The tests on full-sized columns recorded in the foregoing tables furnish the most reliable data for the determination of the strength of columns.

If we apply Rankine's or Gordon's formula to calculate the strength of these columns, we shall find that the results differ from those obtained by experiment.

The following empyrical formulæ represent more nearly the results of tests recorded in the foregoing tables.

Mr. Theodore Cooper has proposed the following formulæ for Phoenix columns :

Although not mathematically correct, the following formula are used to proportion the compressive members of bridges :-1

1 Mr. Theodore Cooper's "General Specifications for Railway and Highway Bridges."

where I the maximum intensity of working stress in pounds

=

per square inch.

the length of the compression member in inches.

r the least radius of gyration in inches.

=

I must not exceed forty-five times the least width of the compression member.

The areas obtained by dividing the live-load stresses by the live load must be added to the areas obtained by dividing the dead-load stresses by the dead load.

The following formulæ are used for steel struts :

Members subjected to alternate stress of tension and compression shall be proportioned to resist each kind of stress. Both of the stresses shall, however, be considered as increased by an amount equal to of the least of the two stresses.

The following formulæ were suggested in Engineering1 for designing struts in which the length does not exceed forty times the least transverse dimensions.

=

min.

2 max.

for

It should be noted that the length in feet, and r = the least radius of gyration in inches. I the safe working stress.

All the foregoing straight-line formulæ should only be used within the limits specified in regard to the ratio of length to least width of section or least radius of gyration.

1 Engineering, January 5, 1892.

CHAPTER XIII.

SIZES OF PLATES AND BARS-JOINTS AND CONNECTIONS.

In designing built-up structures of wrought iron and steel, we make use of certain rolled sections which consist chiefly of plates, angles, T, channel, and flat bars; also of rolled girders, bulb T-irons, and occasionally other specially rolled sections connected together by means of rivets, bolts and nuts, pins, eyes, gibs and cotters, union screws, etc. It is necessary to know how to arrange the lengths and sections of the various riveted joints and other connections in the most convenient manner, not merely with a view to resist the various stresses developed in them, but also to reduce the cost of manufacture, carriage by land and sea to the site of the structure, and its subsequent erection.

The designer will find it convenient to have by him a list of sizes of plates and bars, made by different manufacturers, such as the following: The Butterley Iron Company, Measures Bros., Carnegie, Dalzell Steel and Iron Works, and many others.

Iron and steel plates vary in thickness from 4 to 11⁄2 inch, increasing by of an inch. Plates less than inch are termed sheets, and are generally more expensive. The following maximum sizes from the Butterley Iron Company's list have been selected, and indicate the limits of area, length, and width :TABLE XLIV.