CHAPTER VIII 

 SLAB, BEAM, AND COLUMN DIAGRAMS 



73. Illustrative Problems. In this article the same illustrative 

 problems will be worked out as in Art. 72. It is thought by so 

 doing a good comparison can be made between tables and dia- 

 grams as to their advantages and limitations. The working 

 stresses recommended by the Joint Committee will be employed 

 throughout. 



1. Design a beam to span 40 ft. and to support 600 Ib. per foot (includ- 

 ing weight .of beam). Beam is assumed to be simply supported. 



In Diagram 1, the intersection of the curves f c = 650 and/ s = 16,000 is 

 first found. Tracing down, p is found to be 0.0077, and tracing horizontally 



K |==;1 is found to be 107.3 



6 = 18 in. and d = 27 1/2 in. will be satisfactory. Area of cross-section, 

 6d = (18)(27.5)=495sq. in. 



a a = (495) (0.0077) =3.81 sq. in. 



We shall select four 1 1/8-in. round rods = 3. 98 sq. in. 



Diagram 1 may be also employed to determine the safe resisting moment 

 of a given beam and the greatest unit stresses in the steel and concrete 

 due to a given bending moment. 



To determine the safe resisting moment of a given beam, the value of p 

 should be computed. After finding this value on the lower margin, trace 

 vertically, stopping at the first of the two curves / c = 650 and / a = 16,000 

 (assuming the allowable stresses as recommended by the Joint Committee). 

 Now trace horizontally to either side margin and the value of K is found. 

 Then, M=Kbd 2 . Consider a beam of the above dimensions to have 1 per 

 cent of steel. Tracing vertically from this value on the lower margin, the 

 650 is the first curve to be reached and at a value of K = 117.0 M = 

 (117)(18)(27.5) 2 = 1,593,000 in.-lb. 



To determine the greatest unit stresses in the steel and concrete of a given 

 beam due to a given bending moment, the value of p should be computed 



M 



as before. Also, K should be computed from the formula K = r^. With 



these values of p and K, find the intersection of the vertical and horizontal 

 lines through these values respectively, and from the adjacent steel and con- 

 crete curves the values of f c and / may be estimated. Consider a beam of 

 17 215 



