19 - Design of Timber Floor Joists

› Note 18  Level 1

36

Technical Technical Guidance Note

TheStructuralEngineer November 2012

Design of timber floor joists Introduction

One of the most common structural elements is the timber floor joist. This is normally found in residential properties, but can also be seen in medium sized commercial developments. This Technical Guidance Note will explain the principles behind the design of timber floor joists and provide a worked example. All of the advice given will be in accordance with BS EN 1995-1-1 Eurocode 5: Design of Timber Structures – Part 1-1: General – Common rules and rules for buildings.

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• Design principles

• Applied practice

• Worked example

• Further reading

Design principles Timber is a natural material and is variable both in strength and stiffness. The strength and stiffness of a piece of timber depends on its species, where it was grown, the rate of growth, the number of ‘defects’ (e.g. knots) and the angle of the grain. In order to make effective structural use of timber it needs to be graded and allocated directly or indirectly to a strength class. The strength of a piece of timber also depends on its moisture content and structural timber should be installed when its moisture content is similar to that experienced during growth. Allowances have to be made for this moisture content when the structure is designed. It should be noted that this Technical Guidance Note is solely concerned with the design of solid timber floor joists and not other forms of compound timber floor joists available. This includes Glulam and

Laminated Veneer Lumber (LVL) joists as they are beyond the scope of this note.

Timber floor joist strength grades and classes Softwood timber can be visually graded to General Structural (GS) and Special Structural (SS) grades. These grades are then allocated to a particular Strength Class. With respect to timber floor joists, in the UK they are typically sawn from GS and SS softwoods and are graded in two strength classes respectively: C16 and C24. C16 is the more common grade but weaker class and is therefore easier and cheaper to procure. C24 is a little stronger, but more expensive and is generally used where restrictions such as geometry and depth of floor construction play a significant part in the design of the structure. An example of such an instance would be joists that have long spans or a trimming beam around a large void.

Member sizes Timber joists are cut to pre-defined sizes and are limited in their length from a range of 1.8m to 5.4m. It is possible to have lengths of up to 7.2m however, but they do come at a premium due to their paucity. These lengths are subdivided into increments of 0.3m. In regards to cross-section size, Table 2 provides a list of the most commonly available sections, with both machined and sawn timber sizes shown. It is possible to specify timber sizes of up to 300mm deep, but these are difficult and expensive to acquire. Figure 1 provides guidance on the nomenclature used for timber elements, which are referred to throughout this note.

The material properties of C16 and C24 timber are given in Table 1.

Table 1: Material properties of softwood timber grades C16 and C24 Properties

C16

C24

Characteristic bending strength (N/mm2) – fm,k

16

24

Characteristic shear strength (N/mm2) – fv,k

3.2

4.0

Parallel mean modulus of elasticity (N/mm2) – E0,mean

8000

11000

Mean density (kg/m3)

370

420

Characteristic density (kg/m3)

310

350

•

Figure 1 Nomenclature for timber elements

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Deformation

Table 2: Common sizes of timber floor joists Sawn depth (h) mm

Sawn width (b) mm

Machined depth (h) mm

Machined width (b) mm

150

25

145

22

175

38

170

35

200

47

195

44

225

63

220

60

250

75

245

72

• Short term – less than 1 week e.g.

Exposure conditions

snow loads, maintenance access and accidental loads • Instantaneous – fractions of a second e.g. wind, impact and explosive loads

Timber is a hygroscopic material that absorbs/releases moisture from/to its surrounding environment depending on the amount of moisture in that environment. As the strength and stiffness properties are dependent on the moisture content, it is necessary to account for the environment around the timber. Three service classes have been defined. Examples of typical environments and the respective service class are: • Service class 1 – intermediate floors, warm roofs, internal and party timber frame walls • Service class 2 – ground floors, cold roofs, timber frame walls that are against the outer skin of cladding and all other instances where the timber is protected from direct exposure to water • Service class 3 – external, fully exposed

The figures given in Table 3 provide the values for the factor kmod , which is the factor that is applied to the strength properties of timber and is based on the imposed load (variable action) duration. Note that in the case of load combinations the load condition with the shortest time period defines the value of kmod . When designing timber elements it is important to check for all conditions and to design the element based on the most critical. These conditions along with their respective kmod values are: • Permanent loads with kmod = 0.6 • Permanent loads + long term loads with kmod = 0.7 • Permanent loads + long term loads + medium term loads with kmod = 0.8 • Permanent loads + long term loads + medium term loads + short term loads with kmod = 0.9 • Permanent loads + long term loads + medium term loads + short term loads + instantaneous loads with kmod = 1

Load duration The strength of a piece of timber is dependent of the duration of the load. The longer the duration of the load the higher the strength of timber that must be provided in order to resist that load. To this end there are a number of factors that are applied to the characteristic properties of the timber as defined in Table 1. The UK National Annex to Eurocode BS EN 1995-1-1 classifies load durations as follows: • Permanent – more than 10 years, e.g. selfweight including finishes • Long term – 6 months to 10 years e.g. storage loading • Medium term – 1 week to 6 months e.g. imposed floor loads

For timber floor joists within a building the typical critical condition is the imposed floor load with the self-weight of the joists and super-imposed dead load. This load condition results in a value of kmod of 0.8 as it is subject to an imposed load, which is defined as medium term, as well as self-weight.

Table 3: Values of kmod for solid timber joists Service class

Permanent

Long term

Medium term

Short term

Instantaneous

1&2

0.6

0.7

0.8

0.9

1.10

3

0.5

0.55

0.65

0.7

0.9

The elastic properties of a timber structure depend on the moisture content of the timber and consequently the deflection will be dependent on the service class. To take this into account the factor kdef is applied to the elastic modulus properties of the timber. Table 4 defines these values. Table 4: Values of kdef for solid timber joists Service class

1

2

3

kdef

0.6

0.8

2.00

Enhancement due to shallow member size The way that the grading rules for structural timber work, means that for joists less than 150mm in depth, some enhancement of the strength is allowed. To reflect this, a modification factor kh is applied to bending strength of the timber. If a member is less than or equal to 150mm deep and has a material density of less than 700 kg/m3, then kh factor is defined thus:

150 0.2 kh = a h k

(1)

or 1.3 whichever is the lesser. For all members that are greater than 150mm deep, the value of kh is taken to be 1.0.

Load sharing Timber floor joists are generally placed at fairly close centres with decking/boarding across them which will distribute load between the joists. To account for this, the modification factor ksys is applied to characteristic strength properties of the timber joist which enhances its resistance to bending and shear stress. Provided the floor boards/boarding has staggered connections and are continuous over at least two spans, the value of ksys is taken to be 1.1. In all other instances the value of ksys is taken to be 1.0.

Lateral torsional buckling of timber joists In most instances the risk of lateral torsional buckling affecting a floor joist is not present. This is due to the existence of a floor finish that the joists are supporting acting as a restraint. In the rare condition where the compression face of floor joists is not restrained against bending induced torsional rotation, then the factor kcrit is applied to the bending capacity of the joist. For more

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Technical Technical Guidance Note

TheStructuralEngineer November 2012

information on this, the reader is directed to clause 6.3.3 of BS EN 1995-1-1, which describes the derivation of kcrit.

Design bending strength is defined as:

Applied bending stress

Design shear strength is defined as:

fm,y,d

The applied bending stress to floor joists is associated to its major axis, which is described as ‘y-y’ in Figure 1. To determine the design bending stress, the design bending moment is calculated based on the applied loads and support conditions of the joist as well as its geometry. The equation for determining the design bending stress (σm,y,d) to a timber joist is as follows:

v m,y,d =

M y,d Wy

bh 6

(3)

For a simply supported joist the design maximum shear force is equal to the design reaction. In the case of timber the maximum design shear stress (not average shear stress) needs to be checked against the design shear resistance. The maximum design shear stress of a rectangular section is calculated using:

3V d 2bh

(5)

(6)

The value of fv,d is then multiplied against the effective depth and width of the timber floor joist at the point of support. This is compared against the applied design shear the timber joist has to support. In order to take into account cracking within the timber, the width of the joist is reduced via factor kcr which for solid timber members is taken as 0.67.

The deflections of timber joists should be limited so that any brittle finishes they’re supporting are not damaged. Table 5 provides guidance on the vertical deflection limits for joists that are based on the characteristic imposed loads (variable actions) and dead loads (permanent actions) that are being applied to the floor joists. Creep must also be considered for timber elements as it is a significant factor when assessing serviceability limits. To allow for this, the instantaneous deflection due to the permanent loads is increased by a factor

Worked example

2

Applied shear stress

xd =

k mod $ k sys $ fv,k cM

Serviceability

(2)

Where: My,d is the design bending moment Wy is the elastic modulus of the joist, defined as:

Wy =

fv,d =

k h $ k crit $ k mod $ k sys $ fm,k = cM

(4)

Where: Vd is the design applied shear force h is the depth of section under consideration at the point of support b is the width of the section under consideration If the beam is notched on the same side as the support, the design shear resistance can be considerably reduced and is a detail which should be avoided if possible.

Partial factor due to material variances Like all materials used as structural elements, timber has a partial factor, which is applied to its strength properties due to variances within it. In the case of solid timber elements, the partial factor has a value of 1.3.

Bending strength and shear strength Once the applied forces and subsequent stresses are determined, the design bending and shear strengths of the timber joist need to be calculated. These are compared against the applied design stresses in order to determine the acceptability of the chosen joist size and strength grade.

A timber floor is to span 4.8m and is supporting a characteristic imposed floor load of 2.5kN/m2. The joists are placed at 400mm spacing and have timber boards fixed on top that have a self-weight of 0.15kN/m2. The presence of these boards provides full lateral restraint to the timber floor joists as well as allowing for load sharing between floor joists. The finish to the floor is brittle. Check to see if a 250mm x 75mm C16 timber joist can support this load.

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Table 5: Deflection limits for solid timber joists Use

Deflection limit

Brittle finishes e.g. plasterboard, ceilings, walls

Span/250

No brittle finishes e.g. roofs

Span/150

Accidental e.g. during a fire

Span/20

(1+kdef ).  The instantaneous deflection for imposed (variable) load is increased by a factor (1+ψ2,1kdef ), assuming only one variable load. The sum of these deflections, less any precamber, provides the overall deflection due to bending.

Timber joist span tables

There is also the issue of deflection due to shear. This is rarely a critical condition, but it is prudent to add 10% to the overall deflection to arrive at a final value to allow for it.

Alternatively it is possible to use the Eurocode 5 Span Tables, that have been developed by TRADA. These have a similar set of tables, but again are limited to imposed loads of no greater than 1.5 kN/m2.

Additionally floor joists should be checked to ensure that their vibration performance is acceptable, this can be of concern with joists which span is in excess of 4.0m.

It is possible to refer to timber joist span tables for sizing of joists, such as those included in Table 7 of BS 8103:3 2009. These tables however are limited to imposed loads of 1.5 kN/m2.

Eurocode 0.

Applied practice

BS EN 1995-1-1 Eurocode 5: Design of Timber Structures – Part 1-1: General – Common rules and rules for buildings BS EN 1995-1-1 UK National Annex to Eurocode 5: Design of Timber Structures – Part 1-1: General – Common rules and rules for buildings BS EN 336 2009: Structural Timber – Sizes, permitted deviations BS EN 338 2009: Structural Timber – Strength classes BS 8103:3 2009: Structural Design of Lowrise Buildings Part 3: Code of practice for timber floors and roofs for housing

Glossary and further reading Hygroscopic – Moisture absorbing. Modification factors – Factors that are applied to the characteristic material properties of timber elements.

Precamber – A forced deformation of a member that reduces the effect of deflection following the application of loads.

Further Reading The Institution of Structural Engineers/ TRADA (2010) Manual for the design of timber building structures to Eurocode 5 London: The Institution of Structural Engineers/TRADA TRADA (2009) Eurocode 5 span tables for solid timber members (3rd ed.) High Wycombe: TRADA Porteous, J. and Kermani, A. (2007) Structural Timber Design to Eurocode 5 Chichester: John Wiley & Sons