RECTANGULAR BEAMS 111 



beam, uniformly loaded. Our formula readily gives us the 

 result, using the working stresses given above. 



Z_(4)(16,000)(0.0077)_ 

 d~ 120 



At the same time that the ratio of length to depth is being 

 investigated for moment and shear, there are other conditions 

 which must be considered. For instance, the ratio of length to 

 breadth of beam should not exceed a value of about 25 if the 

 beam is not supported laterally. The reason for this is found in 

 the fact that the upper part of the beam is a column, and to 

 prevent additional stress due to side bending the length should 

 not exceed about 25 times the width. On the other hand, the 

 best shaped beam is one in which b lies between l/2d and 3/4d 

 In any given case, to satisfy all requirements and arrive at, a 

 satisfactory design, two or three trials may be required. 



49. Notation. The notation used in this course in the design 

 of rectangular reinforced concrete beams is summarized as 

 follows : 



f c = unit compressive stress in outside fiber of concrete. 

 f s = unit tensile stress in steel. 

 n = ratio of modulus of elasticity of steel in tension to 



modulus of elasticity of concrete in compression. 

 a s = area of cross-section of steel. 

 b = breadth of beam. 



d = distance from compression surface to axis of rein- 

 forcement. 



M c = resisting moment as determined by concrete. 

 M 8 = resisting moment as determined by steel. 

 M = bending moment or resisting moment in general. 



p = steel ratio = 



A; = ratio of depth of neutral axis to depth of steel. 

 / = ratio of lever arm of resisting couple to depth of steel. 

 V = total shear. 

 v = unit shear. 



v' = unit working shear. 



V 

 v = j-, = average unit shear. 



u = unit bond. 



o circumference of one bar. 



