## Bb

Fig. 5.17. Typical stud wall construction.

The strength of the wall is primarily derived from the studs and all concentrated loading should be located directly over the studs and not in the span area of the header plate. For any loading over the span area, the plate must be checked to confirm whether it can function satisfactorily as a beam or alternatively additional studs can be inserted to carry the load.

When several equally spaced similar members are laterally connected by a continuous load distribution system, EC5 permits the member strength properties to be multiplied by a system strength factor, ksys, as discussed in 2.3.7. In the case of stud walls, provided the sheathing is secured to the studs and plates in accordance with the manufacturer's fixing recommendations, it will function as a continuous load distribution system, allowing the ksys factor to be used. Because the header and sole plates are single members the factor will not apply to these elements, but it will be relevant to the studs, being applied to the compression strength, /c,o,k, and bending strength, /m k. The factor is defined in EC5, 6.7, and where the stud spacing is no greater than 610 mm centre to centre and the sheathing is fixed to the studs in accordance with the fixing manufacturer's recommendations, or in accordance with the design requirements, based on experience in the United Kingdom with such structures where there are four or more wall studs, ksys can be taken to equal 1.1. For stud spacing greater than 610 mm centre to centre or the sheathing is not properly secured, unless it can be demonstrated by calculation, the factor should be taken to equal 1.

5.5.1.1 Design of stud walls subjected to axial compression 5.5.1.1.1 Stud design

(a) Where the relative slenderness ratios Xrely and A.rel,z are >0.3.

This condition will normally apply when there is no sheathing or the sheathing is not adequately secured to the studs and plates and the design requirement will be:

Oc,0,d < kc,z ■ fc,0,d (5.28b) where ac,o,d is the design compressive stress parallel to the grain and Nd tfc,0,d = -f (5.29) A

where Nd is the design axial load on the stud and A is its cross-sectional area; fc,0,d is the design compressive strength of the stud parallel to the grain and

Km where the functions are as previously defined and ksys = 1 for the cases where the sheathing is not adequately secured to the studs.

The design procedure is as described in 5.3.1 for the design of a compression member under axial load. The critical design condition arising from equations (5.28a) and (5.28b) will be the one with the lowest value of instability factor and will be associated with the highest slenderness ratio of the stud.

(b) Where the relative slenderness ratio A.rel,y > 0.3 and A.rel,z < 0.3.

If the sheathing material is properly secured to the studs, kc,z will always exceed kc,y and the design condition will be:

This situation is unlikely to arise in practice, but if it does the values of kc,y and kc,z should be taken to be unity and the design condition will be:

fc 0 d where the functions are as previously defined but the ksys factor used to derive fc 0 d in cases (b) and (c) can be taken to be 1.1 where there are at least four studs and the stud spacing is not greater than 610 mm c/c.

### 5.5.1.1.2 Plate design

The header and sole plates provide lateral restraint to the ends of the studs and also function as bearing members at these positions. Normal fixings between the studs and the plates and the structure will provide adequate lateral restraint and the design condition will generally relate to a design check of the strength of the plates under compression perpendicular to the grain. If there is any loading directly onto the plates between the stud positions, they will also need to be designed for bending and shear forces, as for beams. As stud walls are generally not meant to be loaded in this manner, this design condition has not been considered.

For compression perpendicular to the grain the condition to be satisfied is:

/c.90,d where ac,9o,d is the design compressive stress perpendicular to the grain and ac>o,d = Nd/A where Nd is the design axial load in the stud and A is its cross-sectional area; /c,90,d is the design compressive strength perpendicular to the grain and is defined as:

Km where the functions are as previously defined and /c,90,k is the characteristic compressive strength of the timber or wood-based product perpendicular to the grain. Strength information for timber and the commonly used wood-based structural products is given in Chapter 1; kc,90 is as described against equation (4.22).

In the proposed draft amendment to EC5, summarised in Appendix C, 6.1.5, a major change is proposed for the validation of compression strength perpendicular to the grain. The proposal simplifies the design procedure given in EC5 and will remove the option to be able to design for a large compressive strain condition.

See Example 5.7.6.

5.5.1.2 Design of stud walls subjected to combined out of plane bending and axial compression

This situation most commonly arises when stud walls are subjected to the effect of out of plane wind loading in addition to the axial load being carried. The design procedure for the studs follows the method given in 5.4 for the design of compression members also subjected to bending moment.

5.5.1.2.1 Stud design

This will apply when the cladding cannot provide full buckling restraint about the z-z axis.

(i) For the case where the relative slenderness ratio for bending of each stud is <0.75 (i.e. lateral torsional buckling of the stud will not arise), the design condition will be:

—c,^ + J^^d < 1 (EC5, equation (6.23), with om ,z ,d = 0) (5.35)

—^^ + km ^^ < 1 (EC5, equation (6.24), with omzd = 0) (5.36)

/c,0,d /m ,y,d where the functions are as previously defined and Om,y,d are the design bending stresses about the y-y axis of the stud and om,y,d = My,A/ Wy where My,d is the design bending moment about the y-y axis and Wy = bh2/6 is the associated section modulus of the stud; fm,y,d is the design bending strength about y-y axis and:

Km where the functions are as previously defined and ksys = 1 for the cases where the sheathing is not adequately secured to the studs. (ii) For the condition where the relative slenderness ratio for bending of each stud is >0.75 (i.e. lateral torsional buckling of the stud can arise), the requirements of EC5, 6.3.3(6), must be checked: \ 2

vkcrit fm,y,d/ kc,zfc,0,d where the functions are as previously defined.

For the condition where a stud wall is subjected to combined bending and axial compression, where XreljZ > 0.3 and A.rel,m approximates 0.75, as discussed in 5.4.2, equations (5.35), (5.36) and (5.38) should be complied with.

(b) Where Xrel>y is >0.3 and XreljZ < 0.3.

For this situation, kc z will be unity and on the basis that lateral torsional buckling cannot arise the design condition will be:

kc,yfc,0,d fm,y,d where the functions are as previously defined and the ksys factor can be taken to be 1.1 where there are at least four studs and the stud spacing is not greater than 610 mm c/c.

This situation is unlikely to arise in practice, but if it does the values of kc,y and kc,z will be unity. With the understanding that for this condition the relative slenderness ratio for bending of each stud will also be <0.75, the design condition will be:

fl+ —m^ < 1 (EC5, equation (6.19), with —= 0) (5.40)

\/c,0,d/ fm,y,d where the functions are as previously defined and the ksys factor can be taken to be 1.1 where there are at least four studs and the stud spacing is not greater than 610 mm c/c.

5.5.1.2.2 Plate design

The procedure remains as described in 5.5.1.1.2.

See Example 5.7.7.

5.5.2 Out of plane deflection of load-bearing stud walls (and columns)

The behaviour of stud walls (and columns) with an initial deviation and subjected to axial loading is addressed in EC5 as a strength problem. Out of plane deflection is not considered in the code. There may, however, be a design situation where the out of plane deflection is required and the following methodology is given for calculating this deformation.

(initial out of straightness of member)

(initial out of straightness of member)

(deflection due to out of plane loading)

(deflection under axial and out of plane loading)

(deflection under axial and out of plane loading)

Stud y section

(a) Unloaded wall section

(b) Out of plane loading

(c) Combined axial and out of plane loading

Fig. 5.18. Deflection of wall under vertical and out of plane loading.

When a member with an initial out of plane displacement is subjected to axial loading, due to the additional moment induced in the member by the axial load, the displacement will be amplified. In the case of a stud wall the displacement will comprise an initial deviation from straightness, 50, and, if subjected to out of plane loading, an additional displacement, 5q, as shown in Figures 5.18a and 5.18b respectively.

From EC5,10.2, it is to be noted that the maximum initial deviation from straightness measured halfway along the member, 50, cannot exceed L/300 for solid timber and L/500 for glued-laminated timber or LVL, where L is the length of the member.

Maximum out of plane deflection will occur at mid-height and from classical elastic stability theory it can be shown that if a stud wall comprises members having an initial out of plane deflection S0 (i.e. from the principal y-y axis position shown in Figure 5.18) and each stud is subjected to an axial design load Nd, the out of plane deflection of the wall (or a column) will increase to SN0, where:

In equation (5.41) a is an amplification factor derived from: 1

and PE is the Euler buckling load of each stud about its y-y axis, L is the effective length of the stud, b is the width of the stud, h is the depth of the stud, and £0 05 is the fifth percentile modulus of elasticity of the stud material parallel to the grain.

Although this is an approximate solution, it is accurate to within 2% for values of N/PE less than 0.6, which will be the case when deriving the displacement at the SLS.

For the above condition the increase in wall deflection, SN0, can therefore be written as:

Under the action of out of plane loading only on the wall, and taking shear deformation into account, from the data given in Table 4.7, the deflection Sq per stud at the mid-height of the wall caused by a load of q kN/m2 will be:

where Sq is the out of plane deflection of the stud (in mm), L is the wall height (in metres), E0,m is the mean modulus of elasticity of the stud parallel to the grain (in kN/m2), b is the breadth of the stud (in metres), h is the depth of the stud (in metres), and SP is the lateral spacing of the studs (in mm).

From equation (5.42), when each wall stud is subjected to an axial design load Nd, Sq will be increased to aSq and when added to the out of straightness deflection of the wall, the final deflection SNq will be:

and the net increase in deflection due to the combined axial load and lateral load effect, Snet, will be:

which reduces to

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