{Contributed by P. R. Strong)

General Principles

The general arrangement of reinforcement in the construction of floors and pillars may be seen in Figs. 23 and 39. It will be observed that floor slabs and beams are reinforced with rods close to their lower surfaces, except where beams pass over pillars or where secondary beams are supported by primary beams; or again, where slabs are supported by beams - in which positions the rods are transferred to the upper parts of the concrete, for it is here that the tensile stress is then found.

General Principles 42

Fig. 24.

A section through a floor slab and floor beam is shown in Fig. 24, in which the slab is seen to be one with the beams. Fig. 25 shows another method that may be adopted, in which the beams are distinct from the slabs, the latter being moulded in advance and simply resting upon the beams. In this case, as the slab is not continuous, the reinforcement is not transferred to the upper surface over the supporting beams. The method shown in Fig. 24 has the advantage that the beam is of tee sections, and that the concrete of the floor slab assists in taking the compressional stress, while the concrete in the tensional portion of the beam may be reduced to the minimum; while at the same time the fact that the slab is continuous over its supports affords to it additional strength.

General Principles 43

Fig. 25.

Yet another system, that of Stuart's Granolithic Co., designed by Mr. E. P. Wells, is illustrated in Fig. 26. Continuous rods, carried over the beam, are introduced in the lower part of the floor slabs, which are generally 4 inches thick, the rods being | inch diameter, spaced at such distances apart as will give the necessary total of reinforcement. The concrete is filled in, bay by bay, to half-way across each girder, further reinforcing rods being introduced, as shown in Fig. 26, to connect the bays and take up the tension near the top due to the continuous nature of the rodding. The lengths of these rods vary as may be necessary, and each is cranked or split at the ends to give it a firm grip on the concrete. The longitudinal rods, parallel with the beam, are only introduced to distribute any fixed load or the effect of unexpected impact over several working rods, and are generally placed at 12 inch centres.

General Principles 44

Fig. 26.

It will be noticed that the pillars also are reinforced with rods, and it might be thought that this was unnecessary in a pillar properly loaded, in which there should be no tensile stress; but the rods serve a further purpose, for, besides taking part in the resistance to the load and thus reducing the section of the pillar, they help to bridge over any variations in the strength or elasticity of the concrete, and thus give the material more uniform resistance.

Shearing Stresses

Besides the rods embedded in the slabs and beams there are also vertical members, as in the Hennebique and Wells systems, or inclined members, as in the Kahn system.

In Volume IV. it was shown that besides the simple tensile and compressional stresses in beams there exist shear stresses, both horizontally and vertically, the average horizontal stress being equal to the vertical shear stress per unit of length at all points in the length of the beam. Concrete alone is found to have insufficient resistance to shear, and it is for the purpose of resisting the horizontal shear that the vertical or inclined stirrups are used. Fig. 27 shows the Hennebique stirrup. It is common to use sufficient of these stirrups to take the whole of the horizontal shear, but their employment at the same time materially assists the concrete itself to resist the same stress, in that they tie the layers of concrete together.

Shearing Stresses 45

Fig. 27.

The greatest horizontal shear is at the neutral axis, and in a rectangular beam has been shown to be equal to 3/2 of the average shear. The horizontal shear therefore has greater effect than the vertical shear, while the use of vertical members is particularly necessary in the case of the tee beam; for at the neutral axis, where the shear stress is greatest, the section is reduced to the minimum.

Shearing Stresses 46

Fig. 28.

It is common to make no special allowance for the resistance to vertical shear, and in this case it has to be met by the concrete and increased stress upon the tensional rods. In order to meet both horizontal and vertical shear it would be well to place the stirrups in an inclined position, so that they will offer their section in both directions. The horizontal and vertical shear may, in fact, be regarded as the horizontal and vertical components of diagonal, compressional, and tensile stresses. This is clearly illustrated by the lattice girder, as in Fig. 28, in which all tensional members are represented by full lines, while those in compression arc shown in stout dotted lines, the unstressed members being indicated by small dots.

In a rectangular beam the tensile components of the shear stresses, together with the longitudinal tensile stresses, produce resultant tensile stresses acting in curved lines, as indicated by the full lines in Fig. 29, while the compressive stresses produce similar resultant compression lines as indicated in dotted lines. The effect of the tensile stresses when the beam is loaded to failure is to produce cracks along surfaces at right angles to the tensile stresses, for it is here that the maximum intensity of tensile stresses will be met. That is to say, cracks will be produced along the dotted or compressional lines. Fig. 30 clearly shows this effect. At the centre of the beam, where the tensile stresses are horizontal, the stress has been entirely met by the horizontal reinforcement; but at the ends, where they take an upward direction, cracks have been produced due to the absence of vertical reinforcement. The curved disposition of the tensile stresses could probably be most thoroughly met with the greatest economy of metal by the use of many small rods following these lines; but this method is found to be impracticable, and the many and various "systems" that are in use, or that have been used, are merely so many solutions of the most practicable method of meeting these stresses.