Timber Beam Calculator to EC5

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

Calculation

Beam Geometry





Timber beam designation

:195 x 44 C24​







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



$s$

= 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



SLS Checks

Deflection

Deflection equations







W_SLS

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







u_inst

:2.504036778176098​







u_creep

:2.0032294225408784​







u_final

:4.507266200716977​







span-to-deflection for u_inst

:Span / 1190​







span-to-deflection for u_fin

:Span / 660​



👉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



$f_1>8Hz$

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



$a_{limit}$

. If



$f_1<8Hz$

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,



$f_1$

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



$f_1=\dfrac{18}{\sqrt{\delta}}$

Where:

1. 
   

   $\delta =$
   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,



$a_{limit}$

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



$a$

is given by normal statics formula with modification factors:



$a= \dfrac{P\times k_{dist}\times k_{amp}\times L^3}{48EI}$

Where:

1. 
   

   $P=1kN$
   point load

1. 
   

   $k_{amp}=1.05$
   for simply supported solid timber beams (conservative)
2. 
   

   $k_{\text{dist }}=\max \left\{\begin{array}{l}{k}_{\text{strut}}\left[0.38-0.08\ln \left[14(EI{)}_b/s^4\right]\right]\\ \\ 0.30\end{array}\right]$
   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. 
   

   $(EI{)}_b=$
   flexural rigidity of floor decking perpendicular to the floor beams using
   

   $E_{mean}$
   for
   

   $E$
   .
4. 
   

   $s=$
   beam spacing
5. 
   

   $k_{strut}=$
   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

:3.1739374127754867​







f1

:10.103534431079083​







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

:1.2169257878893276​







Check a

:< 1.8mm 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