Compression members - The Behaviour and Design of Steel Structures to EC3 - page 91

Member buckling resistance .

A eff / A
λ 1

A eff f y

N cr ,y = L cr ,y

12000
( 18.8 × 10 )

10067 / 10400
93.9 × 0.924

λ y = = = 0.724

i y

6.3.1.3(1)

A eff / A
λ 1

A eff f y

10067 / 10400
93.9 × 0.924

N cr , z = L cr , z

6000
( 4.23 × 10 )

λ z = =

i z

= 1.608 > 0.724

6.3.1.3(1)

Bucklingwilloccurabouttheminor( z )axis. ForarolledUBsection(with h / b >
1.2 and t f ≤ 40 mm), buckling about the z -axis, use buckling curve (b) with
α = 0.34

T6.2,T6.1

Φ z = 0.5 [ 1 + 0.34 ( 1.608 − 0.2 ) + 1.608 2 ]= 2.032

6.3.1.2(1)

1
2.032 + √ 2.032 2 − 1.608 2 = 0.305

χ z = 6.3.1.2(1)

N b , z , Rd = χ A eff f y
γ M 1

= 0.305 × 10067 × 275
1.0

= 844 kN > 561 kN = N Ed
6.3.1.1(3)

and so the member is satisfactory.

3.12.2 Example 2 - designing a UC compression member

Problem. Design a suitable UC of S355 steel to resist the loading of example 1 in
Section 3.12.1.
Design axial load. N Ed = 561 kN, as in Section 3.12.1.
Target area and first section choice.
Assume f y = 355 N/mm 2 and χ = 0.5
A ≥ 561 × 10 3 /( 0.5 × 355 ) = 3161 mm 2

Try a 152 × 152 UC 30 with A = 38.3 cm 2 , i y = 6.76 cm, i z = 3.83 cm,
t f = 9.4 mm.
ε = ( 235 / 355 ) 0.5 = 0.814

T5.2

N cr , y = L cr , y

Af y 1

λ 1 =

12000
( 6.76 × 10 )

1
93.9 × 0.814 = 2.322 6.3.1.3(1)

λ y =

i y

N cr , z = L cr , z

Af y 1

λ 1 =

6000
( 3.83 × 10 )

1
93.9 × 0.814 = 2.050 < 2.322
6.3.1.3(1)

λ z =

i z