Load Combinations Part 2 - SLS Actions

#13th episode of the Structural Loads Series

Hello friends, 👋👋

Today we’ll tackle the 2nd part of the load combinations guide - serviceability or SLS load combinations. Last week, we covered ULS, accidental and seismic load combinations. If you missed that article, then you can check it out → here ←.

In today’s article, you’ll learn how to set up SLS characteristic, quasi-permanent and frequent load combinations according to EN 1990, so you know with what loads you need to verify for example the deflection and cracking of a rc concrete beam.

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8 Must-Have Softwares For Structural Engineers

Scroll down, if you are only interested in SLS load combinations.

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Now, back to SLS load combinations…

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Load Combinations According To Eurocode (Part 2 - SLS)

As already mentioned, SLS stands for → serviceability limit states ← and there are 3 actions structural elements might need to be verified for: characteristic, quasi-permanent and frequent.

(We’ll continue with the numbering from last week)

#4 SLS Characteristic Load Combinations

Due to SLS characteristic load combinations structural members are designed for example for deflection.

The formula of SLS characteristic combinations is (EN 1990 (6.14b)):

With,

• G_k = Dead load

• Q_k.1 = Leading variable action

• ψ_0.i = Psi factor of the accompanying actions/loads

• Q_k.i = Accompanying variable action

ψ₀ factors

We find the ψ factors in EN 1990 Table A1.1. Please be aware that every country might define these factors differently in its National Annex.

SLS characteristic load combinations applied to example structure

According to EN 1990 (6.14b) the characteristic load combinations can be written as:

Putting in the values of the characteristic loads and psi factors, we’ll get..

#5 SLS Quasi-Permanent Load Combinations

The SLS quasi-permanent load combinations are used to calculate for example the quasi-permanent moment, which is used to verify cracking of reinforced concrete beams or rc slabs.

The formula of SLS quasi-permanent combinations is (EN 1990 (6.16b)):

With,

• G_k = Dead load

• Q_k.i = Variable actions

• ψ_2.i = Psi factor of variable actions/loads

ψ₁ and ψ₂ factors

Recommended values of ψ₁ and ψ₂ factors according to EN 1990 Table A1.1.

SLS quasi-permanent load combinations applied to example structure

According to EN 1990 (6.16b) in our example the quasi-permanent load combinations can be written as.

And if we put in the values, we will get..

#6 SLS Frequent Load Combinations

The formula of SLS frequent combinations is (EN 1990 (6.15b)):

With,

• G_k = Dead load

• Q_k.1 = Leading variable action

• ψ_1.i = Frequent psi factor of the leading variable action/load

• Q_k.i = Accompanying variable action

• ψ_2.i = Quasi-permanent psi factor of the accompanying variable action/load

SLS frequent load combinations applied to example structure

According to EN 1990 (6.15b) in our example the quasi-permanent load combinations can be written as:

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Final Words

Load combinations are a very important part of structural design. Back when I was still studying at uni, I realized that many of my fellow students had problems understanding how load combinations work.

That’s because there isn’t really a course dedicated to load combinations. At most uni’s, you have to learn it yourself.

But it’s really dangerous if you don’t calculate the design loads correctly with load combinations because ultimately you design your element with wrong loads.

I hope this guide helped to understand load combinations better.

If you missed episode #1 - #12 of this series, then you can find all previous posts → here ←.

See you next Wednesday. ✌️✌️

Cheers,

Laurin. 😎😎