Cross bracing is a traditional means of providing lateral stability to structures.
Richard Henderson of the SCI discusses some of the features of this structural system.
As structural engineers of a certain age will recall from their
student days a cross-braced panel is a statically indeterminate (or
hyperstatic) structural system: the forces in the members cannot
be determined simply by invoking equilibrium at the joints.
Determining the forces used to be an exercise in the application
of virtual work to structural problems.
When cross bracing is used to resist lateral loads, the bracing
members are usually designed as tension only and the designer
assumes that the element which forms the compression member
buckles elastically as the frame deforms so as to shorten the
relevant diagonal. This approach is favoured when analysing
and designing structures by hand as determining the buckling
resistance of the member is avoided. Crossed flats were
traditionally used for this purpose although angle bracing could
be used so the bracing members had some out of plane stiffness
to make handling easier. Cautionary tales regarding finishes
being pushed off by bowing bracing are told, leading to the
adoption of different bracing arrangements.
Flat bar bracing
A flat bar tension only bracing member in a 4 m × 6 m pinjointed
braced panel (say a 130 mm × 10 mm flat), bolted to the
opposing diagonal member at the centre, has a system length
of √13 m, assuming the tension diagonal provides a point of
restraint at the centre connection. (For a detailed assessment see
BS EN 1993-2 Annex D). The out of plane second moment of area
is 1.083 × 10⁴ mm⁴ giving an Euler buckling load:
Ncr = × 210 × 1.0833 × 10
13 × 10
The buckling resistance of the member Nb,Rd is very close to
the Euler load because of the high out of plane slenderness and
has a value of 1.69 kN, assuming S355 material. A compression
force of this magnitude is unlikely to have any effect on a bracing
connection designed for a tension force of 450 kN and is usually
An estimate of the bow in the compression member which is
making no contribution to the lateral resistance of the braced
panel can be made if the panel members are known, assuming
the member buckles into a circular arc. As an example, assume
203 UC 71 columns and a 406 × 178 UB 54 beam framing the
130 ×10 flat cross bracing (Figure 1), with a horizontal design
load of 374 kN applied to the braced panel.
The horizontal displacement of the top of the panel relative
to the bottom is 16.2 mm or 14.6 mm depending on at which
end of the beam the force is applied and the displacement
calculated. The extension of the bracing is about 12.1 mm (taking
the smaller displacement). If the shortening of the opposing
diagonal is taken as the same value, the bow is about 94 mm
(neglecting the elastic shortening of the bracing member under
the axial load). If the flat is unrestrained in the middle, the bow
is about 180 mm. Clearly, such a bow could be sufficient to push
dry lining off a wall concealing the braced panel. The low Euler
load indicates clearly that the member buckles elastically and will
behave satisfactorily when the loads are reversed.
An elastic stick finite element analysis that includes all the
members without somehow allowing for the buckling behaviour
of the bracing will produce a diagonal load in the compression
member which corresponds to its axial stiffness. In such an
analysis, the tension and compression diagonals share the load
and carry a force which is close to half the force in the member
Tubes used as tension only bracing
An alternative form of bracing member consisting of RHS tubes,
also assumed to behave as tension-only, is sometimes adopted.
Consider 90 × 50 × 5 RHS tubes with centrelines in the same
plane with a welded joint in the middle. Assume for the purpose
of this example that the middle joint is pinned and behaves in a
similar way to the crossed flats in providing a point of restraint
in the middle of the compression member. The minor axis
buckling resistance of the RHS for a length of √13 m is 71.6 kN by
calculation. The compression member therefore carries a force of
at least 71.6 kN which the connections must be able to sustain.
The maximum theoretical load on the connection is equal to
the Euler load and is equal to 78.4 kN, about 9.5% higher. If the
connection (perhaps a gusset) is designed for tension only, it
is possible that a load equal to the compression resistance is
sufficient to deform the gusset permanently, compromising its
ability to resist tension when the bracing load is reversed.
The amplified bow in the bracing member that corresponds to
the buckling resistance can be found from back calculation. The
assumed initial bow e0 is given by:
A ( –0.2 )
Figure 1: Braced panel 26