As a preliminary to the theory of the use of reinforced concrete in beams, a very brief discussion will be given of the statics of an ordinary homogeneous beam. Let A B (Fig. 89) represent a beam carrving a uniformly distrib-uted load W; then the beam is subjected to transverse stresses. Let us imagine that one-half of the beam is a "free body" in space, and is acted on by exactly the same external forces; we shall also assume the forces C and T (acting on the exposed section), which are just such forces as are required to keep that half of the beam in equilibrium.

These forces, and their direction, are represented in the lower diagram by arrows. The load W is represented by the series of small, equal, and equally spaced vertical arrows pointing downward. The reaction of the abutment against the beam is an upward force, shown at the left. The forces acting on a section at the center are the equivalent of the two equal forces C and T. Fig. 89. Beam Carrying Uniformly Distributed Load. RESIDENCE FOR MURRAY GUGGENHEIM, ESQ., NORWOOD, N. J.

Carrere & Hastings, Architects, New York. Plan Shown on Opposite Page. FIRST-FLOOR PLAN OF RESIDENCE FOR MURRAY GUGGENHEIM, ESQ., NORWOOD, N. J.

Carrere & Hastings, Architects, New York For Exterior View, See Opposite Page.

The force C, acting at the top of the section, must act toward the left, and there is therefore compression in that part of the section. Similarly, the force T is a force acting toward the right, and the fibres of the lower part of the beam are in tension. For our present purpose we may consider that the forces C and T are in each case the resultant of the forces acting on a very large number of "fibres." The stress in the outer fibres is of course greatest. At the center of the height, there is neither tension nor compression. This is called the neutral axis (see Fig. 90).

Let us consider for simplicity a very narrow portion of the beam, having the full length and depth, but so narrow that it includes only one set of fibres, one above the other, as shown in Fig. 91. In the case of a plain, rectangular, homogeneous beam, the stresses in the fibres would be as given in Fig. 90; the neutral axis would be at the center of the height, and the stress at the bottom and the top would be equal but opposite. If the section were at the center of the beam, with a uniformly distributed load (as indicated in Fig. 89), the shear would be zero. Fig. 90. Position of Neutral Axis. Fig. 91. Neutral Axis in Narrow Beam.

A beam may be constructed of plain concrete; but its strength will be very small, since the tensile strength of concrete is comparatively insignificant. Reinforced concrete utilizes the great tensile strength of steel, in combination with the compressive strength of concrete. It should be realized that the essential qualities are compression and tension, and that (other things being equal) the cheapest method of obtaining the necessary compression and tension is the most economical.