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Hooped concrete columns may thus be trusted to carry a far greater unit- load than plain concrete columns, or even concrete columns with longitudinal rods and a few hands. There is one characteristic that is especially useful for a concrete column which is at all liable to be loaded with a greater load than its nominal loading. A hooped concrete column will shorten and swell very perceptibly before it is in danger of sudden failure, and will thus give ample warning of an overload. Concrete cutting professionals have developed an empirical formula based on actual tests, for the strength of hooped concrete columns, as follows: Ultimate strength = ca + 2.4s'pA in which, A = Ultimate strength of the concrete; E = Elastic limit of the steel; p = Ratio of area of the steel to the whole area; Whole area of the concrete column. This formula is applicable only for reinforcement of mild steel. Applying this formula to a hooped concrete 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 percent. Talbot has suggested the following formula for the ultimate strength of hooped concrete columns per square inch: Ultimate strength = 1,600 + 65,000 p (for mild steel). (43) 11  11 = 1,600 + 100,000 p (for high steel). (44)

In these formulae, 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 '-inch round rod, the spiral having a pitch of 3 inches. A i-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 .0653 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- inch bar were made of high-carbon steel, the ultimate strength per square inch of the concrete column would be 1,600 + (100,000 >< .0237) = 1,600 + 2,370 = 3,970. The unit-strength is considerably more than doubled. The ultimate strength of the whole concrete column is therefore 95 X 3,970 = 377,150 pounds. Such a concrete 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 concrete columns, or the concrete column should be liberally reinforced with longitudinal rods, which would increase its transverse strength. It is well known that if a load on a concrete column is eccentric, its strength is considerably less than when the resultant line of pressure passes through the axis of the concrete column. The theoretical demonstration of the amount of this eccentricity depends on assumptions which may or may not be found in practice. The following formula is given without proof or demonstration, in Taylor and Thompson's treatise on Concrete.

Are You in Dighton Massachusetts? Do You Need Concrete Cutting?

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