RECTANGULAR BEAMS 107 



distributed over the bearing surface, how far should the beam extend 

 beyond the edge of the supports, taking the allowable crushing strength 

 of the concrete at 450 Ib. per square inch? 



34. In the beam of Problem 33, what is the distance from the left reaction 

 to the point beyond which stirrups are unnecessary, assuming the 

 moment calculations to give b = 18 in. and d= 26 in. 



35. (a) Could four 1-in. plain square bars be used in the beam of Problem 

 34? Give reasons, (b) If eight 3/4-in. square bars were used, how 

 many could be bent up to take diagonal tension (allow about 30 per cent 

 more bond stress on the horizontal rods than would be considered safe 

 by formula if three rods can be bent up and at least two bends made at 

 each end of beam)? 



36. In the beam of the preceding problems, at what points may the horizontal 

 rods be bent up if eight 3/4-in. square rods are used? (Student should 

 note that less than eight rods are actually required for moment at 

 the center of the beam.) 



37. At what points in the beam of Problem 36 should the horizontal rods 

 be bent to provide for the diagonal tension in the best possible manner, 

 assuming the resultant reactions 3 in. from the edge of supports (ends 

 of beam 6 in. from edge)? Submit sketch neatly drawn. 



38. In Problem 36 if the horizontal bars were run straight to the end of 

 beam what size and spacing of vertical stirrups would be required to 

 provide thoroughly for diagonal tension? Employ double-looped, 

 square stirrups. Graphical work to be submitted. 



39. (a) What should be the grip of the inclined rods of Problem 37 consider- 

 ing the rods stressed in tension to the allowable value of 16,000 Ib. per 

 square inch? (b) What should be the grip of these rods for the stress 

 they are actually called upon to withstand? 



46. Transverse Spacing of Reinforcement. The amount of 

 concrete between the horizontal bars in a beam should be suffi- 

 cient to transmit to the upper part of the beam the stress which 

 the bars give over to the concrete below 

 them; in other words, the shearing stress 

 along ab, Fig. 52, should equal the amount 

 of stress transmitted by bond along bed. 

 If bond and shearing strengths were equal, 

 ab should equal bed, and the clear space be- 



, 3.1416 ,. 



tween bars should be ~ diameters = 



a 



\ 



1.57 diameters. But shearing strength j? IG 52. 



here employed is controlled by the diagonal 



120 3 



tension and is approximately -, ~ = ~ the bond stress, using the 



oU Z 



values recommended by the Joint Committee. Hence, ab should 

 be (2/3) (1.57) diameters = 1.05 diameters. That is, the mini- 

 mum net distance in the clear between rods is approximately 



