322 REINFORCED CONCRETE 



C s = section-modulus coefficient for steel =jp; 

 C c = section-modulus coefficient tor concrete = ; 



R = coefficient whose values are given. later in tabu- 

 lar form. 



Formulas. Following are the formulas for rectangular rein- 

 forced-concrete beams: 



A = pbd (1) 



k= TJpW+2pn-pn (2) 



(3) 



(4) 

 (5) 



(6) 

 (7) 

 (8) 

 (9) 

 When the economic steel ratio is used, M S = M C \ also, 



k e = { (10) 



n+r e 



*" 



Formulas 7 and 8 furnish the fundamental equations for 

 designing and investigating rectangular reinforced-concrete 

 beams. Formula 7, expresses the resistance of the beam for 

 steel and is to be used when the steel ratio is below its critical 

 value, while formula 8 gives expression to the moment of resist- 

 ance of concrete and governs the design in cases when the 

 amount of steel is above the economic ratio. C s and C c can 

 be determined by formulas 4 and 5, and for finding the economic 

 steel ratio formula 1 1 is available. For n=l2 and n = 15, C s and 

 C c can be taken directly from the accompanying table; also, 

 the economic ratio of steel may be ascertained from this table, 

 as will be explained presently. 



Reinforced-Concrete Tables and Their Application. For 

 n 12 or 15 the accompanying table of properties of reinforced- 



