Response Spectra Analysis

Seismic Action (Section 3.2)

The seismic hazard (a_gR) is described in terms of a single parameter, reference peak ground acceleration on type A ground.

The design ground acceleration of type A ground is

a_{g} = a_{g R} \times γ_{I}

where

γ_{I}

=

the importance factor, and it is given in Table 4.3.

It is considered as low seismicity if

a_{g} < 0.08 g

or

a_{g} S < 0.1 g

where

S

=

the soil factor

General (Section 3.2.2.1)

The horizontal seismic action is described by two orthogonal components assumed as being independent and represented by the same response spectrum. For important structures (i.e., $γ_{I} > 1.0$ ), topographic amplification effects should be taken into account. The methodology given in Annex A of EN 1998-5:2004 is not implemented.

Horizontal Elastic Response Spectrum (Section 3.2.2.2)

For the horizontal components of the seismic action, the elastic response spectrum S_e(T) is defined by the following expressions:

\begin{matrix} 0 \leq T \leq T_{B} & S_{e} (T) = a_{g} \cdot S [1 + \frac{T}{T_{B}} (η \cdot 2.5 - 1)] \end{matrix}

(3.2)

\begin{matrix} T_{B} \leq T \leq T_{C} & S_{e} (T) = a_{g} \cdot S \cdot η \cdot 2.5 \end{matrix}

(3.3)

\begin{matrix} T_{C} \leq T \leq T_{D} & S_{e} (T) = a_{g} \cdot S \cdot η \cdot 2.5 \cdot \frac{T_{C}}{T} \end{matrix}

(3.4)

\begin{matrix} T_{D} \leq T \leq 4 s & S_{e} (T) = a_{g} \cdot S \cdot η \cdot 2.5 \cdot \frac{T_{C} \cdot T_{D}}{T^{2}} \end{matrix}

(3.5)

where

S_e(T)	=	the elastic response spectrum
T	=	the vibration period of a linear single-degree-of-freedom system
a_g	=	the design ground acceleration on type A ground
T_B	=	the lower limit of the period of the constant spectral acceleration branch
T_C	=	the upper limit of the period of the constant spectral acceleration branch
T_D	=	the value defining the beginning of the constant displacement response range of the spectrum
S	=	the soil factor
η	=	the damping correction factor with a reference value of η = 1 for 5% viscous damping. Otherwise, it is calculated as $η = \sqrt{10 / (5 + ξ)} \geq 0.55$
ξ	=	the viscous damping ratio of the structure.

It should be noted that the design ground acceleration a_g is equal to $a_{g R} \times γ_{I}$ and it is directly used in the above equations. Hence, the user-defined a_g value should include important factor γ_I.

Based on selected ground Type, the program reads T_B, T_C, T_D, and S values from the Tables 3.2 and 3.3.

Table 1. Values of the parameters describing the recommended Type 1 elastic response spectra
Ground Type	S	T_B(s)	T_C(s)	T_D(s)
A	1.0	0.15	0.4	2.0
B	1.2	0.15	0.5	2.0
C	1.15	0.20	0.6	2.0
D	1.35	0.20	0.8	2.0
E	1.4	0.15	0.5	2.0

Table 2. Values of the parameters describing the recommended Type 2 elastic response spectra
Ground Type	S	T_B(s)	T_C(s)	T_D(s)
A	1.0	0.05	0.25	1.2
B	1.35	0.05	0.25	1.2
C	1.5	0.10	0.25	1.2
D	1.8	0.10	0.30	1.2
E	1.6	0.05	0.25	1.2

The following clauses and sections are not implemented:

The clauses (5) and (6) regarding elastic displacement response spectrum calculation
Vertical elastic response spectrum (see Section 3.2.2.3)
Design ground displacement (see Section 3.2.2.4)
Design spectrum for elastic analysis (Section 3.2.2.5)

In addition, the program does not apply the behavior factor q to reduce (or scale) results from elastic response spectra analysis. Instead, it provides an option to scale response spectra analysis results for X and Y directions (see the load case dialog).

Criteria for Structural Regularity (Section 4.2.3)

This section introduces definition of regular and non-regular structures both in plan and elevation. Based on structure regularity type, the section provides guidance about selection of structural model type (planar versus spatial) and analysis method (response spectra versus later force procedure). Further information is given in Table 4.1.

The program does not perform building regularity checks mentioned in this section. It is engineer’s responsibility to select structural model type and analysis method.