579. While we have in this country been somewhat slow in acknowledging the worth of concrete-steel construction, there is now a strong interest displayed in the subject; many experiments are being made in our educational and commercial laboratories and the theory of the action of concrete and steel in combination is being rapidly developed. It is natural that in the investigation of a form of construction permitting so many variations in methods of preparation, that the opinions now advanced, based on insufficient data, should be more or less conflicting.
The experiments of M. A. Considere, made in France between 1898 and 1901, which have been made more available to us through the translation and collection of his articles on the subject by Mr. Moisseiff,1 are exceedingly valuable. The effect of the quality of the steel and the concrete, of repeated loads, of changes in volume in hardening, and many other points are carefully analyzed by experiment and theory.
One of the most important deductions drawn by M. Considere is that fibers of concrete within what may be called the sphere of influence of a reinforcing rod of iron or steel, is capable of enduring very much greater elongations without visible fracture than similar concrete without reinforcement. The explanation advanced for this is that the steel so distributes the stress throughout the length of the concrete in tension that the development of insipient fractures or excessive elongations at the weaker sections of the concrete is prevented until each section has taken its maximum load. The conclusion to which this theory leads is that the resistance of the concrete throughout the area of influence of the steel reinforcement, is maintained far beyond that degree of deformation which, in concrete not reinforced, would cause its rupture.
Notwithstanding these conclusions, it is believed that it is sufficient in most cases of design to neglect the tensile strength of the concrete in concrete-steel combinations. This course may be defended by the following considerations. The tensile strength of concrete is, at best, not usually above two hundred to four hundred pounds per square inch. If the stress on the extreme fibers of a beam is three hundred pounds, and we consider that this stress decreases uniformly toward the neutral axis, the mean stress is but one hundred fifty pounds per square inch. Again, if we disregard M. Considered conclusions, we find that since the modulus of elasticity of steel is, say, fifteen times that of concrete, the former is only stressed to forty-five hundred pounds per square inch when the imbedding concrete has reached its ultimate strength.
1 " Reinforced Concrete," by Armand Considere, McGraw Publishing Co., New York.
582. The resistance of concrete to tension may easily be destroyed or impaired by accident, especially when fresh. The properties of concrete vary so much with the materials, the proportions, and the manipulation, and the investigation of the behavior of concrete and steel under stress is as yet so incomplete, as to make refinements in theoretical treatment not only unwarranted but really undesirable for practical purposes, since they lead to the appearance of greater accuracy than is in reality attainable.
It is true that by the judicious selection of values for the constant appearing in formulas for the strength of concrete-steel beams, the results of such formulas sometimes show a remarkable agreement with the results of that series of actual tests for which the constants have been selected; but one has only to recall his experience in other lines, hydraulics for instance, to realize the importance of the almighty constant. The opinion sometimes advanced, that the strength of a given concrete-steel beam may be as accurately derived by formula as can the strength of a steel beam, the writer does not believe to be tenable, at least in the present state of our knowledge concerning the behavior of concrete.
583. To neglect the tensile strength of the concrete will result in a slight increase in the required area of steel reinforcement, and, in so far as the tensile strength of the concrete may be developed, will tend to make the compression side of the beam weaker than the tension side. The only objection to this is that the failure of the beam, though at a higher load, may be more sudden. This possibility, however, seems less serious than the error of depending on the tensile strength of the concrete only to find it lacking at the critical moment.
Since the aim here is to develop a formula that may be used with safety in the design of structures, and since to neglect the tensile strength of the concrete is to add an unknown, though probably small, factor of safety, the tensile strength will not be considered in the following analysis.