This section is from the "Architectural Iron And Steel, And Its Application In The Construction Of Buildings" book, by WM. H. Birkmire.. Also see Amazon: Architectural Iron And Steel, And Its Application In The Construction Of Buildings.
In heavy girders a saving of iron may often be made by reducing the thickness of the flanges towards the ends of the girder, where the strain is less. Then for the area of bottom flange at any point in its length, taking the stations as above, 4 feet and 8 feet, for a load uniformly distributed we have the following formula:
A = W((xy)/(2dkl))
Let d = depth in feet;
W= weight distributed over entire girder in pounds; x = short lever arm in feet; y = long lever arm in feet; l = span in feet; k = taken at 12,000 pounds. We have A = ((80,400xy)/(2x1.66x12,000x24)) = .084xy.
When x = y = 12, then A = .084 X 12 X 12 = say 12 inches, or the area required in the bottom flange at the middle.
When x = 8, then y = 16, and A = .084 X 8 X 16 = 11 inches, or the area required at 4 feet from the middle either way.
When x = 4, then y = 20, and A = .084 X 4 X 20 = 7 ins., or the area required at 8 feet from the middle either way.
In the results just given, the area required in the flanges increases gradually from the points of support each way to the middle of the girder. Then by making the chord or flange angles uniform throughout, and dividing the sum by the width of girder, being 10 inches in this case, the results are:
At the middle three quarters (3/4) of an inch thick.
At four feet from middle five eighths (5/8) " "
At eight feet from middle one quarter (1/4) " "
Or, at middle
4 ft. from "
8 ft. from "
An excess of metal will have to be placed in the plates at eight (8) feet from middle to make up the area, as it requires a one-quarter (J) inch plate the entire length, and within four (4) feet of each end a one-half (1/2) inch plate to make up the three quarters (œ) of an inch section; or use a one-half (1/2) inch plate the entire length, and a one-quarter (1/4) inch plate eight (8) feet each way from middle.
Most girders will work to better advantage in the plates than this example; always remembering that it is not practicable to make the plates for webs and flanges less than one quarter (1/4) of an inch thick.
In calculating the weight of brick walls, the following weights per square foot of surface are generally adopted:
8 inches thick = 77 pounds; 12 " " = 115
16 " " = 153
20 inches thick = 192 pounds;
24 " " = 230 "
28 " " = 268 "
The box girder, as shown in the plate, is connected to a column by the bolts A extending through to a girder on the opposite side. The rivets are countersunk on the bottom at each end D, to allow an even surface for the bearing of heel of girder on bracket and on stone templet.
Secured to the girder is a floor beam, which can be set at any height to accommodate the finished floor of building. The knees should be riveted to girders before being finished, providing the beam can be pushed into knees at right angles to girder; otherwise one knee should be riveted and the other placed on the beam and holes tapped into girder.
At section of box girder, F is the width of top flange, E is the height of webs, B and C are stiffeners, with fillers at the back extending under the same between the chord angles.
Fig. 1 is a single beam with a wrought-iron plate to increase flange area, riveted to flanges with four lines of rivets.
Fig. 2 is a double beam girder, used similarly to Fig. 1.
Fig. 3 is a double channel girder, used similarly to Figs. 1 and 2.
The same formula to be used for these sections as for plate girders; the flange section being taken equal to the area of plate and flange of beam.
The simplest support for a brick wall is two I beams side by side, or any number placed to suit size of wall and weight to be sustained. (See elevation and section of beam girder).
To accommodate the thickness of wall cast-iron separators are placed between webs; for 10 1/2-inch beams and under one bolt is used; for 12-inch beams and over, two bolts.
The separators for beam girders are generally 3/4 of an inch thick, with 3/4-inch-diameter bolts, and made to fit accurately the form of beams. (See section at G for one with two bolts).
Wrought-iron pipe separators are frequently used in the smaller beams with 3/4-inch-diameter bolts, but give very little stiffness to the girder.