SLAB, BEAM, AND COLUMN DIAGRAMS 219 



7. Design a T-beam with span of 40 ft. Assume dead load = 1400 Ib. 

 per foot. Live load = 3000 Ib. per foot. The beam is to be simply supported 

 at the ends and the flange is to be proportioned as well as the web; that is, 

 the flange does not form a part of a floor system already determined. 



From Art. 61, 6' = 18 in. and d=47 in. are suitable dimensions and a 

 thickness of flange of 12 in. is tried. The total bending moment on the 

 beam is 10,560,000 in.-lb. 



'_ 12 _ 0256 

 5~47~ 



By means of Diagram 8, we find that with / c = 650 and -5 = 0.256, the 



value of ^ 2 = 99.2 Then, 



10,560,000 



= = * m ' 



Also, from the diagram, / = 0.892. Then, from Formula (7), Art. 59, 



10,560,000 



aa== (16,000) (.892X47) S<1 ' m " 



The detailed design of this beam has been given at the end of Art. 61. 



8. A continuous T-beam, uniformly loaded, has a bending moment at 

 the center of each span of 358,000 in.-lb. Negative bending moment at the 

 supports and the positive bending moment at the center of span are figured 



by the formula, M = --. The tensile steel at the center of span consists of 



[ - 



four 3/4-in. round rods, b' =9 in. cZ = 15.5 in. Design the supports. 



Diagrams 10 and 11 have been prepared to solve problems involving the 

 determination of stresses for rectangular beams with steel in top and 

 bottom. The formulas used in constructing these diagrams are radically 

 different from those previously employed and an explanation of them will 

 now be given. 



Compressive reinforcement needs to be used only when the compressive 

 concrete, if unreinforced, would be stressed too high. The question then 

 arises of how much compressive reinforcement is needed to reduce the streso 

 in the concrete to within the working limit. Let the following notation be 

 used: 



With no compressive reinforcement ...................... f c , f a , k, j. 



With compressive reinforcement ........................ /c', /', k', }'. 



Formula 2, Art. 33, may be written as follows: 



/ = -_ 



/c n(l-A) 



^ Mk (1) 



'n(l-fc) jda a n(l-k) 

 Referring to Formula 1, Art. 62, and knowing that the fiber stress in the 

 tensile steel of double-reinforced beams may be expressed by f a = ^ 



We also have 



M 



.'. / 



