THE Formula (3) on page 24 of Vol. I, is, of course, applicable this value for "pin" that is, rounded or rough bearings at ends, and for "smooth" that is, turned, planed or smoothed off bearings at ends. These different values have been arrived at largely by experiments, but the reason why the end bearing affects the strength of column can readily be seen in Figures 270 to 274.

Fig 272.

T to every kind and shape of column. The square of the radius of gyration used in this formula, can be found by any of the formulae given in Table I; or if the shape of the column is so unusual that it is not given in Table I, the moment of inertia (i) of the cross-section of the column can be found, and this divided by the area (a) is equal to the square of the radius of gyration, see page 9 of Vol. I.

In Table II are given the different values of n for cast and wrought iron, steel, wood, stone and brick; also the variations in

In Figure 270 we have a column with smooth ends between two forces crushing towards each other ; as a result the column tends to bend, in this case to the right. The bending of the column will, of course, tip its ends, as these are at right angles to the (dotted) longitudinal axis of the column; as a result the further crushing is taken entirely at the edges of the ends, or at points

A and B, marked with arrows in the Figure.

Why smooth end stronger.

Fig. 275.

Fig. 276.

Fig. 276 A.

It will be readily seen that the least pressure at A or B tends to bring the ends back to the horizontal plane and consequently to straighten the column again. For this reason it is that columns with smooth end bearings give way the same as columns with fixed end bearings, as shown in Figure 271. If on the other hand the ends of the column are rounded, as shown in Figure 272, the effect of the crushing at A and B is to constantly increase the bending of the column, as the point of contact against the column simply slips around the circular ends, as the column bends more and more. Such columns break as one curve instead of the triple curve shown in Figure 271. Where there is a pin bearing, as in Figure 273 the effect is, of course, the same as for rounded ends. Rough ends are considered the same as rounded ends, on account of the danger of some roughness or projection on the end of a bearing, which would greatly increase the tendency to bend, as shown at A and B in Figure 274. For this same reason wedging of joints of columns, should never be allowed.

Only those columns should be considered as having smooth ends, where the entire bearing end is perfectly smooth, and forms a true and perfect plane at right angles to the longitudinal axis of the column. In iron and steel columns the ends have to be "planed" or "turned" off, both of which are done by machinery. Planing is, as its name implies, a passing back and forth of a sharp metal planer which removes the surface iron, little by little. Turning is the same as planing but the motion of the planer is circular. Turning is done on circular columns, particularly where there are lugs or projections beyond the bearing surfaces, which would be in the way of a straight planer.

Cast-iron columns are usually made of circular cross-section and hollow. This is the cheapest cross-section there is for any column, and the metal will do more work per square inch, the thinner (within reason, of course,) the shell is made.

Cast-iron columns are also frequently made square in cross-section, and hollow, which does not make a badly proportioned column. All other shapes, however, are bad, and should only be resorted to in unusual circumstances. Such shapes, for instance, are rectangular and hollow, one side (or diameter) being shorter than the other, in this case the neutral axis, when computing the square of the radius of gyration, should be taken parallel to the long side ; then there are H or I shapes, T or Z shapes, etc., all bad and weak. Sometimes a column is made square or rectangular but with only three sides. The column will be greatly strengthened, if at intervals there can be cast on the fourth side a connecting bar.

All hollow castings should be drilled, as already explained, to ascertain their thickness, also near their base to allow any water to escape, which might otherwise freeze and burst the casting. Brackets, and other projections should, by preference, be cast on the column, rather than secured to it by bolts or tap-screws. Of course, they can't be riveted to cast-iron. They should, as far as possible, be of same thickness as shell.

Planing and turning.

Shapes of cast columns.

Fig. 277.

Where there are heavy capitals, bases or other mouldings or ornamental work that greatly increase the thickness of shell, they had better be made separately and slipped on afterwards, and then secured by tap-screws with countersunk heads.

The bearing should always, if possible, be vertically under and over the shell, not flanged out as shown in Figure

275.

Ends of columns are usually flanged out for bolting together, in which case the angles should be well rounded. It is also well to cast on one of the columns a lug as shown on the upper, etched column in as shown in etched part of Figure 276a with upper and lower lugs, and the columns bolted together through the plate.