92 REINFORCED CONCRETE CONSTRUCTION 



of the horizontal unit shear on this plane varies proportionally 



V V 



with the total shear, and is equal to -~ at section A A and to-^ ? 



at section CC. Hence, the total amount of shear on this plane, 



V +V 

 considering uniform variation of shear, is equal to ""Vyr^W* 



V 

 or, when V at BB is the average shear, to -^s. This is the ver- 



tical component of the diagonal tensile stress in a length of 

 beam s. 



When a stirrup is placed at B, Fig. 44, and the distance between 

 stirrups is s, then the vertical component of the diagonal tension 



2 Vs 



to be taken by this stirrup is - -ry This stress causes tension in 



o ]d 



the stirrup, the corresponding horizontal component of the 

 diagonal tension being carried by the horizontal rods. 



The stress in a vertical stirrup is a s f s , hence the cross-sectional 

 area of vertical steel required in a length of s may be taken 

 approximately as 



2 YS 



(Vertical stirrups) (1) 



For stirrups or bars inclined at 45 degrees, the lines on a beam 

 representing the direction in which the diagonal tensile cracks 

 are likely to occur, are crossed more times per unit of length for 

 a given horizontal spacing than would be the case if vertical 

 stirrups were employed; that is, a given amount of inclined steel 

 is much more effective in taking diagonal tension than the same 

 amount of vertical steel. It may be assumed, then, that the 



stress in the inclined bars is approximately . */ and the re- 



sin 4o 



quired area of steel, assuming the steel to take two-thirds of the 

 shear, is 



2 o 7(Vs) 



a = o* j. vi (Inclined bars 45 degree angle) (2) 

 o yy 



For other angles of inclination K, it may be assumed as approxi- 

 mately correct to use the formula 



2 sin K (Vs} ,_ ,. , , /ON 



a, =- -- 7-^7 (Inclined bars any angle) (3) 



o J s ]d 



The recommendations of the Joint Committee for the allowable 

 shearing stresses in beams, both with and without effective web 



