164 BESISTANCE OF MATERIALS 



cross-sectional area of each stirrup rod is .23 'per cent of the total 

 area of the cross section. 



Inclined reenf orcing rods, formed by bending up part of the hori- 

 zontal bottom rods at an angle of 45, are usually too large and too 

 far apart to form an effective web reenf orcement, but a combination 

 of the two, as shown in Fig. 110, constitutes the most effective design. 



97. Reenf orced concrete columns. It is seldom necessary to design 

 reenforced concrete columns by the formulas for long columns. In 

 ordinary construction the ratio of length to least width seldom ex- 

 ceeds 12 or 15, while actual tests show that they may be practically 

 considered as short blocks for ratios up to 20 or 25. The strength 

 of a reenforced concrete column considered as a short block will 

 therefore first be determined, and in exceptional cases this result 

 may then be corrected by applying a general column formula. 



The method of reenforcing concrete columns is either 



1. by means of longitudinal rods extending the full length of 

 the column ; 



2. by means of hoops or spiral bands ; 



3. by a combination of longitudinal rods and hoops or spirals. 

 Let A denote the total cross-sectional area of the column ; A e the 



area of the concrete ; A s the area of the steel ; and p c , p s the safe unit 

 stresses in the concrete and steel respectively. Then the safe load 

 P for the column is given by 



P=P c A c +p s A s . 



The unit deformations of the concrete and steel corresponding to 

 these stresses are 



where E c and E s denote Young's moduli for the concrete and steel 

 respectively. Since the concrete and steel must deform the same 

 amount, s c = *,, and, consequently, 



Ps E* 



^ = 8 = w, 



PC EC 



or p 8 = np c , 



where n denotes the ratio of the two moduli, ordinarily assumed 

 to be 15. 



