— 128 — 
M — ^-( l- x) = ATd to 
AT=S = 
IV X (l 一 X ) 
2 cl 
and substitute for iv f l and d their values, and for x t 2, 4, ß, 8 and 10, S being the 
actual flange stress at the point considered. 
Making tlie substitutions gives for the various values of S, 11.6, 20.8, 27.5, 81.8 
and 33.6 tons. Subtracting each from the one following gives 11.0, 9.2, 6.7, J.3 and 
1.8 tons as the horizontal stresses to be taken up by tlie rivets in the different two 
feet lengths. 
In addition to these horizontal stresses there is in each length a vertical stress 
caused by the two ties pressing on the angle irons. What the amount of tliis vertical 
stress is it would be hard to say, for the stiffness of tlie rails tends to distribute the 
pressure of the wheels over several ties, but if wc assume that two thirds of the 
weight on one wheel or 4,17 tons is supported by the inner angle in a two feet length, 
we will provide for a sufficiently unfavourable case. 
From Table XVIII we find that the working bearing pressure for a rivet on 
a 蚤 " plate is 1.829 tons, and that tlie working bending moment for a rivet of that 
diameter is 0.395 inch ton. 
The total bearing pressure on tlie rivets in the first length is l/(11.6) a -j-(6.26) 2 = 
18.2 tons nearly, which divided by 1.829 gives 8 as tlie number of rivets required for 
bearing. Tlie stress on the inner flange is [/*(5.8) 2 十 (4.17) 2 = 7.15 tons, and the 
lever arm is i (fi x J) — 好"， making the bending moment 7.15 x M = 3.8 inch 
tons, which divided by 0.395 gives 10 as tLe number of rivets required to resist bend- 
ing: this corresponds to a rivet spacing of 2.4", or about three diameters. 
At tli o fifth division tlie stress oil tho inner angle is ， / ^O.ÜJ 2 十 （ 4.17) 2 = 4.3 
tons, and the corresponding bendiug moment 4.3 x fS = 2.28 inch tons, which 
divided by 0.895 gives G as the number of rivets required, corresponding to a rivet 
spacing of 4." A larger spacing would do for the lower flange, but it is scarcely 
worth while to make any difference between the spacings of the upper and lower 
flanges. The change in the spacing from the end of the stringer to tlie centre should 
be made abrupty between stiffeners and not gradually : this is to facilitate tlie 
punching by machinery. 
Generally speaking it is unnecessary except in the caso of very shallow girders 
to calculate the rivet spacing for the flanges, because tlie designer may rely upon 
bis previous experience, but, if he be in doubt, he will break no rule of good design- 
ing by putting in a few extra rivets. 
The stiffeners may be made of 2 士 , ’ x 3" x angle irons, and there should bo 
eight or nine pairs of them. The filling plates will have to be x 2 皆 •び 
In a similar manner may be designed auy plate girder or floor beam. 
