SLABS, CROSS-BEAMS, AND GIRDERS 



139 



practically it is accurate enough to consider these bending 

 moments identical. A greater economy, however, may be 

 obtained from the spacing of rods than is generally obtained in 

 practice. The spacing at the center namely, at aa' or W 

 may be determined on the equally distributed basis but at points 

 intermediate between the center and the edge, the rods might 

 well be spaced so that the number per foot would vary from the 

 required number at the center to zero at the edge, following the 

 law of the parabola. Or, the spacing for the center half of the 

 slab may be the same and then gradually reduce the number 

 of rods per foot to the edge of the slab, using one-half as many 

 rods for the remaining two quarters. 



From a similar approximate analysis regarding the stresses 

 in rectangular slabs of greater length than breadth and rein- 

 forced in both directions, it seems proper to vary the spacing of 

 the reinforcement for each system as already described, provided 

 the panels are not far from square. As a slab becomes oblong in 

 form, however, the relative amount of load carried by the longi- 

 tudinal system becomes rapidly less. 



r 





FIG. 71. 



Consider uniform load over the slab represented in Fig. 71. 

 It is required to find w l and w 2 , the parts of the whole unit load 

 w that is carried by the reinforcement parallel to the strips 

 rr f and ss'. The deflections of these strips of unit width at k 

 are the same, and are proportional to the fourth power of the 

 length of the strip. Thus, 



w 1 b* = w 2 l 4 ' and, since 



or 



'1 



b 4 



I* 



w 



