## N N

Stiffness of each elastic supports = C

span a = t/m, where m is the number of supported elements along the member length

span a = t/m, where m is the number of supported elements along the member length

Fig. 9.3. Plan view on the lateral buckling modes of an elastically supported member.

Fig. 9.3. Plan view on the lateral buckling modes of an elastically supported member.

9.3.2 Bracing of single members (subjected to direct compression) by local support

The method detailed in 9.2.5.2 of EC5 is applicable to the design of bracing members laterally supporting a single member subjected to direct compression, e.g. the compression boom member of a truss, or a single beam under bending moment.

The function of the bracing is to prevent the member from buckling laterally at the bracing positions and by so doing increase its lateral buckling strength. Consequently, when determining the buckling strength of the single member its buckling length should be taken to be the distance between adjacent bracing members.

Consider a compression member of length I braced laterally by elastic supports spaced at equal intervals along its length, each having the same axial stiffness. A plan view on such a member is shown in Figure 9.3a.

Where failure can occur due to the effects of lateral instability, the compression member will buckle about its weak z-z axis and for a perfectly straight member, where it is supported rigidly at bracing positions equally spaced along the length of the member, the failure mode will be as shown in Figure 9.3b. For this condition, the stiffness to be provided at each bracing position will be theoretically infinite and the force in the bracing members and its connections will be zero. Where the stiffness of the bracing and the connections is relatively small, the member will displace laterally but in so doing will reduce the buckling load that can be supported by the member.

To optimise the strength of the member, the design condition to be achieved by the bracing is equivalent to that shown in Figure 9.3b, and this can be simulated by increasing the stiffness of the bracing members for the mode shown in Figure 9.3c

 m = l/a*
0 0