STRENGTH AND ELASTICITY OF REINFORCED CONCRETE. 157 



c = the compressive strength in the extreme outer 



fibre of the concrete, 

 t — the tensile stress in the extreme outer fibre of 



the concrete. 

 f = the stress in the metal reinforcement which 



should not exceed the elastic limit of the metal. 

 p = the ratio of the area of the reinforcement to 



the area of that of the beam, thus, if a = the total 



area of the metal p = — - where b = the breadth 



b h 

 of the beam. 



We assume that a plain section before flexure remains 

 plain during flexure, or if a b, Fig. 11, represents a line per- 

 pendicular to the neutral axis of the beam before flexure, 

 then a b' represents the position of the line after flexure. 

 This is a usual assumption, but it is not strictly true, as 

 can be proved by measuring the strains on the faces of a 

 beam with delicate extensometers, such as Martens' mirror 

 apparatus ; but the assumption is sufficiently approximate 

 in this case, having in view the unavoidable variation in 

 the physical properties of concrete. The form of the stress 

 strain curves obtained by testing beams and prisms in cross 

 breaking, tension and compression are shown on the numer- 

 ous diagrams in the paper, from which it will be seen that 

 the area of the curves (Fig. 12) above and below the neutral 

 axis are approximately: — 



- h x c and — h (1 - x) t respectively. 

 8 10 



It is also clear that : — 



t B t U-*/ 

 f Es /u — x\ / 9 v 



Equating the tensile and compressive forces : — 

 !«.=-l V (l-*)t+Ff...(S) 



