Committee for Specifications for the Design of Committee/Subcommittee Ballot: XXX
Cold-Formed Steel Structural MembersAttachment A
Subcommittee 10, Element Behavior and Direct StrengthDate: November 3, 2008
1.2.2Beam Design
The nominal flexural strength [resistance], Mn, of beams without inelastic reserve shall be the minimum of Mne, Mn, and Mnd as given in Sections 1.2.2.1 to 1.2.2.3. For beams capable of inelastic reserve the nominal flexural strength [resistance], Mn, is defined in Section 1.2.2.4. For beams meeting the geometric and material criteria of Section 1.1.1.2, bandb shall be as follows:
b=1.67(ASD)
b=0.90(LRFD)
=0.85(LSD)
For all other beams, and of the main Specification, Section A1.1(b), shall apply. The available strength [factoredresistance] shall be determined in accordance with applicable method in Section A4, A5, or A6 of the main Specification.
1.2.2.1Lateral-Torsional Buckling
The nominal flexural strength [resistance], Mne, for lateral-torsional buckling shall be calculated in accordance with the following:
(a)For Mcre < 0.56My
Mne=Mcre(Eq. 1.2.2-1)
(b)For 2.78My Mcre 0.56My
Mne=(Eq. 1.2.2-2)
(c)For Mcre > 2.78My
Mne=My(Eq. 1.2.2-3)
where
Mcre=Critical elastic lateral-torsional buckling moment determined by analysis in accordance with Section 1.1.2
My=SfFy(Eq. 1.2.2-4)
where
Sf=Gross section modulus referenced to the extreme fiber in first yield
1.2.2.2Local Buckling
The nominal flexural strength [resistance], Mn, for local buckling shall be calculated in accordance with the following:
(a)For 0.776
Mn=Mne(Eq. 1.2.2-5)
(b)For > 0.776
Mn=(Eq. 1.2.2-6)
where
=(Eq. 1.2.2-7)
Mne=A value as defined in Section 1.2.2.1
Mcr=Critical elastic local buckling moment determined by analysis in accordance with Section 1.1.2
1.2.2.3Distortional Buckling
The nominal flexural strength [resistance], Mnd, for distortional buckling shall be calculated in accordance with the following:
(a)For d 0.673
Mnd=My(Eq. 1.2.2-8)
(b)For d > 0.673
Mnd=(Eq. 1.2.2-9)
where
d=(Eq. 1.2.2-10)
My=A value as given in Eq. 1.2.2-4
Mcrd=Critical elastic distortional buckling moment determined by analysis in accordance with Section 1.1.2
1.2.2.4Inelastic Reserve Capacity
Inelastic reserve is available in any beam where the minimum of Mne, Mn, and Mnd as given in Sections 1.2.2.1 to 1.2.2.3 is equal to My.
The nominal flexural strength [resistance], Mn, of beams with inelastic reserve shall be the minimum of Mne, Mn, and Mnd as given in Sections 1.2.2.4.1 - 1.2.2.4.3.
1.2.2.4.1 Inelastic Lateral-Torsional Buckling
The nominal flexural strength [resistance], Mne, for inelastic lateral-torsional buckling shall be calculated in accordance with the following:
(a)For Mcre 2.78My
(Eq. 1.2.2-11)
where
My =Yield moment as given in Eq. 1.2.2-4
Mcre =Critical elastic lateral-torsional buckling moment determined by analysis in accordance with Section 1.1.2
Mp=ZFy(Eq. 1.2.2-12)
where
Z =Plastic section modulus about the axis of bending
(b)For Mcre 2.78My
inelastic reserve capacity is unavailable and Mne is defined by Section 1.2.2.1
1.2.2.4.2 Inelastic Local Buckling
The nominal flexural strength [resistance], Mn, for inelastic local buckling shall be calculated in accordance with the following:
(a)For 0.776
For sections symmetric about the axis of bending
or for sections with first yield in compression:
(Eq. 1.2.2-13)
where
(Eq. 1.2.2-14)
(Eq. 1.2.2-15)
My =Yield moment as given in Eq. 1.2.2-4
Mcr=Critical elastic local buckling moment determined by analysis in accordance with Section 1.1.2
Mp=Plastic moment as given in Eq. 1.2.2-12
For sections with first yield in tension:
(Eq. 1.2.2-16)
where
(Eq. 1.2.2-17)
, maximum tension strain multiplier
=Compressive strain multiplier as defined in Eq. 1.2.2-14
My =Yield moment as given in Eq. 1.2.2-4
Myc=Moment at which first yield occurs in compression. For sections with first yield in tension the moment at which yielding first occurs in compression in the partially plastified cross-section is Myc; however, Myc = My may be used as a conservative approximation.
Mp=Plastic moment as given in Eq. 1.2.2-12
(b)For > 0.776
inelastic reserve capacity is unavailable and Mn is defined by Section 1.2.2.2
1.2.2.4.3 Inelastic Distortional Buckling
The nominal flexural strength [resistance], Mnd, for inelastic distortional buckling shall be calculated in accordance with the following:
(a)For d0.673
For sections symmetric about the axis of bending
or for sections with first yield in compression:
(Eq. 1.2.2-18)
where
(Eq. 1.2.2-19)
(Eq. 1.2.2-20)
My =Yield moment as given in Eq. 1.2.2-4
Mcrd=Critical elastic distortional buckling moment determined by analysis in accordance with Section 1.1.2
Mp=Plastic moment as given in Eq. 1.2.2-12
For sections with first yield in tension:
(Eq. 1.2.2-21)
where
Myt3=Yield moment when tension fiber is at Cyt times the yield strain as defined in Eq. 1.2.2-17.
=Compressive strain multiplier as defined in Eq. 1.2.2-14
Myc=Moment at which first yield occurs in compression. For sections with first yield in tension the moment at which yielding first occurs in compression in the partially plastified cross-section is Myc; however, Myc = My may be used as a conservative approximation.
Mp=Plastic moment as given in Eq. 1.2.2-12
(b)For d > 0.673
inelastic reserve capacity is unavailable and Mnd is defined by Section 1.2.2.3