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Timber Beam Calculator to EC5's banner
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Timber Beam Calculator to EC5

Verified by the CalcTree engineering team on July 2, 2024

This calculator designs timber bending members, commonly referred to as rafters and joists, by ensuring the beam meets flexural, shear, bearing, deflection and vibration requirements. The calculator takes into account a notch at the support.
All calculations are performed in accordance with:
  1. BS EN 1995-1-1 2004 A2 2014 Design of timber structures - General rules. This code is typically referred to as "Eurocode 5" or "EC5".
  2. BS EN 1995-1-1 2004 A1 2008 UK NA to Design of timber structures - General rules. This is the UK National Annex to Eurocode 5.
  3. IStructE Manual for the design of timber building structures to Eurocode 5
Check out our Timber Design Standards - Eurocode 5 for further explanation about timber design.

Calculation

Assumptions

  1. The calculator accepts all wood types (solid, glulam and LVL of softwood or hardwood)
  2. Input geometry is for rectangular and square sections only
  3. Timber beam is simply supported
  4. Lateral torsional buckling is prevented, which means
    
    in the bending capacity equation
  5. Combined major and minor axis bending check is not included. Axial check is not included.


Material Properties



Strength class
:C14​



fm,k
:14​



fv,k
:3​



fc,90,k
:2​



E0,mean
:7000​


Strength class

The European standard EN 338:2016 outlines a system for strength classes for general use in European design codes applicable to all softwood and hardwood timber for structural use.
The strength classes are tabulated in Table 1 and Table 2 of EN 338 and are designated by the letter "C" for softwood and "D" for hardwood. The strength class also includes a number indicating the value of the edgewise bending strength. For example, timber with strength class C16 is a softwood with a bending strength of 16MPa.


Service class
:3​


Service Class

EC5 Section 2.3.1 outlines a service class system to assign strength values and calculate deformations under the defined environmental conditions. The classes are characterised by the moisture content at 20⁰C temperatures and the relative humidity of the surrounding air.
  1. Service class 1: The moisture content and relative humidity of the surrounding air only exceeds 65% for a few weeks per year. Most softwood will not exceed a 12% average moisture content in this class.
  1. Service class 2: The moisture content and relative humidity of the surrounding air only exceeds 85% for a few weeks per year. Most softwood will not exceed a 20% average moisture content in this class.
  1. Service class 3: Climatic conditions leading to higher moisture content than in service class 2.


Material type
:Solid timber - grade stamped individually​



γ_M
:1.3​


Partial factor for material properties



The partial factor

for material property accounts for model uncertainties and dimensional variations.
EC5 Table 2.3 [2]




Beam Geometry



Timber beam designation
:195 x 44 C14​



h
:{"mathjs":"Unit","value":195,"unit":"mm","fixPrefix":false}​



b
:{"mathjs":"Unit","value":44,"unit":"mm","fixPrefix":false}​



lb
:{"mathjs":"Unit","value":100,"unit":"mm","fixPrefix":false}​



L
:{"mathjs":"Unit","value":3,"unit":"m","fixPrefix":false}​



s
:{"mathjs":"Unit","value":1000,"unit":"mm","fixPrefix":false}​

👉 If calculating for a single member, set

= 1000mm



Notch depth
:{"mathjs":"Unit","value":45,"unit":"mm","fixPrefix":false}​



Notch slope length
:{"mathjs":"Unit","value":200,"unit":"mm","fixPrefix":false}​



x
:{"mathjs":"Unit","value":100,"unit":"mm","fixPrefix":false}​

Beam nomenclature

Beam notch nomenclature



Modification Factors



Load duration
:Long-term​



k_mod
:0.55​


Load duration and moisture content factor



The modification factor

is described in Clause 3.1.3 of EC5 and used in all the ULS capacity equations. It accounts for the effect of moisture content and load duration using different categories of ‘service class’ and ‘load-duration class’.
EC5 Table 3.1 [2]

The load duration classes are defined by the effect of a constant load acting for a certain time period during the life of the structure. Actions are assigned to one of the load durations given below:
EC5 Table 2.1 [2]

EC5 Table 2.2 [2]

👉Tip: as per Clause 3.1.3(2), if your factored design actions (

and

) consists of actions in different load-duration classes, choose

which corresponds to the action with the shortest duration. For example, for a combination of dead load and live load, choose

for a medium-term action.


k,sys
:1​


System strength factor



The modification factor

is described Clause 6.6 of EC5 and used in all the ULS capacity equations. It considers that the continuous load-distribution system is capable of transferring loads from one member to the neighbouring members. For the purpose of this calculator,

is recommended to be taken as 1.1.
BS EN 1995-1-1:2004+A1:2008 Clause 6.6



Support condition
:Discrete support, udl/PL>2h from support, solid softwood​

👉Select continuous support if sections are restrained along the compression flange by battens or floorboards


k_h
:1​


Depth factor



The modification factor

is described in EC5 Clause 3.2 and used in the bending capacity equation for beam depths of solid timber less than 150mm. The characteristic values of bending strength

is increased by

:

kh=min⁡{(150h)0.21.3 [3.1]k_{\mathrm{h}}=\min \left\{\begin{array}{l}\left(\dfrac{150}{h}\right)^{0.2}\\\text{}\\ 1.3\end{array}\right.\ \hspace{1cm}\text{[3.1]}


k_cr
:0.67​


Crack factor



The modification factor

is described in Clause 6.1.7(2) of EC5 and used to decrease the shear capacity. It accounts for drying splits and glue line failure by reducing the width of the cross-section. The recommended values are:
  1. 
    for solid timber and glue-laminated timber
  1. 
    for other wood-based products in accordance with EN 13986 and EN 14374
EC5 Clause 6.1.7(2)



k_v
:0.811812174437201​


Reduction factor for notched beams



The modification factor

is described in Clause 6.5.2 of EC5 and used in the shear capacity equation of a notched beam.
End-notched beams

EC5 Clause 6.5.2

In the formula for

, the factor

accounts for the sheathing material and is provided in EC5 Clause 6.5.2 (2):
EC5 Clause 6.5.2



kc,90
:1.5​


Bearing strength factor



The values of

is described in Clause 6.1.5 of EC5 and is used in the bearing capacity equation. It accounts for the load configuration, possibility of splitting and degree of compressive deformation. The value for

varies between 1.0 and 1.75 depending on the type of timber used (solid timber or glulam) and the support conditions encountered.
For members on discrete support as shown in the diagram below, provided that

,

is taken as:
  1. 
    
    for solid softwood timber
  1. 
    
    for glued laminated softwood timber provided that l ≤ 400mm
Member on discrete support EC5 Figure 6.2 [2]



k_def
:2​


Deformation factor



The modification factor

is described in Clause 3.1.4 of EC5 and used in the deflection equation for creep. It accounts for the effects of creep since timber has the tendency to deform over time, and depends on the material, service class and load duration.
EC5 Table 3.2 [2]



ULS Checks

Bending
Bending check at midspan.


M,Ed
:{"mathjs":"Unit","value":2,"unit":"kN m","fixPrefix":false}​



to be factored and per meter width


σ_m,y,d
:7.17​



fm,y,d
:5.92​



Bending util
:1.2109103018193939​



Bending check
:FAIL​


Bending equations

The design bending strength in the principal y-axis,

is determined by:

fm,y,d=kmod ksys kh fm,kγMf_{\mathrm{m}, \mathrm{y}, \mathrm{d}}=\dfrac{k_{mod}\,k_{sys}\,k_{h}\,f_{m,k}}{\gamma_M}
Where:
  1. 
    
    duration of load and moisture content factor
  2. 
    
    system strength factor
  3. 
    
    depth factor
  4. 
    
    characteristic bending strength
  5. 
    
    partial factor for material properties

The design bending stress

is determined by:

σm,y,d=ME,dZyn\sigma_{\mathrm{m},\mathrm{y},\mathrm{d}}=\dfrac{M_{\mathrm{E},\mathrm{d}}}{Z_yn}
Where:
  1. 
    
    design bending moment
  2. 
    
    section modulus
  1. 
    
    number of beams per meter
Shear
Shear check at the support and if applicable, taking into account a notch.


VE,d
:{"mathjs":"Unit","value":3,"unit":"kN","fixPrefix":false}​



to be factored and per meter width


τ_v,d
:1.01763907734057​



fv,d
:1.0303769906318307​



Shear util
:0.99​



Shear check
:OK​


Shear equations

For this calculator the design shear strength is determined by:

fv,d=kmod ksys kv fv,kγMf_{\mathrm{v}, \mathrm{d}}=\dfrac{k_{mod}\,k_{sys}\,k_v\,f_{v,k}}{\gamma_M}
Where:
  1. 
    
    duration of load and moisture content factor
  2. 
    
    system strength factor
  3. 
    
    reduction factor for notched beams
  1. 
    
    characteristic shear strength
  2. 
    
    partial factor for material properties

The design shear stress,

is:

τd=1.5VE,db hef n kcr\tau_{\mathrm{d}}=\dfrac{1.5V_{E,d}}{b\,h_{{\mathrm{ef}}}\,n\,k_{\mathrm{cr}}}
Where:
  1. 
    
    maximum design shear force (occurs at support since beam is simply supported)
  2. 
    
    beam width
  3. 
    
    is the beam effective depth
  1. 
    
    number of beams per meter
  2. 
    
    crack factor
Bearing
Bearing stress check beneath the beam at its supports.


σ_90,d
:0.6818181818181818​



fc,90,d
:1.2692307692307692​



Bearing util
:0.54​



Bearing check
:OK​


Bearing equations

For this calculator the design bearing strength,

is determined by:

fc,90,d=kmod kc,90 fc,90,kγMf_{\mathrm{c}, 90,\mathrm{d}}=\dfrac{k_{mod}\,k_{c,90}\,f_{c,90,k}}{\gamma_M}
Where:
  1. 
    
    duration of load and moisture content factor
  1. 
    
    bearing strength factor
  2. 
    
    characteristic compressive strength perpendicular to the grain
  3. 
    
    partial factor for material properties

The design bearing stress,

is determined by:

σ90,d=Fc,90,dnAeff\sigma_{90,d}=\dfrac{F_{c,90,d}}{nA_{eff}}
Where:
  1. 
    
    governing design bearing force, which is the design shear force at the bearing support
  2. 
    
    is the effect contact area in compression perpendicular to grain
  1. 
    
    number of beams per meter


SLS Checks

Deflection

Deflection equations

The calculation for

and

are given below. The final deflection,

is taken as the sum of the two to account for both effects.
Components of timber beam deflection


uinst=(1+15.4(L/h)2)⋅(5WSLS32Eb(Lh)3)ucreep =kdef(1+15.4(L/h)2)⋅(5WSLS32Eb(Lh)3)ufinal=uinst+ucreepu_{\text {inst}}=\left(1+\dfrac{15.4}{(L / h)^2}\right) \cdot\left(\dfrac{5 W_{\text {SLS}}}{32 E b}\left(\dfrac{L}{h}\right)^3\right)\\u_{\text {creep }}=k_{def}\left(1+\dfrac{15.4}{(L / h)^2}\right) \cdot\left(\dfrac{5 W_{\text {SLS}}}{32 E b}\left(\dfrac{L}{h}\right)^3\right)\\u_{\text{final}}=u_{\text{inst}}+u_{\text{creep}}
Where:
  1. 
    
    instantaneous deflection due to permanent and variable loads
  2. 
    
    creep deflection due to permanent and variable loads
  3. 
    
    total final deflection due to permanent and variable loads
  4. 
    
    equivalent UDL converted to a point load applied to the middle of the beam, using SLS loads
  5. 
    
    beam length
  1. 
    
    beam height
  2. 
    
    beam width
  3. 
    
    is the elastic modulus
  4. 
    
    deformation factor

Table NA.5 in EC5 outlines that the limit of final deflection is given for a beam span between two supports:
  1. Span/250 with plasterboard finishes
  2. Span/150 without plasterboard finishes
Table NA.5 EC5 limiting values for deflections of individual beams [4]

👉Note, deflection is often the critical case for timber beams which are usually subjected to a uniform distributed load. Shear deflection in the usual case of longer-span beams is not normally significant but is included in this calculator.



W_SLS
:{"mathjs":"Unit","value":2,"unit":"kN","fixPrefix":false}​



u_inst
:3.9349149371338754​



u_creep
:7.869829874267751​



u_final
:11.804744811401626​



span-to-deflection for u_inst
:Span / 760​



span-to-deflection for u_fin
:Span / 250​

👉Note, the designer shall choose the deflection limit. A typical limit is span/250, which means any span-to-deflection ratio with the denominator greater than 250 is OK.

Vibration (applicable for floor beams)

Vibration equations

Unlike some international standards like the Australian Standards, EC5 Section 7.3 provides commentary about vibration requirements.
It states, for residential floors with fundamental frequency

, the floor deflection under a 1kN point load must be less than

. If

than special investigation should be made.
The fundamental frequency can be calculated by modal analysis using an FEA software. Otherwise, for a one-way spanning simply supported beam,

may be approximated as (equation from IStructE Manual of EC5):

f1=18δf_1=\dfrac{18}{\sqrt{\delta}}
Where:
  1. 
    
    instantaneous bending deflection of the floor under dead weight alone
Table NA.6 of EC5 outlines that the limit of floor deflection under a 1kN point load,

is to be taken as:
Table NA.6 Limits for a and b [4]

As per the IStructE Manual for EC5, the deflection under a 1kN point load

is given by normal statics formula with modification factors:

a=P×kdist×kamp×L348EIa= \dfrac{P\times k_{dist}\times k_{amp}\times L^3}{48EI}
Where:
  1. 
    
    point load
  1. 
    
    for simply supported solid timber beams (conservative)
  2. 
    
    is the proportion of point load acting on a single joist, as described in the UK National Annex Section 2.7.2 to EC5.
  3. 
    
    flexural rigidity of floor decking perpendicular to the floor beams using
    
    for
    
    .
  4. 
    
    beam spacing
  5. 
    
    transverse stiffness factor. Use a value of 0.97 in the case of solid timber joists which have a transverse stiffness provided by single or multiple lines of herringbone strutting, otherwise use 1.0.

Frequency check:


Dead load allowance
:{"mathjs":"Unit","value":0.9,"unit":"kPa","fixPrefix":false}​



Instaneous deflection under dead load alone
:4.987615934361485​



f1
:8.059832256318993​



Check f1
:> 8Hz OK​


Deflection under 1kN check:
Floorboard:
  1. 
    
    Thickness_FB
    :{"mathjs":"Unit","value":18,"unit":"mm","fixPrefix":false}​
    
  1. 
    
    E modulus_FB
    :{"mathjs":"Unit","value":4930,"unit":"MPa","fixPrefix":false}​
    
Plasterboard:
  1. 
    
    Thickness_PB
    :{"mathjs":"Unit","value":20,"unit":"mm","fixPrefix":false}​
    
  1. 
    
    E modulus_PB
    :{"mathjs":"Unit","value":2000,"unit":"MPa","fixPrefix":false}​
    


a_limit
:1.8​



a
:1.9123119523975147​



Check a
:>1.8mm NOT OK​


Related Resources

  1. Timber Design Standards - Eurocode 5
  2. Timber Beam Calculator to AS 1720.1
  3. Timber Column Calculator to AS 1720.1

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