KEENFOKCED CONCKETE 



269 



axis is destroyed, and in this case equations (111) and (114) must be 

 modified by neglecting the tensile stress in the concrete. 



The following table gives a comparison , of the preceding theory 

 with experiment. The beams reported in the table were made and 

 tested at Purdue University.* They were 8 in. x 8 in. x 80 in. in size, 

 and were composed of one part cement, two parts sand, and four 

 parts broken stone. In each case the elastic limit of the reenforce- 

 ment was reached before the concrete failed in compression. 



The quantity denoted by K in the last two columns of the table is 

 the quantity in parenthesis in equation (114), viz. 



- v) z 5 nv 3 rk (u v) 2 





f 



12(1-*) 1-v 



COMPARISON OF PARABOLIC THEORY WITH EXPERIMENT 



Problem 178. A reenforced concrete beam 8 in. x 10 in. in cross section, and 

 16 ft. long, is reenforced on the tension side by six J-in. plain steel rounds. The 

 steel has a modulus of elasticity of 30,000,000 lb./in. 2 , and the center of the 

 reinforcement is placed 2 in. from the bottom of the beam. Assuming that 

 E t = 300,000 lb./in. 2 , E c = 3,000,000 lb./in. 2 , and p c = 2500 lb./in. 2 , find from for- 

 mulas (113) and (114) the position of the neutral axis and the moment M. 



NOTE. The moment M corresponds to the moment^- obtained from the consideration 



of the flexure of homogeneous beams ; that is to say, M is the moment of resistance of 

 the beam (see Article 44). 



Problem 179. For a stress p c = 2700 lb./in. 2 on the outer fiber of concrete in 

 the beam given in Problem 178, find the stress p s in the steel reinforcement. 



Problem 180. Using the data of Problem 178, locate the neutral axis and find 

 the value of the moment of resistance M under the assumption that the stresses in 

 the concrete vary linearly. 



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



