A very slight description of one or two common forms of iron girder will be given here, the consideration of the stresses upon them, and of the dimensions required for them, being left for Part IV, but it is necessary to note in this section one or two points that fall within the Elementary Course.
This course merely requires "a knowledge of the best cross section for cast-iron beams in use for floor girders, or as bressummers,1 or as cantilevers,2 and to be able to draw such a section from given dimensions of flanges."
Without going into particulars reserved for Part IV., enough must be said here to show what points have to be considered in determining the general form of a cast-iron beam, whether girder or cantilever.
Such beams consist of an upper flange, uu, Figs. 243, 244, and a lower flange (l l) joined by a web or vertical member (w).
In the case of girders or bressummers supported at each end and loaded, either throughout, or at any point or points in their length, the upper flange is under compression tending to crush, the lower flange in tension, tending to tear across. This is illustrated in Fig. 241, where c c c denotes compression, and t t t tension.
1 A bressummer is a girder over a wide opening, and generally supporting a wall above it.
2 A cantilever is a bearer, of which one end is fixed in the wall, the other end being unsupported.
Fig. 241. Beam or Girder loaded.
In the case of cantilevers, the reverse takes place; loads on the cantilever cause the lower flange to be in compression and the upper flange in tension (see Fig. 242).
The web need not be considered, as but little direct stress comes upon it in either case (see Part IV.)
It has been found by experiment that cast iron will generally be ruptured or torn asunder by a stress of 8 tons per square inch in tension, but that it requires as much as 48 tons per square inch to crush it under compression. In order therefore that the flanges may be of equal strength, so that one may not fail before the other, the tension flange should contain six times as many square inches to resist the tension upon it, as the compression flange contains to resist the crushing stress upon it.
This leads to a section like Fig. 243, for a girder, in which the lower flange (l l), being in tension, contains 36 square inches, and the upper flange (u u), under compression, contains only 6 square inches, so that the tension flange has 6 times the area of the compression flange.
Fig. 242. Cantilever loaded.
Fig. 243. Cross Section of Cast-iron Girder.
Fig. 244. Cross Section of Cast-iron Cantilever.
In Fig. 244, the section for a cantilever, the upper flange is in tension and has six times the area of the lower flange.
The proportion of 6 to 1 for the area of the flanges is generally modified in practice according to circumstances.
The proportion of 1/6 for the compression flange would lead in many cases to very small flanges in which a bubble or flaw in the casting would destroy a large proportion of the area, and therefore of the strength of the flange. Moreover, the compression flange requires to be stiff to prevent lateral bending, and in some cases room is required to rest the load upon it.
For these reasons and others of a theoretical character,1 the area of the compression flange is often made about 1/4 or even as much as 1/3 of that of the tension flange.
Mr. Hurst says the area should be 1/4 1/2 when the load rests on the upper flange or on both sides of the bottom flange and 1/3 if it rests on one side only.