FOR RAILWAY BRIDGES: = 10,000 pounds per square inch, net area.
f, = 8,000 pounds per square inch, gross area, reduced for ratio of length to width of flange.
= 8,000 pounds per square inch net area.
The practice regarding the reduction of allowable compression stress varies somewhat; but the following formula is a conservative one for general use: _ .
1 + 5,000 where f = Fiber stress to be used in compression; f, = Specified fiber stress unreduced; 1 = Length of unsupported flange (in inches); W = Width of flange (in inches).
In ordinary construction, the fact that the two flanges are gener ally made of the same section makes it unnecessary in many instances to consider this reduced compression-fiber stress. If the unsupported length of top flange is long, however, so as to make the section deter, mined for bottom flange insufficient, then both flanges should be made the same as that required by the compression value.
When the girder is short, and the web-plate is not spliced, allow ance is sometimes made for the portion of the compression and tension which the web may carry. In doing this, the net area of the web— deducting rivet-holes—is considered concentrated at the centers of gravity of the flanges, and as reducing the required area of the flanges by an amount equal to t h„ in which t = thickness of web, and = depth. When this assumption is made, therefore, the required area of each flange is — — t in which / is the compression value for the top flange and the tension value for the bottom flange.
There is a considerable saving in the templet and shop work if both flanges are made alike; the extra weight in one flange which may be added, will often be more than offset by the saving in shop work.
It is a very general practice, therefore, to make both flanges alike in section, determining this by whichever flange requires to be the larger.
Economical Depth of Web. It will be seen that the areas re quired for the flanges are dependent on the depth of the web. Where there are no conditions limiting this depth to certain values, it is de sirable, therefore, to fix it so as to give the most economical section.
For a uniformly distributed load, this depth is generally from to of the span. Sometimes several approximations of this depth can be made, and the corresponding areas determined; and then, by computing the weights of flanges and web-plates so determined, the most economical section can be chosen.
In a great many cases, especially in building construction, the economical depth cannot be used, because of conditions fixing this depth with relation to other portions of the construction. In other cases, certain sections of plates and angles must be used in order to obtain quick delivery; and accordingly, the depth must be fixed to harmonize with these sections.
Proportioning the Web. As before stated, the function of the web is to resist the shear.
The student should here note that, as explained under "Statics," the loading which will produce maximum shear is not necessarily the same as that which causes the maximum bending moment.
In highway and railway girders, this loading is always different. In building construction it is very often different, because certain beams may frame into the girder over the support and these beams must be considered in determining the shear although they are not eon sidered in determining the bending moment. Again, a girder may carry a wall, and a portion of this wall may come directly over the end supports of the girder. This portion will materially increase the shear while perhaps not affecting the bending moment.
'The general statement of loads to be considered in determining the shear where all loads are fixed in position, is to include all loads which directly or indirectly can come upon the girder, and to deter mine the maximum end reaction for these loads. (The determination of web shear for moving loads, will be treated under "Bridge Engi neering)." Sometimes the shear at one end is greater than at the other, in which case the section is fixed by the requirements at the end having greatest shear.