CONCRETE AND STEEL IN COMBINATION 31 



Steel has a well-defined elastic limit in tension, as is readily 

 seen by the diagram, and which is at least one-half the ultimate 

 strength. It is represented by the ordinate of the point of 

 tangency between the straight line and the rest of the curve. 

 For medium steel in compression, the transition from the straight 

 line to the curve is more gradual, and the point of tangency is 

 more difficult to locate. If loads are applied which cause stress 

 less than the elastic limit, no appreciable permanent deformation 

 will exist when the loads are removed. Loads causing stress in 

 the steel above this limit will, however, leave a permanent set 

 on their removal. For example, suppose a steel bar is stretched 

 with a force of 50,000 Ib. per square inch of cross-section. The 

 point x will be reached in Fig. 9. The elongation of the bar will 

 be about 0.07 in. per inch of length. If the load is removed, the 

 diagram will go back along some line such as xx' '. The perma- 

 nent set is ox'. If the bar is stretched so that the resulting stress 

 per square inch is less than the elastic limit, then the diagram will 

 go back along the line OA, and no deformation results. Since 

 the line OA is straight, it is clear that below the elastic limit, 

 stress is proportional to deformation. The above illustration 

 could be applied equally well to steel in compression. 



Above the elastic limit the elongation of steel increases at a 

 rate which becomes more and more rapid until finally the condi- 

 tion of perfect plasticity is reached, and the body elongates 

 under a constant force, while the lateral dimensions reduce more 

 and more rapidly. The point B is reached when this action 

 occurs. The piece at this point draws out rapidly, the breaking 

 point C is soon reached, and the piece breaks under a reduced 

 load. For a piece tested in compression, the points B and C are 

 almost identical. 



The modulus of elasticity may be figured theoretically by any 

 stress and its corresponding deformation from to A, but is 

 generally figured near the elastic limit stress since practically a 

 more accurate result can be thus obtained. The modulus of 

 elasticity for steel in both tension and compression is about 

 30,000,000. This value may be taken the same for all grades of 

 steel, the variation being so slight. For medium steel, the elas- 

 tic limit is about 36,000 Ib. per square inch for both tension and 

 compression. 



In the design of reinforced concrete structures, it is necessary 

 to know the relative stresses in the concrete and steel of com- 



