# 000 for Railway Bridges 10

## web, stiffeners, line, angles, inches, shear, flange and stress

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Having determined therefore, the maximum shear, the required h = Depth of web.

The net area is assumed as the gross area.

Crippling of Web, and Use of Stiffeners. The value of to be used depends on the clear distance between the adjacent edges of the top and bottom flange angles, and upon whether or not stiffener angles are to be used.

The distribution of the shear over the web causes compression forces acting at angles of 45 degrees with the axis of the girder, in the manner indicated by Fig. 245. The web, therefore, under these com pression stresses, is subject to failure laterally, just as a long column. The allowable shearing stress must therefore be reduced by a formula similar to the column formula, which may be taken as 12,000 /8 -2 dc 1+ 1,500 in which d c = distance between flanges; and t = thickness of web. Either the web must be made thick enough not to exceed this allowable stress on a, length 1,414 d c, which is the length on a 45-degree line between the adjacent edges of flange angles, or this unsupported length must be reduced by using stiffeners so spaced as to cut this degree length down to limits which will conform to the allowable shear ing stress given by the formula and to the thick ness of web which it is desired to use.

Webs less than inch thick are rarely used. For greater thick nesses, it is a matter of economy generally to use stiffeners. For very heavy loads, however, or for long spans, --inch or w e b s would be used, w ith or without stiffeners, as m i g h t be required.

It will be seen from the above consideration, that, where the shear varies from the end towards the center, the required spacing of stiffeners will increase to wards the center, since the area of the web is constant.

When the shear has reduced to the point where the area of web is sufficient to resist buckling on a length of 1.414 d c, then the stiffeners may be omitted. A convenient diagram for determining spacing of stiffeners is shown in Fig. 246; the use of this diagram will be illus trated by a problem.

Suppose the shear at the end of a girder is 100,000 pounds; and the clear distance between flange angles is 22 inches, and the web which it is desired to use is 30 inches by b inch. The gross area of web is then 11.25 square inches, and the shear per square inch of gross area is 8,900 pounds. Following up the vertical side of the diagram until the line corresponding to 8,900 is found, then following this line until it meets the line of a 1-inch web, and then looking under this inter section to the lower horizontal line, it is found that stiffeners must be spaced about 12 inches apart in order to conform to the above con ditions.

If it was desired to find what thickness of web was necessary in order not to require stiffeners, the flange angles being 22 inches apart in the clear, this would be determined as follows: Follow up the vertical line corresponding to 22 inches as given at the bottom of the diagram, until this line meets the line corresponding to such a thickness of web that the gross area is sufficient to bring the shearing stress within the limit by the horizontal line at this intersection of web-line and vertical through 22.

In this case the nearest intersection is found to be the -1--inch web. The area of a 30-inch by i-inch web is 15 square inches, and this gives a shearing stress per square inch of 6,675 pounds. The allowable stress as given by the diagram is 7,400 pounds; but the web found to give a shearing stress of 7,640 pounds, whereas the allowable shear for a web with angles 22 inches apart is only 6,600 pounds.

It would be found more economical to use a i-inch web with stiffeners, than a i-inch web without stiffeners.

Another use of stiffeners is to stiffen the web at concentrated loads. The most important case under this head is the reaction at the bearings of the girder. Stiffeners are always used here, and they are generally placed so that the outstanding legs will come nearly over the edge of the bearing plate, as illustrated by Fig. 247. Sometimes the special nature of the bearing—as, for instance, the disposition of column members—makes it desirable to place these stiffeners close together, or in three lines instead of two. The fundamental idea is to place the stiffeners so as to distribute the reaction in the most direct way to the bearing. If this bearing is masonry, the stiffeners will be placed so as to give uniform bearing; if a column, they will be placed so as to correspond as closely as possible with the line members of the column. Wherever heavy concentrated loads from beams, other girders, masonry piers, etc., occur, stiffeners should be used to stiffen the web against this concentrated application of load. Stiffeners over bearings should be fitted to both the top and bottom flange angles. Stiffeners at loads on the top flange need be fitted only to the top flange angles.

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