A Mechanical Text-Book; Or, Introduction to the Study of Mechanics And Engineering

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— If the direction of the load be everywhere parallel and vertical, draw a vertical straight line, C D, fig. 124, to represent the total load, amd from its ends draw C O and D O, parallel to two tangents at the points of support of the chain, and meeting in O; those lines will represent the tensions on the chain at its points of support.
Let &., in fig. 123, be the lowest point of the chain. In fig. 124, draw the horizontal line O A; this will represent the horizontal component of the tension o
...f the chain at every point, and if O B be parallel to a tangent to the chain at B (fig. 123), A B will represent the portion of the load sup- ported between A and B, and O B the tension at B.
To express this algebraically, let Kg. 124.
H = A = horizontal tension along the chain at A; 11 = B = pull along the chain at B j P = A B = load on the chain between A and B; i= ZX P B (fig. 123) = Z A O B fig. 124) = inclination of chain at Bj then, P = Htani;E= J (P^ + H^) = H sec i (1.) To deduce from these formulae an equation by which the form of the curve assumed by the chain can be determined when the dis- tribution of the load is known, let that curve be referred to rect- angular, horizontal, and vertical co-ordinates, measured from the lowest point A, fig.


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