Compression members - The Behaviour and Design of Steel Structures to EC3 - page 64

3.5.4 Design procedures

Forthedesignofacompressionmember,thedesignaxialforce N Ed isdetermined
byarationalframeanalysis,asinChapter8,orbystaticsforastaticallydeterminate
structure.Thedesignloads(factoredloads) F Ed arefortheultimatelimitstate,and
are determined by summing up the specified loads multiplied by the appropriate
partial load factors γ F (see Section 1.5.6).
To check the compression resistance of a member, both the cross-section
resistance N c , Rd and the member buckling resistance N b , Rd should generally be
considered, though it is usually the case for practical members that the buckling
resistance will govern. The cross-section resistance of a compression member
N c , Rd must satisfy

N Ed ≤ N c , Rd (3.25)

in which

N c , Rd = Af y /γ M 0 (3.26)

for a fully effective section, in which γ M 0 is the partial factor for cross-section
resistance (with a recommended value of 1.0 in EC3), or

N c , Rd = A eff f y /γ M 0 (3.27)

for the cross-sections that are susceptible to local buckling prior to yielding.
The member buckling resistance N b , Rd must satisfy

N Ed ≤ N b , Rd (3.28)

where the member buckling resistance N b , Rd is given by equation 3.22.
The procedure for checking a specified compression member is summarised
in Figure 3.14. The cross-section is checked to determine if it is fully effective
( A eff = A , where A is the gross area) or slender (in which case the reduced
effectivearea A eff isused),andthedesignbucklingresistance N b , Rd isthenfound
and compared with the design compression force N Ed .
An iterative series of calculations is required when designing a compression
member,asindicatedinFigure3.14.Aninitialtrialsectionisfirstselected,either
by using tabulations, formulations or graphs of design buckling resistance N b , Rd
versuseffectivelength L cr , orbymakinginitialguessesfor f y , A eff / A , and χ (say
0.5) and calculating a target area A . Atrial section is then selected and checked.
If the section is not satisfactory, then a new section is selected using the latest
values of f y , A eff / A , and χ , and the checking process is repeated. The iterations
usuallyconvergewithinafewcycles,butconvergencecanbehastenedbyusingthe
meanofthepreviousandcurrentvaluesof χ inthecalculationofthetargetarea A .
Aworkedexampleofcheckingtheresistanceofacompressionmemberisgiven
in Section 3.12.1, while worked examples of the design of compression members
are given in Sections 3.12.2 and 3.12.3.