Happy Wednesday friends,

Last week I didn't publish a newsletter.

A lot of stuff is happening at the moment. Work is busy as usual, I've met up with a few engineers from Munich that I've connected with on LinkedIn and I am about to move into a very nice apartment with my girlfriend.

So the newsletter will probably be biweekly for the next few weeks. Hope you understand.

Today, we'll look into the tensile capacity of screws.

Let's get into it..

The 4 Steps To Calculate The Tensile Capacity of Screws According To Eurocode

The axial capacity of screws is calculated according to EN 1995-1-1 8.7.2 and the following failure modes should be investigated:

• the withdrawal capacity of the threaded part of the screw
• for screws used in combination with steel plates, the tear‑off capacity of the screw head should be greater than the tensile strength of the screw
• the pull‑through strength of the screw head
• the tension strength of the screw
• the screws used in conjunction with steel plates, failure along the circumference of a group of screws (block shear or plug shear

Failure modes 2 and 4 should never happen as manufacturer do extensive testing to bring their screws to market. At least I have never met any structural engineer do this verification.

Failure mode 5 should not happen if you fulfill the minimum spacing requirements of EN 1995-1-1 Table 8.6.

Therefore we are left with 2 verifications or in other words 2 capacities to calculate:

• withdrawal capacity and
• pull-through strength of the screw head

In this newsletter, we'll calculate the axial capacity of the screwed connection below.

Step #1: Define the geometrical properties of the screws and timber elements

As a screw we use the fully threaded countersunk screw HTS from Rotho Blaas. Rotho Blaas is an international manufacturer of screws and their screws are commonly used in Europe. You can find the data here. The elements and screw have the following dimensions:

• Timber element 1 (OSB): t_osb=t₁=20mm
• Screw length: l_n=50mm
• Pointside penetration thickness in single shear connections (EN1995-1-1 8.3.1.1): t₂=l_n-t_osb=30mm
• Screw diameter d=2.5mm
• Nail head diameter d_h=8.0mm

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

Here are the strength and stiffness properties that we need in the calculation:

• Density OSB: ρ_k.osb=550 kg/m³
• Density timber rafter: ρ_k.r=350 kg/m³

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 #3: Calculate the loads acting on the nail

In this step we need to calculate the characteristic loads that act on the connector. The characteristic area loads are applied to the slabs like the OSB board and transfered to the connection.

We won't show how to calculate the loads and how to do the load transfer in this newsletter, as each calculation of the individual load is an article for itself and load transfer is also a big topic.

In this email, we'll verify the screw for the following point load.

W_k = 0.85 kN

Step #4: Axial design verification of the screw

Before jumping into the calculation I just quickly talk a bit about how you verify connectors in "real life" and which formulas you use.

In reality I mostly go to the manufacturers homepage, pick a screw or nail and look up the shear and tensile capacity from there capacity tables.

If I verify the connectors by hand, I usually pick a product and look up the verification formulas from their ETA declaration. Every load bearing timber connector needs to have an ETA declaration. Otherwise you can't use them for structural purposes.

As you will see in the calculation below, not all formulas are included in Eurocode (in our case the head-pull capacity). But these formulas are included in the ETA. The formulas also verify sometimes from the ones in Eurocode.

Just know that it's ok to use the formulas from the ETA declaration.

First, we'll calculate the embedment strengths of the 2 timber elements.

Characteristic embedment strength for OSB board (EN1995-1-1 (8.39)):

f_ax.k.1 = 3.6 ⋅ 10^-3 ⋅ ρ_k.osb^1.5/(1.5 ⋅ cos(90°) + sin(90°)) N/mm² = 46.4 N/mm²

Characteristic embedment strength for timber element 2 - rafter (EN1995-1-1 (8.39)):

f_ax.k.2 = 3.6 ⋅ 10^-3 ⋅ ρ_k.osb^1.5/(1.5 ⋅ cos(90°) + sin(90°)) N/mm² = 23.6 N/mm²

Minimum density of the 2 timber element:

ρ_k = min(ρ_k.osb; ρ_k.r) = 350 kg/m³

Penetration length minus diameter:

l_ef = t₂ - d = 27.5 mm

Characteristic withdrawal resistance of screws (EN1995-1-1 (8.25)):

F_ax.Rk = min(f_ax.k.1, f_ax.k.2) (π ⋅ d ⋅ l_ef)^0.8 = 1.74 kN

Head pull-through resistance of the nail (given in the datasheet; according to EN 1995-1-1 8.7.2 (6) the pull-through capacity must be determined by tests):

f_head.k = 24.1 N/mm²

Head pull-through capacity (ETA 11/0030):

F_ax.head.k = f_head.k ⋅ d_h² ⋅ ρ_k.r^0.8 = 1.44 kN

Characteristic axial capacity:

F_ax.Rk = min(F_ax.Rk; F_ax.head.k) = 1.44 kN

Design withdrawal capacity:

F_ax.Rd = k_mod ⋅ F_ax.Rk/γ_M = 1.0 kN

Verification:

η = W_d/F_ax.Rd = 0.85

Final Words

Alright, this is how design and verify screws for axial loads according to Eurocode.

I hope this helped.

Enjoy the rest of the week and your weekend.

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)
• Ep. #6: Compression perpendicular to the grain (click here)
• Ep. #7: Shear verification (click here)
• Ep. #8: Deflection verification (click here)
• Ep. #9: Torsion verification (click here)
• Ep. #10: Lateral torsional buckling (click here)
• Ep. #11: Timber beam design (here)
• Ep. #12: Timber column design (here)
• Ep. #13: Vibration analysis of timber floors (here)
• Ep. #14: Timber joist floor (here)
• Ep. #15: CLT floor (here)
• Ep. #16: Timber stud walls (here)
• Ep. #17: CLT walls (here)
• Ep. #18: Timber Connection Design (here)
• Ep. #19: Tensile capacity of nails (here)

#3: The reinforced concrete series (click here)

#4: The engineering mechanics series (click here)

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