220 REINFORCED CONCRETE CONSTRUCTION 



(using the proper value of j) the same as in rectangular and T-beams, we 

 obtain 



ff f'k' , ff M 



^- and/ -- 



Mk ' (2) 



From these equations (1) and (2), the relative reduction in f c due to the 

 addition of compressive steel is found to be 



7 ^ I"* (3) 



, 



''' 



I''* 



Since / and k depend on p, and /' and k' on p r , equation (3) may be employed 

 to show the relative reduction of f c for different percentages of tensile and 

 compressive steel due to the addition of the steel in the compression side of 



the beam. Diagram 10 gives concrete curves for various values of -3 . It 



was found when constructing the diagram that, in some instances, one 

 concrete curve may be employed with sufficient accuracy to represent two 

 and sometimes three percentages of tensile steel. 



Adding compressive steel also reduces the stress in the tensile steel. 

 Using the same notation as above 



M M 



. AZ/L. , 7 

 7. T 



The tensile steel curves, Diagram 11, give this relative reduction for different 

 percentages of tensile and compressive steel. Diagrams 10 and 11 will now 

 be employed in working out the problem stated at the beginning of this 

 discussion. 



Two of the tensile rods on each side of the supports will be bent up and 

 made to lap over the top of the supports, while the other two rods on each 

 side will be continued straight and lapped over supports at the bottom of 

 beam. 



The ratios of steel in tension and compression are the same, and are 

 respectively: 



We will assume -3 =0.1 as before. 

 a 



The stress in the steel and concrete at the support must first be found 

 with no compressive reinforcement. Diagram 1 may be employed when 

 the values sought come within the limits of the curves. In this problem 

 it will be necessary to employ Diagram 2 and do some computing. For 

 p = 0.013, / = 0.847. and k = 0.452 Then 



358 000 

 /a = (0.013)(0.847)(9)( 1 5.5)^ 15 - 50 lb " p 



. (2) (15,050) (0.013) 

 fc**^-^ n , , -- ^ = 865 Ib. per square inch. 



