60 



W. H. WAREEN. 



No tensile resistance must be taken for the concrete. 

 The ratio -^ = 15 



Y-Hp 



Note. — In the bottom line of this diagram for h (1 - x) read h (1 - u). 



The fundamental equations are 2 : — 

 = /;p...(l) 



E c f x 



ex 



T 



e 



f ~ E s \u-x 

 M ^ 73 li- 

 bit 2 



•(2) 



fsP 



..(3) 



x 



/ 2 E 2 . n JE S Us, / A s. 



To find the area of the steel reinforcement in a beam 10 

 inches wide by 20 inches deep to carry 1000 pounds per 

 foot run on a span of 24 feet. 



Take hu = 16 in order to allow sufficient concrete below 

 the steel bars, so that u =0*8 

 ing mo: 

 864000 



The bending moment = 24000 * 24 X 12 = ! 



8 



M 



bh 2 



4000 



= 216 inch fbs. 



M 



= 16000 



3 u~x 



p = 16000 



2*4 - x 



bh 2 ' V 3 / f V 



Take ^ = 0*5 as a first approximation, 

 then p (2*4 - x) = 0*0405 



P 



p = 21Q 



•0405 



1'9 



Let a denote the area of the steel then p 

 .*. a = 4*26 square inches. 



a _ a _ '0405 

 bh 200 1*9 



2 Further Experiments in the Strength and Elasticity of Eeinforced 

 Concrete by W. H. Warren— Proc. Eoy. Soc. N. S. Wales, Sept. 7, 1904. 



