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^rel,m < O.75

1.56 - 0.75 Xrel,m

0.75 < Xrel,m < 1.4

1/^rel,m

L4- < A.rel,m

the bending strength of the member. For this condition, the beam must comply with the requirements of 4.5.1.1.

When Xrei m > 1.4 (1.4 is the value at which the ratio of /m,k/tfm,crit is approximately equal to 2 and is taken to be the elastic limit of the beam material), the beam is considered to fail solely by elastic buckling and the elastic critical bending strength will become the design condition. For relative slenderness values between 0.75 and 1.4 the section will fail in an inelastic manner and EC5 adopts the approximation of a linear relationship between relative slenderness and member strength between these limits.

To take the effect of the reduction in the strength of the beam into account as Xrel m increases, a lateral buckling reduction factor, kcrit, is applied to the design bending strength of the beam such that at the ULS the beam strength, i.e. its design buckling strength, will be obtained from kcrit x the design bending strength.

The value of kcrit to be used is given in Table 4.3.

Where lateral instability effects can occur in beams, the maximum initial mid-length deviation from straightness in the beam permitted in Section 10, EC5, is limited to 1/300 for solid timber and 1/500 for LVL (and glued-laminated timber), where I is the beam length in mm. The design rules in EC5 for strength validation are considered to take the effect of this imperfection into account.

When A.rel,m < 0.75, the design strength will equate to the bending strength of the member, resulting in kcrit = 1. For behaviour within the linear elastic range of the beam, i.e. where amicrit//m,k < 0.51, failure is solely by buckling and the design strength will equal the elastic buckling stress. For this condition, kcrit relates to the relative slenderness ratio as follows:

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