NSC 29
March 18
60
518
My,Ed
Mb,Rd
My,Ed
Mb,Rd
0.6 (1 + 0.8 )= 0.61
kyy = 0.6 (1 + (0.276 – 0.2) ) 800
0.6 (1 + 1.4 )= 1.16
kzz = 0.6 (1 + (2 × 1.536 – 0.6) ) 800
kzy = 0.6 (1 – ) = 0.81
Ncr =
2EI
L2
=
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Technical
Substituting the known values in the above expression:
800
+ + 0.6
= 0.89 > 0.78
1200
15
82.8
In this instance, the simple expression shows that the member
is not satisfactory.
A reasonably simple version
Mike Banfi of Arup proposed a pair of simplified expressions in a
technical note published in 20083. For Class 1 or 2 sections, the
simplified expressions are:
NEd
Nb,y,Rd
+ Cmy 0.85 and
+ Cmz
Mz,Ed
Mc,z,Rd
NEd
Nb,z,Rd
+ 0.78 0.78
+ Cmz
Mz,Ed
Mc,z,Rd
Referring to Table B3, Cmy = Cmz = 0.6. Substituting the known
values:
800
3560
= 0.40 0.85, OK
60
518
+ 0.6
15
82.8
+ 0.6
800
1200
= 0.87 > 0.78. U/S
60
518
+ 0.6
15
82.8
+ 0.78
This second version also indicates that the member is
unsatisfactory.
The full version
Using the expressions in the Standard demands the intermediate
values of non-dimensional slenderness for flexural buckling in
both axes, which are shown in Table 2.
Table 2: Flexural buckling data
The interaction factors follow:
800
3560
3560
800
1200
1200
0.1 × 1.536
(0.6 – 0.25)
800
1200
0.1
(0.6 – 0.25)
1200
kyz = 0.6kzz = 0.6 × 1.16 = 0.70
Then the full interaction expression becomes
800
60
+ 0.70
= 0.42 1, OK
3560
518
15
82.8
+ 0.61
800
1200
= 0.97 1, OK
60
518
+ 1.16
15
82.8
+ 0.81
Using the full expression demonstrates the member is (just)
satisfactory. There are plenty of opportunities to make a mistake
along the way, so careful attention to detail is important.
Software will of course make the job easier. For manual
calculations, the simplified versions of the expressions proposed
by Mike Banfi are recommended, although it may be noted that
there is not much more effort to complete the comprehensive
expressions given in the Eurocode. A tool to verify members
in combined bending and compression is available on
steelconstruction.info, which may be used to confirm the results
presented in the example.
References
1 Georgakis, M. Couchman, G, H.
Steel building design: Concise Eurocodes (P362)
SCI, 2017
2 Manual for the design of steelwork building structures to Eurocode 3
The Institution of Structural Engineers, 2010
3 Banfi, M
Simplified expressions for compression and bending
The Structural Engineer, November 2008
Major axis 47396 0.276
Minor axis 1534 1.536
Afy
Ncr
/Design_software_and_tools#Combined_axial_compression_and_bending_resistance
/
/www.rainhamsteel.co.uk
link