F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

290 Eccentrically loaded columns and slender columns
N 2 - N(Ny + NE(1 + q)) + NENy = 0
where N is the load at material failure of the column; Ny is the squash
load ( = area x yield strength; NE is the Euler load ( = n 2 Elll 2 ); 17 is a
function of the slenderness ratio 1/r, and values of 0.003 (1/r) and 0.3
(l/100r) 2 have been used for 17 in practical design.
It is interesting to compare the steelwork designers' Perry-
Robertson formula with the reinforced concrete designers' eqn
(7.4-6), and observe that both formulae are primarily concerned
with material failure and that, in each formula, the load capacity N is
regarded as being significantly dependent on the column slenderness.
7.8 BS 8110: Part 3 gives a comprehensive set of column design charts,
one of which is reproduced as Fig. 7 .3-1. It can be seen that each of BS
8110's interaction curves refers to a particular set of (e;fcu;fy; dlh) values,
where (! is the steel ratio Asclbh.
The I.Struct.E. Manual (5), on the other hand, uses only two variables
((!/yl/cu; d/h), with the great advantage that only a very small number of
charts are then necessary for design. Explain whether the I.Struct.E.
Manual (5) is justified in using only two variables (!/yl/cu and d/h.
Ans.
In Section 7.1, the authors use three variables: (elfcu;fy and d/h).
Theoretically, it is impossible to use only two variables
((!/yl/cu; d/h). For a detailed explanation, see Example 7.1-7.
References
1 ACI Committee 318. Commentary on Building Code Requirements for
Reinforced Concrete (ACI 318R-83). American Concrete Institute, Detroit,
1983.
2 Nawy, E. G. Columns in uniaxial and biaxial bending. In Handbook of
Structural Concrete, edited by Kong, F. K., Evans, R. H., Cohen, E. and Roll,
F. Pitman, London, and McGraw-Hill, New York, 1983, Chapter 12, Sections
2.5 and 2.6.
3 ACI-ASCE Committee 441. Reinforced Concrete Columns (ACI Publication
SP-50). American Concrete Institute, Detroit, 1975.
4 Evans, R. H. and Lawson, K. T. Tests on eccentrically loaded columns with
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1957' pp. 340-8.
5 I.Struct.E./ICE Joint Committee. Manual for the Design of Reinforced
Concrete Building Structures. Institution of Structural Engineers, London,
1985.
6 Coates, R. C., Coutie, M. G. and Kong, F. K. Structural Analysis, 3rd edn.
Van Nostrand Reinhold, Wokingham, 1988, pp. 304-11 and 326.
7 Smith, I. A. Column design to CP110. Concrete, 8, Oct. 1974, pp. 38-40.
8 Bresler, B. Design criteria for reinforced concrete columns under axial load
and biaxial bending. Proc. ACI, 57, No. 5, Nov. 1960, pp. 481-90.
9 Furlong, R. W. Ultimate strength of square columns under biaxially eccentric
loads. Proc. ACI, 51, No. 9, March 1961, pp. 1129-40.
10 CP 110: 1972. Code of Practice for the Structural Use of Concrete. British
Standards Institution, London, 1972.