The Design of Modern Steel Bridges - TEDI

stress is equal to p 2 E/(Le/r) 2 ), similarly Mcr of a beam can be expressed in
terms of a slenderness parameter lLT as shown in equation (5.7a), namely
Mcr ¼ p 2 EZp=l 2
LT
when Zp is the plastic modulus of the section.
Then
Mcr
MU
¼ p2 E
l 2
LT
The above indicates that M cr/M U depends not just on l LT, but also on:
(1) s y for compact section
(2) s y, and the ratio of the plastic to elastic modulus, Z p/Z e, for non-compact
section.
Zp
MU
We can introduce another slenderness parameter b such that
Then
Mcr
MU
b 2 ¼ l 2
LT
¼ p2 EZp
MU
sy
355
MU
Mp
syMU
b 2 355 Mp
¼ p2E b 2 5700
¼
355 b 2
Using this relationship in equation (5.12) leads to:
MR
¼ 1
2 f1 þ½1þ ZŠ 5700=b2g MU
Rolled Beam and Plate Girder Design 105
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f1 þ½1þ ZŠ 5700=b 2 g 2
22 800=b 2
q
ð5:13Þ
Test results indicate that for small values of the slenderness parameter b, viz.
less than about 30, the limiting moment of resistance M R is not reduced below
M U, the ultimate moment of resistance based on yielding alone. The
imperfection parameter Z is chosen in such a way as to produce:
(1) MR/MU equal to 1.0 for stocky range (i.e. b-values less than about 30),
and
(2) good correlation with test results for higher values of b.
Account should also be taken of the fact that beams fabricated by longitudinally
welding flange and web plates will possess significant longitudinal compressive
welding residual stresses along various parts of the beam cross-section,
thus possibly bringing about an earlier onset of local compressive yielding and
consequent reduction in flexural stiffness. Reference [2] has adopted the