RECTANGULAR BEAMS 



51 



the resultant compression C; hence, the two stresses constitute a 

 couple which is the resisting couple. (This principle comes 

 from one of the three conditions of equilibrium; namely, 2H = 0.) 

 In order to introduce important ideas concerning concrete 

 beams, the perfectly general method of figuring the ultimate 

 resisting moment at any cross-section will be explained. Fig. 



A X' 



27 shows the combined stress-deformation diagram for a given 

 concrete. A plain concrete beam will break in tension because 

 of the low strength of concrete in tension as compared to its 

 strength in compression. BB' then gives this breaking tensile 

 stress and T is represented by the area BOB'. Likewise, C 



A A" 



is represented by the area AOA' this area being determined 

 from the principle that BOB' and AOA' are equal. The next 

 step is to locate the center of gravity of each area and scale the 

 vertical distance between them. The resisting couple is T 7 or C 

 multiplied by this scaled distance. 



Partly to test the correctness of the theory of flexure of concrete 

 beams, Professor Morsch 1 made three beams and several tension and 



1 Of the Zurich Polytechnic, Zurich, Switzerland. 



