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Steel Designers' Manual - 6th Edition (2003)
450 Beams
(a)
unit
load
U—frame
Fig. 16.9 U-frame restraint action. (a) Components of U-frame. (b) U-frame elastic support
stiffness
laterally restrained and the web members, by virtue of their lateral bending stiffness,
inhibit lateral movement of the top chord. It is then only a small step to regard
this top chord as a strut provided with a series of intermediate elastic spring
restraints against buckling in the horizontal plane. The stiffness of each support corresponds
to the stiffness of the U-frame comprising the two vertical web stiffeners
and the cross-girder and deck shown in Fig. 16.9.
The elastic critical load for the top chord is
Pcr EI LE
(16.5)
in which LE is the effective length of the strut.
If the strut receives continuous support of stiffness (1/d LR) per unit length, in
which LR is the distance between U-frame restraints, and buckles in a single halfwave,
this load will be given by
2 2 2 2
Pcr = ( p EI/ L )+ ( L / p dLR)
(16.6)
which gives a minimum value when
025 .
L= p( EIdLR) (16.7)
giving
05 .
Pcr = 2(
EI/ dLR)
(16.8)
or
025 .
LE = ( p/ ÷ 2)(
EIdLR) (16.9)
If lateral movement at the ends of the girder is not prevented by sufficiently
stiff end U-frames, the mode will be as shown in Fig. 16.10. The effective length is
then:
025 .
LE = p( EIdLR) (16.10)
In clause 9.6.4.1.1.2 of BS 5400: Part 3 the effective length is given by
2
= p 2 /
E c Rd
025 .
L = k( EI L )
(b)
unit
load