246 REINFORCED CONCRETE CONSTRUCTION 



Equation 2 gives a means of determining the eccentricity of the 

 resultant force, or x , for which there can be neither tension nor 

 compression at the surface opposite to that near which the thrust 

 acts. To obtain the value of x which gives a zero value to f' G 

 equate the two terms within the brackets, and solve. 



l+n(p+p')~t 2 +24npr z 



or _ t 2 + 24npr 2 J_ (3) 



X ~\+n(p+p') Qt 



If n is assumed to be 15, and, if the steel is embedded in the 



4 

 concrete 1/10 of the total depth from each surface so that 2r = ^ 



formula (3) may be written (since p = p+p') 



(4) 



t 6+90/> 



4 



If the values n = 15 and 2r = ^t are substituted in formula 



(1), this formula becomes 



,W __ __ o 



t 



or if the expression in the brackets is denoted by K, 



WK (6) 



fc = 



bt 



Diagram 13 gives values of K for various values of p and -- 

 The termination of the curves are determined by equation (4). 



/v 



For greater values of y , Case I does not apply; that is, there is 



tension in the concrete and Case II must be employed. 



76. Case II. Tension Over Part of Section. It will be on the 

 safe side and convenient as regards the construction of working 

 diagrams to consider that, when any tension exists in the concrete, 

 the steel carries all the tensile stresses. In this case there are 

 three unit stresses to be determined; namely, maximum unit 

 compression in concrete f c , maximum unit compression in steel 

 /',, and maximum unit tension in steel f s . The general formulas 

 previously developed are not applicable to this case and the 

 following method may be used. 



