650 PKOCEEipNGS OP SECTiON H. 



The central bending nio'tiient is — 



7,000 X 120 



or 105,000 in. pounds. 



Allowing a working stress of 600 lb. per square inch in coni- 

 piession and an idtinu\te stress of 200 11:». per square inch in tension, 

 we have a diagram of stress as in Fig. .'5. The diagram on the left 

 applies as long as the tension at tlie extreme libl'e is less than L'OO; 

 the otlier diagram applies to tlie middle portion of the beam. 



The tensile stresses would no d()\il)t I;e more accurately repre- 

 sented l)y a parabola instead of a straight line, but the difficulty of 

 ■calculation is greater than the possible gain in accuracy would 

 warrant. 



The total Compressive Resistance = C = If ^. x /.-d x h^=^600 

 X 10 X 104;= 30,000 /^. 



The tensile resistance of concrete T = |/', x x il x b = h 200 X 



^ X 10 X 10 == 10,000 X 



T3 , , 200 ^ 



rJut X = fc X = 



600 H 



T=: 10 000^'" 

 '6 



The resistance of the steel i^/', x a =J\ 

 andy; = f\ X n X ^ ~-' = GOO x 1-3 ^ ~^ = 9.000 ^~^ 



hence 30,000 /• = 1 0,000 ^" -f 9,000 ' ~^ 

 3 /t 



and K = .136 ^ = 1153. 



Taking moments about centre of reinforcement — 



M = cAd- — ^ - T id - kd- - X d\ 



= 13,080 (10 - 1.453) - 1.453 flO - 4.3(5 - 0.97) 

 = 111,795 - 6,785 = 105,010 inch lbs. 



The result shows that the tensile strength of 200 lb. is reached 

 at r453 in. below the neutral axis, or 5'81 in. below the Liiiper 

 surface. Below this depth the concrete must have previously cracked, 

 but not necessarily in a visible crack, as Turneaure's and other experi- 

 ments show that the concrete is broken up into a numl^er of small 

 invisible cracks by the distributing action of the reinforcemtnt. 



At any other point in the beam I have computed, the level at 

 which the 200-lb. tension is reached by finding in the s.'une manner 

 as above the moment of resistance corresponding to vai-ious intensi- 

 ties of compressive stress at the upper surface. 



The ilistance y from the centre where this moment is produced is 

 Cidculated in i\\e ordinary way. 



