172 RESISTANCE OF MATERIALS 



The total area of reenforcement in the head for each radial sys- 

 tem is then A = 081 h = 0>628 sq . in . per foot 



Since the diameter of the top is assumed as D = ^ I = 8.75 ft., 

 the total area required for one radial system is 8.75^4 = 5.5 sq. in. 

 The required area of slab rods in one system is then 



equivalent to 18 rods ^ in. in diameter, spaced 5 in. apart. 



Since the four sets of rods overlap where they cross the column 

 top, and since h denotes the distance from the extreme fiber in com- 

 pression to the center of the reenforcement, the total thickness of 

 slab becomes h + 2 d + 1 in. = 9 in. 



Since the hoops around the column head are assumed to be TT 

 times as effective as the same cross-sectional area of radial reen- 

 forcement, the total area of the hoops, neglecting the spider, is 



^j = 0.88 sq. in. If two hoops are used, the diameter of each 



hoop rod may therefore be assumed as | in., giving a total cross- 

 sectional area of 0.88 sq. in. 



It should be noted, however, that the effectiveness of hoop reen- 

 forcement depends on the hoop being placed where it can carry the 

 tensile stress in the column top. Since the outermost hoop of the 

 top is placed as nearly as possible on the line of inflection, there is 

 practically no stress in the slab at this point, except shear, and 

 hence the cross-sectional area of the outer hoop should be neglected 

 in dimensioning the top hoops. 



105. Dimension table. By the use of the above formulas as just 

 explained, the accompanying table has been calculated, giving the 

 required thickness of slab and also the size and number of slab 

 rods for various spans and loads. 



In this table the thickness of concrete below the bottom of the 

 rods has been assumed as about i in., which has been proved by 

 experiment to be sufficient for fireproofing purposes. Some fire- 

 proofing specifications require more, however, in which case it will 

 be necessary to increase the thickness of slab given in the table to 

 the required amount, 



