Beam-columns - The Behaviour and Design of Steel Structures to EC3 - page 337

FromSection7.7.3, N b , z , Rd = 449kN, χ z = 0.346, λ z = 1.490, λ max = 1.490,
N cr , z = 584.4 kN, and w z = 1.5.
ψ = 0, C mLT = 0.6 + 0.4 ψ = 0.6 > 0.4 TB.3

0.1 λ z
( C mLT − 0.25 )

N Ed
χ z N Rk /γ M 1

1 −

1 − 0.1 × 1.490

200 × 10 3
0.346 × 47.2 × 10 2 × 275 / 1.0

=

( 0.6 − 0.25 ) ×

= 0.810

0.1
( C mLT − 0.25 )

N Ed
χ z N Rk /γ M 1

1 −

1 −

200 × 10 3
0.346 × 47.2 × 10 2 × 275 / 1.0

0.1
( 0.6 − 0.25 ) ×

= = 0.873 TB.1

k zy = 0.873 TB.1

N b , z , Rd + k zy M y , Ed

N Ed

M b , Rd = 200 449 + 0.873 × 45.0

121.4 = 0.445 + 0.324 = 0.769 < 1
6.3.3(4)

and the member out-of-plane resistance is adequate.

Beam-column member buckling resistance - more exact approach (Annex A).
The member in-plane resistance was checked in Section 7.7.2, but as for the sim-
plified approach, equation 6.61 should be checked by taking the lateral buckling
resistance in place of the in-plane major axis bending resistance. The interaction
factor k yy also requires re-calculating due to the possibility of lateral buckling.

λ y = 0.960, λ max = λ z = 1.490 TA.1

Using M zx = 111.2 kNm from Section 6.15.2,
λ 0 =

132.8 / 111.2 = 1.093

TA.1

Since cross-section is doubly-symmetrical, using equation 7.37 with

( 5537 × 10 4 + 571 × 10 4 )/ 47.2 × 10 2 i p = ( I y + I z )/ A =

= 113.8 mm,

GI t + π 2 EI w N cr , T = 1

i p

L cr , T

81000 × 15.3 × 10 4 + π 2 × 210000 × 0.0857 × 10 12
4500 2

1
113.8 2

=

= 1636 kN.