REENFORCED CONCRETE 267 



compression, for certain grades of material to be as follows.* The use 

 of this ratio is exemplified in the following article. 



Stone concrete ...... 23 days ... ,8.8 



Stone concrete 90 days ....*.' Q. Q 



Average 77 



Gravel concrete 28 days . . . 8.0 



Gravel concrete 90 days . . . 6.2 



Average 7 ^ 



218. Flexure of reenforced concrete beams. Two general theories 

 of the flexure of reenforced concrete beams have been advanced. In 

 one it is assumed that the stress over any cross section of the beam 

 varies as the distance from the neutral axis, assumed as constant 

 (Articles 41 and 48). In the other the stress acting on any cross 

 section of the beam Pg 7 . .. 



is assumed to vary ^mTR^Axn^p_^^r^ 7 T 



as the ordinates to a ) hi ^ J hit 



parabola ( Fig. 160). 4--" ^^JJI^ t o-ci, 



The following analy- 

 sis is based on the 

 parabolic assumption, and is due to Professor Hatt, of Purdue Uni- 

 versity, the method followed being that of M. Considere.f 



Besides the assumptions of the common theory of flexure (Article 38) 

 and the parabolic distribution of stress, this analysis is based on the 

 following additional assumptions. 



1. The values of the moduli of elasticity obtained from simple ten- 

 sile and compressive tests apply to the materials under consideration. 



2. There is no slipping between the concrete and the steel 

 reenforcement. 



3. There are no initial stresses in the concrete due to shrinkage 

 while setting. 



Let / = length of span, 



b = width of cross section, 

 Ji = depth of beam, 

 hv = distance from compression face to neutral axis, 



* Jour. Western Soc. Eng., June, 1904. + Ibid. 



