Let if, = Moment at one section; = Moment at another section nearer center of girder than the section where 3f, occurs; V = Shear at section where M, occurs; v = Amount of flange stress one rivet can transfer; or it is the stress on one rivet; s — Distance between the two sections; n = Number of rivets between the two sections.
If the above sections be taken close enough together so that the number of rivets required will .he 1 (that is, n = 1), then V can be considered as constant between the two sections, and then the moment = M, + I's (see Article 44, Part I). Substituting in Equation 1, above, there results: which is the formula for the rivet spacing in the vertical parts of the flanges of any girder, providing the flange is not subjected to localized loading. It is to he used for the rivet spacing in both the top and bottom flanges of through girders, but not in the top flanges of deck plate-girders for railroad service. It is to be used, how ever, in the bottom flanges of deck elate girders for railroad service. The dis tance is not ordinarily used, the distance between rivet lines being used instead (see Fig. 145). The.rivet spacing in the cover-plates and horizontal legs of the angles is made to stagger with that in the vertical legs, and usually the staggering is with every other rivet in the vertical flange. The term stagger signifies that the rivets in the top flange are not placed opposite the rivets in the vertical legs of the flange angles—or, that in case there are two lines of rivets in the vertical legs of the angle, a rivet near the outer edge of the cover-plate is placed in the same section where a rivet occurs near the lower edge of the vertical legs of the angle, and vice versa'.
1. Determine the rivet spacing at a section where the shear is 147 200 pounds, the value of one rivet 4 920 pounds, and the effective depth of the section 84I inches.
Ans. 2.82 inches.
2. Determine the stress on a rivet at a section where the shear is 299 400 pounds, the spacing 2i inches, and the effective depth of the girder 841 inches.
Ans. 8 870 pounds.
The rivet spacing is usually determined at the tenth-points; and a curve is'plotted with the 'spacing as ordinates and the tenth points as abscissa:. The rivet spacing at any intermediate point can be determined from this curve. When one-eighth the gross section of the web is considered as flange area, then only that proportion 'of the shear. which is transferred to flanges is to be considered in com
puting the rivet spacing, on account of the fact that some of the shear is transferred directly to the bending moment in the web.
In order to determine the distance between rivet lines, the gauge, or distance out from the back of the angles to the place where the rivets must be placed, must be known for different lengths of legs. Table XXI gives the standard gauges, and also the diameter of the largest rivet or bolt which is allowed to be used in any sized leg. No gauges should be punched otherwise unless your large experience or instructions from one higher in authority demand it, and this should be so seldom that indeed it might be said never to be necessary.
The distance between rivet lines for the girder being designed (see Fig. 146), is, in the first case: In the second case, where s of the web is considered, the above distance is 74.25 — (2 X 21- + 2') = 67.25 inches. The compu tations and the rivet spaces at the tenth point, and at the ends of the cover-plates in the bottom chord of the plate-girder, are shown for each case in Table XXII. The value of v is the value of a i-inch rivet in bearing in a -inch web (see Specifications, Article 40, and Carnegie Handbook, p. 195, second table). This value is 4 920 pounds.
In the first column, 7.9S— indicates that the end of the cover-plate next to the flange is 7.9S feet from the end of the girder, and that this section is taken just to one side of that point, the side being that nearest the end of the girder. In a similar manner, 7.9S+ indicates that the section is taken to that side of the point which is nearest the center of the girder. A like interpretation should be placed on 15.55— and 15.5y-, the point under consideration in this .case being the end of the outer or top cover-plate.
In the fifth column, values are given which indicate that portion of the shear which is transferred to the flanges. For example, 97 700 — 74 700, and the difference between 97 700 and (14.08 - 10.61) 74 700 represents that portion of the shear which is taken up directly by the web in the form of bending moment. An inspection of the headings of the third and fourth columns will tend to make this matter clearer.