V. IS 1893 2015 Static Seismic

Calculate the design lateral force at each node in each global direction by the equivalent static seismic method per the IS 1893 (Part 4) 2015 specification.

Details

The loads at each node are taken as the same in each global direction (i.e., W_xi = W_zi = W_yi). Loads at nodes 2, 8, and 14 are 15 kN ea. Loads at nodes 3, 4, 7, 9, 12, and 13 are 10 kN ea.

Sections used for all members: ISMB 450

Materials used: steel

The structure is modelled in STAAD.Pro considering the following:

Seismic zone factor, Z = 0.36 (ZONE 0.36)
Importance factor, I = 1.0 (I 1.0)
Response reduction factor, R = 5 (RF 5)
Soil site condition = Hard (SS 1)
Structure type is a category 4 (ST 4)
2% Damping (DM 0.02)

Validation

Seismic Load

Seismic Loads as per IS 1893 (Part 4): 2015 specifications are generated along two horizontal directions, global X & global Z and also along vertical direction, global Y.

Time period in X direction: T_x = 0.09734 sec.

Time period in Z direction: T_z = 0.51406 sec.

Time Period, T, is calculated by the Rayleigh Method

As per Table 15 of IS 1893 (Part 4): 2015

Damping Factor (DF) for 2% damping = 1.4

From figure 1 of IS 1893 (Part 4): 2015, for Hard Soil sites for (0 second <T<0.1 second)

Spectral acceleration coefficient value ( $\frac{S_{a}}{g}$ ) in X, Z, and Y directions for 2% damping:

{\frac{S_{a}}{g}}_{x} = D F \times (1 + 15 T) = 1.4 \times [1 + (15 \times 0.09734)] = 3.444

From figure 1 of IS 1893 (Part 4): 2015, for Hard Soil sites for (0.4 second <T<10 second)

{\frac{S_{a}}{g}}_{z} = D F \times \frac{1}{T} = 1.4 \times \frac{1}{0.51406} = 2.723

As per clause 10.2 of IS 1893 (Part 4): 2015

{\frac{S_{a}}{g}}_{y} = \frac{2}{3} \times M a x i m u m o f ({\frac{S_{a}}{g}}_{x}, {\frac{S_{a}}{g}}_{z}) = \frac{2}{3} \times 3.444 = 2.296

As per clause 7.3.2 of IS 1893 (Part 4): 2015

The seismic coefficient in X, Z and Y direction

A_{h_x} = \frac{Z}{2} \times \frac{I}{R} \times {\frac{S_{a}}{g}}_{x} = \frac{0.36}{2} \times \frac{1}{5} \times 3.444 = 0.124

A_{h_z} = \frac{Z}{2} \times \frac{I}{R} \times {\frac{S_{a}}{g}}_{z} = \frac{0.36}{2} \times \frac{1}{5} \times 2.723 = 0.098

A_{h_y} = \frac{Z}{2} \times \frac{I}{R} \times {\frac{S_{a}}{g}}_{y} = \frac{0.36}{2} \times \frac{1}{5} \times 2.296 = 0.083

Node	W (kN)	Design lateral force in X direction Q_x = W_x × A_{h_x}	Design lateral force in Z direction Q_z = W_z × A_{h_z}	Design force in Y direction Q_y = W_y × A_{h_y}
2	15	(15 × 0.124) = 1.860	(15 × 0.098) = 1.471	(15 × 0.083) = 1.240
3	10	(10 × 0.124) = 1.240	(10 × 0.098) = 0.980	(10 × 0.083) = 0.827
4	10	(10 × 0.124) = 1.240	(10 × 0.098) = 0.980	(10 × 0.083) = 0.827
7	10	(10 × 0.124) = 1.240	(10 × 0.098) = 0.980	(10 × 0.083) = 0.827
8	15	(15 × 0.124) = 1.860	(15 × 0.098) = 1.471	(15 × 0.083) = 1.240
9	10	(10 × 0.124) = 1.240	(10 × 0.098) = 0.980	(10 × 0.083) = 0.827
12	10	(10 × 0.124) = 1.240	(10 × 0.098) = 0.980	(10 × 0.083) = 0.827
13	10	(10 × 0.124) = 1.240	(10 × 0.098) = 0.980	(10 × 0.083) = 0.827
14	15	(15 × 0.124) = 1.860	(15 × 0.098) = 1.471	(15 × 0.083) = 1.240

Results

Table 1.
Result Type	Calculations	STAAD.Pro	Difference
${\frac{S_{a}}{g}}_{x}$	3.444	3.444	none
A_{h_x}	0.124	0.124	none
${\frac{S_{a}}{g}}_{z}$	2.723	2.723	none
A_{h_z}	0.098	0.098	none
${\frac{S_{a}}{g}}_{y}$	2.296	2.296	none
A_{h_y}	0.083	0.083	none
Q_x at Nodes 2,8,14 (kN)	1.860	1.860	none
Q_x at Nodes 3,4,7, 9,12, 13 (kN)	1.240	1.240	none
Q_z at Nodes 2,8,14 (kN)	1.471	1.471	none
Q_z at Nodes 3,4,7, 9,12, 13 (kN)	0.980	0.980	none
Q_y at Nodes 2,8,14 (kN)	1.240	1.240	none
Q_y at Nodes 3,4,7, 9,12, 13 (kN)	0.827	0.827	none

STAAD.Pro Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\IS 1893\IS 1893 2015 Static Seismic.std is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 25-Mar-20
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 4 0; 3 3 7 0; 4 6 4 0; 5 6 0 0; 6 0 0 5; 7 0 4 5; 8 3 7 5;
9 6 4 5; 10 6 0 5; 11 0 0 10; 12 0 4 10; 13 3 7 10; 14 6 4 10; 15 6 0 10;
MEMBER INCIDENCES
2 1 2; 3 2 3; 4 3 4; 5 4 5; 7 6 7; 8 7 8; 9 8 9; 10 9 10; 11 2 7; 12 8 3;
13 4 9; 14 2 4; 15 7 9; 16 11 12; 17 12 13; 18 13 14; 19 14 15; 20 12 14;
21 7 12; 22 9 14; 23 8 13;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+08
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-05
DAMP 0.03
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY INDIAN
2 TO 5 7 TO 23 TABLE ST ISMB450
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 5 6 10 11 15 FIXED
DEFINE REFERENCE LOADS
LOAD R1 LOADTYPE Mass  TITLE REF LOAD CASE 1
JOINT LOAD
2 8 14 FX 15 FY -15 FZ 15
3 4 7 9 12 13 FX 10 FY -10 FZ 10
END DEFINE REFERENCE LOADS
FLOOR DIAPHRAGM
DIA 1 TYPE RIG HEI 4
DIA 2 TYPE RIG HEI 7
DEFINE IS1893 2015 LOAD PART4
ZONE 0.36 RF 5 I 1 SS 1 ST 4 DM 0.02
LOAD 1 LOADTYPE None  TITLE STATIC_X
1893 LOAD X 1
LOAD 2 LOADTYPE None  TITLE STATIC_Z
1893 LOAD Z 1
LOAD 3 LOADTYPE None  TITLE STATIC_Y
1893 LOAD Y 1
PERFORM ANALYSIS PRINT LOAD DATA
PRINT ANALYSIS RESULTS
FINISH

STAAD.Pro Output

   LOADING     1  LOADTYPE NONE  TITLE STATIC_X                               
   -----------
   LOADING     2  LOADTYPE NONE  TITLE STATIC_Z                               
   -----------
   LOADING     3  LOADTYPE NONE  TITLE STATIC_Y                               
   -----------
  **WARNING: IF THIS UBC/IBC ANALYSIS HAS TENSION/COMPRESSION
  OR REPEAT LOAD OR RE-ANALYSIS OR SELECT OPTIMIZE, THEN EACH
  UBC/IBC CASE SHOULD BE FOLLOWED BY PERFORM ANALYSIS & CHANGE.
 BASE SHEAR AND TIME PERIOD IN X    
   *********************************************************
   * UNITS - KN    METE                                    *
   * TIME PERIOD FOR X 1893 LOADING =    0.09734 SEC       *
   * SA/G PER 1893=    3.444, LOAD FACTOR= 1.000           *
   * AH PER 1893=    0.124 WEIGHT=      105.00 KN          *
   *********************************************************
   ***NOTE: For Industrial Structures, Static Seismic Load is applied
   per node. Use command: PRINT LOAD DATA to view the applied load at
   each node. Ref. Cl.10.2
 BASE SHEAR AND TIME PERIOD IN Z    
   *********************************************************
   * UNITS - KN    METE                                    *
   * TIME PERIOD FOR Z 1893 LOADING =    0.51406 SEC       *
   * SA/G PER 1893=    2.723, LOAD FACTOR= 1.000           *
   * AH PER 1893=    0.098 WEIGHT=      105.00 KN          *
   *********************************************************
   ***NOTE: For Industrial Structures, Static Seismic Load is applied
   per node. Use command: PRINT LOAD DATA to view the applied load at
   each node. Ref. Cl.10.2
 BASE SHEAR AND TIME PERIOD IN Y    
   *********************************************************
   * UNITS - KN    METE                                    *
   * SA/G FOR Y-DIR CALCULATED AS PER CL.10.2              *
   * FOR INDUSTRIAL STRUCTURES                             *
   * SA/G PER 1893=    2.296, LOAD FACTOR= 1.000           *
   * AH PER 1893=    0.083 WEIGHT=      105.00 KN          *
   *********************************************************
   ***NOTE: For Industrial Structures, Static Seismic Load is applied
   per node. Use command: PRINT LOAD DATA to view the applied load at
   each node. Ref. Cl.10.2
      STAAD SPACE                                              -- PAGE NO.    5
    JOINT            LATERAL          TORSIONAL            LOAD -    1
                     LOAD (KN  )      MOMENT (KN  -METE) FACTOR -   1.000
    -----            -------          ---------
       2     FX        1.860    MY        0.000
       4     FX        1.240    MY        0.000
       7     FX        1.240    MY        0.000
       9     FX        1.240    MY        0.000
      12     FX        1.240    MY        0.000
      14     FX        1.860    MY        0.000
                 -----------        -----------
          TOTAL =      8.679              0.000 AT LEVEL     4.000 METE
       3     FX        1.240    MY        0.000
       8     FX        1.860    MY        0.000
      13     FX        1.240    MY        0.000
                 -----------        -----------
          TOTAL =      4.340              0.000 AT LEVEL     7.000 METE
    JOINT            LATERAL          TORSIONAL            LOAD -    2
                     LOAD (KN  )      MOMENT (KN  -METE) FACTOR -   1.000
    -----            -------          ---------
       2     FZ        1.471    MY        0.000
       4     FZ        0.980    MY        0.000
       7     FZ        0.980    MY        0.000
       9     FZ        0.980    MY        0.000
      12     FZ        0.980    MY        0.000
      14     FZ        1.471    MY        0.000
                 -----------        -----------
          TOTAL =      6.863              0.000 AT LEVEL     4.000 METE
       3     FZ        0.980    MY        0.000
       8     FZ        1.471    MY        0.000
      13     FZ        0.980    MY        0.000
                 -----------        -----------
          TOTAL =      3.431              0.000 AT LEVEL     7.000 METE
    JOINT            LATERAL          TORSIONAL            LOAD -    3
                     LOAD (KN  )      MOMENT (KN  -METE) FACTOR -   1.000
    -----            -------          ---------
       2     FY        1.240    MY        0.000
       4     FY        0.827    MY        0.000
       7     FY        0.827    MY        0.000
       9     FY        0.827    MY        0.000
      12     FY        0.827    MY        0.000
      14     FY        1.240    MY        0.000
      STAAD SPACE                                              -- PAGE NO.    6
                 -----------        -----------
          TOTAL =      5.786              0.000 AT LEVEL     4.000 METE
       3     FY        0.827    MY        0.000
       8     FY        1.240    MY        0.000
      13     FY        0.827    MY        0.000
                 -----------        -----------
          TOTAL =      2.893              0.000 AT LEVEL     7.000 METE