This section is from the book "Modern Buildings, Their Planning, Construction And Equipment Vol5", by G. A. T. Middleton. Also available from Amazon: Modern Buildings.
Taking an ultimate load of 2240 lbs., and applying a factor of safety of 5, the safe load becomes 448 lbs. per square inch; or using a factor of 6, it becomes 373 lbs. In order to obtain a round number, the safe compressional load will here be considered to be 400 lbs. per square inch, assuming that the concrete is 1 2 4 stone concrete of good quality and carefully mixed.
For concrete of coke-breeze, one-third of above value may be taken; or, say, 130 lbs. per square inch.
The above safe values apply to members in direct compression only. For beams, they may be increased by about 25 per cent.; but this will be considered later.
The resistance of concrete in tension is generally accepted to be - of that in compression, and, considering the same qualities as assumed above, the tensile resistance becomes 2240/10 = 224 lbs. per square inch ultimate resistance, or 400/10 = 40 lbs. per square inch safe tensile stress. This value will, however, seldom enter into the calculations of armoured concrete.
Much doubt exists as to the resistance of concrete to this form of stress owing to the difficulty of producing simple shear. The ultimate stress is variously estimated at 120 to 440 lbs. per square inch, and using a factor of safety of 6 the safe stress becomes 20 to 73 lbs. The first of these values is undoubtedly unnecessarily low, and there is not much doubt but that shear resistance is at least as great as the tensile resistance. The Prussian Government regulations allow 64 lbs. per square inch, while the New York regulations allow 50 lbs. per square inch; and it would seem that the latter allowance may safely be made.
" Adhesion " to Metal. - The resistance to sliding between concrete and reinforcing metal varies considerably, according to richness and wetness of concrete, upon the condition of the surface of the metal, upon the length of the embedded metal, and also upon its shape and sectional area. For rough rods just as supplied the resistance is apparently 200 to 500 lbs. per square inch; and these values may be halved if the surface of the metal is turned smooth. This resistance per square inch decreases with the length of the embedded metal, while it increases as the sectional area of the metal increases. The resistance is distinctly improved if the surface of the metal is slightly rusty, and, as was pointed out in Chapter XVII (The Theory Of Arches, Vaults, And Buttresses). Part II. Volume IV., this will have no bad effect upon the preservation of the metal, while the reverse even seems to be the case. Most regulations allow the same resistance to sliding as to shearing, and the safe resistance thus becomes 50 lbs. per square inch.
There is little doubt that the resistance to sliding is great enough under all ordinary stresses in beams, but it does not follow that the same factor of safety is allowed in this case. Many patent reinforcing rods have been introduced to increase this resistance, such as that used in the Ransome system, which is a square bar twisted spirally, and also the patent indented bar and the Kahn bar already described.
The results of experiments show largely divergent results on this property, while for any particular concrete it is greatest at low pressures and decreases as the load increases. Apart from extreme results, values are obtained varying from 2,500,000 to 4,500,000, while 3,000,000 may be considered as a safe average value. The actual value matters little, but it is the ratio of the modulus of elasticity of steel to that of concrete which is of importance in calculation. The modulus of elasticity of steel was given in Volume IV. as 13,500 in inch-ton units; and, multiplying by 2240, this becomes 30,240,000 in inch-lb. units. Representing the latter by Es and that of concrete by Ec, and taking the value of Ec as 3,000,000, Es/Ec = r=10 approximately; that is to say, to produce a certain strain in steel will require a load per square inch 10 times as great as that required to produce the same strain in concrete.
The value 10 is recommended for adoption by many authorities. The Prussian Government regulations state that these moduli are to be taken as 1 15, while the New York regulations fix the ratio as 1 12.
These were discussed in Chapter IV (Ecclesiastical Buildings). Part II. Volume IV. No punching, riveting, or similar work is done upon the metal in the case of armoured concrete, and therefore there is no need to take very low values. Putting the value in lbs. in order to conform with the allowable stress upon concrete, the safe values for steel may be taken as -
Tension, 16,000 lbs. per square inch. Shear, 12,000 lbs. per square inch.
The coefficient of expansion of concrete is approximately 0.0000055, while that of steel is 0.0000066. The difference is apparently sufficiently small to have no appreciable effect upon the adherence between metal and concrete, while the small conductive power of the latter prevents the metal from being affected by any sudden or local rise of temperature.
Concrete shrinks when setting in air, the effect being greater the richer the mixture be in cement. When setting under water the reverse is the case, and here expansion takes place. The greater part of the contraction or expansion takes place during the first week after mixing, and the variation is small at the end of a month.
The shrinkage of concrete when drying in air places the reinforcement in compression and the concrete itself in tension, with the result that before the concrete is put in compression and the steel in tension the stresses have to be reversed. The effect of this is on the side of safety, and its extent need not be considered.