Mathematical and Physical Papers. 221 



F 

 Now for steel in tension t — ^s 



F 



For steel in compression '7 =h^ 



For concrete in tension- = fg 



A y 



F X— di' 

 For concrete in compression - = f^} 



at those distances from the neutral axis at which the reenforcing 

 rods are placed. » 



fs^ . _ Es 



From the foregoing : x — di^ ^ Ec 



X 'c f 



or f i^x-di^f ig g-^^^g g^E, 



* X ' Ec 



Similarly fs = f^e 



Substituting these values of fs^ and f^ in (7) we have : 



2 ' 



^-^f,'{e-l) 



byf, 

 2 +^^ 



^~-re(e-l) 



(5) 



f c y 

 Dividing by fc^ and remembering that t^ = ~ 



' v + As^^^^(e-l)=^. l-^Aj-^. Z(e-1 

 2 ^ ^ X V / 2 x^ ' y X V 



Or, 



+ A,i(x-di^) (e-l)=^VA,(y-di) (e-l) (9) 



bx2 

 2 



Substituting for x, its value h — y 



b(h-yr + 2A,Hli-y-di^)(e-l)=by^ + 2.A,(.y-di)(e-l). ,{10) 



Solving "this equation for y gives 



^ + [Asdi+Asi(h-diO](e-l) 

 ^^ A+(As+Asi)(e— 1) 



which is the correct value of y. 



