This section is from the book "Safe Building", by Louis De Coppet Berg. Also available from Amazon: Code Check: An Illustrated Guide to Building a Safe House.
Caps and bases.
Bottom plates, which usually have to spread the weight are made, as shown in Figure 277 ; as they are often very large, and necessarily therefore quite thick, metal can be saved by gradually reducing the thickness towards the edges, as shown. In such plates a hole should be cast in the centre, to relieve the strain on the plate, when cooling and thereby avoid warping.
No bolts are needed where a bottom plate is used, as shown in Figure 277, as there is no possibility of tipping. Where the spread of base plate has to be very great, flanges as cast on same as shown in section in Figure 278 and in plan in Figure 279. Of course, the flanges can be more numerous. All parts of such a base should be of even thickness. If the casting is unusually large and unwieldy it can be made in two parts, as shown i n Figure 279, but in such cases great care should be exercised with the foundation or substructure, to avoid one-half settling away from the other half. This can be done by thick granite stones, or additional iron plates under the main bottom plate.
The calculation of hollow circular columns is very tedious, particularly as one has to guess at the size and then calculate the strength, often involving several calculations for a single case.
Tables XLV, XLVI, XLVII and XLVIII, have therefore been prepared by the writer to take the place of these calculations, for cast-iron hollow circular columns.
Explanation of Tables XLV to XLVIII.
Across the top of the tables, in the horizontal line, are given the lengths in feet of the columns. Down the left side in the vertical line are the safe loads in tons for each particular shape. The curved lines each represent a hollow circular section, and at the end of each curve is given first, the diameter of column, second the thickness of shell, third the area of cross-section. The latter enables one to pick out the cheapest section from any of the tables, by selecting any curve below and to the right of the one found - which has a smaller area of cross-section. Sometimes by reference to a subsequent table a still cheaper section can be found.
The tables have been calculated for cast-iron, according to Formula (3) ; the columns are supposed to have smoothly dressed ends and true bearings. The value used for (c/f) was 15000 pounds. Any one desiring to use any other value, need only proportion the vertical column of safe loads in tons accordingly; thus, for 12000 pounds we should take 4/5 of the loads as safe, or we could add \ to the load to be carried by the column, and find from the tables the diameter, etc., of column necessary to carry the increased load.
Table XLV gives columns from 3" to 7" diameter of different thicknesses, and from 5 feet to 12 feet long. Table XLVI gives columns from 8" to 10" diameter of different thicknesses, the 8" and 9" columns from 8 feet to 15 feet long, the 10" columns from 10 feet to 20 feet long.
Table XLVII gives columns from 11" to 13" diameter, and Table XLVI11 from 14" to 16" diameter, in both, of different thieknes and from 10 feet to 20 feet long.
An example will best illustrate the use of table.
What is the safe load on a hollow, circular, cast-iron column, with turned ends, 18 feet long, l1" diameter and 1 1/2" thick?
Columns of 11" diameter are given in Table XLVII to which we turn, we find the curve marked 11 - 1 1/2,- 44,8 cuts the vertical line 18 about two-fifth way down between the horizontal lines 150 and 155 our column will therefore safely carry 152 tuns.
Had we calculated our column by Formula (3) we should have had from Table I, section No. 8 for
Example of use of tables.
=5 1/2 2 + 4 2 = 11,56
4 and for V1 = (18.12)2 = 2162 = 46656.
Inserting the values in Formula (3) we have the safe load
44,8.15000 672000 w= = = 303962 pounds,
1+ 46656.0,0003 1 + 1,2108
11,56 or, 151,98 or say 152 tons same as found from table.
Now, is this the cheapest section for that load and length of column. Its area is 44,8 square inches. We now pass to the next curve below and to the right, it is 13- 1-37,7 or a 13" diameter column, 1" thick will be cheaper, as its area is only 37,7 square inches. Then, too, it is stronger, for at 18 feet long it will carry 158 tons cutting the vertical line 18 three-fifth way between 155 and 160. By passing further along, we find also that the 12" diameter 1 1/4" thick column of 42,1 square inches area will be stronger, carrying 161 1/2 tons safely at 18 feet of length.
By referring to the next Table XLVIII, we find some much cheaper sections, than any of these. For the 14" diameter, 3/4" thick column, has only 31,2 square inches area of cross-section, but we find it carries safely only 143 tons and therefore will not answer. However the 14" diameter 1" thick column, has only 40,9 square inches of area and carries 185 tons, and would answer therefore, provided of course, larger diameter is not objectionable. Or, cheapest of all would be the 15" diameter, 3/4" thick column which has only 33,6 square inches of area and carries 161 tons. The 16" diameter, 3/4" thick column would also be economical having only 35,9 square inches of area and carrying 180 tons at 18 feet of length. In wrought-iron construction, any number of shapes of columns are used, from plain flat bars, to the most elaborate combinations of the different shapes rolled, most of which are given, with their areas, squares of radius of gyration, etc., in Tables XIX to XXV. In Figures 280 to 287 are given a few combinations, which are frequently used for columns. Besides those shown there are frequently used combinations of I-beams and channels, or of angles and plates formed in the shape of plate and box-girders stood on end. Figure 280 shows two channels latticed together. A plate might be used in place of latticing if the channels were placed as shown in Figure 281, but in that case the interior would not be accessible for painting.