Theoretically there is an indefinite number of values of r, the ratio of the moduli of elasticity of the steel and the concrete. The modulus for steel is fairly constant at about 29,000,000 or 30,000,000. The value of the initial modulus for concrete varies according to the quality of the concrete, from 1,500,000 to 3,000,000 for stone concrete. An average value for cinder concrete is about 750,000. Some experimental values for stone concrete have fallen somewhat lower than 1,500,000, while others have reached 4,000,000 and even more. We may probably use the following values with the constant value of 29,000,000 for the steel.

Table XIV. Modulus Of Elasticity Of Some Grades Of Concrete

Kind of Concrete

MlXTURE

Ec

r

Cinder....

1:2:5

750,000

40

Broken Stone...

1:6:12

1,450,000

20

,, ,,

1:3:5

2,400,000

12

,, ,,

1:2:4

2.900.000

10

The value given above for 1:6:12 concrete is mentioned only because the value r = 20 is sometimes used with the weaker grades of concrete, and the value of approximately 1,450,000 for the elasticity of such concrete has been found by experimenters. The use of such a lean concrete is hardly to be recommended, because of its unreliability. Considering the variability in cinder concrete, the even value of r = 40 is justifiable, rather than the precise value 38.67.