SLAB, BEAM, AND COLUMN DIAGRAMS 221 



The question now arises, is the stress in the concrete brought down to a 

 value 750 Ib. per square inch (or less) by the introduction of 1.3 per cent of 

 compressive steel. Also, the corresponding value of f s should usually be 

 determined. 



Using Diagram 10 for -v= 0.10 and for p'=0.013 and p = 0.013, the 



relative reduction in the stress in the concrete is found to be 33.3 per cent, 

 or the resulting stress equals 865 (.333) (865) =577 Ib. per square inch. 

 Using Diagram 11, the relative reduction in the stress in the tensile steel 

 equals 4.4 per cent; that is, the maximum tension in the steel is 14,390 Ib. 

 per square inch. The stresses in the concrete and steel are within the 

 allowable and no haunch or additional steel are necessary. 



9. The effective area of a column is 144 sq. in. ; load to be carried is 80,000 

 Ib.; and working stress on the concrete is 450 Ib. per square inch. What 

 percentage of longitudinal bars without hooping will be required? Take 

 n = 15. 



The safe strength of a plain concrete column would be 



144 X 450 = 64,800 Ib. 

 Hence, 



p _ 8 _r5 



F-64J8- 1 ' 23 

 From Diagram 12, for n = 15, and p = 0.017 



p-1.238 



Thus, 1.7 per cent of steel is required, and 



A 8 = (144)(0.017)=2.45 sq. in. 



PROBLEMS 



Unit stresses recommended by Joint Committee are to be used in all the 

 following problems. Solve by using Diagrams. 



75. Determine the cross-section and number of 1-in. round rods required 

 for a rectangular girder to span 20 ft. and to sustain a live load of 2000 

 Ib. per foot. The bending moment is to be figured by the formula 



wl 2 

 M= ~r-. Design this girder by both Diagrams 1 and 7. 



76. Design a slab to span 4.5 ft. and to carry a live load of 300 Ib. per 

 square foot. Slab is to be fully continuous and reinforced in only one 

 direction. 



77. Design the center cross-section of a T-beam, fully continuous, having 

 a span of 16 ft. Maximum shear (not including dead weight of stem) 

 is 13,000 Ib. Maximum moment (not including dead weight of stem) 

 = 628,000 in.-lb. Supported slab is 5 in. thick. The depth of beam 

 (d) is fixed at 18 in. 



78. Solve Problem 77 considering the slab 3 3/4 in. thick. 



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

 center of span of 1,400,000 in.-lb. Negative bending moment at the 



