Ferro-Concrete. 



393 



For a rectangular cross-section we can deduct formulae for the 

 calculations of the dimensions, if the elongation curve of the con- 

 crete is known. In Fig. 2 the line represents the line of the strain, 

 which is identical with the elongation curve of the concrete ; for the 

 compressions are proportionate to the ordinates, while the abscisses 

 represent the corresponding compressive strains. On the side of 

 tension the tensile forces of the reinforcement only act, and will be 

 reduced to the unit of the width. The line from the central axis 

 O to the centre of the reinforcement is defined through strain, which 

 corresponds with the permissible strain of the iron. The area of 

 strain of the iron is a rectangle, the basis of which is of smaller 

 dimensions than the height. Assuming the permissible strain 

 for the concrete to be 750 lbs. per square inch, the maximum area 

 of the concrete is thereby limited above the neutral axis. Under 



I 



• ^ c • SToltt 



K 



Figure II. 



ordinary deflection no external compound forces are present in the 

 longitudinal section ; therefore the tensile and compressive forces 

 must equalise themselves in the cross-section or the contents of the 

 area of compression is equal to the rectangle of the tensile force. 

 If the distance from the centre of gravity of the reinforcement to 

 the top edge of the concrete body equal h, then fe is calculated by 

 means of the function of h and dc, and the moment M, which is 

 equal to the contents of the area of compression multiplied by the 

 distance of the same from the centre of gravity of the reinforce- 

 ment, will be found as the function of hz or h, and fe is found to 

 be proportionate to the square root of M. By this method the 

 dimensions of a construction can easily be determined, while through 

 circumstantial test calculations it is only possible to find the strain 

 of an existing construction. 



The same method can be applied purely analytically by the use 

 of the law of power, whereby the thickness of the concrete and the 

 reinforcement for given strains is obtained proportionally to the 



