This section is from the book "Cyclopedia Of Architecture, Carpentry, And Building", by James C. et al. Also available from Amazon: Cyclopedia Of Architecture, Carpentry And Building.
The modulus of elasticity of ordinary concrete is approximately 2,400,000 pounds per square inch, while its ultimate tensional strength is about 200 pounds per square inch. Therefore a pull of about 1/12,0000 of the length would nearly, if not quite, rupture the concrete. The coefficient of expansion of concrete has been found to be almost identical with that of steel, or .0000065 for each degree Fahrenheit. Therefore, if a block of concrete were held at the ends with absolute rigidity, While its temperature were lowered about 12 degrees, the stress developed in the concrete would be very nearly, if not quite, at the rupture point. Fortunately the ends will not usually be held with such rigidity; but nevertheless it does generally happen that, unless the entire mass of concrete is permitted to expand and contract freely so that the temperature stresses are small, the stresses will usually localize themselves at the weak point of the cross-section, wherever it may be, and will there develop a crack, provided the concrete is not reinforced with steel. If, however, steel is well distributed throughout the cross-section of the concrete, it will prevent the concentration of the stresses at local points, and will distribute it uniformly throughout the mass.
Reinforced-concrete structures are usually provided with bars running in all directions, so that temperature cracks are prevented by the presence of such bars, and it is generally unnecessary to make any special provision against such cracks. The most common exception to this statement occurs in floor-slabs, which structurally require bars in only one direction. It is found that cracks parallel with the bars which reinforce the slab will be prevented if a few bars are laid perpendicularly to the direction of the main reinforcing bars. Usually 1/2-inch or 3/8-inch bars, spaced about 2 feet apart, will be sufficient to prevent such cracks.
Retaining walls, the balustrades of bridges, and other similar structures, which may not need any bars for purely structural reasons, should be provided with such bars in order to prevent temperature cracks. A theoretical determination of the amount of such reinforcing steel is practically impossible, since it depends on assumptions which are themselves very doubtful. It is usually conceded that if there is placed in the concrete an amount of steel whose cross-sectional area equals about 1/3 of 1 per cent of the area of the concrete, the structure will be proof against such cracks. Fortunately, this amount of steel is so small that any great refinement in its determination is of little importance. Also, since such bars have a value in tying the structure together, and thus adding somewhat to its strength and ability to resist disintegration owing to vibrations, the bars are usually worth what they cost.