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Equation (4.32) applies where the member is free to rotate under the applied torsional moment, as will be the case with statically determinate structures. When dealing with statically indeterminate structures, however, depending on the configuration of the member within the structure, the detailing of the end joint(s), the effect of semi-rigid behaviour at the connections etc., the rotation of the member may be less than that derived from equation (4.32), and in such cases the torsion stress will be smaller than the stress obtained from equation (4.31).

The limit state for torsion is the ULS and the EC5 design requirement, given in EC5, 6.1.8, is:

Ttor.d < kshape/v,d (EC5, equation (6.14)) (4.35)

Here rtor,d is the design torsional stress derived from equations (4.29) or (4.31) for circular and rectangular sections, respectively, when subjected to a design torsional moment Td.

/vd is the design shear strength as defined in 4.5.2.1, i.e.

Km where the factors and functions are as described in 4.5.2.1:

kshape is from research by Mohler and Hemner, referred to by Aune in STEP 1 [5]; torsional shear strength is greater than direct shear strength and in EC5 this is taken into account by applying this shape factor to the design shear strength. The value of the factor is given in EC5, equation (6.15), as follows:

(1.2 for a circular section \

min^0.15^) for a rectangular cross-section J (436)

h is the larger cross-sectional dimension. b is the smaller cross-sectional dimension.

4.5.5 Combined shear and torsion

EC5 only addresses members subjected to shear or to torsion but not to a combination of shear and torsion.

When a member is subjected to combined torsion and shear, the respective torsional and direct shear stresses will combine and the section must be designed for the resulting maximum shear stress condition. Limited research has been carried out on this combined stress condition and using the torsional strength relationship in equation (4.35) it is proposed in STEP 1 [5] that the following failure criterion may be taken to apply:

kshape fv, d \ fv,d where the functions are as described in 4.5.2.1 and 4.5.4.

Equation (4.37) assumes an element of stress redistribution, increasing the combined shear resistance of the section. As an alternative, a more conservative approach can be adopted in which the respective shear stresses are added linearly and the failure criterion will be:

kshape fv, d fv,d

Torsional shear stresses will not interact with bending, compression, tension or bearing stresses and when acting in members also subjected to such stresses the torsional shear stress condition need only be checked for compliance with equation (4.35).

4.6 DESIGN FOR SERVICEABILITY LIMIT STATES (SLS)

At the SLS, members must be shown to behave satisfactorily when in normal use and the primary requirements to be checked are deflection and vibration behaviour.

For these states, as stated in 2.2.20.2 and 2.2.25, the partial factors for actions, yg and yq, and the partial material factor, ym, are to be taken as unity.

4.6.1 Deformation

### 4.6.1.1 Deformation due to bending and shear

EC5 requires that the deformation of a beam must be such that the facility it supports will be able to function as designed, that there will be no adverse visual effects, no structural implications (e.g. there will be no damage to non-structural elements due to deformations) and services must be able to function satisfactorily.

The deformation of a timber or wood-based structural beam is made up of several components and when subjected to the SLS design loading the limiting values of these components are shown in Figure 4.17, where the symbols used in EC5 are as follows:

wc is the precamber, where used.

winst is the instantaneous deformation; i.e. the deformation that is permitted immediately under the action of the design load.

Table 4.6 Guidance on limiting values for vertical deflection given in Table 7.2 of EC5 and NA.2.5 of the UKNA to EC5

Document

Element

winst

Wfin

wnet,fin

EC5 Table 7.2

Beam on two supports Cantilever beam

if300 to i/500 1/150 to i/250

i/150 to i/300 i/75 to i/150

i/250 to i/350 i/125 to i/175

UKNA to EC5, NA.2.5

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