These amounts give a total of 24.48 square inches as the approximate net flange area required.
It will be assumed that one-half the total area, or 24.48 _ 2 = 12.24 square inches, is to be taken up by angles. If 12.24 sq. in. is distributed•over two angles, then 12.24 - 2 = 6.12 square inches is the net area for one angle. Of course it is not to be assumed that the area of the angle chosen must be exactly 6.12, but that this 6.12 square inches is the approximate area of the angle to be chosen, and the net area of the angle (see Specifications, Article 149) must not be 2i per cent less than this, although it may he greater.
From Steel Construction, Part I, Table VII, or from the Car negie Handbook, p. 117, a 6 by 6 by 1-inch angle gives a gross area of 8.44 square inches and a net area of 8.44 — 2 X (+ -I- +) X a = 6.94 square inches, Finch rivets being used and so spaced that two rivets are taken out of each angle. (see Specifications, Article 63, and Fig. 139). A 6 by 4 by Winch angle, giving a gross area of 7.47 and a net area of 6.66 square inches, one rivet-hole being out, could have been used, but i inch is too thick to punch, and there fore the above angle is chosen.
The required net area of the cover-plate is now found to be 24.48 — 2 X 6.94 = 10.60 square inches. Since the legs of the angles are 6 inches and the thickness of the web is * inch, the outer edges of the angles are 12* inches apart; and since the cover-plate must extend somewhat over the edges of the angle, and the width of the cover-plate should he in the even inch, the width of the plates must he at least 14 inches, as shown in Fig. 139.
On account of the 1-inch rivet holes to be deducted, the real or ' net width of the cover-plate *is: 2 X n m = 14 — 2 X 1 = 12 inches. The thickness of all the cover-plates at the center is now: 1(l. GJ t — - - _ 11.855 /k A thickness of ; of an inch is decided upon, for the reason that plates are rolled only to the nearest sixteenth of an inch.
The approximate section at the center has now been determined, and is: 2 :1ng!es ti by (i by 1-inch = 13.85 sq. in. net.
('over-plates g inch thick = 10.50 sq. in. net.
Total = 24.38 sq. in. net.
This approximate section must now be examined, and, if it shows too great an excess or a de ficiency, must be revised.
In order to deter mine the effective depth the distance between the centers of gravity of the flanges must first he com puted, the gross areas be ing used. Theoretically, perhaps, the net areas should be used; but this is an unnecessary refinement, since the effect on the final result is of no practical importance.
In computing the center of gravity (see Fig. 140), the axis is taken at the center of the cover-plates, as this reduces the moment of the cover-plates to zero. The distance of the center of gravity of the angles from their back (Carnegie Handbook, p. 117, column 6) is 1 .78 inches: The distance of this center of gravity from the center of the cover-plate, is 1.78 + 0.S7.5 - 2 = 2.22 inches.
The center of gravity is now found to be 16.88 X 2.22 _ 29.13 = 1.286 inches from the center of the cover-plate, and 1.286-0.875 =2=0:84S inch from the back of the angle. The effective depth 5, is 74.25 — 2 X 0.848 = 72.554 inches, and the required flange areas are: The values of the moments, as taken from the curves, must he mul tiplied by 12 in order to reduce them to pound inches.
A total of 24.86 square inches is given by the section approxi mately designed, and the difference between that and the section as above determined is: (24.472 — 24.38) ± 24.472 = 0.38 per cent, and as this is less than 21 per cent (see Specifications, Article 149), it may be used without any further change. If there should have been a deficiency or an excess greater than 21 per cent, then it would have been necessary to revise. In case a revision of section is necessary, the size and thickness of the angles generally remain the same as those taken in the approximate design, the thickness of the cover-plates being decreased or increased as the case may be.