STRENGTH OF PLAIN CONCRETE BEAM. Fig. 25 shows a characteristic stress-deformation diagram for concrete, obtained by testing specimens in direct tension and in direct compression. Notice in Fig. 25 that a stress equal to three fourths of the compressive strength of the concrete gives only one half as much deformation as at failure, and that a stress equal to half of the com pressive strength gives only three tenths as much deformation as at failure.
To show the relationship of Fig. 25 and the principles in the preceding section to the strength of a plain con crete beam, suppose that a beam made of the same concrete as that from which Fig. 25 was deduced is loaded until the stress in the lowest fiber at the center is equal to BB'. The total tensile resistance of the beam is then represented by the area OBB', and the point of application of the resultant tension is at the center of gravity of that area. The total compressive resistance must be equal to the area OBB', and Oaa' is such an area Hence the stress diagram for the ultimate strength of the beam is a'OB', and an' is the compression in the upper fiber at the time of rupture of the beam on the tension side. Fig. 25
shows the wastefulness of using plain concrete as a beam, for the compression, aa', on the upper fiber when the beam fails on the tension side is only about one tenth of AA', the crushing strength of the concrete. The area OAA' represents the compressive strength of the concrete that is available, while only the portion 0.2a' is used. The purpose of adding steel reinforcement is to make available the whole of the compressive resistance of the concrete. The exact amount of steel required to utilize the entire compressive strength of the concrete depends upon the elastic properties of the steel and of the concrete, but steel having a cross sectional area equal to from 1 to 2 per cent of the total area of the beam will develop the entire compressive resistance of the concrete.