### The BS5268 K_{8} factor and built-up timber beams

Every so often a local authority queries calculations produced by SuperBeam on the
grounds that the K_{8} factor of 1.1 has been wrongly applied to a beam built up
from two or three timber members.

The permissible bending and shear stresses given in BS5268 assume that the timber being used will be of the minimum standard required for the stated species/grade. For a single member this assumption is obviously correct. Where two or more members act together it is highly unlikely that all the members will be no better than the minimum. This subject is discussed at length in the Timber Designers' Guide - see our book list for full details.

When designing a timber beam SuperBeam asks how many members are acting together. The options are 'Loading sharing', '1', '2', '3' or '4'.

A load sharing system is defined in BS5268 Part 2 §2.9 as one where four or more members such as rafters or joists spaced at not more than 600mm act together and the loading is shared between them by decking, boarding, battening etc. (certain floors such as those subject to a lot of vibration are not included in this definition). For such systems the K8 factor of 1.1 is applied to the permissible bending and shear stresses, and the mean E-value is used to calculate deflection.

Select '1' for a single member, such as a trimmer. It will be checked using the grade bending and shear stresses, and the minimum E-value is used to calculate deflection.

Select '2', '3' or '4' where 2, 3 or 4 (or more) members are bolted or otherwise fixed together to form a built-up beam, such as double member lintel in timber frame construction or double joist trimmer (in the width field make sure you enter the total width of the member - see the note below). The calculation will be done in accordance with BS5268 Part 2 §2.10.11 which states that "for trimmer joists and lintels comprising two or more pieces connected together in parallel and acting together to support the loads, the grade stresses in bending and shear parallel to the grain, and in compression perpendicular to the grain should be multiplied by the loading-sharing modification factor K8, which has a value of 1.1. The minimum modulus of elasticity modified by the factor K9 (see table 17) should be used for calculation of deflections". If this is queried please draw the attention of the checking authority/engineer to this clause.

When using SuperBeam (and when checking work on site) please note that one 100 x 200 is not the same as 2no 50 x 200. If you have designed a beam on the basis that two members act together, the single member may not be acceptable. To avoid doubt please enter the member width as '2no 50' rather than '100' in such cases.