Second-Order Effects

Owned by Hakan Şahin
Last updated: Sept 30, 2022 by Zeynep Aladağ
3 min read

Symbols

D

 Strength excess coefficient

R

 Carrier system behavior coefficient

θII,i(X)

 (X) second order indicator value defined for each i'th floor in the earthquake direction

θII,max(X)

 (X) maximum second order indicator value defined in the direction of the earthquake

V i (X)

 (X) reduced floor shear force at the i'th storey in the earthquake direction [kN]

hi

 The height of the i'th floor [m]

∆ i , ort (X)

 (X) mean reduced relative storey drift expressing the displacement difference between two consecutive floors in the earthquake direction [m]

wk

 Total weight acting on the kth floor [kN]

β II (X)

 Second order magnification factor

4.9.2.1 - In the direction of the (X) earthquake considered, Equation (4.35) and Second Order Indicator Value   θ II, i (X) shall   be calculated at each i'th storey .

The mean in this relation (∆ i (X) ) will be found according to 4.9.1 as the average value of the reduced relative storey drifts calculated in the earthquake direction in columns and walls on the i'th storey (X) .

4.9.2.2 - If the maximum value of θ II, i (X) calculated for all floors θ II, max (X) satisfies the condition given  in Equation (4.36) , the second order effects should be taken into account in the calculation of internal forces based on design it's not necessary.

In this case, local second order effects can be taken into account in element design according to the current reinforced concrete and steel regulations. In Eq. (4.36) , R and D indicate the load-bearing system behavior coefficient and resistance excess coefficient given in Table 4.1 for the building structural system , and C h indicates a coefficient defined depending on the nonlinear hysteretic behavior of the structural system. C h = 0.5 in reinforced concrete buildings , C h = 1 in buildings with steel and composite columns .

4.9.2.3 - If the maximum value of θ II, i (X)  calculated for all floors i II, max (X) does not satisfy the condition given in Equation (4.36) , the considered (X) earthquake direction the forces will be increased by multiplying the second order magnification coefficient βII (X) defined by Equation (4.37) below .   

Another option that can be applied in this situation is to renew the earthquake calculation by increasing the rigidity and / or strength of the carrier system appropriately.

4.9.2.4 - The above operations will also be performed for the earthquake direction (Y) perpendicular to (X). According to the definition given in 3.3.1 , in buildings with basements surrounded by rigid walls, second-order effects will be taken into account for the upper part of the building above the basement floors .  

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Second Order Effect Coefficient (4.9.2)

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