52 REINFORCED CONCRETE CONSTRUCTION 



compression specimens of the same mix of concrete. 1 From tests 

 on the specimens, he obtained a combined stress-deformation 

 diagram from which he computed the probable resisting moment 

 of the beams. The average of the actual resisting moments of the 

 beams and the moment computed by the theory of flexure agreed 

 very closely. This general theory of the flexure of concrete beams 

 may thus be considered highly satisfactory. 



It should be clear to the student by this time that a great 

 deal of compressive strength cannot be made use of in a plain 



concrete beam. If concrete were only 

 stronger in tension, then the plain con- 

 crete beam might be of some structural 

 value. In order to offset this disadvan- 

 tage of plain concrete, steel is used. In 

 the discussions which follow it will be 

 assumed that the concrete and steel 

 adhere perfectly and therefore deform 

 equally. Many tests show that, under 

 proper design, this is true for all prac- 

 tical purposes. 



32. Flexure Formulas for Reinforced 

 FIG. 27. Concrete Beams. A great many formu- 



las have been proposed from time to time 



to be used in the design of reinforced concrete beams. Of course, 

 the object has been in each case to obtain a formula whereby the 

 resisting moment may be obtained at any cross-section in a 

 sufficiently accurate manner, but at the same time with a view 

 to the ease with which it may be used in practice. As might be 

 expected, many of the earlier formulas considered the concrete to 

 carry its share of the tension which we know now cannot be done 

 with absolute safety. By means of some formulas the ultimate 

 resisting moment of a beam may be computed and the ultimate 

 loads at once determined which will produce this moment. A 

 factor of safety is then applied and the safe load obtained. In 

 other formulas the working loads are found directly. When the 

 ultimate load is obtained from a formula, the utimate strength 

 of the concrete and the elastic limit of the steel (the student 

 will find later that the elastic limit of the steel may determine 

 ultimate strength) must be used. Likewise,- when deriving 

 safe loads, the working strengths should be substituted. 



Unlike steel beams, reinforced concrete beams require a prelim- 



1 From Turneaure and Maurer's "Principles of Reinforced Concrete Construction," 

 2nd edition, page 55. 



