RECTANGULAR BEAMS 99 



Illustrative Problem. A concrete beam is 9 in. X 16 in. in cross-section and 

 the tension reinforcement is 2 in. above the lower face of the beam. Span 

 of the beam is 8.5 ft. Uniform load of 1800 Ib. per foot. If necessary, the 

 web is to be reinforced against diagonal tension using vertical stirrups. The 

 working stresses recommended by the Joint Committee for a 2000 Ib. con- 

 crete will be used. 



V 7650 



61 !b- Per square inch. 



The allowable average shear v ij 35 Ib. per square inch, hence stirrups 

 are necessary. 



The diameter of a stirrup without any prong or hook should not exceed 

 (see table) 



i = (0.012) (14) 



= 0.17 in. 



We will use stirrups bent at the upper end and because of this bending 1/4- 

 in. round bars may be considered secure against slipping. 



Stirrups are unnecessary at a distance from support (assuming j = 7/8) 

 equal to 



8.5 (40) (9) (7/8) (14) . ' 



~2~ 1800 ft * 



The minimum spacing of stirrups (U-shape) will occur at the supports and 

 will be equal to 



_3 (2) (0.049) (16, OOP) (7/8) (14) _ 0f7K . 

 ~2 7650 



Let x = distance from the left support. Then for re = ^ = 1.1 ft., the 



spacing is (4/3) (3. 75) =5.0 in.; and for a: = ^ = 2.1 ft., the spacing is 



(2) (3.75) = 7.5 in. A smooth curve drawn through the points determines the 

 spacing at any part of the beam. In monolithic construction, the first 

 stirrup may be placed one-half the minimum spacing from the edge of the 

 support, and the last stirrup should not be farther distant from the limiting 

 point, where stirrups are unnecessary, than half of the distance between the 

 last two stirrups. In beams simply supported, the first stirrup should be 

 placed one-half the minimum distance from the center of support. 



43. Horizontal Bars Bent Up for Web Reinforcement. The 



ends of the horizontal bars in a reinforced concrete beam may often 

 be bent up to assist in providing for the diagonal tension. In 

 some cases these bent rods may take all such stresses, and 

 vertical stirrups then are not theoretically needed though they 

 are desirable, as shown by tests. 



Plain rods bent up to provide web reinforcement often lack 

 sufficient bond strength to render them fully effective. Where 

 bent up at a considerable angle they should be turned again 

 horizontally and extend some distance along the upper part of 



