A 4 by 3 by angle with an area of 2.87 square inches and a radius of gyration of 1.25 will be assumed. The unit-load P is computed to be 8 750 pounds, and the required area is therefore 22 860 - 8 750 = 2.61 square inches. This does not coincide very closely with the given area, but will be used since this angle comes nearer to fulfilling the condition than any of the other sizes rolled. The joint will require more rivets in bearing than in single shear. It is not necessary to perform the complete computations in order to determine this, since a comparison of the values of a rivet in single shear and in bearing shows that the value in bearing is less than that in single shear, and therefore the number of rivets required in bearing will be greater than that number required in single shear. The number of rivets required in bearing is: = say, 4 shop rivets, and 4g2020 X 1.5 4.00 X 1.5 — 6 field rivets.
75. The Stiffeners. According to Article 47 of the Specifica tions, these should be placed at certain intervals whenever the unit shear is greater than S = 10 000 — 75 X j = 10 000 — 14 800 = —4 800 pounds.
This negative sign signifies that whenever the unit shearing stress is greater than zero, the stiffeners must be placed through out the entire length of the span at distances not to exceed 5 feet.
The diate stiffeners should have the outstanding leg long enough to give good port to the flange angle (see Fig. 155) . The filler bars or fillers are put in so as to allow the stiffener angles to remain straight throughout their entire length; otherwise they will have to be bent as shown in Fig. 156. This bending is called crimping. Stiffeners must also conform to Article 48 of the Specifications. This would require a different sized stiffener at each point, and also a different number of rivets in each stiffener. 'This is not usually done in practice. In practice the stiffener for the first intermediate point is designed, and the remainder are made the same in size and have the same number of rivets. An exception to this is where a stiffener comes at a web splice. In this case the size is usually kept the same, but the number of rivets is changed somewhat to conform to the requirements of the splice design.
The second intermediate stiffener comes at the first tenth-point, and is 6.175 (say 6.2) feet from the end, since it is at the first panel point, or opposite the first panel point, of the lateral system. The first stiffener will be 3.1 feet from the end; and scaling off the value
of the shear at this point (see Fig. 134), it is found to be 108 000 pounds. Here the length 1 to be used in the formula for the unit allowable compressive stress is 74} — 2 X 4 = 72.75 inches, the being the thickness of , the flange angle. The section of the material which according to Article 48 of the Specifications is to be considered as a column, is shown in Fig. 157. The assumed column cannot bend about the axis B—B,but about the axis A —A, and therefore the radius of gyration about the axis A — A must be computed. The moment of inertia of the fillers and the web plates about their own axes is considered as zero.
A 4 by 4 by 1-inch angle with an area of 3.75 square inches will be assumed to be sufficient to withstand the stress. The moment of inertia of this and the filler bars and the web portion is 2(5.55+3.75 X2.12'+3.00 X0.563') =46.70.
The radius of gyration; then, is, ' 46.70 = 1.764, and the unit-stress 15.00 computed with this value and a length of 72.75 inches is 8 140 pounds. The required area is now determined to be 108 000 _ 8 140 = 13.27 square inches. The value 15.00 used in the above computation for the radius of gyration is the value of the area of the angles, the filler bars, and the web portion. A 5 by 31-inch angle with the 5-inch leg out would have given better support to the flange, but would not make so good a job, as it would have extended about b inch be yond. the curved part of the hori zontal leg of the flange angle.
The bearing determines the number of rivets in this case.
The number is 108 000 - 4 920 = 22 shop rivets in the web.
The angle must now be inves tigated in order to see if these 22 rivets can go in one row without being closer together than 2a inches, which is three diameters of the s inch rivet. The total length in which these rivets must be placed is 72.25 inches, and therefore we have 72.25 ± 22 = 3.3 inches as a spacing. Since this is greater than 2ig inches, 22 rivets can be placed in one row. If the spacing as determined above had been less than 2 inches, it would have been neces sary to use two rows of rivets spaced as shown in Fig. 158; and then the distance center to center would he more than 2t1 inches, although the spacing in a vertical line would be less than that.
The four angles at the ends of the girders are called the end stiffeners. These are placed in pairs on opposite sides of the web (see Plate II, Article 74).