Sensitivity to 2^nd order effects acc. EC-EN 1998 4.4.2.2(2)

Eurocode 8 background

According to EC-EN 1998 4.4.2.2(2):

(2) second-order effects (P-delta effects) need not be taken into account if the following condition is fulfilled in all storeys:

where

θ is the interstorey drift sensitivity coefficient;

P_tot is the total gravity load at and above the storey considered in the seismic design situation;

d_r is the design interstorey drift, evaluated as the difference of the average lateral displacements ds at the top and bottom of the storey under consideration and calculated in accordance with 4.3.4;

V_tot is the total seismic storey shear;

h is the interstorey height.

(3) If 0.1 < θ ≤ 0.2, the second-order effects may approximately be taken into account by multiplying the relevant seismic action effects by a factor equal to 1/(1-θ)

(4)P The value of the coefficient θ shall not exceed 0.3

In SCIA Engineer

2nd order sensitivity check is not directly supported in SCIA Engineer. However, all values necessary to perform the check can be obtained easily.

Consider the following, simple example:

P_tot and V_tot can be obtained from detailed storey results as resultant forces per storey for the considered seismic ULS combination:

d_r can be obtained from summary storey results as interstorey drift result for the considered seismic load case:

Please note: displacements from seismic load cases are direct results from FE analysis and must be multiplied by the behaviour factor q when relevant, as it is the case here (EN 1998 4.3.4).

The value of the behaviour factor is q = 1.5.

Storey	Ptot [kN]	Vtot [kN]	dr [m]	q∙dr [m]	h [m]	θ	Check
FL1	5809	83	0.0032	0.0048	4.5	0.075	OK
FL2	3853	66	0.0048	0.0072	4.5	0.093	OK
FL3	1897	50	0.0035	0.00525	4.5	0.044	OK

Tip: copy/paste the relevant results from table results to a spreadsheet (e.g. Excel) to perform the check.