652 PROCEEDINGS OF SECTION H. 



along the centre of the beam. Measurements of extension made in 

 such cases show Httle variation from those made on the ordinary- 

 beam. 



This is as much as to say that the stress in the steel is almost 

 luiiform along the greater part of its length, and is derived from 

 the adhesion of steel to the concrete in the end portions ; allowing 

 oOO lb. per square inch ultimate strength for adhesion, an area of 



-_- = 388 square inches is required. This has to be provided in 



a length of about 18 in., so that the total circumference of reinforce- 

 ment must not be less than 2"15 in. In our beam the reinforcement 

 of 1 square inch could be got approximately by four y^^ in. bars, of 

 which the circumference would be more than 7 in. The factor of 

 safety is then about 3 '28. Working from the pressure line a — a and 

 admitting that the ai'ch consists only of the concrete above the 

 cracked zone shown in Fig. 4, there is no difficulty in finding the 

 extreme fibre stresses in the concrete. 



Ihev are / = — -|- — . 



H = hoiizontal thrust= stress in reinforcement. 

 s = depth of sound concrete. 

 b = breadth of sound concrete. 

 e = eccentricity of thrust. 



The tension at the margin of the cracked zone will now be 

 found to be less than 200 lb. per square inch, except at the central 

 section. 



I consider that the real conditions of stress are intermediate 

 between those due to considering the piece as a beam and as an arch. 



The cracked concrete must press upon the steel, deflecting it 

 downwards and inducing stresses in it as in a suspension cable ; so 

 that neither the diagram of stress in Fig. i nor a uniform stress in 

 the middle portion truly represents the facts. 



A general formula for the intensity of the shearing stress at 

 any level in a cross section is 



S X Gr 



S is the total shearing force at tlie section. 



G is the moment of the area of the section above the level in 

 question about the neutral axis. 



I is the moment of inertia of the whole section. 



h is the breadth at th- given level. 



In calculating I it is convenient to replace the steel by an 

 equivalent width of concreie. 



Thus 1 square inch of steel may be considered equivalent to a 

 strip of concrete 15 in. wide by 1 in. deep at the same level as the 

 reinforcement. 



The diagram of shear at the left end of beam is shown in Fig. 4. 



As the shearing stiength of concrete may easily be about 1,000 

 U). per square inch, it is clear that no failure is likely to take place 

 in this l)eani OAving to jiurc shear. 



