Frames - The Behaviour and Design of Steel Structures to EC3 - page 385

N cr = π 2 × 210000 × 5259 × 10 4 / 5000 2 N = 4360 kN
h
b = 206.2 / 204.3 = 1.009 < 1.2, t f = 12.5 < 100, and so for a S275 steel
UC buckling about the y axis, use buckling curve b.

T6.2

α = 0.34 T6.1

λ y = ( 66.3 × 10 2 × 275 )/( 4360 × 10 3 ) = 0.647 6.3.1.2(1)

Φ = 0.5 ×[ 1 + 0.34 × ( 0.647 − 0.2 ) + 0.647 2 ]= 0.785 6.3.1.2(1)

1

χ y = √

0.785 2 − 0.647 2 = 0.813

6.3.1.2(1)

0.785 +

UsingAnnexA,

1 − 137.2 / 4360
1 − 0.813 × 137.2 / 4360 = 0.994

µ y = TA.1

ψ y = 0 / 144.9 = 0 TA.2
C my = C my ,0 = 0.79 + 0.21 × 0 + 0.36 × ( 0 − 0.33 ) × 137.2 / 4360 TA.2
= 0.786
w y = 567 × 10 3 / 510 × 10 3 = 1.112 < 1.5

TA.1

λ max = λ y = 0.647 TA.1

N Rk = N pl , Rd × γ M 0 = 1823 × 1.0 = 1823 kN 5.3.2(11)

γ M 1 = 1.0 6.1

n pl = 137.2 /( 1823 / 1.0 ) = 0.0753 TA.1

2 − 1.6

1.112 × 0.785 2 × 0.647 − 1.6

C yy = 1 + ( 1.112 − 1 )

1.112

× 0.785 2 × 0.647 2 × 0.0753 − 0 = 1.009 TA.1

0.994
1 − 137.2 / 4360 ×

1
1.009 = 0.798

k yy = 0.785 × 1.0 × TA.1

Substituting into equation 6.61 of EC3,

137.2
0.813 × 1823 + 0.798 ×

144.8
1.0 × 155.9 = 0.834 < 1.0

6.3.3(4)

and so the member resistance is adequate.