Beam-columns - The Behaviour and Design of Steel Structures to EC3 - page 322

whichisasimplelinearextensionoftheuniaxialcross-sectionresistancelimitation
ofequation7.24.ForClass1plasticandClass2compactsections,amoreeconomic
alternative is provided by a modification of equation 7.63 to

M y , Ed
M N , y , Rd

α M z , Ed

M N , z , Rd

β

+ ≤ 1 (7.69)

in which α = 2.0 and β = 5 n ≥ 1 for equal flanged I-sections, α = β = 2.0 for
circular hollow sections, and α = β = 1.66 /( 1 − 1.13 n 2 ) ≤ 6 ) for rectangular
hollow sections, where n = N Ed / N pl , Rd . Conservatively, α and β may be taken
as unity.

7.4.2.2 Member resistance

Thegeneralbiaxialbendingmemberresistancelimitationsaregivenbyextensions
of equations 7.61 and 7.60 for uniaxial bending to

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

N Ed

M b , Rd + k yz M z , Ed M z , Rd ≤ 1

(7.70)

and

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

N Ed

M b , Rd + k zz M z , Ed M z , Rd ≤ 1,

(7.71)

both of which must be satisfied.
Alternative expressions for the interaction factors k yy , k yz , k zy , and k zz are pro-
videdinAnnexesAandBofEC3.TheAnnexBformulationsforthedetermination
oftheinteractionfactors k ij arelesscomplexthanthosesetoutinAnnexA,result-
ing in quicker and simpler calculations, though generally at the expense of some
structural efficiency [28]. Annex B may therefore be regarded as the simplified
approachwhereasAnnexArepresentsamoreexactapproach.Thebackgroundto
thedevelopmentoftheAnnexAinteractionfactorshasbeendescribedin[29],and
that of theAnnex B interaction factors in [30].
For columns in simple construction, the bending moments arising as a result
of the eccentric loading from the beams are relatively small, and much simpler
interaction expressions can be developed with no significant loss of structural
efficiency.Thus,ithasbeenshown[31]thatforsimpleconstructionwithhot-rolled
I- and H-sections and with no intermediate lateral restraints along the member
length, equations 7.70 and 7.71 may be replaced by the single equation

N b , z , Rd + M y , Ed

N Ed

M b , Rd + 1.5 M z , Ed M c , z , Rd ≤ 1

(7.72)