### Trusses - Guidance on methods of analysis.

Generally, in light building trusses secondary stresses are negligible and are often ignored. Secondary stresses in light building trusses may be neglected provided that:

• the slenderness of the chord members in the plane of the truss is greater than 50, and

• the slenderness of most of the web members, about the same axis, is greater than 100.

However, in bridge trusses the secondary stresses can be a signiﬁcant proportion of the primary stresses and must be taken into account. The British Standard for the design of steel bridges, BS 5400: Part 3: 2000, requires the ﬁxity of the joints to be taken into account although axial deformation of the members may be ignored for the ultimate limit state.

The magnitude of the secondary stresses depends on a number of factors including member layout, joint rigidity, the relative stiffness of the incoming members at the joints and lack of ﬁt.

Manual methods of analysis may be used to analyse the stresses, particularly in simple trusses. For simple, statically-determinate trusses,methods of analysis include joint resolution, graphical analysis (Bow’s notation or Maxwell diagram) and the method of sections. The last method is particularly useful as the designer can limit the analysis to the critical sections.

Statically-indeterminate trusses are more laborious to analyse manually;methods available include virtual work, least work and the reciprocal theorem with inﬂuence lines. For a full discussion on these methods of analysis the reader should refer to textbooks on structural analysis.

Computers are nowadays readily available to designers and provide a useful means of analysing the most complex of trusses. In addition, joint and member rigidities can easily be incorporated in the modelling thus avoiding laborious hand calculations in determining out-of-balance moments caused by joint deformations.

Local stresses caused by loads not applied at the panel points, joint eccentricities and axial deformation should generally be calculated and superimposed on the direct stresses. However, stresses due to axial deformation are normally neglected except for bridge trusses and trusses of major importance.

Careful consideration must be given to the out-of-plane stability of a truss and resistance to lateral loads such as wind loads or eccentric loads causing torsion about their longitudinal axis.An individual truss is very inefﬁcient, and generally sufﬁcient bracing must be provided between trusses to prevent instability. In bridges, plan bracing is normally provided between trusses at the chord levels in addition to stiff end portals to prevent lateral instability.

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