A Course on the Stresses in Bridge and Roof Trusses, Arched Ribs and Suspension Bridges (Paperback)

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1883 edition. Excerpt: ...convenient, nor the one commonly used. The method ordinarily used is the usual one for constructing the equivalent polygonal frame, and is the following: Let AK, Fig. 2, represent any span, inclined in this case but ordinarily horizontal, and 1,2, 3, 4, etc., the vertical loads acting along their respective lines of action. In Fig. 3 let the portions 1,2, 3, 4, 5, 6, 7, 8, and 9 of the vertical line 1-9 represent those loads taken by any assumed scale. Since BC Fig. 2. represents the sum of all the applied loads, it is also equal to the sum of the two reactions or shearing stresses at A and K. In the case of the simple beam taken, those quantities will of course be determined by the law of the lever only. Suppose A'C and A'B to represent the shearing stresses or reactions at A and K respectively. Then draw A'P parallel to AK, and on it take any point P. From P draw the radial lines a, b, c, d, /, as shown, and starting from A or AT in Fig. 2, draw the lines a, b, c, d, /, parallel to the lines denoted by the same letters in Fg. 3-Then will Fig. 2 represent the equilibrium polygon for the given span and system of loading. The line AK or PA' is called the closing line of the polygon. Fig. 3. The reaction at A is evidently composed of the numerical sum of the vertical components in / and AK, while that at K is equal to the numerical difference of the vertical components in a and AK. The point P, from which the radial lines are drawn, is called the pole, and the normal distance from the pole to the load line BC, the pole distance. The pole distance evidently represents the horizontal component of stress common to all the members of the polygon. In order that the equilibrium polygon, constructed according to the principles given above, ..