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)

262 Eccentrically loaded columns and slender columns
Step2
Calculate dclh = (= 0.9 x!h $ 1).
Step3
Calculate t~ 1 and t 52 using the strain diagram (see eqns 7.1-9 and 7.1-16
for example).
Calculate /~ 1 and fsz:
Step4
/~1 = Est~l $ 0.87/y
fsz = Estsz $ 0.87/y
Using the dclh value for Step 2 and the steel stresses in Step 3, calculate
(N,M) from eqns (7.1-20) and (7.1-21).
This gives us one point on the column interaction curve for the given
section.
StepS
Assume another value for x/ h and repeat Steps 2, 3 and 4 to obtain
another point (N,M) on the interaction curve.
Step6
Repeat Step 5 to complete the column interaction curve.
Step7
Draw the BS 8110 limit eminlh = 0.05 referred to in Example 7.1-4(b).
Example 7.1-7 (contributed by Dr H. H. A. Wong of the University of
Newcastle upon Tyne)
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 the BS 8110 charts
refer to symmetrically reinforced columns so that (1) A~ 1 = A 52 = Ascl2
and (2) d' = d 2 = h - d. It is also seen from Fig. 7.3-1 that each of BS
8110's interaction curves refers to a particular set of (e; feu ;fy; d/ h) values,
where (} is the steel ratio Asci bh.
(a) Explain whether it is possible to reduce the four variables (e;fcu;[y;
d/h) to three, namely: (elfcu; [y; d/h).
(b) Explain whether it is possible further to reduce the number of
variables to two, namely: (ef/fcu; d!h), as has been done in
Appendix D of the I.Struct.E. Manual [5]. (See Fig. 7.3-2.)
SOLUTION
(a) Yes, it is possible to use only three variables: (elfcu; [y; d!h). To
understand why this is so, we need only consider a few points:
(1) Equations (7.1-3) and (7.1-4) show that aconc and f3conc are
independent of any of these variables.
(2) Equations (7.1-7) and (7.1-11) (eqns 7.1-14 and 7.1-17) show
that the maximum length of the vector a 52 + f3sz (the vector a 51
+ Ps 1 ) is proportional to [y and its direction depends on dlh.
(3) Equations (7.1-7) and (7.1-8) (eqns 7.1-14 and 7.1-15) show