RECTANGULAR BEAMS 95 



The distance from the support to the point where no stirrups 

 are required is helpful in design. This distance for uniform 

 loading may easily be expressed by means of a formula. 



Let v = unit shear. 



v' = unit working shear. (V = corresponding total shear). 

 x t = distance in feet from left support to point beyond which 



stirrups are unnecessary. 

 Z = span of beam in feet. 

 w = uniform load in pounds per foot. 



Then 



V 

 ~ bjd 



Stirrups become unnecessary at section where v = v'. Thus, at 

 the required section 



r XL 



~bjd 



But 



Substituting and solving for x lf we have 



_l v'bjd 

 X *~2~~w~ 



Suppose a 10-ft. beam (6 = 10 in. and d = 2Q in.) is uniformly 

 loaded with 2900 Ib. per foot, and assume v' = 40 Ib. per square 

 inch according to recommendation of Joint Committee for 2000 

 Ib. concrete. Also assume jd = 7/8d. Then, 



10 (40)(10)(17.5) 

 Xl 2 ~ 2900 



= 2.59 ft. 



The following graphical method may be employed to deter- 

 mine the spacing of stirrups in large and important beams: 



Lay off one-half the span to any convenient scale as shown in 

 Fig. 46. Compute the values of s at a number of points (1, 2 

 and 3, for example) and lay off these values on the perpendicu- 

 lars erected at the respective points to the same scale as the span. 

 Draw a smooth curve through the upper ends of the perpendicu- 

 lars. From point a on the curve directly above the point where 

 the first stirrup will be placed, draw a line at 45 degrees to inter- 

 sect with the horizontal line and erect at the point of intersection 



