Ferro-Concrete. 391 



dc and de are thus tensions in the concrete and the iron, which 

 correspond with the same compressions. We must therefore apply 

 the law of the elastic strain for concrete. 



The latest investigations by Considere led to the discovery of 

 quite a new system for the reinforcement of columns, which system 

 is especially recommended for heavily loaded columns, of which, for 

 certain reasons, the diameter must be chosen as small as possible. 

 His publication on " Le beton frette," which is best translated by 

 encircled concrete, appeared some time ago in the French Journal, 

 Genie Civil. They are the results of experiments with concrete 

 cylinders, the reinforcement of which consists of spirally wound 

 iron bars. This system allows a more effective use of the material 

 than the ordinary vertical reinforcement; it is 2.4 times stronger 

 than the latter. The strength of the concrete can thus be increased 

 up to 11,500 lbs. per square inch, and is consequently practically 

 quadrupled. The calculation for reinforced concrete columns should 

 be done in the following manner : — 



The cross-section of the iron is multiplied by 



Ee elasticity of iron 3000000 

 a = — - = _ ^—. 1- = ^ = ID, 



Ec elasticity of concrete 300000 



and the result added to the sectional area of the concrete. Then 

 the strain of the concrete is equal to the loading force, divided by 

 the cross-section of the column, and the strain in the iron conse- 

 quently is ten times the strain in the concrete. On the basis of Euler's 

 breaking formula 



P = ys X e X ], 



and the formula which in bridge construction is known as Rankine's 

 breaking formula, namely : — 



d,. ? 



I -t-o-oooi (i :i)' 



and further on the basis of the formula for the strain of the concrete 

 (and of the cast iron) 



dk = K (i - e - 1000*^) 



the calculation of reinforced concrete bodies under compression can 

 easily be made. 



Deflection. 



In demonstrating the deflection in ferro-concrete constructions, I 

 will first refer to the ordinary bending : — 



The fluxure equations with the homogeneous bodies with constant 

 coefficients of strain are obtained as mentioned before, on the assump- 

 tion that the vertical sections, straight before the bending, also 

 remain straight after the bending, although that assumption is incom- 

 patible with the presence of the shearing strains, as the latter cause 



