What are the use cases of these Ultimate limit state (ULS) equations - Eurocode0 4

[Pretty Girl7]

Whats the difference between 6.9a and 6.9b? (EuroCode0, Clause 6.4.3.2, page 47)

It states, 6.9a - for general format, and 6.9b for combination of effects.
But, I see both equations contain γ[sub]i[/sub] ψ[sub]i[/sub] Qk[sub]i[/sub]. So that means both equations can be used for combinations.

Why it says, one for general and other one for combinations. Is there any different use case?

 

[centondollar]

What you quoted may be interpreted as jargon of the regulator. To put it simply, Eurocode postulates that design values are multiplied by different factors depending on if they are leading or accompanying actions. Normally, you would make combinations until you run out of actions to place as "leading actions". The national annexes to Eurocode typically contain tables listing the combination factors and load combination equations (dead weight, leading and other variable actions) to be used in design, so you should take a look at those. Identifying all cases (e.g., uplift due to wind etc.) is of course left to the engineer.

 

[ThomasH]

I think that 6.9a and 6.9b shows basically the same thing but in different formats. Neither of them is very "user friendly" in my opinion.
If you go to Annex A1 instead, specifically A1.3 things will hopefully get clearer. There a a few tables in that chapter that may help you. And, as already mentioned, don't forget the National Annex. There are often additional info in those.

/Thomas

 

[HTURKAK]

6.9a is the general format of effects of actions . The effects could be ( internal force , moment, shear , ..deflection etc)

In general , the combination of effects of actions is directly based on the design values of all actions and so 6.9b is used.










Tim was so learned that he could name a
horse in nine languages: so ignorant that he bought a cow to ride on.
(BENJAMIN FRANKLIN )

 

[Pretty Girl7]

@HTURKAK
So, in theory, it's like the first equation (6.9a) fits inside the second equation.

say, first equation = γS[sub]d[/sub]E
so the second equation is = Ed = (γS[sub]d[/sub]E1)+(γS[sub]d[/sub]E2) .... etc

But practically, we only have to use the second equation (6.9b) to test the ULS, is that right?

 

[HTURKAK]

6.9a is the general format of effects of actions implicitly states that , if you are uncertain for the leading variable action, you should try each variable action (imposed, wind, snow, temp.) leading variable action and the others accompanying to get the most unfavorable comb.

In most cases , the leading variable action is certain and we apply 6.9b.

Apparently, and this thread also shows that EN 1990 (EC 0) needs to be simplified with a summary for common cases.








Tim was so learned that he could name a
horse in nine languages: so ignorant that he bought a cow to ride on.
(BENJAMIN FRANKLIN )

 

[GeorgeTheCivilEngineer]

6.9a is just explicitly showing γ_Sd - which is the fudge factor... sorry, the 'Partial factor associated with the uncertainty of the action and/or action effect model'

γ_F = γ_Sd x γ_f

Most of the time you just get a value of γ_F from the relevant Standard or National Annex for a particular action or material(for example, permanent actions γ_G = 1.35) and you don't need to worry what the value of γ_Sd is 99.9% of the time. It has a recommended value between 1.05 to 1.15. Such fudge factors do pop up, especially in assessment codes, but the likely main purpose in the Eurocodes was to allow a simple way for National Annexes to align with their existing standards with a simple tweak.

In theory it also allows for reduction in the fudge factor as action/action effects become better understood.