The Design of Beams: General Notes
4.4 LOAD-SHARING SYSTEMS .1 Lateral distribution of load
When a beam system has adequate provision for lateral distribution of loads, e.g.
by purlins, binders, boarding, battens, etc., it can be considered to be a load-sharing system. In such a system a member less stiff than the rest will tend to deflect more than the other members. As it does, the load on it will be transferred laterally to the adjoining stiffer members. Rather than give load-relieving factors, this load sharing is dealt with in BS 5268-2 by permitting higher values of Ethan Eminand increases in grade stresses in the design of certain components.
In the special case of four or more members occurring in a load-sharing system and being spaced not further apart than 610 mm (as with a domestic floor joist system) the appropriate grade stresses may be increased by 10% (factor K8of 1.1), and Emean(and Gmean) may be used in calculations of deflection (although BS 5268- 2 calls for the use of Eminif a flooring system is supporting an area intended for mechanical plant and equipment, or for storage, or for floors subject to consider- able vibration such as gymnasia and ballrooms).
Factor K8applies to bearing stresses as well as bending, shear and, where appro- priate, to compression or tension stresses parallel to the grain.
In the case of two or more members fastened together securely to form a trimmer The Design of Beams: General Notes 65
joist or lintel, the grade stresses in bending and shear parallel to the grain and com- pression perpendicular to the grain (i.e. bearing) may also be increased by 10%
(factor K8). Also, Eminmay be increased by factor K9. See section 2.3.
Where members are glued together to form a vertically laminated member having the strong axis of the pieces in the vertical plane of bending, the bending, tension and shear parallel to grain stresses may be increased by factor K27while Eminand compression parallel to grain may be increased by factor K28(see section 7.3.2). Compression perpendicular to grain stresses may be increased by K29=1.10.
There are some inconsistencies when comparing K8with K27and K28(for com- pression parallel to the grain). For example, if a trimmer consists of two softwood members nailed together, the grade stresses for bending and shear parallel to the grain may be increased by K8=1.10, whereas if the members were glued together the relevant factor is K27with a value of 1.11. If a compression member comprises two pieces nailed together then no increase may be taken for grade stress for com- pression parallel to the grain but if the pieces are glued together then a K28value of 1.14 may be incorporated. With compression perpendicular to the grain, at an end bearing for example, factor K8=1.10 may be used for two or more members acting together, i.e. they may be either constrained to act together by a strong trans- verse bearer or nailed together or glued together.
This should not be a serious matter for a designer; although, if designing a two- piece column which also takes a bending moment and is supported at one end on an inclined bearing surface, it may seem odd to increase the bending strength parallel to grain for load sharing but not the compression strength parallel to grain.
Also, when considering an end bearing, the bearing strength perpendicular to grain component may be increased for load sharing, but not that for the bearing strength parallel to grain, even though the bearing stresses being considered are at the same position!
It is not normal to design glulam members (horizontally laminated) as part of a load-sharing system. However BS 5268-2 recognizes the statistical effect within each member of four or more laminates by giving various coefficients K15to K20
(see Table 7.1).
In the case of a built-up beam such as a ply web beam, BS 5268-2 recognizes the load-sharing effect by permitting the use in designs of factors K27, K28and K29
as for vertically glued members. In applying K27and K28to the grade stresses it is
Fig. 4.1
accepted that the number of laminates, N, is appropriate to the number of members in each flange. In applying K28 to Eminthe value of N is appropriate to the total number of solid timber members in the cross-section. Because K29 is the factor which relates to bearing, the same comment given above for vertically laminated members also applies to ply web beams.
Very often, ply web beams are placed at 1.200 m centres with secondary nog- gings fixed at regular intervals between them at the level of the top and bottom flanges. As such, many practising engineers have considered this to be a load- sharing system. Some engineers have used Emean in calculating deflections while some have used Ederived from Emin¥K28. The extent to which a ply web beam system can be taken as a load-sharing system is discussed in Chapter 8 in relation to Eand Gvalues and in section 19.7.3 in relation to finger jointing.
4.4.2 Concentrated load. Load-sharing system
When a concentrated load such as that specified in BS 6399-1:1996 acts on a floor supported by a load-sharing system, clause 4.1 of BS 6399-1 permits the concen- trated load to be disregarded in the design of the supporting members. When the concentrated load acts on a flat roof or sloping roof (sections 3.6 and 3.8) it must be considered, particularly for short-span beams.
In a load-sharing system lateral distribution of the load will reduce the effect on any one member, particularly if the decking is quite thick and the effect can
‘spread’ (sideways and along the span) through the thickness of the decking. A conservative assumption with a typical domestic or similar floor construction is that 50% of the concentrated load will act on the member directly under the load with the adjacent members taking 25% each.
For domestic floors BS 5268-2 states that the concentrated load defined in BS 6399-1 should be taken as medium term. BS 5268-3 allows the concentrated load acting at ceiling or rafter level to be taken as short-term duration (K3=1.5) as this is taken to be a person walking on or in the roof.
Other concentrated loads (as from partitions) must be given special considera- tion. One case which is open to discussion is illustrated in Fig. 4.2. The usual ques- tions are whether or not the joists B supporting the partition should be designed using Emean on the assumption that they are part of a load-sharing system and The Design of Beams: General Notes 67
Fig. 4.2
whether or not the two joists A will carry a share of the load from the partition.
Providing it will not lead to significant differential deflection between joists A and B it is probably better to assume that joists B support the total weight of the par- tition and a share of the floor loading, excluding any imposed loading under the
‘footprint’ of the partition, with an Evalue of EN. It is prudent to carry out an addi- tional deflection check to ensure that under dead loading only the deflections of joists A and B are similar and that any difference is unlikely to be noticeable.