About the Book
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. 1887 Excerpt: ... of the figure), on the objective path of the resultant of the forces, (8), (1), and (2). Secondly, from any point, E, in X c, erect a perpendicular, E 0v equal in length to the unit of scale, and join, X 0v c 0v This unit of scale, which is an arbitrary unit, has in this case been made equal to the perpendicular, OF, let fall from the pole, 0, on the line of forces. Thirdly, through the points, a, and c0, draw lines parallel toi'o; and from any point, G, on the resultant line of action through, set off two lines, G a;, and G yv parallel respectively to, c0, and X Ov The intercept, xlyv cut off by these two lines on the line through, a," will determine the moment required. It is important to notice that the position of, F F, the resultant force of the system, (8), (1), (2), is independent of the form of arch or other structure to which those three forces may be applied. The moment about the point, a, will remain the same, no matter how the form of the structure may be varied to which it may belong, provided that it represent the same fixed point in space. Draw a vertical line through the point, a, and let it intersect the line of action of the resultant, F F, in a point, a, . Let u be a third point on the vertical line, a, a. Construct, as shewn, two forms of arch passing respectively through the points, a, and For sections made through the three forms of arch passing through points, o, av a2, placed on the same vertical line, it will be seen that the bending moments vary in nature and amount. The bending moment relatively to the point, a," situated in the first type of arch, is graphically represented by, ti% and tends to turn the part-rib of the arch from right to left The moment relatively to the point, a2, situated on the third form of arch, is ...
