Expansion and Contraction

EXPANSION AND CONTRACTION. The coefficient of expansion of steel and concrete are so nearly equal that there is no likelihood of any serious stresses being developed by differences of expansion and contraction of the steel and the concrete. The coefficient of expansion for steel is 0.000,006,5 per 1° F., and that for concrete varies from 0.000,005,5 for a 1:2 mixture to 0.000,006,5 for a 1 : 3 : 6 concrete.

In large structures built of plain concrete it is necessary to provide joints to prevent unsightly contraction cracks (§ 385-86); but with reinforced concrete these joints may be farther apart, and in some cases are entirely omitted. There is no well-established practice as to the proper distance between expansion joints or as to the method of constructing them.

Reinforcing to prevent Contraction Cracks.

Strictly speaking, no amount of reinforcement can prevent contraction cracks; but by the use of sufficient reinforcement the cracks can be forced to take place at such frequent intervals as to be quite invisible and conse quently to be of no importance, either as affecting the appearance of the concrete or as permitting the entrance of water or gas sufficient to corrode the steel.

In determining the amount of reinforcement required to prevent contraction cracks, three stresses in the steel must be considered, viz.: (1) the stress due to the cooling of the cement after the rise of temperature caused by the chemical action of setting (§ 348); (2) for concrete setting in air the stress due to the shrinkage of the con crete in hardening (§ 385); and (3) the stress due to changes in temperature of the atmosphere.

1. The first stress would probably be appreciable only in a very thick wall built rapidly, and is usually neglected.

2. Concrete setting in air shrinks 0.000,4 per unit of length. At points where the tensile strength of the concrete is least, this shrinkage will cause tension in the steel; and at points where the concrete is strongest, it will cause compression. The maximum tension that can come upon the steel from this shrinkage is equal to the tensile strength of the concrete, say 200 lb. per sq. in. (§ 406); and the cross sectional area of steel required to prevent a crack from opening up is equal to the tensile strength of the concrete divided by the elastic limit of the steel, or 200 _ 30,000 = 0.0067 = 0.67 per cent. Of course, if steel having a higher elasti limit is used, a proportionally smaller per cent will be required.

3. The amount of steel to prevent the opening up of cracks due to a change in the temperature of the atmosphere is computed as follows: For a drop in temperature of 100° F. the temperature stress in the steel will be 100 X 0.000,006,5 X 30,000,000 = 19,500 lb. per sq. in. If the elastic limit of the steel is 30,000, then there is available to resist the tension produced by the shrinkage of the concrete 30,000 — 19,500 = 10,500 lb. per sq. in.; and if the tensile

strength of the concrete is assumed to be 200 lb. per sq. in., then the steel required to prevent a contraction crack is 200 - 10,500 = 0.019 = 1.9 per cent. If steel having an elastic limit of 40,000 lb. per sq. in. is employed, only 0.97 per cent will be required; and if 60,000-pound steel, only 0.5 per cent will be required. These results are rather extreme, since a large change of temperature was assumed, and since a low elastic limit was sssumed for the steel. If a steel having a high elastic limit is used, it may be wise to use a deformed bar so as to distribute the deformation as much as possible.

The conclusion of the above discussion is that to resist the stresses due to a change of temperature of 100° F. requires 1.9 per cent of mild steel. The above computations are only approximate since the shrinkage during hardening is not known accurately, and since the change of temperature of the mass of concrete is not usually known with any considerable accuracy. On account of these uncer tainties and of the relatively large amount of steel required, it is comparatively rare that the attempt is made to prevent contraction cracks by reinforcing the concrete, although it has been done very successfully in a few cases.* The steel to resist thermal stresses should be placed near the surface, particularly if only one face is exposed to the atmosphere. Obviously, the reinforcement inserted to resist contraction can not rightly be expected to resist also the stresses due to the load.

Oontraction Joints.

For the reasons stated above, the usual practice is to divide continuous reinforced-concrete structures into units separated by contraction joints. The units are usually made somewhat longer than the distance at which cracks occur in non-reinforced walls (§ 386), and each section is reinforced to take up the shrinkage and thermal stresses within itself. Formerly these expansion joints were placed not more than 25 feet apart; but now the distance between them is usually 50 or 60 feet. In reinforced concrete buildings, the contraction joints are usually spaced at equal distances both longitudinally and transversely, and extend from the foundation to the roof. They are usually formed by fin ishing a section of wall or floor against a vertical form and allowing the concrete to set before concreting the succeeding section. The joints are therefore simply planes of weakness, and divide the columns, girders and beams vertically into halves.

For the method of making expansion joints in more massive structures, see § 387.