Hwq

mean, f

• At the final mean value condition,

Ief, fin

The maximum design stress on the tension side of the web will be: • At the instantaneous condition,

Ief,in\

• At the final mean value condition,

^w,fin,t,d — (Ot,2) — ( 1-(^2,fin - 0.5hf,t) 1 ' 1 '

<ef,fin

As the web has been transformed in the equivalent section, to obtain the stress in that element the calculated stress must be multiplied by the modular ratio for the appropriate condition.

The design requirement in EC5, 9.1.2(9), is that the design stresses obtained from equations (7.43) and (7.44) mustbe less than or equal to the design compressive bending strength of the web material, fc,w,d, and those from equations (7.45) and (7.46) must be less than or equal to the design tensile bending strength,ft,w,d. Where timber is used for the web,

^w,c,d ^ fc,w,d GwXd < ft,w,d and and k mod fc,w,d —

where the functions are as previously described and /m,k is the characteristic bending strength obtained from Table 1.3; ksys is in accordance with the requirements of 2.3.7.

Where timber is not used for the web, unless compressive and tensile bending strengths are given for the material being used, the in-plane compressive and tensile strengths of the material should be used.

(b) Web shear stress check.

Although there is no stated requirement in EC5 to carry out a shear stress check across the section, the greatest shear stress will arise in the web and the shear strength f f k of this member should be checked. The maximum shear stress will arise at the NA position and the value at this position,rv d, is determined as follows:

• At the instantaneous condition,

^ef.inst^w

• At the final mean value condition,

Vd Sf,fin,NA

Ief,finbw where the functions are as previously defined, and Vd is the design shear force at the position of maximum shear, SfjinstjNA, and Sfjfin>NA are the first moments of the area of the section above the NA about the neutral axis at the instantaneous and at the final mean value conditions, respectively, and bw is the thickness of the web.

The design requirement for the shear strength will be

where fv.d is the design shear strength of the web material.

(c) Horizontal shear stresses in the glued joints between the web and the flanges. The shear stress in the web is transferred to the flanges in the composite section through the glued interface connection at positions 1-2 shown in Figure 7.7. The glue in the connection will be able to take the stress and the limiting design condition for a flange comprising wood-based panels will be the rolling shear strength of the flange. The shear stress along the interface is assumed to be uniform and will be derived as follows:

• At the instantaneous condition:

Vd Sf,inst

Ief,instbw

• At the final mean value condition:

Ief,finbw where the functions are as previously defined and:

Vd is the design shear force at the position of maximum shear, and Sf inst and Sf fin are the first moments of the area of a flange about the neutral axis at the instantaneous and the final mean value conditions, respectively. For each condition there will be a value for the compression and for the tension flange, and the larger of the values should be used.

For an internal I-shaped section the design requirements of EC5 are given in EC5, 9.1.2(6), which are

/ fv,90,d for bw < 8hf\ Tmean.d < _ /8hf\a8 - ^ 0, (EC5, equation (9.14)) (7.55) \fv,90,d ^b1 J for bw > 8hf J

Km where the symbols are as previously described and hf is the flange thickness associated with the first moment of area used to derive the horizontal shear stress.

For sections where bw < 8hf the effect of stress concentrations at the glued junction between the flange and the web can be ignored. When bw > 8hw, however, stress concentration effects have to be included for and this is achieved by the power function

For a U-shaped end beam section, the same expressions will apply but with 8hf substituted by 4hf.

7.3.2.6 Deflection at the SLS

For these structures the deflection is calculated as described for glued thin web beams in 7.3.1.2, and the web depth for shear deflection calculations should be based on the depth of the web in the thin flanged beam, hw.

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