Ancient and modern engineering and the Isthmian canal

123. Beams of Combined Steel and Concrete.[2]—A reference has already been made to a class of beams and arches recently come into use and now quite widely employed, composed of steel and concrete, the former being completely surrounded by and imbedded in the latter. These composite beams are very extensively used in the floors of fire-proof buildings as well as for other purposes. Arches of combined concrete and steel were probably first built in Germany and but a comparatively few years ago. During the past ten years they have been largely introduced into this country, and many such structures have not only been designed but built. The most prominent design of arches of combined concrete and steel are those of the proposed memorial bridge across the Potomac River at Washington, for which a first prize was awarded as the result of a national competition in the early part of 1900. So far as the bending or flexure of these composite beams and arches is concerned, the theory is identically the same for both, the formulæ for each of which are given below. In order to express these formulæ the following notation will be needed:

P is the thrust along the arch determined by the methods explained in the consideration of arched ribs.

l is the distance of the line of the thrust P from the axis of the arched rib.

E₁ and E₂ are coefficients of elasticity for the two materials.

A₁ and A₂ are areas of normal section of the two materials.

I₁ and I₂ are moments of inertia of A₁ and A₂ about the neutral axes of the composite beam or arch sections.

k₁ and k₂ are intensities of bending stress in the extreme fibres of the two materials.

h₁ and h₂ are total depths of the two materials.

d₁ and d₂ are distances from the neutral axes to farthest fibres of the two materials; distances to other extreme fibres would be (h₁-d₁) and (h₂-d₂).

W₁ and W₂ are loads, either distributed or concentrated, carried by the two portions.

W = W₁ + W₂ is total load on the beam or arch.

The application of the theory of flexure to the case of a beam or arch of two different materials, steel and concrete in this case, will give the following results:

M = Pl; hence M₁ = q₁Pl and M₂ = q₂Pl.    (59)

These formulæ exhibit some of the main features of the analysis which must be used in designing either beams or arches of combined steel and concrete. In the use of these equations care must be taken to give the proper sign to the bending moment M. They obviously apply to the combination of any two materials, although at the present time the only two used in such composite structures are steel and concrete. If the subscript 1 belongs to the concrete portion, and the subscript 2 to the steel portion, there may be taken E₁ = 1,500,000 to 3,000,000 and E₂ = 30,000,000. Hence e = 20 to 10.

The purpose of introducing the steel into the concrete is to make available in the composite structure the high tensile resistance of that metal. A very small steel cross-section is sufficient to satisfactorily accomplish that purpose. The percentage of the total composite section represented by the steel will vary somewhat with the dimensions of the structure and the mode of using the material; it will usually range from 0.75 per cent to 1.5 per cent of the total section. The large mass of concrete in which the steel should be completely imbedded serves not only to afford a large portion of the compressive resistance required in both arches and beams, but also to preserve the steel effectively from corrosion. Many experiments have shown that it requires but a small per cent of steel section to give great tensile resistance to the composite mass.