112 REINFORCED CONCRETE CONSTRUCTION 



2 = total circumference of bars, 

 s = horizontal spacing of stirrups, 

 i = diameter of stirrup bar. 

 w = uniform load in pounds per foot. 

 I = span of beam in feet. 

 Xj = distance in feet from support to point beyond which 



stirrups are unnecessary. 

 I' = required length of bent bars for bond strength (above 



a point O.Gd from upper surface of beam). 

 x 2 = distance from support to point where w 2 bars may 

 be bent up leaving sufficient steel to carry the tension. 

 m = number of bars actually required for moment at 



center of beam. 

 m 2 = number of these bars to be bent. 



' 50. Formulas. For convenience in working the problems 

 which follow, the formulas which apply to rectangular reinforced 

 concrete beams will be re-stated. 



a 



or bd* = ~-., or/.= 

 or 5*= or/. = 



Note. If a beam is over-reinforced, its resisting moment 

 depends on M c , and if under-reinforced on M 8 . If it is desired 

 to find the fiber stresses in concrete and steel for a beam already 

 designed [with an amount of steel differing from the amount 



determined by the formula p = 7 ^r 1, the formulas /. 



h f/Lj. i* J 



fc We / 



= ri and f c = , ., , 2 (or f c =^r) should be used, where M is 

 the external bending moment in each case. For a given external 



