SLABS, CROSS-BEAMS, AND GIRDERS 165 



Also, 



358,000 



= 56 ">' p 



Allowable compression in concrete at the support is thus satisfactory, and 

 no haunch is necessary. 



The value of /' can always be determined as above, but it is seldom 

 desired as the working strength of the steel in compression cannot be 

 reached without exceeding the compressive strength of the concrete in 

 which it is embedded. With n = 15, the allowable stress in the steel cannot 

 exceed 15 times the compressive strength of the concrete. 



Illustrative Problems. A continuous T-beam with 6' = 14 in., and 

 d = 26.5 in. has a negative bending moment at the supports of 2,000,000 

 in.-lb., and has equal spans of 18 ft. Reinforcement at supports consists 

 of 7/8-in. round rods. Eight bars are in tensile and four in compressive 

 part of beam. Hence, 



Ratio tension steel, p = * =0.0130 



Ratio compression steel, p r = = 0.0065 



2 



With these values of p and p f and n = 15, also assuming -^- = 0.1, we 

 obtain from equations (3) and (5), L = 0.243, and from equation (4). 



2,000,000 

 /c = (14) (26.5) 2 (0.243) = lb ' P ei sc l uar 



which is excessive, only 750 lb. per square inch being allowed, or a stress 

 15 per cent greater than at the center of span. 



d' 

 For depth of haunch assume -3 =0.1 and try d = 29 in. For this depth of 



beam the ratios of steel in tension and compression change to 

 p = 0.0130 (~~'-\ =0.0119 



The corresponding value of L = 0.233 and ^ = 0.0104. The maximum com- 

 pression in the concrete 



2,000,000 



/c= (147(29^(0^33) 



and maximum tension in steel 



2 000 000 



/a = (14)(V(0.0104) - 1MO< ' lb ' P er S 1 Uare inch 



This stress is allowable and the depth of haunch from top of beam of 29 in. 

 will be accepted. 



Using the formula (4) 



M l = (750) (14) (26.5) 2 (0.242) =1,780,000 in.-lb. 

 M 2 = 2,000,000 in.-lb. 



