CORRUGATED BAR COMPANY, INC. 



GENERAL FORMULAS FOR BEAMS 



REACTIONS, BENDING MOMENTS, SHEARS AND DEFLECTIONS 

 CAUSED BY VARIOUS APPLIED LOADS 



The classes of beam loading given on the following pages cover the majority of 

 cases occurring in reinforced concrete design. The formulas may be applied to a beam 

 of any material, although it should be noted that those for deflection and maximum 

 safe load require modification for use in connection with reinforced concrete beams. 



In the application of deflection and maximum load formulas to reinforced concrete 

 beams account must be taken of the fact that the moment of inertia of the section 

 and the modulus of elasticity of the material enters into the computations, thereby 

 introducing elements of uncertainty that do not exist in the case of homogeneous 

 beams, at least not within the limits of working stresses. Bearing this fact in mind it 

 will be necessary to make certain assumptions before applying these formulas. These 

 assumptions may be stated briefly as follows: 



1. The moment of inertia is considered substantially uniform throughout the 

 length of the beam, and shall be taken as that of the section of the beam at the center 

 of the span. 



2. The section shall be considered intact from top of beam to center of steel. 



3. The modulus of elasticity of the concrete shall be taken as the average or secant 

 modulus up to the working compressive stress. 



For such a beam the moment of inertia of a section is the moment of inertia of the 

 concrete about the neutral axis plus n times the moment of inertia of the steel about the 

 same axis, or 



= — j Jc^-\-{l — ky-\-Snp{l — k)n I for rectangular beams. 



" ¥ ^~ {^~l ) ( ^'"0 ''^^' (1 -^^)'+32>n(l -/.O^l for T-beams 



The value of the modulus of elasticity to use in the deflection formula is that of 

 the concrete, or 



n 



It is recommended, from the consideration of test data, that 8 or 10 be used for n 

 to secure fair agreement between computed and measured deflection. A more com- 

 plete discussion of the subject of deflection of reinforced concrete beams will be found 

 in "Principles of Reinforced Concrete Construction" by Turneaure and Maurer. 



The maximum safe load formula given in the following cases applies only to homo- 

 geneous beams. To obtain the maximum safe load for a reinforced concrete beam, 

 equate the maximum external moment to the internal resisting moment of the section 

 and solve for-^i^. For example, in the case of a uniformly loaded rectangular beam 



supported at the ends, ifm=-^ and the resisting moment of the section is Kb<P, 

 then W^ 



^ 12/2 



\yy. 



