. He...
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