HORIZONTAL TIMBER DIAPHRAGMS FOR WIND AND EARTHQUAKE RESISTANCE

This paper discusses the principles of horizontal timber diaphragm behaviour under in-plane loading, gives guidance on analysis, design and details, and reviews relevant research. Plywood, particle board and solid timber boarding are all relevant sheathing materials for wind and earthquake resistance, provided that appropriate stiffness is provided and the design provisions ensure that brittle failure modes are suppressed.


INTRODUCTION
This paper is one of a series of papers on the design of timber structures for wind and earthquake resistance, resulting from the work of a joint committee of the New Zealand Timber Society and the New Zealand National Society for Earthquake Engineering (Williams, 1986).
This paper discusses the behaviour and design of horizontal timber diaphragms which will perform well in both wind and earthquake loading.There are two alternative contrasting design approaches that may be adopted for diaphragms, both of which relate to the high degree of non-linearity which readily occurs in diaphragms under earthquake loads as discussed below.
(1) Suppression of Non-linearity The distribution of loading through the diaphragm to the vertical structure and the control of deflections can be much more easily and reliably predicted if significant non-linearity in the nail deformations is suppressed.In the majority of buildings this will be the preferable and economical procedure.
The seismic force factors for parts and portions of buildings in the New Zealand loadings code {NZS 4203) should be used, and the design of diaphragm nailing for the lateral loads derived using the appropriate seismic force factors will generally ensure that the response of the diaphragm is predictable.
Potential brittle failure of the chords of diaphragms and around openings in the diaphragm must still be prevented.In this approach the inelastic (non-linear) behaviour of the diaphragm at design loads is allowed for explicitly in calculating the loads, load distribution and deflections.The energy absorption and ductility of the diaphragm implied by the elasticity may be utilised to reduce the loadings generated within the diaphragm (by the use of appropriate  1986), the achievement of a ductile failure mode is essential.This is achieved by providing adequate extra strength for all other failure modes to ensure that failure occurs through nail deformation.
Premature failure of the chords, in framing around openings, in shear panels, or in the diaphragm connections to vertical structure must be prevented by capacity design procedures= Control of deformations that will occur in the inelastic structure must ensure that inter-storey drifts at any location along the diaphragm are not excessive.

RESEARCH INTO DIAPHRAGM BEHAVIOUR
A great deal of research has been done into various aspects of timber diaphragms involving a variety of materials and sheathing patterns.
Brief descriptions of a selection of research reports have conveniently been published in two publications by the Applied Technology Council (1980Council ( , 1981)).In this present paper we will restrict our attention to a few papers particularly pertinent to the subject of this paper.(1984) and Jain and Jennings (1984) .both these papers confirm that diaphragm flexibility modifies the response characteristics of structures, in some cases increasing the forces compared with those obtained assuming rigid diaphragms.

Analysis
Diaphragms act to distribute the horizontal loads imposed on the building to lateral load resisting elements such as frames or shear walls (Fig 1).Timber

Web
buckling is typically prevented by the stiffening effect of the framing members to which the sheathing is connected.For typical floor diaphragms, the thickness of material required to carry vertical loads normally ensures that buckling of the sheet material will notvoccur under lateral loading.
Most diaphragms are relatively deep beams, with length to depth ratios seldom exceeding 3.0.
There is evidence that the girder analogy is inappropriate for deep beams made from materials which behave isotropically through a large part of their useful load carrying history.GIRDER ANALOGY

Flange Stresses
The flanges are normally designed to provide the entire resistance to flexural stresses in the diaphragm (ie the bending contribution of the web is neglected).
The force in the flanges is therefore equal to the moment in the diaphragm divided by the distance between the centres of the flanges.
The flange force determined by this procedure is the upper limit of the force.
The size of flange members can be derived by dividing the flange force by the allowable stress for the flange members, with allowance for combined loading effects.
The length of most diaphragms requires most flange members to be spliced.
Splices should be located as far as possible from positions of maximum moment and should be designed and detailed to carry the flange force at the splice location in addition to any other loading effect present in the flange member.
Ductile connection systems should be used to prevent failure of the flanges, and compression splices must be capable of transferring compressive flange forces without buckling.

Web Stresses
The web of the diaphragm, similar to the web of a girder, is required to carry the shearing forces induced in the diaphragm by the applied loads.For timber sheathed diaphragms the available size of sheets requires the web sheathing to be spliced frequently.
These splices are located over framing members, principally provided to carry the gravity loads on the floor.
A blocked diaphragm is one in which all panel edges occur over, and are nailed to, framing members.Splicing may be accomplished by using typical full depth blocking, reduced depth blocking laid on edge or on flat, or plywood strips.
Forces applied to diaphragms are usually uniform along the length of the diaphragm, and therefore the critical shear condition for diaphragms without openings occurs at the reactions.
The critical shear condition dictates the thickness and boundary nailing of the diaphragm. Where where area of flanges (m ); d = distance between centre lines of flanges (m).
Diaphragms may be subjected to horizontal loads from any direction and the "flange to web" shear transfer for forces in one direction can become the "force reaction" transfer for horizontal loads at 90 degrees to the previous direction.

3.5
The Effects of Diaphragm Stiffness The stiffness of diaphragms is important for the behaviour of structures under lateral loads because (i) it affects the distribution of hori zontal loading to the vertical members resisting those loads, and

Flange-web shear transfer
The shear to be transferred from the flange to the web is directly related to the lateral shear in the web.The distribution of lateral forces to the various vertical load resisting elements is physically complex, and hence is open to various analytical interpretations.
The distribution of lateral loads is determined by the flexibility of the diaphragm relative to the flexibility of the lateral load resisting system.
As an alternative to using complex computer programs (Section 2.0), the two extreme alternative simplifying assumptions are (a) infinitely stiff vertical elements with a flexible diaphragm, and (b) an infinitely rigid diaphragm with flexible vertical elements.
Timber diaphragms are rarely of sufficient stiffness to permit the assumption of a rigid diaphragm and the distribution of lateral forces should be calculated using the beam-on-elasticsupport analogy.The analysis of a beam on elastic supports is readily calculated using microcomputers, where the diaphragm stiffness properties are used for the beam properties, and the properties' of the supports are selected to model the stiffness properties of the vertical members which provide the horizontal restraints.
An alternative , but conservative, approach is to design the diaphragm for shears at the ends as determined for simply supported spans and for shears over internal supports as determined for full continuity.

Effects
These four components of deflection are described below for the case of simply supported diaphragms sheathed with panels eg plywood or particle board:

Bending contribution
The bending contribution to deflection is where e is the nail deformation under the applied load (m); h is the length of a sheathing panel (m); b is the width of a sheathing panel (m).
Equation ( 6) is that given by the ATC (1981), who derive it in two different ways.
It will be noted that it is slightly at variance with the formula given by NZS 3603:1981.

Splice slip contribution
The rotation of the end plane of the diaphragm is proportional to the change in length of the flange due to slippage in the splices.If the change in rotation at the support is assumed to be proportional to the distance from the support compared to the total length (correct for a splice at midspan), then the deflection has been shown (ATC, 1981) to be

Large openings
The analysis of diaphragms with large openings is complex and requires finite element programs to establish the stress distribution around openings.Dean et al. (1984) have proposed a simplified "shear transfer" method for finding the shear distribution, which is based upon equilibrium considerations assuming (a) The framing transmits all direct stresses and is rigid; Connections must be provided between discontinuous blocking to transmit frame forces in the direction of the discontinuous blocking.

Higher
nail densities must be provided in panels carrying greater shear loads.
The increased nail densities should result in the shear stiffness being similar to a uniform less densely nailed diaphragm.Providing the opening size is small relative to the overall diaphragm dimensions the increase in overall diaphragm deflection should be small.
The largest frame forces are generated in the direction parallel to the longer sides of the opening and it is preferable to arrange the continuous framing in this direction.

Nailing
Permissible nail loads in diaphragms should be restricted to ensure that effectively elastic behaviour at design earthquake load levels is ensured f as discussed in Section 1. Nail loads will thus be reviewed in the light of the findings of Collins (1986).

Detailing
Some typical construction details for diaphragms are given in Appendix A, and further guidance on detailing may be obtained from Ref 2.

CONCLUSIONS has
In the foregoing text an attempt been made to highlight those aspects of the design of horizontal timber diaphragms that require attention in order to ensure good performance under earthquake and wind loading. The

"
Spencer, Holmes-Miller Partners Ltd, Fig 1.STRUCTURAL CONCEPT Fig 2.GIRDER ANALOGY The magnitude of the shear per unit length between the flange and web is given by v = VQ/I kN/m (l) where V = shear in member at section under consideration; Q = first moment of area of flange (m ) ; I = moment of inertia (m ).

Fig 5 .
Fig 5. ALLOCATION OF PANEL SHEARS AND FRAME FORCES SURROUNDING AN OPENING.