## Timber Design Standards - Eurocode 5

This article discusses and summarizes the basic design procedure for timber elements as outlined in EN Eurocode 5, which covers the design approaches, calculation and analysis of structural strengths and material properties of timber materials. Every country, sometimes even states, have unique design methods, which often leads to scattered calculations, incoherency in design and wasted time. As such, this piece was written to help engineers who may need to use Eurocode 5 and wish to develop a basic understanding of its concepts without reading the entire document.

### Ultimate Strength Limit State

EC5 [1] uses a similar approach to AS1684 and AS1720 for ultimate strength limit state design. The general equation for calculating design capacities is:

*R _{d} = k_{mod} (R_{k} ÷ γ_{M})*

R_{k} is the characteristic design capacity and *γ _{M}* is the “partial factor”. This parameter accounts for differences due to material type in design value calculation:

### Modification Factors

The modification factor k_{mod }in EC5 accounts for the effect of moisture content and load-duration using different categories of ‘service class’ and ‘load-duration class’. There are 3 service classes and 5 load-duration classes; climatic loads like snow and wind vary between countries therefore, EC5 allows nation annexes to assign country-specific load-duration classes in the national annexes:

Effects of other parameters are not accounted for by *k _{mod }*in EC5. Instead, each expression to be satisfied supplements its own modification factor. For example, for design compression capacity parallel to the grain, AS1720 uses

*N*where

_{d,c}> ϕ k_{1 }k_{4 }k_{6 }k_{12 }f’_{c }A_{c}*k*,

_{1 },k_{4 }*k*and

_{6}*k*are modification factors; EC5 uses

_{12 }*σ*where

_{c,90,d}< k_{c,90}f_{c,90,d }*k*is the modification factor accounting for the effect of load configuration, splitting and deformation. The theory behind these equations are the same (as they both use elastic analysis), but the selection criteria for modification factors and their numerical values are different.

_{c,90 }A component covered in EC5 but not in AS1684 or AS1720 is the cracking of timber. The strength performance of timber systems mainly depends on shear connectors (joints and fasteners) that create combined actions between adjacent members. These connections are often the first to fail upon reaching the ultimate strength limit. Clause 6.1.7 of EC5 accounts for the influence of cracks for shear resistance of members in bending using the factor *k _{cr, }*which varies depending on the type of timber material.

### Serviceability Limit State

Deflection limits in EC5 are also based on elastic analysis methods, similar to Australian standards. It recommends the use of deflection limits relative to the beam span, and directs engineers to refer to national annexes for specific values.

It does not offer any structural models like AS1684 and instead provides formulae for modulus of elasticity, slip moduli and shear moduli to be used to calculate deflections. The most significant difference between EC5 and the Australian standards is the inclusion of vibration control for timber flooring systems.

**Fundamental Frequency f**_{1}

_{1}Fundamental frequency, or natural frequency, is an inherent property of all materials; it is the frequency at which objects vibrate in free, unrestrained condition. When the frequency of external forces (including human activities, such as walking or running, machinery, wind, seismic activity, etc.) is equal to the fundamental frequency, resonance occurs.

In structures, resonance must be avoided at all costs. It leads to amplified deflections and perceivable oscillations that cause annoyance and discomfort. In extreme cases, total structural collapse may occur. The Tacoma Bridge incident is an example of structural failure due to resonance: the frequency of the wind loads caused vibrations equal to the fundamental frequency of the bridge. It led to uncontrollable deflections and the bridge eventually collapsed. EC5 provides a formula for estimating the fundamental frequency using the floor’s material properties (bending stiffness, mass and span). However, studies have shown differences when compared to experimentally obtained values. Engineers should use experimentally verified values if they are available.

To prevent such phenomena, EC5 suggests that the fundamental frequency of residential flooring systems should be above 8 Hz. Studies show that the frequency of day-to-day human activities are between 1 - 8 Hz [2,3], hence the flooring systems are at risk if their fundamental frequency is within this range.

**Additional Limits**

If the fundamental frequency is lower than 8 Hz, “special investigation” is required and additional limits must be satisfied. These limits are:

*w *is the maximum instantaneous deflection caused by a concentrated vertical static load F (summation of forces acting on the floor represented as a single point load). represents the damping ratio, the measure of vibration absorbance of a material (obtained experimentally). v is the velocity of the floor’s vibration under a unit load and it is calculated using the following equation found in EC5 Clause 7.1.3:

Where m, b, l represent the mass, width and length of the floor respectively and n_{40} is the number of fundamental frequencies under 40Hz (obtained experimentally or approximated using formula in EC5 Clause 7.1.3). Additionally, EC5 encourages engineers to follow the provided figure of recommended relationship between parameters a and b:

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### References

[1] European Committee for Standardization, Eurocode 5: Design of timber structures - Part 1-1: General - Common rules and rules for buildings. EN 1995-1-1, Brussels, Belgium, 2004.