To facilitate the erection, connections of beams to columns should always be by a shelf having the proper shear angles under, rather than by side connections. Another advantage in this form of connection is that the deflection of the beam does not cause so much bending stress in the column. As will be seen from Fig. 106, if a deep beam or girder were connected by angles in the web, a deflection in the beam would cause the top to tend to pull away from the column; and, if the beam were held rigidly by side angles, considerable bending stress in the column would result.

Selection of Sections. The particular form of column section will vary with the conditions.

1. The first consideration is usually the amount of load; certain forms cannot be used without excess of metal if the loads are light; and conversely, certain other forms cannot be used economically if the loads are very heavy.

2. The next point to be considered is the way the beams come to the column. If the framing is symmetrical and on four sides, any of the sections could be used; in such a case, however, it would be simpler to avoid single or double angles for use as columns.

If the connections are eccentric, then a section stronger in the direction of eccentricity should be chosen, and one that will admit of easy connections. If a heavy girder comes in on top of a column, then the metal must be specially arranged to meet this condition. The consideration of these points will be taken up and illustrated in detail under the head of "Connections."

3. In the case of wall columns, the architectural details, - such as size of pier, relation to ashlar line, thickness of walls, etc., - by limiting the dimensions of column, generally affect the choice of form of section.

4. Other architectural conditions, such as, shape and size of finished column, relations to partitions, provision for passage of pipes, wires, etc., have to be considered in the general choice, as it is desirable to adopt the same type throughout even if the limitations affect only certain columns.

5. The condition of the steel market as regards delivery of certain shapes within the required time, is always a factor. A delay of several months may sometimes be saved by proper consideration of this point.

Calculation of Sections. The type of column having been decided on, the calculation of sections is the next step.

The effect of connections is as important in the case of cast-iron columns, as in that of steel columns, and typical details are shown in Plates X and XI, Figs. 108 to 111.

Plate XII, Fig. 112, shows a cast-iron ribbed base designed for a square column similar to that shown by Fig. 110.

Fig. 113 shows a cast-iron base designed for a steel column, the section of which is indicated by the hatched lines. An important feature of all cases of this type is to have the metal arranged so as to conform to the metal of the column that rests upon it.

A good many designers give a slight pitch downward to the brackets forming the seats of beams. This is of advantage in avoiding the tendency, which would otherwise occur, of the beam to bear most heavily on the other edge when deflection under loading takes place.

There are several types of column formulae in general use; and, as noted under "Building Laws and Specifications," there is a variation in the legal requirements of different cities in this respect.

Gordon's formula is perhaps the oldest and most generally used. This is as follows: f = 12500

1 + l2/ar2 where f = safe fibre strain reduced for length and radius of gyration; l = unsupported length, in inches; r = radius of gyration, in inches; a = a constant, of the values below:

= 36,000 for square bearing;

= 24,000 for pin and square bearing;

= 18,000 for pin bearing.

Plate X. Cast Iron Columns

Columns Part 2 0500122

Fig. 108

Columns Part 2 0500123

Fig. 109.

Plate XI. Cast Iron Columns

Columns Part 2 0500124

Fig 110

Columns Part 2 0500125

Fig 111

The formula used by the Carnegie Steel Company for the calculation of capacity of Z-bar and box-section columns is as follows: f = 12,000 for lengths of 90 times the radius of gyration.

f = 17,100 - 57 l/r for lengths greater than above.

Cooper's formula is as follows: f= 16,000 - 58 l/r.

This formula, while similar in form to the one used by the Carnegie Company for lengths above 90 radii, is applied by Cooper to all lengths.

The American Bridge Company use the following formula for all lengths: f = 17.0000

1 + l2/11,000 r2.

The results given by these formulae vary considerably, the variation increasing under certain conditions of length and of radius of gyration, and being greater with large values in ratio of length to radius of gyration.

The student should work out the areas of column required by these formulŠ for different values of l/r, to become familiar with their differences.

Columns, Diagrams, and Tables. The most useful diagram for the calculation of capacity of columns and of required areas under concentric loading is one which gives the allowable unit-stress according to the formula to be used. Such a diagram would be made by laying off vertical ordinates representing different values of radius of gyration, and horizontal ordinates representing length of column in feet. On this diagram curves could be plotted, corresponding to a number of formulae.

Plate HI

Cast Iron Ribbed Bases

Columns Part 2 0500126

In practice this diagram would be used as follows: Assume a certain section which the judgment of the designer indicates as approximately correct. Calculate the radii of gyration, and, this