168 



RESISTANCE OF MATERIALS 



center to center of columns. For practical purposes the diameter 

 D of the column top may therefore be assumed as 



which is approximately the mean of the above values. 



There is another condition, however, which also affects the 

 diameter of the top, namely, the distribution of slab reenforce- 

 ment. If the column top is too small, there will be portions of the 

 slab which contain no reinforcement, as shown by 'the triangular 



areas #, 5, c, d (Fig. 112). 

 The arrangement shown in 

 Fig. 113, however, has no 

 such gaps ; it requires that 



o 



d-* 



I 



FIG. 112 



FIG. 113 



or JJ = 



== = 0.414*, 



which determines the minimum diameter of column top. If, then, 

 D is assumed as 



D = l = O.4375 I, 

 16 



a slight overlap of the reenforcing rods is assured. 



100. Efficiency of the spider hoops. The efficiency of tensile re- 

 enforcement in the form of hoops as compared with direct reen- 

 forcement may be obtained approximately as follows : 



In the case of column tops as here considered, take a diametral 

 section of the top and consider half of one hoop and the portion of 

 the material reenforced by this segment, as shown in Fig. 114. Let 

 w denote the radial stress, or pressure on the inside of the hoop 

 per unit of length, expressed in pounds per linear inch of hoop. 

 Also let r denote the radius of the hoop, A its cross-sectional area, 

 and p the unit stress in the metal. Then the radial force acting on 

 any portion of the hoop of length As is wAs, and the component of 

 this force perpendicular to the plane of the section is wAs sin a. 

 Or, if A# denotes the projection of As on the diameter, then 

 As sin a = Az, and this component of the force therefore becomes 



