19 - Design of Timber Floor Joists.pdf

36
Design principles
TheStructuralEngineer
November 2012
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
›
Note 18 Level 1
Technical
Technical Guidance Note
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.
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.
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/mm 2 ) – f m,k 16 24
Characteristic shear strength (N/mm 2 ) – f v,k 3.2 4.0
Parallel mean modulus of elasticity (N/mm 2 ) – E 0,mean 8000 11000
Mean density (kg/m 3 ) 370 420
ICON
LEGEND
• Design principles
• Applied practice
• Worked example
• Further reading
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.
Characteristic density (kg/m3 ) 310 350 Figure 1 • Nomenclature for timber elements

Table 2: Common sizes of timber floor joists
Sawn depth
(h) mm
Sawn width
(b) mm
Exposure conditions
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
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
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
Table 3: Values of k mod for solid timber joists
• Short term – less than 1 week e.g.
snow loads, maintenance access and
accidental loads
• Instantaneous – fractions of a second e.g.
wind, impact and explosive loads
The figures given in Table 3 provide the
values for the factor k mod , 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 k mod . 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 k mod values are:
• Permanent loads with k mod = 0.6
• Permanent loads + long term loads
with k mod = 0.7
• Permanent loads + long term loads +
medium term loads with k mod = 0.8
• Permanent loads + long term loads +
medium term loads + short term loads
with k mod = 0.9
• Permanent loads + long term loads +
medium term loads + short term loads +
instantaneous loads with k mod = 1
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 k mod of 0.8
as it is subject to an imposed load, which
is defined as medium term, as well as
self-weight.
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
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37
Deformation
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 k def is
applied to the elastic modulus properties
of the timber. Table 4 defines these values.
Table 4: Values of k def for solid timber joists
Service
class
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 k h 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/m 3 , then k h factor is defined thus:
150 . 02
kh
= a k
h
1 2 3
k def 0.6 0.8 2.00
or 1.3 whichever is the lesser.
For all members that are greater than
150mm deep, the value of k h is taken to
be 1.0.
(1)
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 k crit is applied to
the bending capacity of the joist. For more

38
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 k crit .
Applied bending stress
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:
My,d
vm,y,d =
(2)
Wy
Where:
My,d is the design bending moment
is the elastic modulus of the joist, defined as:
Wy
Wy
=
bh
2
6
Applied shear stress
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:
3Vd
xd
=
2bh
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.
(3)
(4)
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.
›
Note 18 Level 1
Technical
Technical Guidance Note
Design bending strength is defined as:
kh $ kcrit $ kmod $ ksys $ fm,k
fm,y,d
=
(5)
c M
Design shear strength is defined as:
kmod $ ksys $ fv,k
fv,d
=
(6)
c M
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.
Worked example
Serviceability
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
A timber floor is to span 4.8m and is supporting a characteristic imposed floor load of
2.5kN/m 2 . The joists are placed at 400mm spacing and have timber boards fixed on top
that have a self-weight of 0.15kN/m 2 . 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.

Table 5: Deflection limits for
solid timber joists
Use Deflection limit
Brittle finishes
e.g. plasterboard,
ceilings, walls
No brittle finishes
e.g. roofs
Accidental
e.g. during a fire
Span/250
Span/150
Span/20
(1+k def ). The instantaneous deflection
for imposed (variable) load is increased by
a factor (1+ψ 2,1k def ), assuming only one
variable load. The sum of these deflections,
less any precamber, provides the overall
deflection due to bending.
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.
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.
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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
39
Timber joist span tables
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/m 2 .
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/m 2 .
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