Civil Engineering Reference
In-Depth Information
P
σ
Work done = internal energy
⇒
stability
P
dyn
=
λ
P
stat
P
stat
= G
k
+
k
+
Q
k
ε
Figure 12.6
Linear elastic-perfectly plastic material model
σ
u
dyn
Figure 12.8
Work done versus internal energy © Arup
Key elements should be designed in accordance with the
following guidance:
ε
Figure 12.7
Bi-linear elasto-plastic material model with strain
The element should be designed for an accidental loading of
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hardening
34 kN/m² applied to the width of the element and any supported
cladding.
Any element that provides lateral restraint vital to the stability of
The dynamic effects may be taken into account utilising a
dynamic load factor as described above, or alternatively may
be calculated directly through energy balance between the
strain energy capacity of the structure and the work done by
the applied load, expressed dynamically (
Figure 12.8
).
Performance criteria for the limiting ductilities to which
members and connections may be subjected are found for seis-
mic design in ASCE 41 (American Society of Civil Engineers,
2006), which have been adapted for progressive collapse ana-
lysis in UFC 4-023-03 (United States Department of Defense,
2010) and may be adopted in an alternative loadpath analysis.
Data for simple connections in steel construction, however, are
limited, and performance criteria which account for the contri-
bution of the structural slab are not generally available.
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a key element should itself also be designed as a key element for
the same accidental loading.
The accidental loading should be applied to the member from
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all horizontal and vertical directions, in one direction at a time,
together with the reactions from other building components
attached to the member subject to the same accidental loading, but
limited to the maximum reactions that could reasonably be trans-
mitted considering the breaking resistances of such components
and their connections.
The applicable accidental loadcase assumed should be that given
■
above (equation 12.1), except in buildings predominantly used for
storage or where the imposed load is otherwise of a permanent
nature. In such cases the full imposed load should be used.
The imposed accidental load of 34 kN/m
² should be applied in
combination with the dead load using a partial load factor Ψ = 1.0
together with (typically) Ψ = 0.5 for the imposed load and Ψ = 0.2
for the wind load.
12.9.3 Key element design
Approved Document A states that where the notional removal
of columns/lengths of load-bearing walls would result in a
collapse that exceeds the limits on the tolerable area at risk
of collapse (i.e. where horizontal and vertical tying has been
implemented in a building whose structural grid is large, or
where it has not been possible to show suffi cient resilience in an
alternative loadpath analysis), the element should be designed
as a 'key element'. Key elements are designed for enhanced
loads to provide an additional level of robustness and decrease
the likelihood of failure under a range of accidental loads to
which the element might reasonably be subjected. Inasmuch
as the protection of the element has been shown to be crit-
ical to ensuring a disproportionate collapse does not occur,
Approved Document A recommends key element design only
as the method of last resort if horizontal and vertical tying or
alternative loadpath analysis alone is insuffi cient.
■
In adopting a key element approach, there are two essential
aspects to which the structural engineer must give considera-
tion in the design. The fi rst is that the rules for key element
design were fi rst developed in the wake of the Ronan Point col-
lapse when structural grids were much smaller than in modern
practice. In the late 1960s a 6 × 6 m grid was typical, the limit
of 70 m² given in the Fifth Amendment corresponding to two
such perimeter bays. In Eurocode 1 this limit is increased to
100 m²: this does not refl ect a greater tolerability of risk but
is merely a necessity refl ective of increasing structural spans,
corresponding to two perimeter bays on a 7.5 × 7.5 m grid.
However, even with this increase the limiting area of collapse is
frequently exceeded purely by virtue of the grid size, which in
