Equivalent Static Method

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).

Design Seismic Base Shear: Section 7.2.1

The total lateral force (or design seismic base shear) along principal directions is determined from:

V_B = A_hW

where

W	=	seismic weight of the building (Section 7.4.2)
A_h	=	design horizontal acceleration spectrum value (Section 6.4.2) using the fundamental natural period T_a (Section 7.6) in the considered direction of vibration.

Seismic Weight (W): Section 7.4

Total seismic weight of building is summation of seismic weight of all floors. In calculation of floor seismic weight, Section 7.4.1 states that full dead load and approximate amount of imposed load (&.3.1 and 7.3.2) should be included in this calculation. This is not implemented in the program. Note that the program calculates seismic weight from building mass information. For this reason, engineer needs to modify mass information to account for live loads. On the other hand, modifying building mass also alter dynamic characteristics of structure (i.e., periods and modes).

Design Horizontal Acceleration Spectrum Value (A_h): Section 6.4.2

The term A_h is defined in Section 6.4.2 as follows:

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

The term Z is zone factor and its defined as follows:

Table 1. Zone Factor Z
Seismic Zone	II	III	IV	V
Seismic Intensity	Low	Moderate	Severe	Very Severe
Z	0.10	0.16	0.24	0.36

where

$(\frac{Z}{2})$	=	for converting MCE (maximum considered earthquake) to DBE (design basis earthquake)
I	=	importance factor (Table 6)
R	=	response reduction factor (Table 7). It is defined separately for each direction.

The term

(\frac{S_{a}}{g})

is average response acceleration coefficient and it is defined as follows (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
$\frac{S_{a}}{g} = \{\begin{matrix} \begin{matrix} 1 + 15 T & 0.00 < T < 0.10 \end{matrix} \\ \begin{matrix} 2.50 & 0.10 \leq T \leq 0.67 \end{matrix} \\ \begin{matrix} \begin{matrix} \frac{1.67}{T} & 0.67 \leq T \leq 4.00 \end{matrix} \\ \begin{matrix} 0.42 & T > 4.00 \end{matrix} \end{matrix} \end{matrix}$

Table 2. Multiplying Factors for Obtaining Values for Other Damping (Clause 6.4.2)
Damping, percent	0	2	5	7	10	15	20	25	30
Factors	3.20	1.40	1.0	0.90	0.80	0.70	0.60	0.55	0.50

Noted that values for $\frac{S_{a}}{g}$ given above is valid for 5% damping.

Fundamental Natural Period Calculation (T_a): Section 7.6.2

7.6.2.a. Bare MRF building (without any masonry infills):

T_{a} = \{\begin{matrix} 0.075 h^{0.75} & f o r R C b u i l d i n g s \\ 0.080 h^{0.75} & f o r R C - S t e e l C o m p o s i t e M R F b u i l d i n g \\ 0.085 h^{0.75} & f o r s t e l l M R F b u i l d i n g \end{matrix}

7.6.2.b. Building with RC structural walls:

T_{a} = \frac{0.075 h^{0.75}}{\sqrt{A_{w}}} \geq \frac{0.09 h}{\sqrt{d}}

where

A_w	=	the total effective area (m²) of walls in the first story of the building given by: $A_{w} = \sum_{i = 1}^{N_{w}} [A_{w i} \{0.2 + {(\frac{L_{w i}}{h})}^{2}\}]$
h	=	height of buildings in meters
A_wi	=	effective cross-sectional area of wall "i" in first story (m²)
L_wi	=	length of structural was "i" in the first story in the considered direction of lateral forces (in meters)

The value of L_wi/h to be used in the above equation shall not exceed 0.9. This implementation does not enforce this condition.

7.6.2.c. All other buildings:

T_{a} = \frac{0.09 h}{\sqrt{d}}

where

h	=	height of buildings in meters
d	=	base dimension of building along considered direction of lateral force (in meters)

All conditions defined in 7.6.2a, 7.6.2b, and 7.6.2c are implemented. Also, note that fundamental natural period can be directly obtained from an Eigenvalue analysis.

Distribution of Design Forces: Section 7.6.3

Calculated base shear is distributed to floors (vertical distribution) in accordance with the following equation:

Q_{i} = V_{B} \frac{W_{i} h_{i}^{2}}{\sum_{j = 1}^{n} W_{j} h_{j}^{2}}

where

Q_i	=	design lateral force at floor "i"
W	=	seismic weight at floor "i"
h_i	=	height of floor "i" measured from base
n	=	number of stories

Orthogonal Load Cases: Section 6.3.2.2

Orthogonal cases (combining 100% of load case in one direction and 30% in other) is supported.

Design Vertical Earthquake Load: Section 6.3.3

Vertical earthquake loads are not calculated in the program.

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

Equivalent Static Method

Design Seismic Base Shear: Section 7.2.1

Seismic Weight (W): Section 7.4

Design Horizontal Acceleration Spectrum Value (Ah): Section 6.4.2

Fundamental Natural Period Calculation (Ta): Section 7.6.2

Distribution of Design Forces: Section 7.6.3

Orthogonal Load Cases: Section 6.3.2.2

Design Vertical Earthquake Load: Section 6.3.3

Torsion (or Accidental Torsion): Section 7.8

Design Horizontal Acceleration Spectrum Value (A_h): Section 6.4.2

Fundamental Natural Period Calculation (T_a): Section 7.6.2