Technical
Figure 7: U-frame
action in purlin
restraint
NSC 25
June 18
The rule considered the necessary restraint at a plastic hinge
and may be expressed as:
Is
If
where,
fy is the design strength of the portal frame member
Is is the second moment of area of the purlin or rail in its major axis
If is the second moment of area of the frame member
B is the span of the rail or purlin
L1 and L2 are the distances each side of the plastic hinge to the
eaves or points of contraflexure, as shown in Figure 8.
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B(L1+L2)
L1L2
fy
190 × 103
Figure 8: Lengths L1 and L2 used to check restraint member stiffness
As an illustration, for a rafter (Figure 8), and a span of 35 m, a
reasonable assumption is that L1 = 3.5 m and L2 = 4 m
Assuming the member is a 457 × 191 × 67 UB, then If =
29400 cm4. If the rafter is S355 and the span of the purlin is 7 m,
the stiffness requirement for the purlin becomes:
Is
29400 × 104 × 355 × 7000 × (3500 + 4000)
190 × 103 × 3500 × 4000 × 104
= 206cm4
This order of inertia is provided by a 170 mm deep purlin, so
normal frame arrangements appear to be adequate.
Unorthodox situations
The selection of purlins and side rails is normally made based
on the span and loading on the member without any recourse
to the check illustrated above. For orthodox construction, the
relationship between the selected member and the stiffness
necessary to provide u-frame action appears to be satisfactory. An
issue can arise if the portal frames are long span, but nevertheless
spaced at typical centres. Since the purlin (or rail) selection is
based on the span and spacing of the secondary members, the
purlins and rails selected for a long span frame may be the same
as would be chosen for an orthodox span, but clearly the demands
on stiffness are much higher.
The general advice is that orthodox frames with usual member
sizes function satisfactorily with the ‘normal’ sizes and spacing
of secondary steelwork. Situations where more care is needed
are long span frames, and where the secondary steelwork is not
continuous.
References
1 Horne, M, R and Ajmani, J,L.
Failure of columns laterally supported on one flange: Discussion
The Structural Engineer, Vol 50, No. 7, July 1973
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