Beam-columns - The Behaviour and Design of Steel Structures to EC3 - page 335

N Ed
χ z N Rk /γ M 1

> C mz 1 + 1.4

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

= 0.550 × 1 + 1.4 × = 0.893 TB.1

k zz = 0.893 TB.1

N b , z , Rd + k zz M z , Ed

N Ed

M c , y , Rd = 200 449 + 0.893 8.1 32.7 = 0.445 + 0.221 = 0.666 ≤ 1

6.3.3(4)

and the member resistance is adequate.

Beam-column member resistance - more exact approach (Annex A).
From Section 7.7.2, λ y = 0.960

λ max = λ z = 1.490 > 0.960 = λ y TA.1

N cr , z = π 2 EI z / L cr , z = π 2 × 210000 × 571 × 10 4 / 4500 2 N = 584.4kN.

qL 4
185 EI z =

3.2 × 4500 4
185 × 210000 × 571 × 10 4 = 5.92mm,

| δ x | =

M z , Ed ( x ) = 8.1kNm

π 2 EI z | δ x | N Ed

N cr , z L 2 M z , Ed ( x ) − 1

C mz = C mz ,0 = 1 +

π 2 × 210000 × 571 × 10 4 × 5.9
4500 2 × 8.1 × 10 6

200
584.4 = 0.804 TA.2

= 1 + − 1

w z = W pl , z

W el , z = 119 78 = 1.526 > 1.5,

200 × 10 3
47.2 × 10 2 × 275 / 1.0 = 0.154

N Ed
N Rk /γ M 1 =

n pl = TA.1

2 − 1.6

w z C mz λ max − 1.6

≥ W el , z
W pl , z w z C mz λ 2

C zz = 1 + ( w z − 1 ) n pl − e LT

max

1.5 × 0.804 2 × 1.490 2

2 − 1.6

1.5 × 0.804 2 × 1.490 − 1.6

= 1 + ( 1.5 − 1 )

× 0.154 − 0 = 0.958 > 0.667 = 1 / 1.5

TA.1