RECTANGULAR BEAMS 109 



of beam for all rods greater than 5/8 in. in diameter will be 

 governed by the first formula and for 5/8-in. rods and less ; by 

 the second formula. 



Where two layers of rods are used, there is less danger of 

 vertical than of horizontal splitting so that usually the rods may 

 be placed directly over each other, providing merely sufficient 

 space for the mortar to run between them. The Joint Com- 

 mittee specifies a limiting clear space of 1/2 in. 



47. Depth of Concrete Below Rods. Prof. Charles L. Norton 

 of the Insurance Engineering Experiment Station has made a 

 careful study of the thickness of concrete which is essential to 

 thoroughly protect embedded steel from the direct action of 

 flames, and recommends 2 in. for maximum conditions. An 

 excessive thickness of concrete, however, adds to the danger of 

 cracking, because the tension in the concrete increases with the 

 depth below the steel and with but slight corresponding gain 

 in strength to the beam. Also, flat slabs are found to be affected 

 to a less depth than projecting members such as beams and 

 columns. The Joint Committee suggests that "the metal, in 

 girders and columns be protected by a minimum of 2 in. of con- 

 crete; that the metal in beams be protected by a minimum of 

 1 1/2 in. of concrete; and that the metal in floor slabs be pro- 

 tected by a minimum of 1 in. of concrete." 



The following depths of concrete below the steel may be em- 

 ployed under ordinary conditions, but wherever conditions are 

 especially hazardous, the recommendations of the Joint Com- 

 mittee should be followed: 



SLABS 



Depth to steel (d~) Depth below center of steel 



3 in. and under in. 



Between 3J in. and 4 in 1 in. 



4f in. and over 1^ in. 



BEAMS AND GIRDERS 



Depth to steel (d) Depth in the clear below steel 



10 in. and under 1 in. 



Between 10 in. and 20 in 1 J in. 



20 in. and over 2 in. 



48. Ratio of Length to Depth of Beam for Equal Strength in 

 Moment and Shear. With given working stresses in concrete 

 and steel, there is a definite ratio of length to depth of beam 

 which will give equal strength in moment and shear. Let us 

 first consider beams simply supported. 



