## The combination of the horizontal seismic components

## The combination of the horizontal seismic components

(OP)

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

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

## RE: The combination of the horizontal seismic components

## RE: The combination of the horizontal seismic components

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

## RE: The combination of the horizontal seismic components

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).

## RE: The combination of the horizontal seismic components

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 ?

## RE: The combination of the horizontal seismic components

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 .

## RE: The combination of the horizontal seismic components

1. ELFLet'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 directionV

_{x}(EQx) = 100 kNa) For earthquake in global y directionV

_{x}(EQy) = 20 kNFor 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. RSALet'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 directionmode 1 - V

_{x1}(EQx) = 95 kNmode 2 - V

_{x2}(EQx) = 5 kNmode 3 - V

_{x3}(EQx) = 1 kNmode 4 - V

_{x4}(EQx) = 31 kNmode 5 - V

_{x5}(EQx) = 2 kNTo get the value for earthquake in x you need to do an SRSS:

V

_{x}(EQx) = (95^{2}+5^{2}+1^{2}+31^{2}+2^{2})^{0,5}= 100,08 kNb) For earthquake in global y directionmode 1 - V

_{x1}(EQx) = 2 kNmode 2 - V

_{x2}(EQx) = 19 kNmode 3 - V

_{x3}(EQx) = 1 kNmode 4 - V

_{x4}(EQx) = 1 kNmode 5 - V

_{x5}(EQx) = 8 kNTo get the value for earthquake in y you need to do an SRSS:

V

_{x}(EQx) = (2^{2}+19^{2}+1^{2}+1^{2}+8^{2})^{0,5}= 21 kNFor 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).## RE: The combination of the horizontal seismic components

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 .

## RE: The combination of the horizontal seismic components

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

## RE: The combination of the horizontal seismic components

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,

## RE: The combination of the horizontal seismic components

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 .

## RE: The combination of the horizontal seismic components

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 ?

## RE: The combination of the horizontal seismic components

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).

## RE: The combination of the horizontal seismic components

Clear , thank you so much for your response .

Great forum. Best resource by far!!!