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)

260 Eccentrically loaded columns and slender columns
M
Fig. 7.1-9
eccentricity in design is to exclude part of the curve, K 1 K 2 , as shown
in Fig. 7.1-9.
Example 7.1-5
In the paragraph preceding eqn (7.1-1), it was pointed out that, using BS
8110's simplified stress block, the depth de= 0.9x for de :5 h (i.e. for xlh :5
1/0.9). For cases where xlh > 1/0.9 (i.e. >1.111) explain:
(a) how the (a,/3) values are to be determined; and
(b) how the use of the column interaction diagram in Fig. 7.1-6 is
affected in design.
SOLUTION
When the bending moment M is small compared with the axial load N, the
neutral axis may fall sufficiently far outside the column section for xi h to
exceed 1.111. When this happens, de is no longer equal to 0.9x; instead
del h = 1 for all values of xi h ;:::: 1.111.
(a) (a,/3) values for xlh > 1.111. aeone and f3eone are calculated from eqns
(7.1-3) and (7.1-4) but with xlh taken as 1.111 (that is, even when
xlh actually exceeds 1.111). a, 2 and /3, 2 are calculated as usual from
eqns (7 .1-7) to (7 .1-9), none of which require any modification.
Similarly, a, 1 and /3, 1 are calculated as usual from eqns (7.1-14) to
(7.1-16).
(b) Column interaction diagram in Fig. 7.1-6. Using the information in
(a) above, the reader should verify that:
(1) for x/h = 1.111, (a,/3) = (0.591, 0.020);
(2) for x/h = 1.5, (a,/3) = (0.626, 0.008);
(3) for x!h ;:::: 1.983, (a,/3) = (0.650, 0).
That is, as x/h increases beyond 1.111, the point (a,/3) progressively
approaches the a axis, until at xlh = 1.983 when both A~ 1 and A, 2
then reach the design strength 0.87/y in compression. For x/h =