The gross area of the angles being 12,86 square inches, and that of the cover-plates 12.25 square inches, the center of gravity of the section is found, by a method similar to that previously employed, to be 1.10 inches from the center of the cover-plate, or 1.10 0.438 = 0.662 inch from the back of the flange angles. This makes the effective depth 72.93 inches.
For this section, the true live-load flange stress is (1 340 000 X 12) - 72.93 = 221 000 pounds, and the actual dead-load flange stress is (275 000 X 12) - 72.93 = 45 400 pounds. The actual areas required for the 1'iVe and dead load are 22.10 and 2.27 square inches, which are obtained by dividing the above flange stresses by 10 000 and 20 000 pounds, respectively. The total required area is the sum of the two areas above, and is equal to 24.37 square inches. The total area required in the flange angles and cover-plates is therefore 24.37, less * the gross area of the web, 3.47, which leaves 20.90 square inches. The same angles as decided upon before will be used. This gives a required area for the cover-plates of 20.90 10.61 = 10.29 square inches. The required thickness is then 10.29 - (14 2) = 0.857say inch. The following section of the flange will therefore be decided upon: As the total net area above is within 21 per cent of the required net area, that section will he taken (see Specifications, Article 149). Note that in this case, the thickness of the cover-plates in the final design is the same as that determined in the preliminary design. Also note that the total net area is about 4 square inches, or 20 per cent,less than in the flange as first designed, in which case none of the area of the web was considered as withstanding the bending moment.
The -inch cover-plate on the top flange will extend the entire length of the grider, and is therefore 62 feet 9 inches long. The lengths of the other cover-plates are: For i-inch plate at the bottom, L = 61.7:i lu.5o 21.11 43.5 feet.
For each 1-inch plate, L = 61.75 _ 28 5 feet.
1'2L11 One foot should be added to each of the above lengths at each end, thus making the total lengths 45 feet 6 inches and 30 feet 6 inches, respectively.
1. If the span is 63 feet center to center, compute the length of the cover-plate. The section consists of two angles 6 by 6 by - in.; one cover
plate 14 by -1 in.; and one cover-plate 14 by in.; two rivet-holes being taken out of each angle and each cover-plate.
2. If the span is 87 ft. 9 in. center to center, compute the length of the cover-plate if the flange consists of two angles 6 by 6 by - in., and four cover plates 16 by 38s in., two rivet-holes being taken out of each angle and each cover-plate.
In determining the area of plates, the tables in the Carnegie Handbook, pp. 245 to 250, are convenient. In order to obtain plates whose widths are greater than 121 inches, see the note in the right hand column on page 250, Carnegie Handbook. For another pres entation of the above subject-matter, see "Steel Construction," Part IV. pp. 252, 254, and 261.
The spacing of the rivets in the flanges is a matter of considerable importance; the shear is transferred from the web to the flanges, where it becomes flange stress. This is done by the rivets, each rivet taking as much flange stress as is allowed by the Specifications. The conditions are similar to those shown in Fig. 143, where V represents an object exerting a pull on a long, thin plate A A which has, at various points along this length, small objects F attached to it by means of pegs r r. These small objects F hold the plate A A in equilibrium. Here V represents the shear which tends to cause the movement; AA, the web; r r, the rivets; and 2F the amount of flange stress taken by each rivet.
At section c c the total amount in the web to be trans formed is 2F; at section b b it is 10F. From this it is seen that enough rivets r r must be put in between the sections b b and c c to take up 10F 2F = SF; hence it is proved that the rivets between any two sections of the flange take up the difference in flange stress between those two sections.
The discussion just given will be the means of giving us the number of rivets required between any two sections; but it does not give us the rivet spacing between these two sections. In order to determine the rivet spacing at any particular point, the following analysis is presented (see Fig. 144).