FORMULAS FOR REINFORCED CONCRETE 

 DESIGN 



It is recognized by all authorities on the design of reinforced concrete structures, 

 that the common theory of flexure does not apply for wide ranges of stress. For 

 stresses in excess of those commonly used in design the relation between stress and 

 deformation is not uniform and this divergence becomes more pronounced as the 

 stress increases. Under these conditions the parabola is the curve which most nearly 

 expresses the relation between stress and deformation and is the relation which should 

 be used in the discussion of experimental or test data to obtain accuracy of results. 



In the design of structures, however, the stresses used are low, a condition for which 

 it can safely be assumed that the deformation of any compression fibre in a beam is 

 proportional to its distance from the neutral axis. The error in this assumption is 

 small and is on the side of safety. 



The formulas which follow are for working loads and assume a straight line varia- 

 tion of stress to deformation of concrete in compression. Tension in the concrete is 

 neglected. 



* STANDARD NOTATION 



(a) Rectangular Beams. 



The following notation is recommended: 

 fa = tensile unit stress in steel, 

 /c = compressive unit stress in concrete. 

 Ea = modulus of elasticity of steel. 

 Eo = modulus of elasticity of concrete. 



Es 

 " =^ 



M = moment of resistance, or bending moment in general. 

 Aa = steel area. 

 b = breadth of beam. 

 d = depth of beam to center of steel. 

 k = ratio of depth of neutral axis to depth d. 

 z = depth below top to resultant of the compressive stresses. 

 j = ratio of lever arm of resisting couple to depth d. 

 jd =d—z = arm of resisting couple. 



p = steel ratio = tt 

 bd 



ih) T-Beams. 



6 = width of flange. 



h' = width of stem. 



t = thickness of flange. 



(c) Beams Reinforced for Compression. 



A' = area of compressive steel. 



p' = steel ratio for compressive steel. 



fa' = compressive unit stress in steel. 



C = total compressive stress in concrete. 



* From: Transactions of Am. Soc. of C. E. Vol. LXXXI, December, 1917. 



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