Technical
26 NSC
Mar 20
Assuming S355 steel, from the Blue Book7, a 356 × 406 UC 467
has a resistance Nb,z,Rd of 17.1 MN with a buckling length of 4 m.
A 356 x 406 UC 287 has a resistance Nb,z,Rd of 10.6 MN for the same
buckling length. These section sizes will be adopted for the lower
and upper lengths of column respectively. Relevant properties
for the upper column length are given in Table 2.
Effect of bending moment
Based on a 4 m storey height, for the minor axis, the elastic
critical load is
Ncr =
EIz
L
× 210 × 10 × 3.87 × 10
= = 50,131 kN (50.13 MN)
16
The amplifier due to axial loads is:
N50.13
cr
= = 1.27
Ncr – N50.13 – 10.5
Ed
The initial bow imperfection is given by:
eo =
We
A ( – 0.2)
The non-dimensional slenderness and initial bow imperfection
are then:
=
Aƒy
Ncr
3.66 × 10 × 345
= = 0.502
50.13
1940
366
eo = × 0.49 × (0.502 – 0.2) = 0.784 cm = 7.8 mm
The amplified bow is 9.9 mm or about 10 mm. At the splice
position, say 1.2 m up the column, the proportion of the
maximum bow is given by sin(π × (1.2/4.0)) = 0.81. The design
minor axis bending moment at the splice due to strut action is
therefore:
Mz,Ed = 0.81 × 0.01 × 10,500 = 85.1 kNm.
A similar calculation for the major axis strut moment gives
My,Ed = 49.3 kNm. If the reactions from the floor beams at the
relevant floor levels are equal on opposite sides of the column,
the strut moment is the only bending moment on the splice.
The axial and minor axis bending stresses are given by:
ƒtot = ƒc+ƒb = 10.5 = 287 + 43.9 MPa
3.66 × 10
+ 85.1 × 10
1940 × 10
The cross section is always in compression at the splice.
Material for 25% of compressive force
Typical details of splices are given in The Green Book, which have
been modified slightly for this example. The proposed
arrangement is shown in Figure 1.
According to BS EN 1993-1-8 para 6.2.7.1(14), splice materials
should be provided to transmit at least 25% of the maximum
compressive force in the column (10.5 MN), which is 2625 kN, The
bolts and splice plates will be verified against this design force.
Assuming ƒy = 345 MPa for the splice material (over 16 mm thick),
the area required is 7610 mm2. With two flange cover plates, the
area provided is 14000 mm2 (fastener holes can be ignored
according to BS EN 1993-1-1 para 6.2.4(3)).
M30 property class 8.8 bolts have been chosen: three pairs in
each flange in single shear and one pair in the web in double
shear, on each side of the joint. Choosing property class 10.9
bolts does not reduce the number of bolts required. The
resistances of a bolt are given in the Blue Book as 215 kN in single
shear and 431 kN in double shear.
The shear resistance of the bolts in the flanges of the upper
half of the joint is reduced by the presence of packs, which are
21.5 mm thick. The reduction factor βp is given by clause 6.6.1(12)
as
p = 9d = 0.89
8d + 3tp
= 9 × 30
8×30 + 3×21.5
The shear resistance of the bolts in the flanges of the upper
half of the joint is therefore
215 × 0.89 = 191 kN
With the particular geometry of the bolt groups shown in
24
Property Value
Major axis second moment of area Iy (cm4) 999000
Minor axis second moment of area Iz (cm4) 38700
Major axis elastic modulus Wy (cm3) 5070
el,Minor axis elastic modulus Wz (cm3) 1940
el,Area A (cm2) 366
Flange thickness tf (mm) 36.5
Web thickness tw (mm) 22.6
Yield strength ƒy (MPa) 345 (16 ≤ tf ≤ 40)
Imperfection factor, α for rolled section
0.49 (minor axis)
with h/b ≤ 1.2, tf ≤100 mm
0.34 (major axis)
Table 2: Design parameters
/The_Blue_Book
/Steel_section_sizes
/Design
/The_Green_Books