With regard to the method of drawing a section in its right proportions, nothing can be more simple. The depth in case of a girder (generally about 1/12 to 1/10 the span) being known, and the size of the lower flange having been calculated, the upper flange is drawn so as to have 1/4 to 1/6 the area of the lower flange. This is for a girder or bressummer; for a cantilever the flanges are reversed.
For example, in the girder whose central section is shown in Fig. 245, the depth given is 19 inches, the area of the lower flange 18 inches by an average of about 2 1/4 inches = 40 inches, the area of the upper flange should therefore be 1/4 of 40 inches =10 inches. The upper flange is now drawn 6 inches wide and 1 1/2 inches thick at the ends, but averaging about 1 3/4 inches thick, so that its area is 6 x 1 3/4 inches = about 10 inches. The web is gradually tapered, its thickness at the bottom being equal to that of the lower flange, and at the top equal to that of the upper flange, so that there are no sudden changes in the thickness of the metal, which would lead to unequal contraction while cooling, and consequent rupture at the junctions of the unequal parts. For the same reason both the flanges and the web are often made of the same thickness throughout, as in Figs. 244, 246. The method of calculating the strength of girders, their shape in longitudinal section and plan, and other points connected with their construction, will be described in Part IV.
1 See Part IV.
Elevations of Cast-iron Girders and Cast-iron Cantilevers.
A girder supported at the ends and uniformly loaded throughout its length, if it is to be of equal strength throughout, requires a section of larger area at the centre than at any other point. The section may be gradually smaller and smaller as the ends are approached.
The reason for this is that the stresses upon the girder are greatest at the centre and diminish gradually towards the end. If it were made of equal section throughout the girder would be unnecessarily strong except at the centre, and material would be wasted so far as the strength is concerned. This may, however, sometimes be necessary in order to afford space for the loads.
There are two ways of effecting the reduction of material.
The material may be reduced from centre to ends by reducing the depth of the girder, leaving the flanges the same width throughout as in Fig. 248. This is the most common form, and is convenient when anything is to rest upon the lower flange.1
Figs. 247, 248, 249 are the elevation, plan, and cross section at centre of a cast-iron girder of uniform strength, of which the section is varied by reducing the depth.1 b. Girder of uniform strength and uniform depth. - The width of the flanges may be reduced from the centre of the girder to the ends, leaving the depth the same throughout.
Figs. 250, 251 are the elevation and plan of a cast-iron girder of uniform depth in which the section is reduced towards the ends by gradually narrowing the flanges.2