162 RESISTANCE OF MATERIALS 



Moreover, equating the external moment M to the moment of the 

 stress couple, we have 



Substituting the value of x in either one of these expressions, say 

 the first, we have 



whence, solving for 



For practical work assume ft = 15, p c = 500 lb./in. 2 (factor of 

 safety of 5), and p s = 15,000 lb./in. 2 (factor of safety of 4). 

 Substituting these numerical values in the above, the results take 

 the simple form 



180 



where If denotes the total depth of the beam in inches, d is the 

 diameter of the reenforcement in inches, and M is the external 

 moment in inch-pounds per inch of width. 



In designing beams by these formulas first find A, then A, and 

 finally H. 



96. Calculation of stirrups, or web reenforcement. For a beam 

 reenforced with horizontal rods only, that is, having no vertical or 

 web reenforcement, the ultimate shearing strength is found to be 

 about 100 lb./in. 2 , calculated as the average shearing stress on the 

 cross section. The working stress in shear for the concrete is there- 

 fore assumed to be 25 or 30 lb./in. 2 , equivalent to a factor of safety 

 of 3 or 4. 



If the average shear on any cross section exceeds 30 lb./in. 2 , 

 vertical, or web, reenforcement is required, usually supplied in the 



