Civil Engineering Reference
In-Depth Information
5.6.4
Resistance of a cross-section to combined compression
and uni-axial bending
Design for a combination of load along the
x
-axis and bending about the
y
- or
z
-axis is based on an interaction curve between resistance to com-
pression,
N
Rd
, and resistance to bending about the relevant axis,
M
Rd
. The
method is explained with reference to Fig. 5.11. The plastic resistance
N
pl,Rd
is given above.
The complexity of hand methods of calculation for
M
pl,Rd
and other
points on the curve has been a disincentive to the use of composite
columns. It is quite easy to prepare a spreadsheet to do this. However, it
should be noted that when a rolled I- or H-section is represented by three
rectangles, as in the algebra given in Reference 17 and outlined below,
results will differ slightly from those by hand calculation, unless the
corner fillets are allowed for.
The assumptions are those used for calculating
M
pl,Rd
for beams: rectan-
gular stress blocks with structural steel at a stress
±
f
yd
, reinforcement at
±
f
sd
, and concrete at 0.85
f
cd
in compression or cracked in tension. Full
shear connection is assumed.
The complexity appears in the algebra. For major-axis bending of the
section shown in Fig. 5.10(a), there are five possible locations of the
plastic neutral axis, each leading to different expressions for
N
Rd
and
M
Rd
.
A practicable method is to guess a position for the neutral axis, and
calculate
N
Rd
by summing the forces in the stress blocks, and
M
Rd
by
taking moments of these forces about the centroid of the uncracked sec-
tion. This gives one point on Fig. 5.11. Other points, and hence the curve,
are found by repeating the process.
Figure 5.11
Polygonal approximation to M-N interaction curve
