COLUMNS 169 



Then 



and the additional intensity of compressive stress due to eccentric 



loading is seen to be equal to -p -7-^ The above formula may 



A. t 



be used for columns of plain concrete. 



65. Columns with Longitudinal Reinforcement.* Since the 

 modulus of elasticity of a material is the ratio of stress to de- 

 formation, it follows that for equal deformations the stresses in 

 the steel and concrete of a concrete column will be as their 

 moduli of elasticity. Thus, 



= !*, or /, = /, 



Jc &e 



Let A denote total cross-section of column. 

 A c denote cross-section of concrete. 



A s denote cross-section of steel. 

 ^ 



p denote steel ratio= *- 



J\_ 



f' c denote stress in concrete. 

 f 8 denote stress in steel. 



n denote j- 



&c 



P f denote total strength of a plain column for the stress / c . 

 P denote total strength of a reinforced column for the 



stress /.. 



Then, P'=f c A 



or P =f c A c +f s A s =f c (A - pA) +f c npA 



Thus, P=f c A[l + (n-l)p] (1) 



from which also 



The relative increase in strength caused by the reinforcement is 



Tests of columns made at the Massachusetts Institute of 

 Technology, the Watertown Arsenal, the University of Wisconsin, 

 and the University of Illinois, on columns with vertical steel bar 

 reinforcement, indicate that the steel may be counted upon in 

 design to take its portion of the loading as computed from equa- 



