Hello friends, đđ
Today weâll 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 â here â.
In todayâs article, youâll 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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Scroll down, if you are only interested in SLS load combinations.
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Now, back to SLS load combinationsâŚ
Load Combinations According To Eurocode (Part 2 - SLS)
As already mentioned, SLS stands for â serviceability limit states â and there are 3 actions structural elements might need to be verified for: characteristic, quasi-permanent and frequent.
(Weâll 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,
Gk = Dead load
Qk.1 = Leading variable action
Ď0.i = Psi factor of the accompanying actions/loads
Qk.i = Accompanying variable action
Ď0 factors
We find the Ď 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, weâll 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,
Gk = Dead load
Qk.i = Variable actions
Ď2.i = Psi factor of variable actions/loads
Ď1 and Ď2 factors
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,
Gk = Dead load
Qk.1 = Leading variable action
Ď1.i = Frequent psi factor of the leading variable action/load
Qk.i = Accompanying variable action
Ď2.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:
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.
Thatâs because there isnât really a course dedicated to load combinations. At most uniâs, you have to learn it yourself.
But itâs really dangerous if you donât 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 â here â.
See you next Wednesday. âď¸âď¸
Cheers,
Laurin. đđ