Depth = 0.005 X 61 ft. 9 in. + 0.543 — 72.5• • The depth might be taken as 72 inches, but 74 inches will be decided upon, as this will decrease the area of the flange and also will not affect the total weight to any great extent, The unit-stress for shear is 9 000 pounds per square inch (see Specifications, Articles 40 and 41).
The maximum shear in the girder occurs at the end, where it is 117 S00 pounds. The area required for the web is then 117 800 _ 9 000 = 13.09 square inches, and the required thickness is 13.09 74 = 0.177 inch. This latter value cannot be used, since, on account of Ar ticle S2 of the Specifications, no material less than s inch can be used. The web plate will therefore be taken as 74 in. by in. in size.
Some engineers insist that the net section of the web should be considered. Consider Fig. 136, the shear being trans ferred to the webby the end rivets. The web will not tend to shear along the section B—B, in which case the rivet-holes should be subtracted; but it will shear along section A—A, a section which is unaffected by the rivet-holes. The web splice should come at one of the stiffeners, and will therefore be considered in Arti cle 76.
73. The Flanges. This portion of the girder is usually built either of two angles or of two angles and one or more plates. In heavy girders where the flange areas are large, additional area is ob tained by using side plates or side plates and four angles. Sometimes two chan nels are used in the place of side plates and angles. Fig. 137 shows the different methods of constructing the top flanges of girders. The lower flanges are usually of the same construction. Fig. 137 b has the web extending beyond the upper stir faces of the upper flange angles. This is done in order that the ties may be dapped over it, and thus prevent the labor usually required for cutting holes in the lower face of the tie in order to allow for the projecting rivet-heads. Fig. 137 g is usually uneconom ical, since the thinness of the channel web requires a great many rivets to sufficiently transmit the shear from the web to the flange, and also since the cover-plates must be very narrow.
Specifications usually state that the flanges shall have at least one-half of the total flange area in the angles, or that the angles shall be the largest that are manufactured. The largest angles are not usually employed, since their thickness is greater than three-quarters of an inch and therefore the rivet-holes must be bored, not punched.
The reason for this is that the depth of the rivet-hole is too great in proportion to its diameter, and on this account the dies used for punching frequently break. Also, the punching of such thick material injures the adjacent metal, which makes it undesirable. In reality the flange area of only the short span girders is small enough to allow the flange area to be taken up by the angles.
In choosing the thickness of the cover-plates, care should be taken so that the outer row of rivets will not come closer to the outer edge of the plate than eight times the thickness of the thinnest plate. In case eight times the thickness of the plate is greater than 5 inches, then 5 inches should be the limit. Also, the distance between the inner rows of rivets should not exceed thirty times the thickness of the thinnest plate. These limitations are placed by Article 77 of the Specifications, and Fig. 13S indicates their significance.
The determination of the required flange area depends upon the distance between the centers of gravity of the flanges; and in order to determine this exactly, the area and composition of the flanges should be known. The above condition requires an approximate design to be made, the supposition being that the flanges consist of two angles and one or more plates as shown in Fig. 138.
The distance back to back of angles will be taken as 74 + 2 X = 74j inches. Article 74 of the Specifications requires i'6 inch; inch is better practice, since the edges of the web plate are very liable to overrun more than inch. Some specifications require inch.
In the computation of the approximate flange area, the center of gravity of each flange will be assumed as one inch from the back of the angles. The approximate effective depth is then 74} less 2 X I inch, which equals 721 inches. The approximate stresses in the flange areas are: The approximate flange areas are now obtained by dividing these amounts by the allowable unit-stresses for dead and live load, which are (see Specifications, p. 8, Article 31): 20 000 and 10 000 pounds per square inch respectively; and the resulting areas are: For dead load, 4' 600 = 2.2A square inches. 2V000 For live load, 22102 000 — 22.20 square inches.