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)

266 Eccentrically loaded columns and slender columns
which may be either in compression, inactive or in tension,
depending on the value of the xlh ratio (see Fig. 7.1-6);
b = the width of the column section;
d2 = the depth from the surface to the reinforcement A 52 (see Fig.
7.1-6);
d' =the depth to the reinforcement A~ 1 (see Fig. 7.1-6);
feu = the characteristic strength of the concrete;
/~ 1 = the stress in the reinforcement A~ 1 (compressive is +ve; tensile
is -ve) which should not be taken as more than 0.87/y;
fsz = the stress in the reinforcement As 2 (compressive is +ve) which
should not be taken as more than 0.87/y;
f = the characteristic strength of the reinforcement;
h = the depth of the column section in the plane of bending; and
x = the neutral axis depth measured from the more highly
compressed face.
Equations (7.3-1) and (7.3-2) were derived earlier as eqns (7.1-18) and
(7.1-19). Using these equations in design involves a process of trial and
error to see if a value of x can be found such that the right-hand sides of the
equations are not less than the left-hand sides. For convenience in design,
BS 8110: Part 3 provides a comprehensive set of design column interaction
diagrams for use as design charts, for both rectangular and circular
columns. One such design chart is reproduced in Fig. 7.3-1 and it is worth
noting that:
(a) BS 8110's design charts are based on the rectangular-parabolic stress
block (Fig. 4.4-3) and not on the simplified stress block (Fig. 4.4-5).
50
45
40
35
NE 30
- .c
E
~25
.a 20
"Z-
15
10
5
~ ~ l
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
' ·~
~ h'-. I
~
• Q
_a
. .!
t:'-~
~ ::'~s~
. N.1
~ :Kr--.-
~ 'K ~
~· :<.
K.
.,..;. ,_
-·< .·
~v
K~ ~-..
) ;-
....... /.
-4~ I
"'"6,.,
~ t....
!"'.~)
~
;..!'-...
f'x K
.-
~ K
' ~
v v
/
_/.
r(
r--b--1 1-
f~l
d 2 1-
l Asc }-
• 2 •
<II., L....-.- 1-
~ r~ !'-... o·" 1-
r> .><-. 'h feu 40
.
o·1 fy 460
r-. f'.. •
1-
---
).. K.~
K~ " -..e.:s
d/h 0·85
~ --~ ~~ -~ "-"" ~ I ·-
~--
;--·) ----~-- )- __ "S .... 7K~~
v. vv v
7
v T
./. /, /
0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
M/bh2 (N/mm2)
Fig. 7.3-1 Column design chart-BS 8110
/