Hi friends,

I have taken it a bit slower on Structural Basics the last 3-4 weeks, because I am super busy at my full-time job right now, working many extra hours. My first triathlon Ironman 70.3 Zell am See is only 2 weeks out. So I also spent many hours training each week to get the kilometers in.

And then there was also Festwoche happening which is a beer festival like Oktoberfest in my hometown Kempten. It's great. I go to the festival every year, because you meet many people you haven't seen in a long time and the vibe is just great.

But we are back and today we’ll look at the verification of compression perpendicular to the grain of timber.

This verification we only need to do for timber, because timber has different strength properties parallel and perpendicular to its grain.

Parallel to the grain the properties are great, but perpendicular to it very weak.

Compression perpendicular to its grain needs to be checked whenever timber beams are exposed to point loads, like when you connect a column to a beam or at supports when timber beams "sit" on top of columns/walls.

So today, I am gonna show you how you verify timber for compression perpendicular to its grain according to Eurocode. This verification is one of the most critical design checks of timber elements, because the strength perpendicular to its grain is so weak. There's a few things we engineers can do to increase the capacity which I'll mention later in the newsletter.

Now, let’s get into it...

The 4 Steps To Verify Timber For Compression Perpendicular To Its Grain

Let's use the connection of the primary beam to column from the canopy structure that we also used in the last episodes as an example to show the calculation steps.

Step #1: Define the material properties of the timber element

We first define the material properties of the timber beam. In this tutorial, we'll use C24 as the timber material.

For small structures like this which aren't exposed to big loads, C24 is enough.

We summarized all timber materials in ep. #2 about timber material properties or I also published it to the blog as a table (click here).

Here are the strength and stiffness properties of C24.

The partial safety factor is found in EN 1995-1-1 Table 2.3 as:

γ_M = 1.3

The beam is classified according to EN 1995-1-1 2.3.1.3 as service class 2 (assumption in this tutorial).

Then we'll verify the timber beam for a design load of load duration class short-term (EN 1995-1-1 Table 2.1) which leads to a modification factor (EN 1995-1-1 Table 3.1) of:

k_mod = 0.9

Step #2: Define the geometrical properties of the timber elements

The beam has the following cross-sectional properties:

• Cross-sectional height h=20cm
• Cross-sectional width w=14cm

And the column has the following cross-sectional properties:

• Cross-sectional height h=14cm
• Cross-sectional width w=14cm

Step #3: Calculate the loads and internal forces acting in the timber element

First, we need to calculate the characteristic loads that act on the roof area of the canopy. The area loads are applied to the roof panels (could be OSB boards or trapezoidal steel sheeting). These panels then transfer the loads to the secondary beams. From the secondary beams the loads travel to the primary beams which then transfer the loads to the columns. This video explains transfering vertical loads in detail (click → here ←).

We won't show how to calculate the loads in this newsletter, as each calculation of the individual load is an article for itself. I've written detailed articles and published video tutorials about loads, which you can follow to understand how to calculate these loads:

• ​Dead load​
• ​Live load​
• ​Snow load​

In this email, we'll design the primary timber beam for a vertical design reaction forces of:

P_d = 65 kN

Step #4: Verify the timber element for compression perpendicular to its grain

Now we can verify the timber beam for compression perpendicular to its grain.

According to EN 1995-1-1 (6.3) compression perpendicular to its grain is verified as:

σ_c.90.d ≤ k_c.90 ⋅ f_c.90.d

With,

• σ_c.90.d as the compression stress at the contact/support area
• k_c.90 as a factor taking into account the load configuration, possibility of splitting and degree of compressive deformation
• f_c.90.d as the design compressive strength perpendicular to the grain

Characteristic compression resistance perpendicular to the grain (see step #1):

f_c.90.g.k = 2.5 MPa

Design compressive resistance perpendicular to the grain:

f_c.90.d = k_mod ⋅ f_c.90.g.k/γ_M = 1.73 MPa

For midsupports/internal supports like in our example k_c.90 is calculated according to EN 1995-1-1 (6.5):

k_c.90 = (2.38 - l/250) ⋅ (1+ h/6l) = 2.25

With,

• l as the contact length of the support; in our case the contact length equals the cross-sectional height of the column (l=14cm)
• h as the cross-sectional height of the beam (h=20cm)

For endsupports k is calculated according to EN 1995-1-1 (6.4):

k_c.90 = (2.38 - l/250) ⋅ (1+ h/12l)

Note, that these formulas might be defined differently in your National Annex. For instance, in Germany there are different formulas.

Design compression stress:

σ_c.90.d = P_d/(14cm ⋅ 14cm) = 3.32 MPa

Verification according to EN 1995-1-1 (6.3):

η = σ_c.90.d /(k_c.90 ⋅ f_c.90.d) = 85%

Final Words

Often the design check for compression perpendicular to its grain leads to a utilisation ratio of > 100%.

Here are things that you can do, so the utilisation becomes < 100%:

• Increase the width of the beam and column for a wider contact are (-> stress decreases)
• Increase the contact length l
• Reinforce the timber beam with screws. In many cases it's economically better to keep the dimensions of a beam small but add reinforcement to timber beams. This increases the compressive strength perpendicular to its grain. We'll do a future episode on how to calculate screw reinforcement.

Alright, this is how we design timber beams for compression perpendicular to its grain according to Eurocode.

I hope this helped.

Enjoy the rest of the week and your weekend.

I’ll see you next Wednesday for the next newsletter.

Let’s design better structures together,

Laurin.

P.S. If you want to learn more, here are a few ways I can help you:

#1: I teach you everything you need to know about load calculation. It's the most important fundamental of structural engineering. ​Without knowing the loads of a building you can't design the structural elements. Click → here ← to learn.

#2: Previous episodes of the timber design series:

• Ep. #1: Welcome to the timber design series (click here)
• Ep. #2: Timber material properties (click here)
• Ep. #3: Tension verification of timber (click here)
• Ep. #4: Compression verification of timber (click here)
• Ep. #5: Bending verification of timber (click here)

#3: The reinforced concrete series (click here)

#4: The engineering mechanics series (click here)

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