The combination of the horizontal seismic components 3

[Refaatfaraj]

Dear Colleagues
According to EC8 – Clause (4.3.3.5.1 ) , The combination of the horizontal components of the seismic action (Ex & Ey ) shall be applied when the dynamic analysis is used.
May I know if this condition shall be taken in consideration in (Static Method Analysis – Equivalent Lateral Force Method ) or not ?
Any help will be appreciated

 

[hardbutmild]

Yes, this should be considered when using Equivalent Lateral Force Method.

 

[Refaatfaraj]

Hi hardbutmild
Thank you for your response .
May I know if this condition EC8- ( Clause 4.3.3.5.1) is applicable in low seismicity zones ?
Knowing that I always take the accidental eccentricity (5%) in my Consideration .
Note : Capture from the code is attached
Tkanks inadvance

 

[hardbutmild]

I haven't done much of the low ductility structures, but as 4.3.3.5.1 (1) would suggest:
In general the horizontal components of the seismic action shall be taken as acting simultaneously.

The exception to that is the last point of that clause where the combination is not needed:
"For buildings satisfying the regularity criteria in plan and in which walls or independent bracing systems in the two main horizontal directions are the only primary seismic elements (see 4.2.2), the seismic action may be assumed to act separately and without combinations (2) and (3) of this subclause, along the two main orthogonal horizontal axes of the structure."

Other than satisfying that, you need to ensure that all of the reinforcement is of ductility class B or C (if your structure is even RC) and nothing else I believe (keep in mind that your behaviour factor is equal to 1,5 and not some higher value).

 

[HTURKAK]

Where did you read that sentence; (The combination of the horizontal components of the seismic action (Ex & Ey ) shall be applied when the dynamic analysis is used.) ?

Let me explain my interpretation of 4.3.3.5 Which is the Combination of the effects of the components of the seismic action. That is, how to combine the effects after analysis performed.

Simultaneous occurrence of two components ( Ex and Ey ) can be analyzed only by a time-history analysis,in Eurocode 8 is defined to be non-linear . The other analysis methods ( Static Method , RSA ..) give estimates of the peak values of seismic load effects.

4.3.3.5.1 , (2)

a) The structural response to each component shall be evaluated separately, using the combination rules for modal responses given in 4.3.3.3.2.
That is, for each direction seperate analysis shall be performed.

Pls look to the formula,(4.16) This means SRSS combination of the effects in two orthogonal directions..

b) The maximum value of each action effect on the structure due to the two horizontal components of the seismic action may then be estimated by the square root of the sum of the squared values of the action effect due to each horizontal component

That is ,Ed = SQRT ( EX**2 + EY**2 (+EZ**2 ) EZ is added if applicable..

(3) As an alternative to b) and c) of (2) of this subclause, the action effects due to the combination of the horizontal components of the seismic action may be computed using both of the two following combinations:
That is ,

Ed= EX + 0.3EY + 0.3EZ
Ed= 0.3 EX + EY + 0.3EZ
Ed= 0.3 EX + 0.3EY + EZ


The analysis performed with taking the accidental eccentricity (5%) will not provide exemption for combination of the effects. The exemption stated in the code 4.3.3.5.1 (8) which Mr. hardbutmild (Structural) stated..

Does this respond answers to your question ?

 

[Refaatfaraj]

hardbutmild / HTURKAK

Thanks for your answer and your willing to help.

May I conclude the subject from your posts :

1. In RSA method (CQC/SRSS) for modes combination shall be used without applying the clause ( 4.3.3.5.1 (3)) .
2. In Static Analysis (Equivalent Lateral Force Method , we have to deal with each horizonal seismic component separately without any combination of the component of the seismic action .
3. The Combination of the effects of the components of the seismic action(4.3.3.5.1(3)) can be applied only for nonlinear analysis e.g(pushover analysis ).

Please , advise me if any missing understand .

 

[hardbutmild]

I think you misunderstood completely so I'll try to explain it with an example.

1. ELF
Let's say that you got from the analysis that the shear force in the direction of a wall at the bottom of a wall is:
a) For earthquake in global x direction
V_x(EQx) = 100 kN
a) For earthquake in global y direction
V_x(EQy) = 20 kN

For design you need to combine them:
100 + 0,3*20 = 106 kN (this is governing for ELF)
0,3*100 + 20 = 50 kN
100 - 0,3*20 = 94 kN
0,3*100 - 20 = 10 kN

So you need to design for V_x(Ed) = 106 kN (for DCL you design for this value, for DCM you need to increase this by 50% , for DCH even more usually).

2. RSA
Let's say that you checked the first 5 modes and got from the analysis that the shear force in the direction of a wall at the bottom of a wall is:
a) For earthquake in global x direction
mode 1 - V_x1(EQx) = 95 kN
mode 2 - V_x2(EQx) = 5 kN
mode 3 - V_x3(EQx) = 1 kN
mode 4 - V_x4(EQx) = 31 kN
mode 5 - V_x5(EQx) = 2 kN
To get the value for earthquake in x you need to do an SRSS:
V_x(EQx) = (95²+5²+1²+31²+2²)^0,5 = 100,08 kN

b) For earthquake in global y direction
mode 1 - V_x1(EQx) = 2 kN
mode 2 - V_x2(EQx) = 19 kN
mode 3 - V_x3(EQx) = 1 kN
mode 4 - V_x4(EQx) = 1 kN
mode 5 - V_x5(EQx) = 8 kN
To get the value for earthquake in y you need to do an SRSS:
V_x(EQx) = (2²+19²+1²+1²+8²)^0,5 = 21 kN

For design you need to combine them:
100,08 + 0,3*21 = 106,3 kN (this is governing for RSA)
0,3*100,08 + 21 = 51 kN
100,08 - 0,3*21 = 93,7 kN
0,3*100,08 - 21 = 9 kN

So you need to design for V_x(Ed) = 106,3 kN (for DCL you design for this value, for DCM you need to increase this by 50% , for DCH even more usually).

 

[HTURKAK]

hardbutmild explained the case with numbers . A pink star for this explanation to Mr. hardbutmild . But this explanation based on 4.3.3.5.1 (3) (As an alternative to b) and c) of (2) of this subclause, the action effects due to the combination of the horizontal components of the seismic action may be computed using both of the two following combinations ).

complementary to this explanation is, the use of 4.3.3.5.1 b) The maximum value of each action effect on the structure due to the two horizontal components of the seismic action may then be estimated by the square root of the sum of the squared values of the action effect due to each horizontal component.

That is, V(Ed) =sqrt ( 100,08**2 + 21**2)= 103 kN .

For this case, you may use 106,3 kN or alternatively 103 kN .

 

[Refaatfaraj]

Thank you for all of you especially to Mr . hardbutmild for his detailed explanation .
I think everything related to ( EC8 clause 4.3.3.5.1) is clear to me .
Truly appreciated

 

[Agent666]

Note you also need to satisfy clause 4.3.3.3.2 to use the SRSS modal combination like hardbutmild provided the example for.

If you don't satisfy the inequality noted, then you need to use a CQC combination (Complete Quadratic Combination) of the modal response.

Most analysis programs will do this for you. Just need to tick the right analysis option. CQC deals with combining closer spaced modes better as I understand it,

 

[Refaatfaraj]

Dear Agent666
Thank you to refer to code requirement in clause ( 4.3.3.3.2 ) . this condition I usually check it in the dynamic analysis table in RSA software . Of course SRSS can be applicable if clause ( 4.3.3.3.2(1) ) is valid that means ( Tj/Ti) should be less than or equal to ( 0.90) . otherwise (CQC) must be used .

 

[Refaatfaraj]

Dear hardbutmild
Please , could you point me to the code clause which mentioned that the base shear in (DCM) increase by (50%) and for DCH even more usually whereas in DCL used the same value ?

 

[hardbutmild]

I said that you need to increase the shear force because I was thinking about a RC wall.
Note that this is only for reinforced concrete!
In concrete of higher ductility, you always want to avoid shear failure (for steel that's not the case!).
It's clause 5.4.2.4. (7) and (8) for DCM and 5.5.2.4. (7) for DCH.

Basically, this is a capacity design rule, in short if you have DCM or DCH reinforced concrete structure, you need to somehow increase the shear in every element (just shear, for every element a different rule exists).

 

[Refaatfaraj]

Dear hardbutmild

Clear , thank you so much for your response .
Great forum. Best resource by far!!!