The encyclopdia britannica; a dictionary of arts, sciences, literature and general information . total moment at?^ Wi, due to three loads, is the sumotC +mn +mo ofthe intercepts ML 0) a -4— %; 4L -X Fig. 49. which the triangle sides cut off from the vertical under Wi. As theloads move over the girder, the points C, D, E describe the parabolasMl, M2, M3, the middle ordinates of which are fWii, fWii/, and JWs/.If these are first drawn it is easy, for any position of the loads, todraw the lines BC, BD, BE, and to find the sum of the interceptswhich is the total bending moment under a load. The lo
The encyclopdia britannica; a dictionary of arts, sciences, literature and general information . total moment at?^ Wi, due to three loads, is the sumotC +mn +mo ofthe intercepts ML 0) a -4— %; 4L -X Fig. 49. which the triangle sides cut off from the vertical under Wi. As theloads move over the girder, the points C, D, E describe the parabolasMl, M2, M3, the middle ordinates of which are fWii, fWii/, and JWs/.If these are first drawn it is easy, for any position of the loads, todraw the lines BC, BD, BE, and to find the sum of the interceptswhich is the total bending moment under a load. The lower portionof the figure is the curve of bending moments under the leading Wi has advanced a distance a only one load is on the girder,and the curve AF gives bending moments due to Wi only; as Wiadvances to a distance a+6, two loads are on the girder, and thecurve FG gives moments due to Wi and W2. GB is the curve ofmoments for all three loads W1+W2-I-W3. Fig. 51 shows maximum bending moment curves for an extremecase of a short bridge with very unequal loads. The three lightly. dotted parabolas are the curves of maximum moment for each ofthe loads taken separately. The three heavily dotted curves arecurves of maximum moment under each of the loads, for the threeloads passing over the bridge, at the given distances, from left toright. As might be expected, the moments are greatest in thiscase at the sections under the 15-ton load. The heavy continuousline gives the last-mentioned curve for the reverse direction ofpassage of the loads. With short bridges it is best to draw the curve of maximumbending moments for some assumed typical set of loads in the wayjust described, and to design the girder accordingly. For longerbridges the funicular polygon affords a method of determiningmaximum bending moments which is perhaps more very great accuracy in drawing this curve is unnecessary,because the rolling stock of railways varies so much that the precisemagnit
Size: 1636px × 1527px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1910, booksubjectencyclo, bookyear1910
