Beam-columns - The Behaviour and Design of Steel Structures to EC3 - page 332

N Ed
χ y N Rk /γ M 1

< C my 1 + 0.8 = 0.90

200 × 10 3
0.693 × 47.2 × 10 2 × 275 / 1.0

×

1 + 0.8 ×

= 1.060

TB.1

so that k yy = 1.052

N b , y , Rd + k yy M y , Ed

N Ed

M c , y , Rd = 200 900 + 1.052 × 45.0 132.8

= 0.222 + 0.356 = 0.579 < 1 6.3.3(4)

and the member resistance is adequate.

Beam-column member resistance - more exact approach (Annex A).

λ max = λ y = 0.960 TA.1

N cr , y = π 2 EI y / L cr = π 2 × 210000 × 5537 × 10 4 / 9000 2 = 1417kN.

Since there is no lateral buckling, λ 0 = 0, b LT = 0, C mLT = 1.0 TA.1

C my = C my ,0 = 1 − 0.18 N Ed / N cr , y = 1 − 0.18 × 200 / 1417 = 0.975 TA.2

w y = W pl , y

W el , y = 483 433 = 1.115,

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 y C my λ max − 1.6 w y C my λ 2

C yy = 1 + ( w y − 1 ) n pl − b LT

max

≥ W el , y
W pl , y

2 − 1.6

1.115 × 0.975 2 × 0.960 − 1.6

= 1 + ( 1.115 − 1 )

1.115

× 0.975 2 × 0.960 2 × 0.154 − 0
= 0.990 > 0.896 = 1 / 1.115 TA.1