RECTANGULAR BEAMS 87 



elasticity of concrete has a wide range, depending upon the 

 materials used, the age, the range of stresses between which 

 it is considered, as well as other conditions. It is recom- 

 mended that in all computations it be assumed as one- 

 fifteenth that of steel, as, while not rigorously accurate, this 

 assumption will give safe results." 



The yield-point of ordinary mild steel purchased in the open 

 market cannot safely be fixed at a higher value than from 30,000 

 to 32,000 Ib. per square inch, although frequently, and in fact in 

 the majority of cases, a value of at least 35,000 to 40,000 Ib. 

 per square inch will be found. Since the yield-point of steel is 

 regarded as its ultimate strength when used in reinforced concrete 

 beams, the maximum working stress of 16,000 Ib. per square inch 

 recommended by the Joint Committee, gives, it would seem, a 

 factor of safety of at least about 2 with respect to a steel-tension 

 failure. In well-designed beams, however, where the concrete 

 used is of high grade, the steel stress at failure will considerably 

 exceed its elastic limit, the high crushing strength of the concrete 

 enabling the steel to elongate very considerably before final 

 failure occurs through the crushing of the concrete. For the 

 above reason, the working stress of 16,000 will be found to give 

 a much greater factor of safety than 2 generally somewhere 

 between 21/2 and 3. 



The elastic limit of good concrete is between one-half and two- 

 thirds its ultimate strength. Considering 2000 Ib. per square 

 inch as the ultimate strength in concrete, the elastic limit will 

 be about 1000 to 1300 Ib. per square inch. The working stress 

 of 650 Ib. per square inch gives the beam, then, a factor of safety 

 as regards elastic limit of concrete of about 2, and as regards the 

 ultimate strength of concrete, from 4 to 5 (this value is greater 



2000 



than > since above the elastic limit the stress in concrete does 



ooU 



not vary even approximately in the same ratio as the increase in 

 the loading) . 



Thus t the elastic limit of a reinforced concrete beam is deter- 

 mined by the concrete (minimum factor of safety about 2) and 

 its point of failure by the steel (minimum factor of safety between 

 21/2 and 3), which may be regarded as satisfactory conditions. 

 The greater uniformity and reliability of the steel, as compared 

 to the concrete, should be noted in this connection. 



7 



