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The nominal
flexural strength is the smallest value computed based on the following
limit states of LTB, FLB, and WLB (LRFD F1 and Appendix F1).
1. For l £ lp
2. For lp < l £ lr
For the limit state of LTB
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(5.32)
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For the limit state of FLB and WLB:
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(5.33)
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3. For l > lr
For LTB and FLB:
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(5.34)
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For WLB:
For l of the web > lr, design as a plate
girder (see Chapter 9).
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Mp
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= plastic moment = ZFy
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Mcr
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= buckling moment
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Mr
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= limiting buckling
moment, equal to Mcr
when l = lr
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l
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= controlling
slenderness parameter
= minor axis slenderness ratio Lu/ry for LTB
= flange width-thickness ratio b/tf for FLB
= web depth-thickness ratio for h/tw for WLB
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lp
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= limiting slenderness
parameter for compact sections
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(largest value of l for which Mn = Mp)
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lr
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= limiting slenderness parameter for
sections with slender elements
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(largest value of l for which buckling is
inelastic)
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Fcr
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= critical stress
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Sx
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= section modulus
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Z
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= plastic modulus
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Lu
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= unbraced length
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ry
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= radius of gyration
about minor axis
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The
quantity Cb is a factor
to take into account the non-uniform bending moment distribution over an
unbraced segment (LRFD F1.2a).
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(5.35)
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MA
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= absolute value of moment at quarter
point of the unbraced segment
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MB
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= absolute value of moment at mid-point
of the unbraced segment
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MC
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= absolute value of moment at
three-quarter point of the unbraced segment
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Mmax
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= absolute value of maximum moment in
the unbraced segment
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The lp and lr values corresponding to FLB and WLB have been
summarized in Table 5.3. The slenderness parameter lp corresponding to LTB
for doubly symmetric I shapes bent about major axis is (LRFD F1.2a)
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(5.36)
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The slenderness parameter lr corresponding to LTB
for I shapes bent about the major axis is (LRFD F1.2a)
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(5.37)
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where
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(5.38)
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(5.39)
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E
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= modulus of elasticity
of steel (29,000 ksi)
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G
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= shear modulus of steel (11,200 ksi)
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A
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= cross-sectional area (in.2)
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FL
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= smaller of (Fyf
- Fr) or Fyw
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J
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= torsional constant (in.4)
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Cw
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= warping constant (in.6),
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Iy
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= moment of inertia about minor axis (in.4)
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It should
be noted that there are no LTB lp and lr limits for any I shape bent about its minor
axis (LTB is not a problem in this case).
The critical stress for Fcr LTB for bending about the major axis is given by
and for FLB
of the rolled shapes is given by
When the bending is about the major axis, the
limiting buckling moment Mr
for LTB and FLB is given by
and for
WLB is given by
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(5.43)
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For
bending about the minor axis, Mr
needs to be evaluated for FLB only, and its value is specified by
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(5.44)
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