It has been found that the strength of a column is very greatly increased and even multiplied by surrounding the column by numerous hoops or bands or by a spiral of steel. The basic principle of this strength can best be appreciated by considering a section of stovepipe filled with sand and acting as a column. The sand alone, considered as a column, would not be able to maintain its form, much less to support a load, especially if it was dry. But when it is confined in the pipe, the columnar strength is very considerable. Concrete not only has great crushing strength, even when plain, but can also be greatly strengthened against failure by the tensile strength of bands which confine it. The theory of the amount of this added resistance is very complex, and will not here be given. The general conclusions, in which experimental results support the theory, are as follows:

1. The deformation of a hooped column is practically the same as that of a plain concrete column of equal size for loads up to the maximum for a plain column.

2. Further loading of a hooped column still further increases the shortening and swelling of the column, the bands stretching out, but without causing any apparent failure of the column.

3. Ultimate failure occurs when the bands break or, having passed their elastic limit, stretch excessively.

Hooped columns may thus be trusted to carry a far greater unit-load than plain columns, or even columns with longitudinal rods and a ew bands. There is one characteristic that is especially useful for a column which is at all liable to be loaded with a greater load than its nominal loading. A hooped column will shorten and swell very perceptibly before it is in danger of sudden failure, and will thus give ample warning of an overload.

Considere has developed an empirical formula based on actual tests, for the strength of hooped columns, as follows:

Ultimate strength = c'A + 2As'pA.(42) in which, c' = Ultimate strength of the concrete; s' = Elastic limit of the steel; p = Ratio of area of the steel to the whole area;

A = Whole area of the column.

This formula is applicable only for reinforcement of mild steel. Applying this formula to a hooped column tested to destruction by Professor Talbot, in which the ultimate strength (c') of similar concrete was 1,380 pounds per square inch, the elastic limit of the steel (s') was 48,000 pounds per square inch; the ratio of reinforcement (p) was .0212; and the area (A) was 104 square inches; and substituting these quantities in Equation 42, we have, for the computed ultimate strength, 409,900 pounds. The actual ultimate by Talbot's test was 351,000 pounds, or about 86 per cent.

Talbot has suggested the following formulae for the ultimate strength of hooped columns per square inch:

Ultimate strength

= 1,600 + 65,000 p (for mild steel)

(43)

,, ,,

= 1,600 + 100,000 p (for high steel)

(44)

In these formulŠ, p applies only to the area of concrete within the hooping; and this is unquestionably the correct principle, as the concrete outside of the hooping should be considered merely as fire protection and ignored in the numerical calculations, just as the concrete below the reinforcing steel of a beam is ignored in calculating the strength of the beam. The ratio of the area of the steel is computed by computing the area of an equivalent thin cylinder of steel which would contain as much steel as that actually used in the bands or spirals. For example, suppose that the spiral reinforcement consisted of a 1/2-inch round rod, the spiral having a pitch of 3 inches. A 1/2-inch round rod has an area of .196 square inch. That area for 3 inches in height would be the equivalent of a solid band .0053 inch thick. If the spiral had a diameter of, say, 11 inches, its circumference would be 34.56 inches, and the area of metal in a horizontal section would be 34.56 X .0653 = 2.257 square inches. The area of the concrete within the spiral is 95.0 square inches. The value of p is therefore 2.257 ¸ 95.0 = .0237. If the 1/2-inch bar were made of high-carbon steel, the ultimate strength per square inch of the column would be 1,600 + (100,000 X .0237) = 1,600 + 2,370 = 3,970. The unit-strength is considerably more than doubled. The ultimate strength of the whole column is therefore 95 X 3,970 = 377,150 pounds. Such a column could be safely loaded with about 94,300 pounds, provided its length was not so great that there was danger of buckling. In such a case, the unit-stress should be reduced according to the usual ratios for long columns, or the column should be liberally reinforced with longitudinal rods, which would increase its transverse strength.

DETAIL OF RESIDENCE AT CLEVELAND, OHIO

DETAIL OF RESIDENCE AT CLEVELAND, OHIO.

ENCLOSED OPEN AIR PORCH IN RESIDENCE AT CLEVELAND, OHIO

ENCLOSED OPEN-AIR PORCH IN RESIDENCE AT CLEVELAND, OHIO.

Frost & Granger, Architects, Chicago, 111. For Further Exteriors, See Vol. 1, Page 314; for Interior Views, See Opposite Page.

DINING ROOM IN RESIDENCE AT CLEVELAND, OHIO

DINING ROOM IN RESIDENCE AT CLEVELAND, OHIO.

Frost & Granger, Architects, Chicago, 111. Note the Absence of any Hanging Fixture. Other Details of Same House Shown on Opposite Page.