General aspects

7.5.1.1 Basis of analysis and design

The assumption here is that such buildings are designed according to contemporary Partial Coefficient Limiting States Design practices, such as those specified in the model codes of the European Committee for Standardization [4,18,106–108]. Consistency with such codes requires that linear elastic response analysis be used to estimate internal forces in components that are the resulting effects of individual or combined design load cases; and that characteristic strength and stiffness properties of the CLT are apparent values used in conjunction with geometric prop-erties determined from gross-dimensions of elements (Section 2.1). For example, the second moment of area to be used in combination with E _0,mean or E _90,mean from Table 7.1 is the element width multiplied by h³ /12, and the section modulus used in combination with f _m,k from the same table is the element width multiplied by h² /6 (where h is the panel thickness).

7.5.1.2 Load paths and robustness

Load paths in timber plate superstructures are quite transparent. Vertical force transfers occur directly from floors and roof plates to plates that form walls, with force in walls accumulating

A

A

B

C

D

Fig. 7.6: Examples of metal fasteners, ties, and connectors (A = shear connector; B = anchor tie, anchor bolt not shown; C = fasteners for attaching shear connectors/ties to CLT; D = self-tapping metal screws)

7.5 STRUCTURAL ANALYSIS AND DESIGN  93

through the heights of superstructures. According to the platform construction method, horizon-tal force transfers also occur cumulatively from level to level through the heights of superstruc-tures. Two important aspects to consider with respect to the load flows between storeys are the rigidity of those storeys in plan and in elevation. Once assembled, unless plan shapes are irregular or very elongated, storeys within superstructures like those in Figs. 7.3 and 7.4 are quite rigid both in plan and in elevation. This means that floor platforms tend to behave as rigid, rather than as flexible diaphragms. The simplified approaches outlined in Subsections 7.5.1.3 and  7.5.1.4 for designing floors and walls are based on not making specific presumptions about the rigidity of horizontal diaphragms and adopts the worst interpretation of how forces may flow from floor platforms to walls. The question of how to consider the behaviour of walls and the effect of their behaviour on rigidities of complete storeys is more complicated. In-plane rigidities of individual wall segments, and therefore complete walls and assembles of walls, depend on the following:

• The extent of wall openings

• How wall segments are interconnected

• How wall segments are connected to horizontal elements that are floors, the roof, and the top of the foundation

• The extent to which walls that are directly within a load path are stiffened and strengthened by transverse walls

Often, it is conservatively assumed that walls or segments within them are not stiffened or strengthened by transverse walls. Two extreme cases are considered. In the first, walls are cut from single pieces of CLT (Fig. 7.7 ). In the second, they are assembled from CLT plate segments (Fig. 7.3). These two scenarios can result in distinctly different behaviour mechanisms in terms of distortion, and therefore flexibility and internal force flows within walls subjected to rack-ing forces that result from lateral design loads on superstructures. Figure 7.8 illustrates the two extreme cases. Intermediate cases will also exist depending on factors such as whether or not edges of abutting CLT panels in segmented walls are mechanically interconnected. Therefore, when performing wall design (as discussed in Subsection 7.5.1.4) the influences of construction details on the racking deformation mechanism and strength of CLT panels and their perimeter connections must be considered.

Structural robustness of multi-storey building construction needs to be considered. In super-structures like those discussed in this chapter, the honeycombed nature of their arrangements Fig. 7.7: Conceptualization of force flows resisted by CLT walls

formed by floor and wall plates promotes even redistribution of forces flowing from one sto-rey to another. Therefore most, if not all, walls in the various stosto-reys participate in resisting effects of other than locally applied design loads. Superstructures like those in Figs. 7.3 and 7.4 contain much structural redundancy and forces would be redistributed relatively benignly were particular structural elements to fail during any type of loading event. Consequently, the general likelihood of progressive collapse is very limited, and timber plate systems such as the ones discussed in this chapter are highly robust, if properly designed and constructed. The most likely system-level vulnerabilities are connections that link storeys together, such as the roof to the walls or the superstructure to the foundation. Therefore, close attention should be given to selection and design of shear and hold-down connections resisting sliding and uplift due to wind and seismic loads. Connections used at level-to-level interfaces should contain redundancy and ductility. In the case of hold-down anchoring between elevated storeys, the flow of forces should be whenever possible directly from wall to wall, rather than from walls to floor platforms sandwiched between them.

Discussion here applies directly to situations where elevator and staircase shafts are constructed from CLT or comparable timber panels. In such instances, no specific distinctions need to be made for the purposes of structural analysis between wall elements forming those shafts and other wall elements.

7.5.1.3 Design of floors

Floor plates are designed considering them to act as one-way spanning elements (i.e. ignoring that panels are interconnected at abutting side edges, as seen in Fig. 7.9). This consideration reflects that the edge-to-edge joints are made using simple carpentry lap joints fastened by screws or just screws. Such joints are intended to transfer shear forces but not moment forces that result from vertical loads on floors. This approach tends to be conservative. Most often, ser-viceability performance-related bending deflection criteria control the required plate thickness.

The deflection criteria take the form of the maximum acceptable ratio of deflection to span and are selected to avoid damage to non-structural elements of buildings (e.g. 1/500). In some cases

Top CLT connection

Top CLT connection Base CLT

connection Base CLT connection

CLT wall panel

(a)

(b)

CLT wall panel CLT wall panel

Floor platform

Floor platform Floor platform

Floor platform

Fig. 7.8: Racking behaviour of CLT walls: (a) one-piece wall; (b) segmented wall

7.5 STRUCTURAL ANALYSIS AND DESIGN  95

such criteria are intended as indirect control of floor motions resulting from building use, like effects of footfall impacts. However, neither static deflection nor simplified dynamic analyses are robustly reliable ways of ensuring satisfactory vibration serviceability of CLT floors [109].

For the types of buildings discussed, installation of floating floors over CLT slabs is common and is an effective solution to vibration serviceability problems.

When designing floor plates for strength it is necessary to consider both bending and shear strength. Design strengths such as those in Table 7.1  take into account the layered nature of plates (Fig. 7.10). Bending strengths are based on the assumption that only CLT laminations with lumber oriented parallel to the plane in which bending moments occur resist forces. How-ever, such complexity is ignored during normal design, because it is integrated into the apparent design properties (Table 7.1).

The explicit design consideration required with respect to ensuring floors behave adequately as horizontal diaphragms depends on factors like floor layouts and plate element connections as discussed in Subsection 7.5.1.1.

7.5.1.4 Design of walls

Using CLT panels as walls provides interesting architectural options, because their in-plane stiffness and strength allow them to resist gravity, uplift, and racking design forces; to span gaps in facades; and to create overhanging storeys (Fig. 7.7 ). These applications have often been beyond the capabilities of more traditional timber construction methods (e.g. light-frame, post and beam) because of the requirement of large dimensions of elements, difficulties connecting elements, and affiliated high costs. CLT walls can consist of panels with or without stiffening ribs or as double-skin box elements with multiple glulam webs (Fig. 7.5). The use of stiffened Fig. 7.9: One-way span analogy for design of CLT floors

M M

Compression  Distribution of normal

stresses due to bending within the cross-section

 Distribution of shear  stresses within the

cross-section

 Rolling-shear   Rolling-shear  Traction

V V

Fig. 7.10: Analogies used to represent internal stress distributions due to moment and shear  forces

plates usually permits economical construction of walls that can resist high vertical compression forces at the lower storeys of tall and slender superstructures.

When superstructures are not structurally slender, it is often possible to use a number of quite simple approaches to estimate the flow of the horizontal forces (i.e. wall racking forces) that are caused by lateral design loads (i.e. equivalent static wind or seismic forces) to the walls. In cases where floor plans and wall openings are replicated between storeys, and the extent of openings is limited, buildings are essentially symmetrical about a vertical plane passing through the cen-troid of the building’s footprint. In such cases, it is often adequate to:

• ignore the resistance of walls that are not parallel to the vertical plane in which the super-structure’s response is being evaluated and

• assume that the floor platforms and roof behave as completely flexible diaphragms (pro- jected load area method) or as perfectly rigid diaphragms (relative wall stiffness method),

and to take the worst outcome from those extreme case assumptions as the design force.

In other instances, like when systems are not essentially symmetric on plan but storeys are replicated, the same approach can be taken to estimate components of horizontal force flows to the walls. However account has to be taken of interactions between those forces and ones that are associated with bending and shear distortion in planes coincident with a vertical plane passing through the centroid of the building’s footprint. In such instances it is also necessary to add components of horizontal force flows that occur because of torsional distortion about the superstructure’s vertical axis (i.e. effects of torsion force due to plan eccentricities).

The approaches outlined above, or similar ones, will usually provide a sufficient basis for decid-ing whether a builddecid-ing design concept is feasible, or if a more refined follow-up structural analysis is necessary. When further investigation is necessary, a finite element analysis may be required to represent CLT panels in walls and floors, the roof substructure and connections between elements, and any other substructures in the superstructure and foundation. A refined analysis will, for example, account for interactions between walls that do not lie in the same plane (Fig. 7.11). In many instances a refined follow-up analysis will not be required, but it is unwise to assume that is the case.

The combined effects of vertical and horizontal force flows for various design load combina-tions (e.g. effects of factored dead and seismic loads) will determine the minimum required dimensions of wall panels and connections. Unless a specific rule is mandated by locally appli-cable design codes, use of the summation of the ratios of the factored force effects to the fac-tored resistances approach is suggested:

Tension + Racking:___T  _f 

T _r  + R___ _f 

 R_r ^≤ 1.0 (7.1)

Compression + Racking:

(

)

≤ 1.0 (7.2)

where T  _f  is the factored tension force, T _r  is the factored tension resistance, C  _f  is the factored compressive force, C _r  is the factored compressive resistance (accounting for either crushing or buckling), R _f  is the factored racking force, and R_r  is the factored racking resistance.

7.5 STRUCTURAL ANALYSIS AND DESIGN  97

The foregoing does not apply without modification to hybrid superstructures in which multi-storey assemblies of CLT plates work in combination with substructures of other types. This exclusion applies, for example, when a building has primary lat eral load-resisting systems con-structed from RC or reinforced masonry.

7.5.1.5 Design of connections

Figure 7.12 shows an illustrative example of connection types and locations in a timber plate superstructure that require structural design.

Because suitable metal fasteners, connectors, and anchors are mostly proprietary products, their design properties must usually be acquired from manufacturers or third-party technical organizations that conducted tests on behalf of manufacturers. Consequently, engineers must

Seismic actions:

Realistic analogue: Effective tube

Seismic or wind and heavy roof 

Foundation

Wind and light roof 

Realistic analogue: Effective tube

Fig. 7.11: Interaction of wall panels directly in load paths with other walls to resist effects of lateral loads

Screw connections:

1 wall panel-to-panel 2 floor panel-to-panel 3 wall corner 

4 floor-to-wall junction

Hold-down connections:

5 wall-to-foundation

6 wall-to-floor-to-wall (using anchors) 7 wall-to-wall (using tie strap)

Shear connections:

8 wall-to-foundation 9 wall-to-floor 

4

4 6

5 8

9

9 3

2

1

4 7

3

Fig. 7.12: Example locations and types of connections requiring structural design

assure themselves that the available information is consistent with the needs of specific design projects and applicable design codes. This necessity will, for example, ensure that available design information is based on the appropriate definition of capacity (in terms of the associ-ated failure mechanism), deformation at failure, ductility ratio, and indexing effects of factors like duration and loading-type. Data in the public domain mostly indicate that connections in CLT made using slender self-tapping screws have high ductility when used to resist shear flows between panels [110], but it is prudent to check that such behaviour apply to particular product brands.

When installed in systems of the type discussed in this chapter, screws and other dowel-type fasteners usually have design capacities that are higher than for products like glulam that is manufactured from the same grade and species of lumber, because of the already mentioned toughening that CLT possesses from cross-laminating of lumber.

Figure 7.13a shows the suitability of sample connectors for joining wall panels at building cor-ners, and Fig. 7.13b shows the same for attaching floor or roof plates to tops of walls. In each application, desirable connections minimize the likelihood of causing delamination type split-ting of CLT (i.e. avoid wedging the layers apart).