Response Spectra Analysis

This section explains the implementation of response spectra according to IS 1893 (Part 1): 2016, 6th Revision. For further information, refer to IS 1893-1 (2016): Criteria for Earthquake Resistant Design of Structures, Part 1: General Provisions and Buildings (Sixth Revision).

Structural Response Factors (S_a/g): Section 6.4.2

For rocky or hard soil sites
$\frac{S_{a}}{g} = \{\begin{matrix} \begin{matrix} 1 + 15 T & 0.00 < T < 0.10 \end{matrix} \\ \begin{matrix} 2.50 & 0.10 \leq T \leq 0.40 \end{matrix} \\ \begin{matrix} \begin{matrix} \frac{1.00}{T} & 0.40 \leq T \leq 4.00 \end{matrix} \\ \begin{matrix} 0.25 & T > 4.00 \end{matrix} \end{matrix} \end{matrix}$
For medium soil sites
$\frac{S_{a}}{g} = \{\begin{matrix} \begin{matrix} 1 + 15 T & 0.00 < T < 0.10 \end{matrix} \\ \begin{matrix} 2.50 & 0.10 \leq T \leq 0.55 \end{matrix} \\ \begin{matrix} \begin{matrix} \frac{1.36}{T} & 0.55 \leq T \leq 4.00 \end{matrix} \\ \begin{matrix} 0.25 & T > 4.00 \end{matrix} \end{matrix} \end{matrix}$
For soft soil sites
$\frac{S_{a}}{g} = \{\begin{matrix} \begin{matrix} 1 + 15 T & 0.00 < T < 0.10 \end{matrix} \\ \begin{matrix} 2.50 & 0.10 \leq T \leq 0.67 \end{matrix} \\ \begin{matrix} \begin{matrix} \frac{1.67}{T} & 0.67 \leq T \leq 4.00 \end{matrix} \\ \begin{matrix} 0.42 & T > 4.00 \end{matrix} \end{matrix} \end{matrix}$

Base Shear Modification: Section 7.7.3

This section states that base shear calculated per response spectra case (or time history) should be modified per base shear calculated from the equivalent seismic load case (i.e., ${\bar{V}}_{B} / V_{B}$ ).

The same modification should also be applied to member forces, displacements etc. This is not directly enforced by the program. However, the program provides scale factors in the response spectra load case dialog in which they can be used for scaling results.

Modes to be considered: Section 7.7.5.2

It is the engineer's responsibility to confirm that 90% mass participation is included in response spectra analysis (i.e., Eigenvalue analysis). There is no missing mass correction feature provided by the program if the subspace iteration method is selected for Eigenvalue analysis. On the other hand, the Ritz vector solution includes missing mass correction directly (i.e. static load correction), therefore use of the Ritz vector solution is recommended for this purpose.

Modal Combination: Section 7.7.5.3

Both CQC and SRSS methods are implemented for modal combination of results.

Torsion (or Accidental Torsion): Section 7.8

The 5% eccentricity rule is implemented for response spectra eccentric load case (eccentricity percentage can be changed in Diaphragm Mass dialog). The following design eccentricity is enforced for floors

e_di = 1.0e_si ± 0.05b_i

where

e_di	=	dynamic eccentricity
e_si	=	static eccentricity at floor "i" defined s distance between center of mass and center of rigidity
b_i	=	floor plan dimension of the floor "i" perpendicular to the direction of force

Implementation Details

Response spectra analysis for vertical direction is not implemented in the program.
Orthogonal response spectra cases are not supported in the program.
The design horizontal seismic coefficient A_h is defined according to the following equation:
$A_{h} = \frac{(\frac{Z}{2}) (\frac{S_{a}}{g})}{(\frac{R}{I})}$

or

$A_{h} = (\frac{Z I}{2 R}) (\frac{S_{a}}{g}) = γ (\frac{S_{a}}{g})$

Structural response spectra factor $\frac{S_{a}}{g}$ is used in response spectra analysis and it is not modified according to the above equation. In other words, the scaling factor $γ = \frac{Z I}{2 R}$ is not considered in the response spectra analysis. On the other hand, the program provides scale factors in the response spectra load case dialog in which the above scaling factor can be applied accordingly.