Timber Roof Truss Analysis

Timber Frame Houses: Design Principles

Dr Robert Hairstans

19 August, 2009

2 Wood is a natural, heterogeneous, anisotropic, hygroscopic composite material.

Its structural properties are highly variable as a result of a whole range of influencing factors.

What has to be considered is the level of effect the influencing factors have in relation to the structural properties of the

timber section being considered.

If it can be considered negligible in the overall scale of investigation then it can be ignored.

When designing with timber it is important to have an appreciation of what affects its strength:

Density

Moisture content

Temperature

Time

Grain deviation

Knots

DESIGN PRINCIPLES: Material Properties

a) Cell wall organisation of a mature tracheid

b) Diagrammatic representation of a wedge shaped segment cut from a five year old hardwood tree showing the principal structural features

Cellular and structural features of timber

3DESIGN PRINCIPLES: Material Properties

Influence of grain deviation on failure mode of small clear samples in bending

b) Cross grain tension example

a) Failure types of clearwood in bending with

span parallel to the grain c) Splintering tension example

Simple tension

Cross grain tension

Splintering tension

Brash tension

Compression

Horizontal shear

4DESIGN PRINCIPLES: Material Properties

Influence of grain deviation & knots on failure mode of larger samples in bending

b) Localised cross grain tension

b) Diagonal example

Diagonal

Compression near a

knot

Localised cross-grain tension

5DESIGN PRINCIPLES: Strength Class & Grading

Property Symbol UnitsStrength class

C16 C24 C27

Characteristic bending strength, fm,k

N/mm

16 24 27

Characteristic tensile strength

parallel to the grain,ft,0,k 10 14 16

Characteristic tensile strength

perpendicular to the grain,ft,90,k 0.5 0.5 0.6

Characteristic compressive

strength along the grain,fc,0,k 17 21 22

Characteristic compressive strength

perpendicular to grain,fc,90,k 2.2 2.5 2.6

Characteristic shear strength, fv,k 1.8 2.5 2.8

Mean value of modulus of

elasticity parallel to the grain,E0,mean 8000 11000 11500

Fifth percentile value of modulus

of elasticity,E0,05 5400 7400 7700

Mean value of modulus of elasticity

perpendicular to the surface grainE90,mean 270 370 380

Mean value of shear modulus, Gmean 500 690 720

Characteristic density, rka

kg/m

310 350 370

Mean density, rmeanb 370 420 450

a Used for calculating the strength of mechanically fastened connectionsb Used for calculating weight

Characteristic values for some common strength classes of solid softwood

(British Standards Institution (BSI), 2003)

6DESIGN PRINCIPLES: European Structural Code of Practice

EN 1990

EN 1991

EN 1992 EN 1993 EN 1994

EN 1995 EN 1996 EN 1999

EN 1998EN 1997

Structural safety,

serviceability and

durability

Actions on structures

Design and detailing

Geotechnical and

Seismic design


Ultimate limit states are those associated

with the collapse or with other forms of

structural failure. Ultimate limit states

include: loss of equilibrium; failure through

excessive deformations; transformation of

the structure into a mechanism; rupture;

loss of stability.

Serviceability limit states include:

deformations which affect the appearance

or the effective use of the structure;

vibrations which cause discomfort to

people or damage to the structure;

damage (including cracking) which is likely

to have an adverse effect on the durability

of the structure.Instance where serviceability limit state has been breached

Instance where ultimate limit state has been reached


Advantages of Eurocode:

Facilitate further the free trade of construction products and services within EuropeProvides the designer with more scope for design input.Facilitate a wider selection of materials and components.Provides more guidance on the design of built up components facilitating the incorporation of new engineeredproducts and allow future products to be integrated for use.

Result in timber design which is economic, serviceable and ultimately safer.

Disadvantages of Eurocode:

More complicated design code and contains hundreds of design expressions for predicting the resistance ofstructural components.

Factors, have the potential to affect significantly the economics of one construction material over anotherdepending on the numerical value selected.

M = 1.3

Due to the inherent flaws in

timber, partial safety factor:

Comparison between poor and high quality design expressions

(Byfield and Nethercot, 2001)


Consider a beam in bending (y-y axis only)

10

DESIGN PRINCIPLES: European Structural Code of Practice

Consider a beam in bending (y-y axis only)

dymdym f ,,,, s

where m,y,d = maximum design bending stress about y axis

= My,d/Wy

fm,y,d = khkcritksyskmodfm,k/M

My,d - Bending moment

Wy - Section modulus

fm,k - Characteristic bending strength

kh - Depth or width factor

kcrit - Factor used for lateral buckling

ksys - System strength factor

kmod - Strength modification factor for duration of load and moisture content

M - Partial factor for material properties

11

DESIGN PRINCIPLES: Responsibility

The Engineer has overall responsibility for:

Strength, Stability & Structural serviceability

Primary concern is load bearing elements

Duty of care concerning durability

Meet the requirements of the client and the relevant Building

Regulations

12


Building use and location

Determine the imposed loadsRequirements for resistance to disproportionate collapseRequirements for the corrosion protection of metal fastenersProtective treatment of timber.

Methods of introducing system robustness

a) Ring beam over lintel providing redundancy to system b) Tying of system together

13


Design life

A design life for the building should be specified. A properly designed and maintained timber building can last for centuries, but most commonly a design life of 50 years is specified.

Timber frame systems can also be used for less permanent structures where a design life of 10 years may permit the use of higher strength properties.

Initial

value

Performance

indicatorNormal maintenance Repair

ULS

SLS

Visible damage

Serviceability

level

Time

Evolution with time of a structure

14


Design situations

The building must be designed to have adequate strength, stability and

structural serviceability in the following situations:

During construction (the execution phase).In designated use throughout its design lifeIn accidental design situations

Timber frame under construction

15

DESIGN PRINCIPLES: Design procedures

Developer

Architectural Information

Roof Truss System

Supplier

Initial Design

Timber Frame Supplier

Final Design

Floor System Supplier

Initial Design


Collation of design

information

Developer

Certification of structural

design


Preliminary layout of

building

Timber Frame Designer

Final Design


Indemnification of Design


Initial Design

Floor System Supplier

Final Design

Roof Truss System

Supplier

Final Design

16


Architects

Layouts

Building layout

Initial System Dimensioning & Sizing

Designation of Wall Types (Load Bearing & Non-Load-bearing).

Roof & Floor Orientations & Spans

Initial Make-Up of Timber Frame Walls:

Wall thickness & details

Timber grade & dimension

Sheathing material & arrangement

Fixing specification

Calculate Actions:

Self Weight

Imposed Loads (Wind, Snow, Live etc)

Yes

Select Floor Type & Initial Make-Up

Specification:

Solid Timber Joist

Engineered Wood Joist

Rim Beam Material

Decking Make-Up

Select Roof System Type & Initial

Make-Up Specification:

Trussed Rafter

Stressed Skin Panels

Prefabricated timber joists

Solid timber

Yes

Check Stud & Lintel

Specification

No

No No

Yes Yes

Accept

No

Check Stud

Specification

Check Racking Resistance

Building Stability

Requirements

Check Overturning

& Sliding

Specify Holding down

Straps & Shear Fixings

Yes No

Detail Connections

Does wall contain

openings?

Are ULS and SLS

criteria satisfied?

Roof System

1. Detail Connections

2. Check Member Sizes 3. Check Bracing & Holding Down

Are ULS and SLS

criteria satisfied?

Does capacity exceed

applied actions?

Does capacity exceed

applied actions?

Wall Diaphragm

Check Wall Panel

Overturning & Sliding

Floor System

1. Detail Connections

2. Check Member Sizes

3. Check Bracing


Timber composites

a) LVL b) LSL c) PSL

a) Fink c) Attic

Truss type

Floor options

a) Solid section b) I-Joist

17

DESIGN PRINCIPLES: Wind loading & system overturning

The principles of timber platform frame design are such

that it is normal to consider system stability in two parts:

1. Overall system resistance to sliding and overturning

as a result of the applied wind action:

Timber frame buildings are relativelylightweight, therefore it is necessary to verify

their overall stability under wind loading with

respect to overturning, sliding and roof uplift,

both during the execution phase and after

completion.

During the execution phase the weight of theroof tiles should be excluded.

For the majority of circumstances the selfweight of the system results in a holding down

moment and, as a result of friction, a resistance

to sliding, both of which are greater than the

applied overturning and sliding forces.

A point for further consideration is the commonpractice of levelling due to poor foundation

tolerances by inserting proprietary plastic

shims, this reduces frictional resistance to

sliding to an unknown level and as a result

additional resistance to sliding may require to

be specified.

Proprietary shims reducing level of frictional

resistance

Timber frame during construction

18

DESIGN PRINCIPLES: Wind loading & system overturning

2. The transmission of applied shear to the foundation:

Applied wind loading on a building is transferred to the foundations by diaphragm action. The side walls, considered to be simply supported at roof and foundation, transfer one half the total

wind load to the roof level.

The roof diaphragm, acting as a deep horizontal beam, transmits the load to the end shear walls, whichin turn transfer the load to the foundation via shear connections and holding down straps.

Temporary bracing during construction for stabilityTransmission of applied shear to foundation

19

DESIGN PRINCIPLES: Wind pressure

Recommendations for low rise timber frame:

Use a single reference height ze equal to the totalheight of the building above the ground (EC1-1-4

Figure 7.4).

Base the external pressure coefficients for walls onthe height of the wall to the eaves, rather than dividing

the wall height into zones.

For overturning, sliding, roof uplift and rackingresistance calculations involving more than one value

of coefficient of pressure cpe on the roof, first apply a

single conservative value to the whole roof. If the

structure fails, calculate the overturning moment or

the sliding, uplift or racking force more accurately.

To check structures during the execution phase theseasonal factor cseason may be used to modify the

basic wind velocity (EC1-1-4 4.2(3)). For the

execution phase it is expected that a value for cseasonbased on a 2 year erection period will be specified in

the National Annex to BS EN 1991-1-6#10.5. For small

scale timber frame projects a 1 year period might be

considered appropriate, for which the corresponding

value of cseason is 0.749. This reduces the wind

pressure by a factor of 0.749 = 0.56.

20

DESIGN PRINCIPLES: Wind pressure

For certain pitches of roof two sets of external pressure coefficients are given, and the critical coefficients maydiffer for different verifications.

Verification

Wind coefficient zoneComments

F G H I J

Wind perpendicular to the ridge q = 0Overturning

about z-z-0.5 -0.5 -0.2 -0.4 -0.5

Sliding +0.7 +0.7 +0.4 -0.4 -0.5

Roof uplift N/A N/A N/A -0.4 -0.5Calculate uplift on more severe side of ridge,

resisted by half the roof weight*

Racking +0.7 +0.7 +0.4 -0.4 -0.5Use for horizontal racking load and for uplift

which reduces vertical load on wall panels

Wind parallel to the ridge q = 90Overturning

about z-z-1.1 -1.4 -0.8 -0.5

Sliding N/A N/A N/A N/AWind friction forces may generally be

disregarded (see EC1-1-4 5.3(4))

Roof uplift -1.1 -1.4 N/A N/AAssume roof trusses are separate members and

check worst case

Racking -1.1 -1.4 -0.8 -0.5Use for horizontal racking load and for uplift

which reduces vertical load on wall panels

* If necessary a more accurate calculation using the moments about the opposite eaves exerted by all

the wind coefficient zones may be used in conjunction with the restoring moment of the whole roof.

Illustrative values of cpe,10 for overall stability and racking resistance verifications

Wind zones on a 30 duopitch gable roof (EC1-1-4 7.2.5)

21

DESIGN PRINCIPLES: Masonry shielding

Both testing and experience in the UK have demonstrated that within certain limits masonry walls will reduce the wind load

onto the timber frame of buildings.

BS 5268-6.1:1996 (British Standard Institution (BSI), 1996) makes allowance for this applying a wind load reduction factor.

The IStructE Manual for the design of timber building structures to Eurocode 5 provides guidance to the application of a similar

factor in Eurocode (IStructE & TRADA Technology, 2007) to

reduce the applied wind action.

The resulting reduced wind load Fw is considered to act uniformly over the entire area of the adjacent timber frame wall.

When the wind blows on or off a gable wall the total wind load

on or off the adjacent timber frame wall should be calculated as:

Fw = kmasonryFmasonry + Fspandrel

where kmasonry = wind shielding reduction factor.

Fmasonry = total wind load on or off the masonry

wall excluding the spandrel area

Fspandrel = wind load on or off spandrel.

In other cases it should be calculated as:

Fw = kmasonryFmasonry

where kmasonry = wind shielding reduction factor

.

Fmasonry = total wind load on or off the masonry

wallMasonry clad timber frame houses

22


Since kmasonry depends on the proportion of openings in the wall it may differ on

windward and leeward faces, therefore it must be used in conjunction with the

surface pressure method of EC1 (see EC1-1-4 Clause 5.3(3)).

kmasonry may be used only in accordance with the following conditions:

only the first four storeys of masonry not exceeding 10m in total height can be considered to contribute wind shielding

the external dimensions of the masonry walls are used to calculate the wind loads

the masonry walls are constructed in accordance with BS EN 1996-1-1:Eurocode 6 Design of Masonry Structures (EC6-1-1) and BS EN 1996-2: Eurocode 6.

Design of masonry structures (EC6-2) from a material designated in EC6-1-1.

the mortar conforms to the relevant part of BS EN 1996-1-1 with a minimum strength class of M4

the masonry walls are at least 100 mm thick and have a minimum mass of 75 kg/m

the masonry cladding is connected to the timber frame with wall ties that have sufficient strength and stiffness to transfer wind forces to the timber frame wall

manufactured in accordance with BS EN 845-1

kmasonry is applied to the wall as a whole up to eaves level, to the top of the fourth storey of masonry or up to 10m of masonry, whichever is less.

kmasonry should not be applied to the design of individual elements, for example studs.

kmasonry should not be used when checking the execution phase.

High Movement (HM) Wall Tie (dimensions in mm)

FT Wall Tie (dimensions in mm)

Courtesy of Cullen Building Products

23


Percentage of

shielded wall

occupied by

openings

Number of storeys shielded by masonry

1 and 2 3 4

A B C A B C D E F

0 0.45 0.60 0.75 0.50 0.68 0.85 0.60 0.74 0.88

10 0.50 0.64 0.78 0.55 0.71 0.87 0.64 0.77 0.89

20 0.56 0.68 0.80 0.60 .074 0.88 0.69 0.80 0.91

30 0.61 0.72 0.83 0.65 0.78 0.90 0.73 0.83 0.93

40 0.66 0.76 0.85 0.70 0.81 0.92 0.77 0.86 0.95

50 0.71 0.80 0.88 0.75 0.84 0.93 0.81 0.89 0.96

60 0.77 0.84 0.90 0.80 0.87 0.94 0.86 0.92 0.98

70 0.82 0.88 0.93 0.85 0.91 0.96 0.90 0.95 1.00

>70 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

KEY

A: For masonry walls with buttresses or returns of length >= 550 mm and spaced at not more than 9 m centres

B: For masonry walls with buttresses or returns of length >= 550 mm at one end only, wall length = 950 mm and spaced at not more than 9 m centres

E: For masonry walls with buttresses or returns of length >= 950 mm at one end only, wall length

24


Additional ties required at door and window openings (courtesy of Cullen Building Products)

Maximum net surface wind pressures for the FT range of brick / timber wall-ties

(courtesy of Cullen Building Products)

25

DESIGN PRINCIPLES: Overturning

The overturning calculation can be illustrated considering the previous

example:

AF, AG = total area of roof region F, G etc

z-z = centre line of structural wall beneath roof

aF,aG, etc = horizontal distances between z and centre of areas AF,

AG etc.

hF,hG, etc = vertical distances between z and centre of areas AF, AGetc.

b, = plan dimensions of structural walls = roof pitch

qp = peak velocity wind pressure (without masonry shielding

reduction)

Fbuilding,k = characteristic dead weight of building (excluding the tile

weight in the execution phase) Wind zones on a 30 duopitch gable roof (EC1-1-4 7.2.5)

26


For wind perpendicular to the ridge the clockwise design overturning moment about z-z is

M0,d = 1.5[qpcosa(0.5AFaF + 0.5AGaG + 0.2AHaH + 0.4AIaI + 0.5AJaJ)

+ qpsina(-0.5AFhF - 0.5AGhG - 0.2AHhH + 0.4AIhI + 0.5AJhJ)

+Fw,total,khe/2]

where Fw,total,k = total characteristic wind force on windward and leeward walls, after allowing for any

masonry shielding in completed phase.

The design restoring moment about z0-z0 is

MR,0,d = GFbuilding,kb/2 = 0.45Fbuilding,kb

with the partial load factor for permanent load, G, taken as 0.9 according to BS EN1990:2002, Table A1.2(A).

Fbuilding,k = characteristic dead weight of building (excluding the tile weight in the execution phase)

27


For wind parallel to the ridge the clockwise design overturning moment about z-z isM90,d = 1.5[qpcosa(1.1AFaF + 1.4AGaG + 0.8AHaH + 0.5AIaIJ)

+ Fspandrel,total,k(he + hr/3) + Fw,total,khe/2]

where Fw,total,k = characteristic wind force on windward wall for end-of-terrace building or total wind force

on windward and leeward walls for detached building, excluding the spandrel area of the

gable walls.

Fspandrel,total,k = characteristic wind force on windward spandrel for end-of-terrace building or net wind

force on windward and leeward spandrels for a detached building. For hip-ended buildings

or buildings with a flat roof Fspandrel,total,k = 0.

he = height to eaves

hr = height of roof from eaves

The design restoring moment about z90-z90 is

MR,90,d = GFbuilding,k/2 = 0.45Fbuilding,k

with the partial load factor for permanent load, G, taken as 0.9 according to BS EN1990:2002, Table A1.2(A).

28


If Md > MR,d

A restraining or holding down method should be specified.

The restraints should provide a total design restraining force along each wall of (Md-MR,d)/b or (Md-MR,d)/.

Timber frame holding down methods

29

DESIGN PRINCIPLES: Sliding

The sliding calculation can be illustrated considering the previous example,

where Fw,total,k and Fspandrel,total,k are as previously defined.

For wind perpendicular to the ridge the design sliding force is

Fd = 1.5[qpsina(-0.7AFhF 0.7AGhG 0.4AHhH + 0.4AIhI + 0.5AJhJ) + Fw,total,k]

For wind parallel to the ridge the design sliding force is

Fd = 1.5[Fw,total,k + Fspandrel,total,k]

The maximum value of Fd is Fd,max.

The Engineer is therefore recommended to specify positive restraints around all the structural perimeter walls providing a total design restraining

force of at least Fd,max.

If friction is utilise, a coefficient of 0.25 is recommended and a partial factor of 0.9 should be applied to the characteristic dead weight of the

building; any further lateral resistance still required may then be provided

by more positive restraints.


30

DESIGN PRINCIPLES: Roof uplift

It is generally regarded as good practice to attach every trussed rafter to the wall plate with truss clips, whether or not there is a possibility of roof uplift.

Truss clips make a significant contribution to the strength of the horizontal diaphragm in the ceiling plane.Truss clips reduce the potential damage skew nailing can cause to connector plates, rafters or wall plates by offering a positive fixing on two planes.

Truss clips

31


For wind perpendicular to the ridge the simplest approach is to calculate

the uplift force on the more severely loaded side of the ridge and

compare this with half the roof weight. In this case:

Fd = 1.5qpcosa(0.4AI + 0.5AJ)

The design resisting force applied by half the roof weight is:

Rd = 0.5 G Froof,k = 0.45Froof,k

with the partial load factor for permanent load, G, taken as 0.9

according to BS EN 1990:2002, Table A1.2(A).

If necessary a more accurate calculation can be calculated using the

moments exerted by all the wind coefficient zones in conjunction with

the restoring moment of the whole roof.

If Fd > Rd specify truss clips to attach the roof trusses to the head binder

or top rail of the wall panels.

The truss clips should provide a total design restraining force of at least

(Fd Rd) on each side of the roof.Wind zones on a 30 duopitch gable roof (EC1-1-4 7.2.5)

32


For wind parallel to the ridge the design uplift force should be calculated

for one side of a single truss in the most severely loaded zone:

Fd = 1.5qpcosa(1.1AF + 1.4AG) x 10s/2e

where s = trussed rafter spacing

e = the cross-wind building width or twice its

height, whichever is smaller.

The design resisting force applied by the roof weight on one truss is

Rd = 0.5sGFroof,k/2 = 0.225sFroof,k/

with the partial load factor for permanent load, G, taken as 0.9

according to BS EN1990:2002, Table A1.2(A).

Each truss, at least in the most severely loaded roof zones, should be

restrained by a truss clip at each eaves point with a design resistance to

uplift of at least (Fd Rd), determined as for wind perpendicular to the ridge.


33

DESIGN PRINCIPLES: Racking Requirements

2. The transmission of applied shear to the foundation:

Applied wind loading on a building is transferred to the foundations by diaphragm action. The side walls, considered to be simply supported at roof and foundation, transfer one half the total

wind load to the roof level.

The roof diaphragm, acting as a deep horizontal beam, transmits the load to the end shear walls, whichin turn transfer the load to the foundation via shear connections and holding down straps.

(a) Area of gable wall transferring

wind load to front racking wall

Racking load on first floor front wall from wind on gable wall

b) Diaphragm action of roof trusses and ceiling

transferring wind on gable wall to front wall

34


Standard timber frame wall panel

Structurally graded C16 framing members, specified with nowane, cross-section 38mm x 89mm, 38mm x 140mm or 44 x 97mm(depth governed by thermal insulation requirements and method of

insulation).

Stud spacing 600mm (maximum); where possible spacing shouldmatch joist centres which are normally 600mm but may be 400mm

or 450mm to reduce joist depth.

Top and bottom rails nailed to studs with a minimum of 3.0mmgalvanised smooth round steel wire nails or 3.1mm machine-driven

galvanised steel nails, 75mm long , 2 no. per 89 mm stud or 3 no.

per 140 mm stud.

External sheathing 9.0 mm thick OSB/3; fastened to studs with3.0mm galvanised smooth round steel wire nails or 2.8mm

galvanised machine-driven steel nails; for Class 2 buildings fastened

to studs with 3.35mm galvanised smooth round steel wire nails or

3.1mm galvanised machine-driven steel nails; all at least 50mm

long, spaced at 150mm on perimeter, 300mm on internal studs.

12.5mm thick gypsum plasterboard suitable for 30 minutes fireresistance fastened to the internal face with 2.65mm plasterboard

nails or plasterboard screws at least 40mm long, maximum fastener

spacing 150mm around perimeter and on internal studs if relevant.

35


Internal walls are constructed in a similar manner to external walls except that 12.5mm plasterboard is used on both sides and the stud size may be reduced to 38mm x 63mm.

If they are required to carry vertical or horizontal loads the stud depth should increase to at least 72mm, and if necessary an additional layer of structural sheathing materials may be introduced beneath the plasterboard to

provide additional racking resistance.

Internal & external panels Party wall

36


Timber frame party walls consist of two separatewall panels with a gap between them.

Normally they are sheathed only on the interiorface of each unit with two layers of plasterboard,

19.5 mm thick and 12.5mm thick respectively, the

joints being staggered.

It is particularly important that the inner layer isfixed to the framing with specified fasteners at the

specified spacings.

In order to provide sufficient racking resistance itmay be necessary to specify solid timber diagonal

braces in the cavity, taking care to preserve a gap

of at least 50mm.

Alternatively structural sheathing on the innerside of each leaf can be specified, but this can

result in drumming as it is not tied to masonry orother cladding, and it is therefore normally

avoided.

Any additional bracing must be accompanied byadequate holding-down arrangements to prevent

party wall panels from overturning.

Typical timber frame party wall

Gypsum plasterboard

Designed as two individual wall units separated

by a cavity, the sound performance is comparable

to that of a 240 mm thick concrete wall. Each wall

unit has plasterboard linings on its sides and is

filled with insulation between the wall studs.

Standard external (EX) timber frame wall panel

37

DESIGN PRINCIPLES: Racking Design (BS5268)

Current UK design method BS 5268-6.1 has beenused successfully for over 20 years.

It is a permissible stress design method wherestructures are designed so that materials are kept

within their elastic limits.

Racking resistances are based on the results oftested wall assemblies and are expressed in terms of

kN/m.

Test panel were constructed from Hem-fir, handdriven clout nails and outdated sheathing materials.

Modification factors K101, K102 & K103 are applied tothe basic racking resistance to account for variations

in nail diameter, sheathing thickness and nail

spacing.

Modification factors K104, K105, K106 & K107 are appliedto the basic racking resistance to account for

variations in wall dimensions, the presence of framed

openings and applied vertical loading.

Basic racking resistances for a range of materials and

combinations of materials

38

DESIGN PRINCIPLES: Unified European Code of Practice Design Method

Currently Eurocode 5 contains a Method A & Method B for racking design.

At present the U.K National annex to EC5 specifies the use of Method B, a conversation of BS 5268.

The conversion process has been ineffectual and it is widely accepted that method B gives inaccurate results.

As a result work has been on-going to create a unified Method C.

Forces acting on sheathing- to- frame fasteners

under idealised linear-elastic behaviour).

Forces acting on sheathing to frame fasteners

under idealised plastic behaviour

39

DESIGN PRINCIPLES: Plastic Design Method

L1 L

LLLLL 5.05.012

1

15.05.05.0 LLL

0F

FLr nt ,

FLr nb ,

0M

15.01 , LrLHF nb

22,2, 15.0115.0 LrLrHF nbnb

215.0

H

L

05.05.0 2

H

L

H

L

H

L

H

L

H

L

5.02

5.05.0411

H

L

H

L11

2

At top rail,

At bottom rail,

(at bottom rail)

H

F

40

DESIGN PRINCIPLES: BSI, UKTFA & Edinburgh Napier University Collaboration

Range of panels tested in accordance with BS EN 594:1995 (150/300mm nail spacing unless specified).

Standard (C-1,C-2) 300mm Studs - 300mm

sheet widths (C-3,C-4,C-5,C-

6)

75/150 spacing - Double end

studs (C-7,C-8,C-9,C-10)

50/100 spacing - Double end

studs (C-11,C-12,C-13,C-14)

50/100 spacing - double end studs -

double sheathed (C-15,C-16)

1200mm Panel width (C-

17, C-18,C-19,C-20)

41


Points of note from testing

Vertical restraint of windward stud through

hold down strap detail.

Vertical restraint of windward stud through

hold down strap detail.

Racking rig set-up Hydraulic ram

42

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

Standard 300mm Sheet widths

300mm Sheet

widths -VIL

Dense Nailed 75

Dense Nailed 75

-HD

Dense Nailed 50

Dense Nailed 50

-HD

Double Sheathed 50 -HD

Double Sheathed

50

1.2m Panel

1.2m Panel -

HD

Av

era

ge r

ackin

g s

tren

gth

(kN

)

Average Test value

Average/Design calculated value -1.156kN fastenener capacity*1.2 mod. factor

Load at 7.2mm deflection measured from test


Test results (150/300mm nail spacing unless specified).

Average Ultimate strength value, Fmax, for each panel configuration NB. VIL refers to the application of a Vertical Imposed Load, HD refers to the inclusion of Holding Down detail

Failure Mode A lead stud lifting and sheathingbreaking away from bottom rail

A AA

B

A

B

B

A

A

B

Failure Mode B Sheathing buckling out of plane

Failure Mode A or B

A

43


The following are critical to the racking

performance of timber frame panels:

1. Connection between the sheathing and

timber studs.

2. Bottom runner to sole plate connection

detailing.

3. Method of holding down.

4. Sole plate to substrate connection.

Floor slab

Facing

brick

Wall Panel

Sole Plate

Footer

Wall

Footing

Foundation

Floor slab

Facing

brick

Wall Panel

Sole Plate

Footer

Wall

Footing

Foundation

Timber frame construction in section

44

t1 t2

(a)

(b)

(c)

(d)

(e)

(f)

dtfF khRkv 1,1,,

dtfF khRkv 2,2,,

4112

1

,

1

2

2

1

23

2

1

2

1

221,1,

,

Rkaxkh

Rkv

F

t

t

t

t

t

t

t

tdtfF

4

)2(4)1(2

205.1

,

2

1,1,

,1,1,

,

Rkax

kh

Rkykh

Rkv

F

dtf

MdtfF

4

)21(4)1(2

2105.1

,

2

2,1,

,22,1,

,

Rkax

kh

Rkykh

Rkv

F

dtf

MdtfF

42

1

215.1

,

,1,,,

Rkax

khRkyRkv

FdfMF

Fv.Rk = min

The lateral load carryingcapacity of a nailed sheathing-

to-timber connection can be

calculated using the equations

laid down in EC5 Section 8.2.2.

Equations in EC5 are set upbased on the minimum fastener

spacings, edge and enddistances specified in EC5

Table 8.2.

By adhering to these values itis ensured that failure of the

connection shall occur in a

predictable ductile fashion asillustrated by the range of

possible failure modes specified

by EC5 Clause 8.2.2 Equation

8.6 (Figure 2.18).

DESIGN PRINCIPLES: Sheathing to timber connection

Where

Fv,Rk is the characteristic load-carrying capacity per shear plane per fastener;

fh,k is the characteristic embedment strength in the timber member;

ti is the timber or board thickness or penetration depth, with i either 1 or 2;

d is the fastener diameter;

My,Rk is the characteristic fastener yield moment;

is the ratio between the embedment strength of the members;

Fax,Rk is the characteristic withdrawal capacity of the fastener.

45

DESIGN PRINCIPLES: Holding down detail

Where



t1 is the timber or board thickness or penetration depth.




Typical holding down details (courtesy of Cullen Building Products)

dtfF khRkv 1,, 4.0

4215.1

,

,1,,,

Rkax

khRkyRkv

FdfMF

EC5 Section 8.2.3 Steel-to-timber connections - For a thin steel plate in single shear:

Timber frame holding down strap

(a)

(b)

Fv.Rk = min

t1

t1

46

NAIL SPECIFICATION

6No. 3.35 x 50mm stainless steel annular ring shank nails (ST-PFS)

4No. 3.35 x 50mm stainless steel annular ring shank nails (ST-PFS-M)

Holding Down Strap (ST-PFS/ST-PFS-M) Performance (courtesy of Cullen Building Products)

DESIGN PRINCIPLES: Holding down detail

47

DESIGN PRINCIPLES: Sole plate to substrate connection details

KMN 72 Shot Fired Dowel Masonry anchor

Masonry anchor Express nails fasteners

48

(c)

(d)

(e)

dtfF khRkv 1,1,,

41

42

,

2

1,

,

1,,

Rkax

kh

Rky

khRkv

F

tdf

MdtfF

Fv.Rk = min

DESIGN PRINCIPLES: Sole plate to substrate connection details

Where



t1 is the timber or board thickness or penetration depth;




43.2

,

,,,

Rkax

khRkyRkv

FdfMF

EC5 Section 8.2.3 Steel-to-timber connections - For a thick steel

plate in single shear:

t1

t1

t10

1000

2000

3000

4000

5000

6000

Ch

ara

cte

risti

c late

ral lo

ad

carr

yin

g c

ap

acit

y -

N

Fastener Type

Caculated value based on characterisitc properties

Characteristic values from test

49

DESIGN PRINCIPLES: System continuity

Party wall Party wall strap

50

DESIGN PRINCIPLES: System continuity

Where:

R is the total racking force of each of the

building units

sd is the available design shear transfer from

the party wall connector

Q

R

Q R s x No. of storeys

sd

sd

sd

sd

sd

sd

sd

sd

sd

sd

sd

sd

sd

sd

sd

sd

sd

sd

R R R

Characteristic load carrying capacity, sk = 1.6kN

Characteristic load carrying capacity, sk = 3.2kN

Acoustic wall strap (courtesy of Cullen BP)

51

DESIGN PRINCIPLES: Racking resistance in asymmetric buildings

Where several walls parallel to the wind direction resist the wind load on a timber platform frame building it is normally assumed that they share the load in proportion to their strength.

Assumption: strength of a wall is proportional to its stiffness and that the horizontal diaphragms create a stiff structure.

id

iddv

idvR

RFF

,

,,

,,

where Fv,d,i = design load on racking wall i

Fv,d = total racking load

Rd,i = design racking resistance of wall

52


If the shear walls on one side of a building are significantly less strong and stiff than those on the other side then the share of the load which they carry may be greater:

G.C

C.R

A

A

B B

aSteel Goal

Post (B)

Steel Goal

Post (A)b

W

L

a

Plan of timber frame system

In such cases it is assumed that the building acts like a rigid box which resists

both the shear force of the wind load and a

torsional moment.

This torsional moment is equal to the wind load multiplied by the distance between the

geometrical centre of the building and the

buildings centre of rotation (CR) measured perpendicular to the wind direction.

Wind direction

53


x3

R1

(x1 = 0) R3

R2

xmean

x

x2

(0,0)

For building plans on an x-y grid with an origin (0, 0) in one corner, the distance

of the CR from the origin for wind perpendicular to the x-axis is calculated from

the formula:

id

iid

R

xRx

,

,

where Rd,i = design resistance of racking wall i which is

parallel to the wind direction

= distance of CR from origin, measured along

x-axis

xi = distance of wall i from origin, measured

along x-axis

)()()( 332211 xxRxxRxxR Therefore:

hence

321

332211

RRR

xRxRxRx

Wind direction

54


The resulting torsional moment, is resisted by all the walls, with each

wall contributing to the total moment in proportion to its (stiffness) (lateral displacement) (perpendicular distance to the centre of rotation), i.e.

2

,, )( iidxmeandv zRkxxF

x3

R1

(x1 = 0) R3

R2

xmean

x

x2

(0,0)

where

Fv,d = design racking load on building (sum of wind force

on windward and leeward walls)

xmean = distance of geometrical centre of building from the

origin, along x-axis

kx =a constant calculated from the above equation

zi =perpendicular distance of any racking wall i from CR, i.e.

)( ixx )( iyy or as appropriate.

The additional load which each wall perpendicular to the x-axis takes to

resist the torsional moment is then:

Ftor,d,i = kxRd,ixi

The total load carried by each wall perpendicular to the x-axis is then:

Fd,i = Fv,d,i + Ftor,d,i

And it is checked that:

Fd,i Rd,i

Wind direction

55

DESIGN PRINCIPLES: Additional racking due to masonry

Masonry cladding with a minimum height of 2.4m and a minimum width of 600mm attached by suitable wall ties to storey height timber frame walls can increase their racking resistance.

The walls ties and their fasteners should have a design horizontal shear strength of at least 225N at deformations of 5mm or more and a characteristic horizontal shear stiffness of at least 30N/mm for deformations up to 5mm.

The additional racking resistance, Fv,masonry,Rd, provided by the masonry subject to the conditions above, is:

Fv,masonry,Rd = minimum of

masonrymasonry

Rdv

q

F

,25.0

where Fv,Rd = design racking resistance of attached timber frame wall in kN

masonry = length of masonry wall in mqmasonry = 0.75 kN/m for 4.4 ties/m (e.g. 600 mm horizontally, 380 mm vertically)

= 0.6 kN/m for 3.7 ties/m (e.g. 600 mm horizontally, 450 mm vertically)

56

DESIGN PRINCIPLES: Design of wall studs

Wall stud design verifications:

1. Combined compression and bending stress (strength check):

2. Column stability (to prevent buckling as a column):

3. Lateral torsional stability (to prevent torsional instability as in a beam) :

1ff d,y,m

d,y,m

2

d,0,c

d,0,c

s

s

1,,

,,

,0,,

,0,

s

s

dym

dym

dcyc

dc

ffk 1,,

,,

,0,,

,0,

s

s

dzm

dzm

dczc

dc

ffk

1,0,,

,0,

2

,,

,

s

s

dczc

dc

dymcrit

dm

fkfk

c,0,d Design compressive stress along the grain

m,y,d Design bending stress about the principal y-axis

m,z,d Design bending stress about the principal z-axis

fc,0,d Design compressive strength parallel to the grain

fm,y,d Design bending strength about the major y-axis

fm,z,d Design bending strength about the minor z-axis

kc,y or kc,z Instability factor

kcrit Factor used for lateral buckling

Wall studs in-situ

Wall studs in-situ

57


Wall stud design information:

For simplicity it is normally assumed that a stud resists the fullvertical load and full net wind load i.e. sheathing is ignored.

For the calculation of kcrit about the stronger y-y axis a value of0.85 may be used for the effective length, where is the length ofthe stud within the frame.

In the traditional UK design of buildings not exceeding fourstoreys it is normally assumed that wall studs are fully restrained

against buckling about their weaker axis by their connection to the

sheathing.

However in cases such as party wall where sheathing is limited,the load capacity is reduced, so some caution is recommended,

particularly for buildings above four storeys.

To support the ends of lintels single or multiple studs will berequired at each end. If they are made of the same material and

section as the main wall studs the total number required is at least

equal to the number of wall studs removed by the opening.

Beneath a window sill studs are normally provided in the positionthat the full height wall studs would have been.

Wall studs aligned with I-joists

Wall studs supporting lintel over opening

58


Notching and drilling of studs

Wall studs should not be notched.

Unless otherwise justified by calculation, drilling of studs should conform to the following requirements:

Holes should be drilled on the centreline, avoiding knots.Hole diameters should not exceed one quarter of the stud depth.Holes should be no nearer than 150 mm and no further than a quarter of the stud length from either the top or bottom of the stud.

Centre-to-centre hole spacing should be at least 4 hole diameters.

Deflection

The effect of axial load on the horizontal deflection of a wall stud subject to wind loading may be generally be ignored, except in the

case of slender studs subject to high wind loads, when ignoring

axial load may result in excessive deflection.

Bearing strength of bottom rails

The bearing strength of the bottom rail should be verified.Intermediate studs should be checked rather than edge studs as they carry more load.

Wall studs under an opening

Continuity across a goal post

59

DESIGN PRINCIPLES: Design of lintels

Lintels above windows, doors and patio windowsmay consist of two solid timber members fastened

together with nails, screws, dowels or bolts, a

single LVL or hardwood member, or where

necessary a bolted steel flitch beam.

For lintels consisting of two or more solid timbermembers securely fastened together so that both

members can share the load the strength

properties including the bearing strength may be

increased by a factor ksys of 1.1.

A deflection limit of wfin 250 under dead +imposed load is recommended.

Screw size: 3.1mm dia. 75mm long galvanised screws at 300mm centres staggered mid distance between edge and centreline. No screw closer than

60mm to end of lintel.

Lintel over opening

60

DESIGN PRINCIPLES: Design information for Roofs

Before designing a roof the Engineer should assemble the following data:

site location, height, ground roughness and reference to any unusualwind conditions

overall site plan indicating any adjacent buildings or features whichmight affect the wind loading

height of building from ground level to eavesbuilding type and whether access to the roof is required for purposesother than maintenance or repair

intended use of roof spacereference to any unusual environmental conditions which may affectsteel or timber

the type of any preservative treatment requiredplan and elevations of roof including overhangs and other eaves details,window lights, hatches, stairwells, chimney, and support details (nature,

position and breadth) including intermediate supports (e.g. load-bearing

walls)

type and weight of roof tiles or coveringweight of any sarking, insulation materials and plasterboardthe size and position of all water tanksthe weight and position of any permanent ancillary equipment to besupported on the ceiling joists

preferred spacing of raftersany limitations on member size, e.g. to accommodate insulation or tomatch existing members, or minimum thicknesses for fixing ceiling

boards or sarking

rafter bracing method to be used (solid timber bracing or sarking using aspecified panel product, or possibly steel ties in the case of larger roof

structures)

limitations on vertical deflection for rafters and ceilings joists, and onhorizontal deflection at the eaves relative to the gable walls.

any unusual site conditions (e.g. low loading limit) which may affect thedesign and assembly method

Sarked attic trusses

Roof layout drawing

61

DESIGN PRINCIPLES: Design information for Roofs

The Engineer in turn should obtain the following output

information from the roof designer:

the basis of design, including any design assumptionsmade not covered below

detailed drawings showing all trussed rafters in the roofand their positions and spacing

timber strength classes or grades and species, and cross-sectional dimensions

the type, sizes and positions of all jointing devices withtolerances, or the number of effective teeth or nails

required in each member at each joint

the positions and sizes of all bearingsthe loadings and other conditions for which the trussedrafters have been designed

the positions, fixings and sizes of any lateral supportsnecessary to prevent buckling of compression members

such as rafters and struts

the location and support method for tanks and ancillaryequipment or loads, plus the capacity and magnitude of

any additional loads assumed, e.g. weight of water

the reactions to be accommodated at the bearings foreach separate action (see Table 7.1) or load case (see

Table 7.2) including asymmetrical snow loads and

exceptional snow drifts where relevant

maximum initial and final deflections of rafters and ceilingjoists

instructions concerning the fixing of any girder trusses orother special connection details

Type A

Roof truss details from MiTek Software (Designed by Donaldson Timber

Engineering Ltd)

62

DESIGN PRINCIPLES: Roof system points of note

Glued joints

Split ring

Double sided toothed-plate

Dowel

Bolt

Punched metal plate

Nail

Forc

e, F

(kN

)

Slip (mm)

TS 100 truss shoe

Steel truss shoe

Bolted connection of steel truss shoe

Example of truss nail plates

Experimental load slip curves for joints in tension parallel to the grain (Racher, 1995)

63

DESIGN PRINCIPLES: Roof system bracing

Bracing of the system forms two basic functions:

1. Stability bracing holds the trusses firmly in place and

keeps them straight so that they can resist all the

loads applied (with the exception of wind).

2. Wind bracing, often required in addition to stability

bracing so wind forces on the roof and walls can be

withstood.

Eurocode guidance for bracing in the plane of the rafters

and the ceiling of trussed rafter roofs which fall within

certain dimensional limits will be contained in in BS PD

6693: Complementary information for use with Eurocode

5. British Standards Insittuion. London.

Outside these limits the roof designer should design the

rafter bracing in accordance with EC5 9.2.5.3 and the

ceiling bracing using the EC5 method described in sub-

section 5.5.2.

BS5268-3:1998Standard bracing for rafter and web members

of duopitch trussed rafters

64

DESIGN PRINCIPLES: Roof system designed for lifting

Bracing element

fixed to headbinder

of system

Diagonal Bracing Element to be

fixed to Gable Panel

Longitudinal Bracing

Element to be fixed to

Gable Panel

Gable Panel

System

Truss

On-site applicationBracing detail

Lifting of roofReinforced bracing

The upgraded bracing would function as

bracing once the roof is in service and

would improve the structural integrity of

the system as it is an over-specification.

In accordance with BS 5268:1998 Part3 Annex A.1 all bracing members are ofminimum width 89mm and minimum

depth 22mm and the following pointsfrom the code are noted due to their level

of importance:

1. All bracing members are nailed toevery trussed rafter they cross with

two 3.35mm diameter galvanized wire

nails with a minimum length equal to

the bracing thickness plus 32mm.Therefore, the minimum nail length to

be used is 77mm.

2. Where bracing members areprovided in two pieces, they are lap

jointed over at least two trussed

rafters and nailed as described

above.

65

Recommended texts:

IStructE & TRADA Technology (2007) Manual for the design

of timber building structures, The Institution of Structural

Engineers, ISBN 978 0 901297

Porteous & Kermani (2007) Structural Timber Design to

Eurocode 5, Blackwell Publishing, ISBN 978 14051 4638 8

66

Centre for Timber Engineering

Edinburgh Napier University

10 Colinton Road

Edinburgh EH10 5DT

United Kingdom

http://cte.napier.ac.uk/

[email protected]

Timber Roof Truss Analysis

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