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by linearly interpolating between the values in the table immediately above and below the required value.

Lateral restraint can be provided by blocking or strutting the beam at positions along its length, as illustrated in Figure 4.7, and for these situations the effective length will be based on the beam length between adjacent blocking/strutting positions. Where the beam is supported laterally along the length of its compression flange, e.g. due to

Fig. 4.7. Examples of the provision of lateral support.

(a) Tensile stresses at notch (b) Compressive stresses at notch

Fig. 4.8. Notch subjected to bending.

(a) Tensile stresses at notch (b) Compressive stresses at notch

### Fig. 4.8. Notch subjected to bending.

flooring structure secured to the compression flange, and the beam is relatively rigid across its depth (e.g. a solid timber beam), it can be considered to be fully restrained and £crit will be unity. The lateral restraint must provide adequate strength and stiffness to the beam and guidance on these requirements is given in Chapter 9.

### 4.5.1.3 Bending of notched members

When members are notched, stress concentrations can arise at the notch position and, depending on the stress condition, the effects have to be taken into account in the design.

For members having a notch and subjected to bending, as stated in EC5, 6.5.1(2), the stress concentration effect can be ignored when:

(i) bending will result in tensile stresses at the notch and the slope at the notch is less than 1:10, i.e. tan a < 0.1 (see Figure 4.8a);

(ii) bending will result in compressive stresses at the notch (see Figure 4.8b).

Where a beam has a rectangular cross-section, its grain runs essentially parallel to the member length and there is a notch at the support, the effect of stress concentrations has to be taken into account and this is considered in 4.5.2.1.

4.5.2 Shear

When a beam is loaded laterally and subjected to bending, shear stresses will also arise. In accordance with elastic bending theory, shear stresses will be generated parallel to the longitudinal axis of the beam and, to achieve equilibrium, equal value shear stresses will be generated in the beam perpendicular to the longitudinal axis as shown in Figure 4.9a.

The value of the shear stress at any level in the cross-section of a beam, as derived from elastic theory, is

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