390 Report S.A.A. Advancement of Science. 



Assuming that the assumptions are correct, the line AB shows 

 the cross-section after the change of form, and the line CD represents 

 the same cross-section before the change of form. The compressive 

 or tensive strains in the concrete above and below the neutral axis 

 respectively, are values depending upon the changes of form of the 

 body equally increasing from O to AC and from O tO' 

 BD. These are represented by two curves OE and OF 

 which in a body of rectangular cross-section are nothing 

 else than the law of the change of form of the concrete 

 through compression or tension, and the latter was constructed by 

 accepting on the one hand O a and OA, on the other hand O /3 and 

 OB as co-ordinate lines for the strains and changes of form respec- 

 tively. As the reinforcement takes part in the changes of form of 

 the concrete, u is accepted that the cross-sections K and I of the 

 iron bar are removed to H and G in the line CD, which enables 

 the strain to be determined as a value depending on the modulus 

 of elasticity. As all relations connecting the strains with the changes 

 of form are known, one can succeed through two conditions to deter- 

 mine the elastic powers in the horizontal direction, which are trans- 

 mitted between the two intercepts divided by the line AB, one being 

 the moment, the other the projection. The problem is therfore solved 

 as soon as it is possible to determine the equation of the curves OE 

 and OF. 



In the following I will refer to the different strains appearing 

 in different structures, in order to prove the probability of the 

 assumptions above mentioned. The most simple of all strains is 

 resulting from compression, and this has to be specially dealt with 

 in the statical calculation of columns. 



Compression. 



The compressive strength of concrete depends entirely upon 

 the proportion of the mixture, the shape and the height of the test 

 bodies. With small concrete bodies the strength is very great, it 

 diminishes with the increasing proportion of the height to the width ; 

 the strength of the cubic bodies is known as the cubiform strength 

 of the concrete. In the high test bodies, the rupture occurs through 

 removing the sliding resistance in inclined planes, and the compressive 

 strength, which generally cannot be taken into account, then appears 

 very small, when dividing the crushing load by the sectional con- 

 tents. The purpose of the reinforcement in the columns is thus to 

 prevent that sliding to inclined planes. Round iron vertical bars 

 interlocked with horizontal iron hoops, are usually employed for the 

 reinforcement of columns. This arrangement affords the advantage 

 that by the eccentrical loading of the columns, it can still sustain 

 tensile strains. For the compressive strain on the axis, the calcu- 

 lation is made under the supposition that the concrete and the iron 

 are equally compressed. Thus if fc means the sectional contents 

 of the concrete, fe that of the iron, dc and de the corresponding 

 strains of both materials, the load P will be : — 



P = fc X dc4- fe X de 



