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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
Parameter Hand Calculation STAAD.Pro Difference Comments
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

STAAD Input

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
DEFINE REFERENCE LOADS
LOAD R1 LOADTYPE Mass  TITLE REF LOAD CASE 1
JOINT LOAD
8 FX 49.035
3 6 FX 98.07
END DEFINE REFERENCE LOADS
FLOOR DIAPHRAGM
DIA 1 TYPE RIG HEI 3
DIA 2 TYPE RIG HEI 6
DIA 3 TYPE RIG HEI 9
LOAD 1 LOADTYPE None  TITLE RS_X
SPECTRUM SRSS 1893 X 0.036 ACC DAMP 0.05
SOIL TYPE 1
PERFORM ANALYSIS PRINT ALL
PRINT MODE SHAPES
PRINT ANALYSIS RESULTS
FINISH

STAAD Output

 1893 RESPONSE SPECTRUM LOAD     1 
     RESPONSE LOAD CASE      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
     SRSS          MODAL COMBINATION METHOD USED.
     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  
     RESPONSE LOAD CASE     1
        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
  -----------------------------------------------------------
                                                             MOMENTS ARE ABOUT THE ORIGIN
   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