USEFUL DATA 



805 — 747 l'<^/o 

 tion of /o to 747 will then be ssSi^,r 7-^%- Entering Diagram 5, on the left 



margin, with Tt^ and moving to the right to the "concrete curve," thence downward, 

 the amount of compressive steel to effect the reduction in/o is found to be 0.20% or 



(14) (34) (0.002) =0.95 sq. in. 



Combined Bending and Direct Stress. In the design of columns, arch rings, 

 etc., the resultant of the external forces does not always coincide with the center of 

 gravity of the cross section of the member. In such cases consideration must be given 

 to the combined action of bending and direct stress. For reinforced concrete members 

 the general formula for extreme fibre stress where compression exists over the entire 

 section, is 



A + {n-l)poA-^h-\-nI, 



W= Total direct load. 



A 



Po = Percentage of reinforcement = -^ 



A 



y = Distance from center of gravity of section to extreme fibre, 

 /o = Moment of inertia of concrete section about the gravity axis 

 /s = Moment of inertia of steel area about the gravity axis. 

 The other symbols are as given in the standard notation, pages 5 and 6. 

 It is in the case of rectangular sections with symmetrical reinforcement, that we 

 most frequently meet with problems involving bending and direct stress and Dia- 

 grams 6, 7, 8a and 8b, will be found to greatly facilitate the solution of such 

 problems. 



In the case of a homogeneous material no tension exists on the cross section when 

 the resultant falls within the middle third. For a concrete section reinforced with steel 

 bars the conditions are altered somewhat and the resultant may fall slightly outside 

 the middle third without producing tension on the section. In those cases where com- 

 pression exists over the whole section Diagram 6 may be employed, but where there 

 is tension over part of the section Diagrams 7 and 8a or 8b should be used. 



Case I. No Tension on the Cross Section. Consider a column 18 inches 

 square, reinforced with 4^1 in. square bars, carrying a load of 150,000 lb. concen- 

 trated 1 in. from the center of the column. Find the maximum unit stress in the 

 concrete. 



A 4 



Percentage of reinforcement, Po= tt^ = (18) (18) ^ 1-23% 



The eccentricity Xo=l in. 



and 1=^ = 0.0555 



Entering Diagram 6 with y = 0.0555, tracing vertically to po = 1.23% and then to 

 the left margin find JS"' = 1 . 09, a factor by which the average unit stress must be multi- 

 plied to find the maximum unit stress. 



13 



