Beam-columns - The Behaviour and Design of Steel Structures to EC3 - page 341

Beam-column member resistance - simplified approach (Annex B).
Checksarerequiredagainstequations6.61and6.62ofEC3.Fromtheappropriate
parts of Sections 7.7.2-7.7.4,

k yy = 1.052, k zz = 0.893, k zy = 0.873, N b , y , Rd = 900 kN,
M b , Rd = 121.4 kNm, M z , Rd = 32.7 kNm, and N b , z , Rd = 449 kN.
k yz = 0.6 k zz = 0.6 × 0.893 = 0.536

TB.1

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

N Ed

M b , Rd + k yz M z , Ed M z , Rd = 200 900 + 1.052 × 45.0 121.4 + 0.536

× 8.1

32.7 = 0.222 + 0.390 + 0.133 = 0.745 < 1

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

N Ed

M b , Rd + k zz M z , Ed M z , Rd = 200 449 + 0.873 × 45.0

121.4

+ 0.893 × 8.1

32.7 = 0.445 + 0.324 + 0.221 = 0.990 < 1
and the member resistance is adequate.
Beam-column member resistance - more exact approach (Annex A).
Checks are required against equations 6.61 and 6.62 of EC3. Relevant details are
taken from the appropriate parts of Sections 7.7.2, 7.7.3, and 7.7.4.

M y , Ed
χ LT M pl , y , Rd

M z , Ed

b LT = 0.5 a LT λ 0

M pl , z , Rd = 0.5 × 0.997 × 1.093 2

121.4 × 8.1

45

×

32.7 = 0.0546

TA.1

λ 2
0
5 + λ 4
z

M y , Ed
C my χ LT M pl , y , Rd = 10 × 0.997

c LT = 10 a LT

1.093 2
5 + 1.490 4 ×

45
0.990 × 121.4 = 0.449

×

TA.1

λ 0
0.1 + λ 4
z

M y , Ed
C my χ LT M pl , y , Rd

M z , Ed
C mz M pl , z , Rd

d LT = 2 a LT

1.093
0.1 + 1.490 4 ×

45
0.990 × 121.4 ×

8.1
0.804 × 32.7

= 2 × 0.997 ×

= 0.0500 TA.1

λ 0
0.1 + λ 4
z

M y , Ed
C my χ LT M pl , y , Rd = 1.7 × 0.997 ×

1.093
0.1 + 1.490 4

e LT = 1.7 a LT

45
0.990 × 121.4 = 0.138

× TA.1