General Principles of Reinforced Concrete Design

These experiments were performed upon beams comp(Aed of 1:3:6 concrete. A 1:2:4 con crete would permit of a slightly larger percen age of steel, on account of the greater com pressive strength of the concrete.

Tests for adhesion have also shown that the use of rods of a greater diameter than/ 200 of the length of the beam are liable to pull out of the concrete without breaking. This is due to the want of proper adhesion between the rod and the concrete, in comparison with the strength of the rod itself. Tests have also shown that beams whose depth is greater than the length, or span, when reinforced with horizontal rods, or with rods bent over at the ends and not provided with anchor plates, will fail when loaded to the breaking point, in a man ner similar to that shown in Fig. 40. This is due to diagonal tension produced in the beam as a result of the combined vertical and horizontal shear together with the direct tensile stress.

The theoretical discussion of formulas and their deviation will not be discussed in this volume. The theories regarding flexure in re inforced concrete beams are based upon mathe matical principles, as well as the principles of mechanics. Therefore the detailed design of any important work—especially when compara tive costs must be considered and where failure would result in serious disaster to property or life—should be under the immediate supervision of an engineer trained in these principles and competent to apply them with judgment to the work in hand.

If a study of these theories is desired, refer ence to Church's "Mechanics of Engineering" will show the so-called straight line theory; while the bulletin on "Tests of Reinforced Con crete Beams, Series of 1905," by Professor Arthur N. Talbot of the University of Illinois, gives a demonstration of the parabolic theory.

Simple, Practical Rules for Design.

Several empirical formulas, or working rules based on experience and observation in actual practice as distinguished from refined theoretical calcula tions, have been suggested for different types of design, and their authors claim that they closely follow the results of reliable tests. These formulas should be used with care and applied only to the class of work that supplied the data from which they were derived.

Mr. Homer A. Reid, in his volume on "Con crete and Reinforced Concrete Construction," presents two simple approximate working formulas for the design of beams. These are

Wason's formula and Ransome's formula.

Wason's Formula. This formula is "based on the following assumption: that there is a perfect bond between the steel and the concrete within the limits of the working stresses of the combination. That the steel takes the entire tensile stress and the concrete the entire com pressive stress. That the neutral axis is as sumed to be half-way between the center of the reinforcing bars and the top of the beam. That the center of pressure of the concrete under compression is considered as being two-thirds of the height from the neutral axis to the top of the beam. The distance from the center of pressure of the concrete in compression to the center of the reinforcement, equals of the distance from the top surface of beam to the reinforcement." d=Effective depth of beam (top to reinforcement). 1= Span in inches.

F. =

Total stress in steel.

W =

Total uniform load in pounds.

Then, taking the center of pressure as the center of moments, the resisting moment, m=idb"..

The bending moment of a freely supported beam under a uniformly distributed load is m Equating these two moments, and solving for we obtain: =_ 61CI Example. Determine amount of steel required for a beam of ft. span to carry a total uniform load of 12,500 lbs., assuming an effective depth of 14 inches, and using a unit-stress for the steel of 16,000 lbs. per square inch.

Since ft. = 150 inches, we have : F 150 — 19,500 lbs.

° 19,500 Area of Steel = sq. in.

16,000 Two bars give an area of sq. in.

After determining the total stress in the metal, the area of the reinforcement is deter mined by dividing the total stress by a safe working stress to determine the area of metal. Bars of proper size are selected to make up this area, a convenient spacing selected, and the area of the concrete adjusted to resist the com pression. Mr. Wason uses 16,000 lbs. per square inch tension on the steel; and for a 1:3:6 con crete, an average of 500 lbs. per square inch in compression on the concrete; and requires 32 square inches of concrete in the upper third of the beam for each square inch of steel (in the lower part). This averages very nearly 1 per cent of reinforcement.