

32 REINFORCED CONCRETE CONSTRUCTION 



pression members under like distortions; and in beams, it is 

 necessary to find the position of the neutral axis and the required 

 percentage of steel. These may easily be determined if the 

 modulus of elasticity is known for both the concrete and the 

 steel. The modulus of elasticity for steel we already know. 

 Let us now discuss the method of determining the modulus for 

 concrete. 1 



With concrete we have an entirely different material to deal 

 with as regards elasticity. Fig. 10 shows a typical stress- 

 deformation diagram for concrete in compression. As you can 



see, the compression curve is slightly 

 curved almost from the beginning, the 

 curvature gradually increasing toward 

 the end in approximately the shape of 

 a parabola. A release of load at even 

 moderate stresses will show some 

 permanent set, as OF, indicating im- 

 perfect elasticity. After a few repe- 

 titions of such loads, however, there 



DeformaTion 



-p iG 1Q will be no further set, and the stress 



deformation diagram line will become 



straight up to the load applied, as YA, for example. There is 

 a limit of stress beyond which repeated applications of the 

 same load will continue to add to the permanent deformation, 

 and the specimen will ultimately fail. This limit is found to 

 be from one-half to two-thirds the ultimate strength and is 

 called the elastic limit. Point S is the breaking-point and 

 ultimate strength. 



For very low stresses, up to perhaps 300 to 400 Ib. per square 

 inch, the variation of the curve from a straight line is so small 

 that it may be considered straight, and an average straight line 

 may be drawn, as OT } and its slope taken as the modulus of 

 elasticity. For higher stresses, the total deformation is OB and 

 the modulus elasticity becomes 



I" 



(J 



- 

 ~OB 



This ratio will be less than the slope of the line OT. 



Later in the course when referring to these two methods of 

 calculating the modulus, the slope of the tangent OT will be 

 called the initial modulus and the slope of the line OA, the 

 secant modulus. 



1 Discussion as given in Turneaure and Maurer's "Principles of Reinforced Concrete Con- 

 struction," 2nd edition, page 20. 



