May 8, 1916 Tcsts of Rezfiforced-Concrete Slabs 233 



APPLICATION OF RECTANGULAR-BEAM THEORY TO DESIGN OF 

 SLABS UNDER CONCENTRATED LOADS 



The usual rectangular-beam design formulas may be applied to the 

 design of slabs by merely substituting for b its value as determined by 

 these investigations, b^o.yL. The corresponding formulas then be- 

 come — 



FOR SLABS UNDER CENTRAL 

 FOR RECTANGULAR BEAMS CONCENTRATED LOADS 



(i) M,=y,fjtjbd^ M,=y,fj^jU.d^ 



(2) M=pfjbd' M=pfjy-Ld^ 



(3) p=h 



joa. 



bd "jLd 



(4) P= f /f — \ p= 



(5) k=^-\ 2pn-^{pn)' — pn f^='\/2pn-\-{pny—pn 



It is interesting to note that in substituting for M^ and Mg in formulas 



PL 

 I and 2 their value ^ — , the L's cancel, showmg that the safe load-carrying 



capacity of the slab is independent of the span; thus — 



PL 7 7 



1 becomes — = ^fJij—Ld^ or P=—fJijd'^ 



2 becomes ?^=pfjlLd'' or p=plAf jd^ 



The above investigations were made on slabs the width of which was 

 twice the span length, so that the stress at the extreme edges was very 

 small. The conclusions must therefore be applied to such cases only. 

 When the ratio of width of slab to span length is less than 2, these conclu- 

 sions may or may not apply, and additional investigations are now being 

 made to determine the proper value of effective width to use under such 

 conditions. 



