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Bracing member ^ stabilising force ^ system

Bracing member ^ stabilising force ^ system

Reaction force of bracing system due to combination of bracing member and external loading

External loading on bracing system

Nd Nd Nd Bracing members

' Bracing system with a Nd Nb Nd+Nb flexural stiffness EI

• Compression/bending member

Fig. 9.5. Bracing system for a series of compression or bending members.

a a a a a where qd is the maximum value of the equivalent lateral load per unit length on the system.

Under the effect of q the additional lateral deflection of the bracing system, zq, will be:

and the deflection at mid-span will be:

The maximum bending moment due to the equivalent lateral load will be qdi2/n2 and equating this to the maximum bending moment in the axially loaded bracing system:

qAl2

Although the additional deflection z1 is a function of qd, if it is restricted to a small enough value that its effect can be considered to be negligible, equation (9.10) reduces to:

Equation (9.11) gives the value to be used in equation (9.8) for the maximum lateral load per unit length acting on the bracing system at mid-length. Because of the approximation used in the derivation of equation (9.11) the lateral force on the bracing system will be underestimated. However, as it can also be argued that all of the compression members in the system are unlikely to have the maximum value of initial out of straightness permitted in EC5, the lateral loading will be reduced, offsetting the effect of the underestimate.

In EC5, qd is referred to as the internal stability load per unit length and is applied as a uniform load along the full length of the bracing system. It is obtained from EC5, equation (9.37), incorporating a modification factor kf,3, which can be considered to relate to function (n2/t)a0 in equation (9.11), as well as an additional factor kt:

• qd is the uniformly distributed internal stability load per unit length to be imposed on the bracing system.

• n is the number of compression or bending members to be supported by the system.

• Nd is the mean design compressive force in each compression or bending member. Where the members are rectangular beams subjected to bending moment, equation (9.1) will apply.

• kt is a factor that adjusts the out of tolerance allowance for members greater than 15 m long and is equal to:

• kf,3 is a modification factor and, as required by NA.2.10 of the UKNA to EC5, will be:

50 - when compression or bending members are spaced at <600 mm c/c, 40 - when compression of bending members are spaced at >600 mm c/c.

• t is the span of the bracing system.

Where compression or bending members form part of the bracing system, for example as shown in Figure 9.5, these members will be subjected to additional axial forces, Nb, arising from the effect of the lateral loading on the bracing system. For the loading configuration shown, the mean design compression force in the bracing system members will be adjusted as indicated.

Depending on the number and location of bracing systems being used to provide the lateral stability, the bracing members may be in tension or compression and the bracing system must also be designed for the combination of internal and external loading that will result in the maximum deflection/stress condition. For the example shown in Figure 9.5, where only one bracing system is used and the external loading is acting in the direction indicated, the loading combination leading to the greatest lateral deflection condition will be when the bracing members are functioning in tension.

It is normally more economic to design bracing members to function in tension rather than compression, and this can be achieved by providing a bracing system at kf,3t kf,3t

where:

system systems system

Fig. 9.6. Multiple bracing systems for a series of compression or bending members.

system systems system

Fig. 9.6. Multiple bracing systems for a series of compression or bending members.

each end of the system of braced members together with internal bracing system(s), if required, as shown in Figure 9.6.

With this type of configuration, the gable bracing systems are designed to support external loading in addition to an element of lateral stability loading, and the internal bracing system(s) provide support structure designed to enable the attached bracing members to function in tension.

To conform with the assumption used in the theoretical approach that the lateral deformation is kept small such that its effect can be ignored, EC5 requires that the maximum deflection in a bracing system due to qd combined with any other external loading the system has to withstand (e.g. wind loading) does not exceed i/500.

See Example 9.7.3.

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