# V. IS 1893 2002 Response Spectrum

Calculation of base shear and its distribution along the height for response spectrum method in IS 1893 (Part 1) : 2002.

## Problem

A three story building is modelled in STAAD.Pro considering the following:
• Seismic zone factor, Z = 0.36
• Importance factor, I = 1
• Response reduction factor, R = 5
• Soil site conditions = Hard

The generated model is subjected to a response spectrum load along global X direction. The base shear and its distribution along height reported by STAAD.Pro is verified against hand calculation.

Natural Frequency/Time Period Information & Mode Shapes (Obtained from output file)

Table 1. Natural Frequencies/Time Period
Mode Frequency (cyc/sec) Time Period (sec)
1 3.332 0.30014
2 9.103 0.10986
3 12.435 0.08042
Table 2. Mode Shapes
Mode Story Level/Joint Numbers X-Trans Y-Trans Z-Trans X-Rot Y-Rot Z-Rot
1 Roof/Joints 7 & 8 1 0 0 0 0 0
2nd Floor/Joints 5 & 6 0.86603 0 0 0 0 0
1st Floor/Joints 2 & 3 0.5 0 0 0 0 0
2 Roof/Joints 7 & 8 -1 0 0 0 0 0
2nd Floor/Joints 5 & 6 0 0 0 0 0 0
1st Floor/Joints 2 & 3 1 0 0 0 0 0
3 Roof/Joints 7 & 8 1 0 0 0 0 0
2nd Floor/Joints 5 & 6 -0.86603 0 0 0 0 0
1st Floor/Joints 2 & 3 0.5 0 0 0 0 0
Table 3. Mode Participation Factor Calculation
Story Level Weight Wi (KN) Mode 1 Mode 2 Mode 3
ϕ Wi × ϕ Wi × ϕ 2 ϕ Wi × ϕ Wi × ϕ 2 ϕ Wi × ϕ Wi × ϕ 2
Roof 49.035 1 49.035 49.035 -1 -49.035 49.035 1 49.035 49.035
2nd Floor 98.07 0.86603 84.932 73.553 0 0 0 -0.86603 -84.932 73.553
1st Floor 98.07 0.5 49.035 24.518 1 98.07 98.07 0.5 49.035 24.518
Summation 245.175 183.00 147.11 49.035 147.105 13.138 147.106
Modal Weight Mk × g 227.66 16.345 1.173
Modal Weight Participation (In %) 92.85 6.667 0.479
Mode Participation Factor Pk ∑Wi × ϕ / ∑ Wi × ϕ 2 1.244 0.3333 0.0893
Mode 1 Mode 2 Mode 3
Sa/g 2.5 (time period < 0.4 s) 2.5 (time period < 0.4 s) 2.2063 (1 + 15 × 0.08042 as time period < 0.1 s)
Ak (Z/2 × I/R × Sa/g) 0.09

(0.36/2 × 1/5 × 2.5)

0.09

(0.36/2 × 1/5 × 2.5)

0.0794

(0.36/2 × 1/5 × 2.2063)

Story Level Weight Wi (KN) Mode 1 Mode 2 Mode 3 Story Shear due to all modes i.e. SRSS of all modes
ϕ Qi (Ak × ϕ × Pk × Wi) Vi (∑Qi) ϕ Qi (Ak × ϕ × Pk × Wi) Vi (∑Qi) ϕ Qi (Ak × ϕ × Pk × Wi) Vi (∑Qi)
Roof 49.035 1 5.490 5.490 -1 -1.471 -1.471 1 0.3478 0.3478 5.69
2nd Floor 98.07 0.86603 9.509 15.0 0 0 -1.471 -0.86603 -0.6025 -0.2546 15.073
1st Floor 98.07 0.5 5.490 20.49 1 2.942 1.471 0.5 0.3478 0.0932 20.542
Base Shear 20.54

## Comparison

Table 4. Comparison of results
Story shear (kN) Roof 5.69 5.69 none
2nd 15.07 15.07 none
1st 20.54 20.54 none
Base shear (kN) 20.54 20.54 none

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\IS 1893\2002\IS 1893 2002 Response Spectrum.STD is typically installed with the program.

``````STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 08-Feb-17
END JOB INFORMATION
INPUT WIDTH 79
SET SHEAR
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 3 0; 3 3 3 0; 4 3 0 0; 5 0 6 0; 6 3 6 0; 7 0 9 0; 8 3 9 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 2 5; 5 3 6; 6 5 6; 7 5 7; 8 6 8; 9 7 8;
START USER TABLE
TABLE 1
UNIT METER KN
PRISMATIC
COLLUMN
1e+09 0.000847246 0.001 0.001 0.001 0.001 0.5 0.5
TABLE 2
UNIT METER KN
PRISMATIC
BEAM
0.001 1e+09 0.001 0.001 0.001 0.001 0.5 0.5
END
DEFINE MATERIAL START
ISOTROPIC CONCRETE
E 2.17185e+07
POISSON 0.17
DENSITY 23.5616
ALPHA 1e-05
DAMP 0.05
TYPE CONCRETE
STRENGTH FCU 27579
G 9.28139e+06
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 3 TO 5 7 8 UPTABLE 1 COLLUMN
2 6 9 UPTABLE 2 BEAM
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORTS
1 4 FIXED
8 FX 49.035
3 6 FX 98.07
FLOOR DIAPHRAGM
DIA 1 TYPE RIG HEI 3
DIA 2 TYPE RIG HEI 6
DIA 3 TYPE RIG HEI 9
SPECTRUM SRSS 1893 X 0.036 ACC DAMP 0.05
SOIL TYPE 1
PERFORM ANALYSIS PRINT ALL
PRINT MODE SHAPES
PRINT ANALYSIS RESULTS
FINISH
``````

``` 1893 RESPONSE SPECTRUM LOAD     1
MODAL WEIGHT (MODAL MASS TIMES g) IN KN           GENERALIZED
MODE           X             Y             Z              WEIGHT
1       2.276565E+02  0.000000E+00  0.000000E+00    1.471050E+02
2       1.634500E+01  0.000000E+00  0.000000E+00    1.471050E+02
3       1.173519E+00  0.000000E+00  0.000000E+00    1.471051E+02
DYNAMIC WEIGHT X Y Z   2.451750E+02  0.000000E+00  0.000000E+00 KN
MISSING WEIGHT X Y Z  -3.177132E-06  0.000000E+00  0.000000E+00 KN
MODAL WEIGHT X Y Z   2.451750E+02  0.000000E+00  0.000000E+00 KN
MODE    SPECTRAL ACCELERATION       DESIGN   SEISMIC   COEFFICIENT
----    ---------------------     ------------------------------
X           Y           Z
1           2.50000                0.0900      0.0000      0.0000
2           2.50000                0.0900      0.0000      0.0000
3           2.20632                0.0794      0.0000      0.0000
STAAD SPACE                                              -- PAGE NO.    6
PEAK STORY SHEAR
STORY           LEVEL IN METE           PEAK STORY SHEAR IN  KN
-----           -------------           -------------------------
X                  Z
3                   9.00               5.69               0.00
2                   6.00              15.07               0.00
1                   3.00              20.54               0.00
BASE                  0.00              20.54               0.00
RESPONSE SPECTRUM VALUES - UNITS ( METE SECOND )
------------------------
DIRECTIONAL VALUES:                 SCALE FACTOR =    1.00
X =  0.04   Y =  0.00   Z =  0.00          DAMPING FACTOR = 0.050
PERIOD  VS.  ACCELERATION
0.3001          24.5166
0.1099          24.5166
0.0804          21.6366
MODE                 ACCELERATION-G     DAMPING
----                 --------------     -------
1                      2.50000       0.05000
2                      2.50000       0.05000
3                      2.20632       0.05000
STAAD SPACE                                              -- PAGE NO.    7
MODAL BASE ACTIONS
MODAL BASE ACTIONS        FORCES IN KN   LENGTH IN METE
-----------------------------------------------------------
MODE     PERIOD        FX          FY          FZ          MX          MY          MZ
1      0.300       20.49        0.00        0.00        0.00        0.00     -122.93
2      0.110        1.47        0.00        0.00        0.00        0.00        4.41
3      0.080        0.09        0.00        0.00        0.00        0.00       -0.56
PARTICIPATION FACTORS
MASS  PARTICIPATION FACTORS IN PERCENT         BASE SHEAR IN KN
--------------------------------------         ------------------
MODE    X     Y     Z     SUMM-X   SUMM-Y   SUMM-Z       X        Y        Z
1   92.85  0.00  0.00   92.855    0.000    0.000     20.49     0.00     0.00
2    6.67  0.00  0.00   99.521    0.000    0.000      1.47     0.00     0.00
3    0.48  0.00  0.00  100.000    0.000    0.000      0.09     0.00     0.00
---------------------------
TOTAL SRSS  SHEAR     20.54     0.00     0.00
TOTAL 10PCT SHEAR     20.54     0.00     0.00
TOTAL ABS   SHEAR     22.05     0.00     0.00
TOTAL CSM   SHEAR     20.54     0.00     0.00
```