CONCRETE DESIGN 303 



distance between two ties should not exceed the width, or 

 diameter of the column. If the ties are spaced too far apart, 

 the column is apt to fail by the reinforcement bulging. 



In Fig. 3 (V) is shown a column reinforced with hooped 

 reinforcement. This type of reinforcement consists of either 

 a steel spiral or a separate steel hoop that is about 2 in. from 

 the surface of the column, as shown at b. 



Some columns have both styles of reinforcement just 

 mentioned. 



In the design, as given here, A c is the effective area of the 

 concrete. The effect of fire is to injure the concrete for a 

 depth of about 1% in. from the surface. Therefore, in 

 investigating a column already built, first deduct 1$ in. all 

 the way around the column from the total area of the con- 

 crete so as to get the effective area of the concrete. For the 

 same reason, after a column is designed, add a coat 1 in. on 

 all sides for fire protection. The reinforcement to protect 

 it from fire should be embedded at least 2 in. in the concrete. 



In a hooped column, the effective area should not only be 

 limited to 1 in. from the surface, but should further be 

 limited to the concrete within the hooping. Outside of the 

 hooping, of course, at least 2 in. of concrete must be placed. 



In height, columns should be less than fifteen times their 

 least dimension. 



Straight Reinforcement. Let A c represent the effective 

 area of cross-section of concrete, in square inches; A s , the 

 area of cross-section of steel in square inches; E c , the modulus 

 of elasticity of concrete; E s , the modulus of elasticity of steel; 

 F c , the safe compressive stress per unit area of concrete; 

 F s , the safe compressive stress per unit area of steel; n, the 



ratio , and W, the total load on column. 



EC 



The design formulas are as follows: 

 W = F C (A f + nA s ) 



F s = nF c 



Any values of F c and n as may be required may be used. 

 The Joint Committee uses 450 Ib. for F c and 15 for n for 

 grade of concrete as specified in discussing beams. These 

 values are used here for the sake of example. 



