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In the above relationships the functions kmod, ksys and kM are as previously defined and /v,g,k, /t,90,g,k and /c,90,g,k are the characteristic shear strength, the characteristic tension strength perpendicular to the grain and the characteristic compression strength perpendicular to the grain respectively. Values of the strength properties for GL 24, GL 28 and GL 32 are given in Table 6.2.

Figure 6.6 shows the effect of the reduction factor, km a, when applied to glulam beams of homogeneous glulam compliant with the strength classes given in Table 1 of BS EN 1194:1999. For tensile stresses parallel to the tapered edge, the factor is represented by a dashed line and for compression stresses parallel to the tapered edge, by a solid line. It can be seen that the value of kma is primarily dependent on the angle of taper of the beam and the largest strength reduction will always be associated with the condition where the tapered face is subjected to tension. For example, when using a beam with a taper of 10°, irrespective of the strength grade of the glulam, the bending strength will only be approximately 35% of the non-tapered beam of the same depth when subjected to tension bending stresses parallel to the tapered edge, compared to approximately 70% when it is subjected to compression bending stresses on the same face.

Where the relevant stress being considered is a compression bending stress, the effect of lateral instability will also have to be taken into account and for such conditions:

Om,0,d — kcrit /m,d and/or am,a,d — kcritkm,a /m,d (6.1°)

In equation (6.10) the functions are as previously defined and kcrit is the lateral torsional instability factor referred to in 4.5.1.2. An approximate conservative value of kcrit will be obtained by assuming a uniform beam depth of h¿.

If the benefit of the size factor is to be taken into account or the design condition arises from some loading arrangement other than those referred to in Table 6.5, the position and value of the maximum stress condition will have to be obtained by trial and error, calculating the stresses at intervals along the beam length.

Because of the tapered profile, deflection calculations are more involved than those required for beams with a uniform profile and equations to calculate the flexural and shear deflection for this type of beam when subjected to a uniformly distributed load or a point load at mid-span are given in Annex 6.1. They are based on the deflection equations for tapered beams given in the Timber Designers' Manual [7]. The maximum deflection is taken to occur at the centre of the beam span, which is acceptable for design purposes.

See Example 6.7.3.

6.4.2 Design of double tapered beams, curved and pitched cambered beams

These types of beams are shown in Figure 6.7 and are rectangular in cross-section.

The critical design checks for these beams are the same as those referred to in 6.4.1 for single tapered beams. At the ULS the maximum shear stress and the maximum bending stress condition must be validated, and at the SLS the deflection behaviour must be shown to be acceptable. With these profiles, however, in addition to design checks in the tapered area of the beam, the stress condition in the apex zone must also be validated, taking into account the effect on material strength arising from:

• residual stresses caused by the production process,

• stress distribution and volume effects,

• the combination of shear stresses in the zone and radial tension stresses perpendicular to the laminations caused by bending.

The stressed volume in the area of the apex affected by the radial stresses referred to above is illustrated in Figure 6.7, and in EC5 it is called the apex zone. The zone must be limited to a maximum of 2/3 Vb, where Vb is the total volume of the beam.

6.4.2.1 Bending and radial stresses in the apex zone -for double tapered and pitched cambered beams

In the apex zone of double tapered beams and of pitched cambered beams, the bending stress distribution is complex and non-linear and is shown in Figure 6.8 for a double pitched beam. The bending stress at the apex will be zero and the bending stress distribution will be as shown in Figure 6.8c. The radial stress induced in the section

(a) Curved beam

Beam volume = Vt

(a) Curved beam ha ha

Fig. 6.7. Apex zones for curved, double tapered and pitched cambered beams are shown shaded.

(c) Pitched cambered beam

Fig. 6.7. Apex zones for curved, double tapered and pitched cambered beams are shown shaded.

h Apex zone

, shaded h Apex zone

, shaded

Fig. 6.8. Bending and radial stresses in the apex zone of a double tapered beam: (a) elevation of a double tapered beam; (b) section at apex; (c) bending stress at apex; (d) radial stress at apex.

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