310 CONCRETE DESIGN 



ring thickness usually increases more rapidly, and while no 

 definite proportions can be laid down, it is usually at least 

 twice as thick at the skewbacks as at the crown. 



One of the points yet to be considered is the amount 

 of steel reinforcement to be used. As was said, this rein- 

 forcement usually is placed in two layers, one layer near 

 the intrados and the other near the extrados. If the arch 

 carried only a dead load and the conditions were absolutely 

 uniform, only one layer of reinforcement would be neces- 

 sary; but, in actual practice, as even the changes of temper- 

 ature cause large variations in stress, two layers of rein- 

 forcement are used unless a very careful analysis of stresses 

 has been made to prove that they are not needed. The 

 amount of steel in each layer is kept uniform throughout its 

 length. The cross-sectional area ot steel in each layer is equal 

 to -j^j of 1% of the area of the arch-ring section at the crown. 



Thus, suppose that the thickness of an arch at the crown 

 is 24 in. For a width of 1 ft., the area of the arch-ring 

 section is 24X12 = 288 sq. in. The area of the steel in the 

 top or bottom layer per foot of arch width is therefore 



288 X = 1.152 sq. in. The area of a |-in. round bar is 



.6013 sq. in. Therefore, one $-in. round bar placed near the 

 extrados and one |-in. round bar placed near the intrados, 

 every 6 in. in width along the bridge, will be found sufficient. 



The distance from the center of the bars to the surface 

 of the intrados and extrados, that is, the depth to which 

 the bars are to be embedded in the concrete, is another 

 question that must be decided. The nearer the reinforce- 

 ment is to the surface, the more efficient it will be. On the 

 other hand, the reinforcement must be embedded deep 

 enough, so that it will not tear loose and so that it will be 

 protected from fire and rust. As a general rule, the distance 

 from the center of the steel reinforcement to the surface of 

 the arch ring should be from 2 to 3 in. 



The two layers of reinforcement are laced together by light 

 steel rods that are run from one layer to the other. No uniform 

 method is followed in designing these shear members, as they 

 are called, and the amount of material used also varies greatly. 



