RECTANGULAR BEAMS 125 



deflection is quite uniform during this period. But as the 

 concrete fails in tension near the center of the beam, there occurs 

 a second or readjusting stage: the steel carries more and more 

 of the tensile stresses and the deflection diagram is a curve. 

 From this point on till the steel reaches its yield point, the de- 

 flection is again quite uniform. Since deflection depends on the 

 stress at all sections, the deflection formulas for homogeneous 

 beams cannot be used for reinforced concrete without modifica- 

 tion because of the variable action of the concrete in tension 

 throughout the length of the beam. 



Fig. 62 gives the general form of a deflection diagram for a 

 reinforced concrete beam. The portion AB shows the deflection 

 before the concrete has begun to fail in tension, BC shows the 

 deflection during the readjusting stage, and 

 CD the deflection with the steel near the 

 center of beam carrying practically all the 

 tension. 



The deflection formulas presented in "Prin- 

 ciples of Reinforced Concrete Construction" 

 by Turneaure and Maurer yield results in fair 

 agreement with actual measured deflections 

 and undoubtedly are the best so far proposed. 

 These formulas have been obtained semi- A - _ ~ 

 rationally from the deflection formulas for FIQ 62 



homogeneous beams and thus assume the 

 material of the beam to obey Hooke's law (stress is proportional 

 to deformation) . Concrete in compression obeys the law very 

 closely up to working stresses, but for concrete in tension the 

 assumption is far from the actual conditions. Since tension in 

 the concrete is considered in the above mentioned deflection 

 formulas, the assumption of a linear stress-deformation relation, 

 which is made for simplicity, should be regarded as a rough ap- 

 proximation. 



The modulus of elasticity of the concrete in the type of formulas 

 mentioned above should be taken as about the average or secant 

 modulus up to the working compressive stress in the same. 

 Although initial moduli of concrete for compression and tension 

 are nearly equal, the deflection of a beam depends on the elonga- 

 tions and shortenings of all the fibers, and hence not upon the 

 initial modulus but on some sort of a mean value. The resulting 

 value of n should also be governed by the value as chosen from 



