A

Iy where Iy is the second moment of area of the cross-section about the y-y.

The term Iy /z is referred to as the section modulus about the strong axis and is denoted by the symbol Wy. The value of Wy is dependent on the distance from the y-y axis and the values used in design for z are the distances to the extreme tension and compression fibre position on the section. Adopting the symbols defined in Chapter 2, the design bending stress, am,y,d, at the extreme fibre position in the rectangular section shown in Figure 4.3 when bent about its strong axis by a design moment, Md, will be

Fig. 4.3. Cross-section of a rectangular beam.

z where

Iy bh3 2 bh2

Similar expressions may be derived for the design bending stress about the z-z axis (the weak axis) at the extreme fibre positions based on the design moment about that axis and the Wz section modulus.

When a member is subjected to bending, provided that there is no reduction in strength due to lateral torsional instability of the section, its design strength will be based on the bending strength of the member material. Lateral torsional instability affects a member bent about the y-y axis when the compression face of the member is not fully restrained against lateral movement and the relative slenderness for bending, ^rei.m, about this axis is >0.75. The design procedure for members that are not affected by lateral torsional instability is addressed in 4.5.1.1.

Where the relative slenderness for bending of a member about the y-y axis exceeds 0.75, the design procedure for taking the effect of lateral torsional instability into account is given in 4.5.1.2.

The procedure for determining the relative slenderness ratio for bending of a member about its strong axis is given in 4.5.1.2.

4.5.1.1 Bending (where the relative slenderness ratio for bending about the major axis is <0.75)

When a member is subjected to uni-axis bending about its y-y axis and the relative slenderness ratio for bending about this axis is <0.75, the design condition for bending is that the maximum bending stress in the section shall not exceed the design bending strength of the timber or wood-based structural material used for the member. This is achieved by compliance with equation (4.4a):

For a member subjected to uni-axis bending about its z-z axis, lateral torsional instability will not occur and the design condition is again that the maximum bending stress in the section must not exceed the design bending strength of the timber or wood-based structural product material used for the member. For bending about this axis, equation (4.4b) must be satisfied:

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