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with

where the symbols are as previously described and/or shown in Figure 7.3; /v,90,d is the design planar (rolling) shear strength of the web, /r,k is the characteristic planar (rolling) shear strength of the web, and

(bw for box beams\ for I-beams J

7.3.1.2 Displacement at the serviceability limit states (SLS)

Because of the different time-dependent properties of the components in the section, the requirements of 2.3.4.1 must be taken into account.

At the instantaneous condition the deformation analysis is undertaken using the design value of the combination of actions for the SLS, i.e. either equation (2.24) or

(2.25), depending on whether the characteristic or the frequent combination of actions will apply. As the creep behaviour of the member is not relevant at this condition, in accordance with the requirements of EC5, 2.2.3(2), the mean value of the appropriate modulus of elasticity,Emean, and shear modulus, Gmean, must be used to derive the stiffness properties.

For the final deformation analysis the loading will be the same as that used for the instantaneous deformation and the creep effect on displacement behaviour is achieved by using the reduced stiffness properties given in equations (2.34) and (2.35), i.e.

Emean

Emeanfin = , ^T"1 . (EC5, equation (2.7)) (2.34)

G mean

where the functions are as follows:

• Emean,fin is the final mean value of the modulus of elasticity;

• Emean is the mean value of the modulus of elasticity;

• Gmean,fin is the final mean value of the shear modulus;

• Gmean is the mean value of the shear modulus;

• kdef is the deformation factor for timber and wood-based products and, for connections, it will be as defined in Section 2.3.2. Values for kdef for timber and some wood-related products are given in Table 2.10.

If the composite section is to be installed at or near its fibre saturation point, but functioning in an environment where it is likely to dry out under load, as required by EC5, 3.2(4), the value of kdef obtained from Table 2.10 must be increased by 1.0.

When deriving the deflection due to bending, the second moment of area used in the deflection equation will be the value of the transformed section for the condition being considered, i.e. the value at the instantaneous or the final deformation. When deriving the shear deflection, the shear area will be the actual cross-sectional area of the webs and not the transformed area.

Taking the flange material as the material selected for use in the equivalent section approach, on the above basis, the second moment of area to be used in a deformation calculation arising from flexure will be as follows:

(a) The instantaneous condition:

(b) The final deformation condition:

/ —mean,w ^ / 1 + kdef,f \ 4f,fin = If + —- ——- Iw (7.6)

For these structures, the deflection is calculated in the same way as explained in Chapter 4 for rectangular beams, ensuring that shear deformation is taken into account. There are several methods available for deriving the shear deformation of thin web beams and using the approximate method given in Roark's Formulas for

Stress and Strain [2] in which the form factor for the beam is taken to be unity and all of the shear is considered to be carried solely by the web(s), the shear deflection at the instantaneous condition can be written as: Md u = G-^ (7.30)

G w,mean Aw where u is the instantaneous shear deformation of the beam at mid-span, Md is the design moment at mid-span, Gw>mean is the mean value of the shear modulus of the web material, andAw is the cross-sectional area of the web(s) in the section (before transformation).

In Table 7.1 equations are given for the deflection of simply supported and cantilever composite beams at the instantaneous and the final deformation conditions due to the effects of bending and shear.

Based on the above, if at the SLS a simply supported thin webbed box beam of span £ is subjected to a design loading of qd (kN m), the mean value of the modulus of elasticity of each flange is Ef, the transformed second moment of area is Ief>inst at the instantaneous condition and Iefjfin at the final deformation condition, with two webs, having a total cross-sectional area Aw, and a mean shear modulus of Gw, where kdefjf and kdef,w are as defined in equation (7.2), the deflection at mid-span due to the SLS design load will be as follows:

At the instantaneous condition:

At the final deformation condition:

f 5l4(1 + kdef.f) f £2 WO+kdefw)\\ ufin = n 384EfIef,fin + l T){-GAT)) (732)

where kdef f is the deformation factor for the flange material at the relevant service class, and kdef,w is the deformation factor for the web material at the relevant service class.

See Example 7.5.1.

7.3.2 Glued thin flanged beams (stressed skin panels)

When a stressed skin panel is subjected to out of plane bending it will function as a thin flanged beam. Stressed skin panels are structural elements in which the web is normally formed using timber sections aligned with the direction of span and the facing panels are formed from wood-based materials such as plywood, OSB or particleboard. The thickness of each flange is normally determined from the bending stress when functioning as a beam spanning across the panel webs.

The panels may be on one or both sides of the beam. End blocking between the webs is commonly used to provide lateral torsional restraint at these positions, and where flange splices are required these can be achieved by finger or scarf jointing or by the use of splice plates supported by timber noggings fitted within the box structure.

The connection between the flange and the webs can be glued or formed by mechanical fasteners. If mechanical fasteners are used (e.g. nails, screws, etc.) there will

Table 7.1 Bending and shear deformation of a simply supported or a cantilever composite beam at the instantaneous and at the final condition

Load case

Bending deflection

Shear deflection

Uniformly distributed load

(udl) of qd (kN/m) run along the span:

At mid-span:

At mid span:

Instantaneous condition

8 Aw G w,mean

Final deformation condition

5qd^4(1 + kdef) 384Emean,f Ief,fin

8 Aw Gw,mean

Point load Vd at mid span:

At mid span:

At mid span:

48 Emean,f Ief,inst

4 Aw G w,mean

Final deformation condition

48 Emean, f ^ef, fin

4 AwGw,mean

Point load Vd at the end of a cantilever:

At the end of the cantilever:

At the end of the cantilever:

3 Emean, f ^ef, inst

Aw Gmean,w

Final deformation condition

Vd^3(1 + kdef) 3 Emean, f ^ef, fin

Aw G mean,w

Note: (1) In the above expressions Aw is the cross-sectional area of the web(s) in the section (before transformation);

(2) where a more accurate assessment of the shear deflection is required and the I or box section have flanges of the same thickness and the webs of the box section are both of the same thickness, the deflection expression given in Table 7.1 for the shear deformation should use the area of the section (i.e. the web and the flanges) rather than just the web area and should also be multiplied by the following form factor, F, given in Roark's Formulas for Stress and Strain [2],

Note: (1) In the above expressions Aw is the cross-sectional area of the web(s) in the section (before transformation);

(2) where a more accurate assessment of the shear deflection is required and the I or box section have flanges of the same thickness and the webs of the box section are both of the same thickness, the deflection expression given in Table 7.1 for the shear deformation should use the area of the section (i.e. the web and the flanges) rather than just the web area and should also be multiplied by the following form factor, F, given in Roark's Formulas for Stress and Strain [2],

where D1 is the distance from the neutral axis to the nearest surface of the flange, D2 is the distance from the neutral axis to the extreme fibre, b is the transformed thickness of the web (or combined web thicknesses in box beams), bwt is the width of the flange, and r is the radius of gyration of the section with respect to the neutral axis.

be slip between the flange and the web, and the effect on the design must be taken into account. The more common practice is to use glue and in the following analysis the theory only applies to rigid joints formed by using glued connections, as covered in EC5, 9.1.2.

As with glued thin webbed beams, glued thin flanged beams also use different materials to form the composite section and the equivalent section approach referred to in 7.3.1 is again used in the analyses. In the following sub-sections, the transformed section has been based on the use of the flange material and assumes both flanges have the same modulus of elasticity.

Compression

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