126 REINFORCED CONCRETE CONSTRUCTION 



experiments on actual deflection, so that this term becomes to 

 some extent a sort of empirical coefficient-making correction for 

 various errors in the deduction of the deflection formulas. 



Turneaure and Maurer 1 recommend that 8 to 10 be used for n 

 in the formulas which they have derived, and which are given 

 below. They also state that the formulas presented are the 

 result of modifying the deflection formulas for homogeneous 

 beams in accordance with the following assumptions: 



1. The representative or mean section has a depth equal to the 

 distance from the top of the beam to the center of the steel. 



2. It sustains tension as well as compression, both following 

 the linear law. 



3. The proper mean modulus of elasticity of the concrete equals 

 the average or secant modulus up to the working com- 

 pressive stress. 



4. The allowance for steel in computing the moment of inertia 

 of the mean section should be based on the amount of steel 

 in the mid-sections, since stirrups and bent-up rods do not 

 affect stiffness materially for working loads. 



The following are the deflection formulas for rectangular rein- 

 forced concrete beams: 



Dss *L. . (1) 



E. bd* a 



(2) 

 n 



From equations (2) and (3) , the value of a for any values of p 

 and n may be computed, and then the deflection from equation 

 (1). The notation employed in the above formulas is as follows: 



D = maximum deflection (if desired in inches, the units 



specified below should be used) . 

 6 = breadth of the beam (inches). 



d = depth of the beam to the center of the steel (inches) . 

 W = total load (pounds). 

 I = span (inches). 

 p = steel ratio. 

 E s = modulus of elasticity of the reinforcing steel (pounds 



per square inch). 

 n = ratio of the moduli of elasticity of steel and concrete. 



1 In Turneaure and Maurer's "Principles of Reinforced Concrete Construction," 2nd 

 edition, pages 116 to 123. 



