Compression members - The Behaviour and Design of Steel Structures to EC3 - page 96

3.12.8 Example 8 - checking a member with intermediate
axial loads

Problem. A5mlongsimplysupported457 × 191UB82compressionmemberof
S355steelwhosepropertiesaregiveninFigure3.28ahasconcentricaxialloadsof
N Ed and2 N Ed atitsends,andaconcentricaxialload N Ed atitsmidpoint.Atelastic
buckling the maximum compression force in the member is 2000 kN. Determine
the compression resistance.

Solution .
From Section 3.12.1, the cross-section is Class 4 slender and A eff =
10067 mm 2 .

N cr , z = 2000 kN.

10067 × 355
2000 × 10 3 = 1.337

A eff f y
N cr , z =

λ z =

For a rolled UB section (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 ( 1.337 − 0.2 ) + 1.337 2 ]= 1.587 6.3.1.2(1)

1

χ z = √

1.587 2 − 1.337 2 = 0.410

6.3.1.2(1)

1.587 +

N b , z , Rd = χ A eff f y
γ M 1

= 0.410 × 10067 × 355
1.0

= 1465 kN 6.3.1.1(3)

3.13 Unworked examples

3.13.1 Example 9 - checking a welded column section

The14.0mlongweldedcolumnsectioncompressionmemberofS355steelshown
inFigure3.30(a)issimplysupportedaboutbothprincipalaxesateachend( L cr , y =
14.0 m), and has a central brace that prevents lateral deflections in the minor
principalplane( L cr , z = 7.0m). Checktheadequacyofthememberforafactored
axial compressive force corresponding to a nominal dead load of 420 kN and a
nominal imposed load of 640 kN.

3.13.2 Example 10 - designing a UC section

Design a suitable UC of S275 steel to resist the loading of example 9 in
Section 3.13.1.