Structural Design of Timber Posts to EC 5

In timber frame construction, a post is one of the most basic structural elements that can be found.  Timber posts are vertical elements, when utilized in any timber frame are principally subjected to both axial compressive actions and bending moments along one or both axes. In other words, a timber post is the equivalent of a column, but in this case the term ‘post’ refers to timber or steel.

Designing a timber post require the same level of appreciation as would be required in the design of vertical elements or columns formed from other materials. Extreme fibre stresses and buckling from applied actions is a major concern. Perhaps, even more complicating is the anisotropic nature of timber, which for vertical elements has a significant impact on the assessment of their performances as a structural material. The performance of a timber post is governed by its geometry as well as the magnitude of the applied design actions. They’re very prone to instability from buckling hence, this is typically the governing aspect of their design.

Previous codes of practices tend to adopt the permissible stress design philosophy in the design of timber elements due to the highly probable nature of timber as a structural member. In the Eurocodes, however the limit state design philosophy was introduced, hence the approach described in this article is based on limit state design. This article would assume that the reader is well familiar with terminologies and the use of coefficients present in Eurocode 5 (part 1) or at the very least has read a previous article on timber joist (See: Structural Design of Timber Joist to EC 5).

To design a timber post, requires the designer to consider each and every component that would impact on the performance of the timber when utilized as a vertical element against applied stresses. These components are explained below:

Slenderness

Timber is a naturally occurring structural material with natural imperfections. When designing vertical elements subjected to compressive stresses, the impact of this imperfections in estimating the slenderness ratio of the timber section becomes apparent. To account for the naturally occurring flaws that may be present in timber, the estimated slenderness ratio must be converted to relative slenderness ratio before it can be applied to design calculations.

The effective slenderness ratio is defined as:

\lambda =\frac { { L }_{ e } }{ i } 

Where:

• λ is the slenderness ratio of the post
•  L_e is the effective length of the post with respect to the axis being considered
• i is the radius of gyration of the post with respect to the axis being considered.

The slenderness ratio is estimated in both axis of the timber post. Should the post be overloaded, the axes with the higher slenderness ratio would have more pronounced buckling. As must’ve being understood, buckling governs the design of slender vertical elements and this is assessed by determining their relative slenderness which is not only dependent on the timber section but the effective length. 

Support Condition

The effective length L_e, of a timber post is dependent on the support conditions. This is based on Euler’s theory of instability and the buckled shape of a post as actions are applied on it. Table 1 provides a guide on estimating the effective lengths of post for typical support conditions.

Geometric Imperfections

Timber elements are not only prone to natural imperfections but also those that may be created from fabrication. Eurocode 5 recognizes this and rather than assuming timber elements to be perfectly straight and without blemish, a consideration is given to how the timber will warp and deform as the design actions are being applied to it as well as other imperfection that may occur during mill preparation. This is explained within Clause 6.3.2 of Eurocode 5 (part 1). Equation 6.2.1 and 6.2.2 are utilized in estimating the slenderness ratio λ_rel, that is used in determining the design resistance of the timber section with respect to the axes under consideration. These equations are subsequently reproduced below as:

{ \lambda  }_{ rel,y }=\frac { { \lambda  }_{ y } }{ \pi  } \sqrt { \frac { { f }_{ c,0,k } }{ { E }_{ 0.0.5 } }  } 

{ \lambda  }_{ rel,z }=\frac { { \lambda  }_{ z } }{ \pi  } \sqrt { \frac { { f }_{ c,0,k } }{ { E }_{ 0.0.5 } }  } 

Where:

• f_c,0,k is the characteristic compressive strength of the timber parallel to the grain
• E_0.05 is the fifth percentile of the modulus of elasticity of the timber parallel to the grain
• λ_y and λ_z are the slenderness ratios for the post as calculated previously

Where the value of the relative slenderness as calculated from the above equations is less than 0.3, then the post is considered ‘stocky’ hence not susceptible to a buckling failure and would rather fail through crushing. However, if relative slenderness exceeds 0.3 then the post is ‘slender’ and the failure mechanism would be through buckling.

Member Verification

There are about three verifications that should be enough to justify the adequacy of a timber post. These are explained as follows:

Design for Compressive Stress

To design against compression, the applied design compressive stress is compared with the design strength of the chosen timber section. The applied compressive stress is determined by dividing the applied axial action with the cross-sectional area of the timber section. This is defined as σ_c,0,d  in Eurocode 5.

Determining the compressive strength of a post depends on the post being either stocky or slender. For stocky posts, the compressive strength is equal to the design compressive stress parallel to the grain f_c,0,d , determined using equation 2.17 of Eurocode 5 (part 1).  The equation is reproduced below as:

{ f }_{ c,0,d }={ k }_{ mod }\frac { { f }_{ c,0,k } }{ { \gamma  }_{ M } } 

Where the timber post is ‘slender’ and buckling dominates the design, the compressive strength of the section is determined through the application of a buckling strength reduction factor designated as (k_c,y or k_c,z) depending on the axis under consideration. This factor is determined through equation 6.25 & 6.26 of Eurocode 5 (part 1). These equations are reproduced below:

{ k }_{ c,y }=\frac { 1 }{ { k }_{ y }+\sqrt { { k }_{ y }^{ 2 }-{ \lambda  }_{ rel,y }^{ 2 } }  }

{ k }_{ c,z }=\frac { 1 }{ { k }_{ z }+\sqrt { { k }_{ z}^{ 2 }-{ \lambda  }_{ rel,z }^{ 2 } }  }

The variable k_y and k_z relates to the straightness of the timber post and can be determined from equation 6.27 and 6.28 of the Eurocode 5(part 1). These equations are also reproduced below

{ k }_{ y }=0.5\left[ 1+{ \beta  }_{ v }\left( { \lambda  }_{ rel,y }-0.3 \right) +{ \lambda  }_{ rel,y }^{ 2 } \right] 

{ k }_{ z }=0.5\left[ 1+{ \beta  }_{ v }\left( { \lambda  }_{ rel,z }-0.3 \right) +{ \lambda  }_{ rel,z}^{ 2 } \right] 

β_v is a coefficient that relates to the timber material, given as 0.2 for solid timber and 0.1 for glued laminated timber.

Having determined the reduction factors, the compressive strength of the timber section is given as the lesser of reduction factors multiplied by the design compressive strength parallel to the grain. This can be expressed as

{ f }_{ c,0,d }={ { k }_{ c }k }_{ mod }\frac { { f }_{ c,0,k } }{ { \gamma  }_{ M } } 

Design for Flexural Stress

By default, applied actions on timber posts are rarely concentric, hence the result is a applied bending moment from eccentricity, which the timber post must resist in addition to the applied axial compressive force. This is addressed by comparing the design bending strength of the timber post against the applied bending stress. The procedure is basically the same as for horizontal timber element such as timber joists, now using the appropriate coefficients.

Design for Combined Action

Eurocode 5 requires that a combined action review is carried out for all timber post subjected to multiple stresses to determine how it will perform under the application of applied actions. This is done through a procedure known as the ‘unity check’. Here, the individual applied stresses are compared against the design strengths of the post and, if the summation of the ratios are found to be less than or equal to one, the element is deemed to perform satisfactorily. Carrying out this check depends on the classification of the post with respect to slenderness.

For stocky posts equation 6.19 and 6.20 of Eurocode 5 (part 1) applies. The equation assumes that the timber element allows plastic behaviour to occur. The equations are reproduced below.

{ \left[ \frac { { \sigma  }_{ m,0,d } }{ { f }_{ m,0,d } }  \right]  }^{ 2 }+\left( \frac { { \sigma  }_{ m,y,d } }{ { f }_{ m,y,d } }  \right) +{ k }_{ m }\left( \frac { { \sigma  }_{ m,z,d } }{ { f }_{ m,z,d } }  \right) \le 1

{ \left[ \frac { { \sigma  }_{ m,0,d } }{ { f }_{ m,0,d } }  \right]  }^{ 2 }+{ k }_{ m }\left( \frac { { \sigma  }_{ m,y,d } }{ { f }_{ m,y,d } }  \right) +\left( \frac { { \sigma  }_{ m,z,d } }{ { f }_{ m,z,d } }  \right) \le 1

Where k_m is a factor applied to timber design to account for plastic behaviour since Eurocode 5 assumes limit state design. Clause 6.1.6 of Eurocode 5 (part 1) defined the value of k_m as follows:

• Elements formed from solid timber, Glulam and LVL k_m =0.7
• Other types of engineered timber k_m =1.0

In slender post, plastic behaviour does not develop hence, the post cannot be considered under the level of the unity review. Extreme fibre stresses will govern the design posts equation 6.19 and 6.20 of Eurocode 5 (part 1) applies. Here, equations 6.23 & 6.24 applies and is hereby reproduced below.

{ \left[ \frac { { \sigma  }_{ m,0,d } }{ { { k }_{ c,y }f }_{ m,0,d } }  \right]  }^{ 2 }+{ k }_{ m }\left( \frac { { \sigma  }_{ m,y,d } }{ { f }_{ m,y,d } }  \right) +\left( \frac { { \sigma  }_{ m,z,d } }{ { f }_{ m,z,d } }  \right) \le 1

{ \left[ \frac { { \sigma  }_{ m,0,d } }{ { { k }_{ c,z }f }_{ m,0,d } }  \right]  }^{ 2 }+\left( \frac { { \sigma  }_{ m,y,d } }{ { f }_{ m,y,d } }  \right) +{ k }_{ m }\left( \frac { { \sigma  }_{ m,z,d } }{ { f }_{ m,z,d } }  \right) \le 1

Instability

Finally, the overall instability of the timber post could be of crucial concern if there is a risk of lateral torsional buckling. This is often the case when the timber post is subjected to a significant bending moment along its major axis and having a relative stiffness ratio of less than 0.75. In this instance equation 6.35 of Eurocode 5 (part 1) is applicable. However, this check is beyond the scope of this article. 

Worked Example

There is a new requirement for a timber floor within a newly refurbished building. The clear headroom of the floor is 3.0m. It is proposed that 250mm x 250mm C24 timber posts would be used to support the timber floor. Assuming the posts are pinned at both ends and is fully braced in both directions, verify that one of the edge posts can support the applied actions. The characteristic applied actions on this post are 50mm eccentric, and is as follows:

• Permanent Actions = 15.6kN
• Variable Actions = 106kN

Sources & Citations

• Regan C.O (2021) ‘Design of Timber Post, The Structural Engineer -Technical Guidance Note (level 2) 95(2), pp. 24-27.
• Institution of Structural Engineers and TRADA (2007) Manual for the design of timber building structures to Eurocode 5, London: IstructE Ltd
• BS EN 1995-1-1:2004 Eurocode 5: Design of timber structures. General. Common rules and rules for buildings

Thank You!