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V.IS 1893 2016 Response Spectrum Vertical

Calculation of base shear for vertical motion of oscillation by response spectrum method in IS 1893 : 2016 (Part 1).

Details

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

  • Seismic zone factor, Z = 0.36
  • Importance factor, I = 1.2
  • Response reduction factor, R = 5
  • Soil site conditions = Hard

The dimension of the columns is 0.2m x 0.1 m and material is concrete

The generated model is subjected to a response spectrum load along global Y direction.

Natural frequencies / time period and mode shapes are obtained from the STAAD.Pro output file.

Table 1. Natural frequency / time period
Mode Frequency (cyc/sec) Time Period (sec)
1 9.913 0.10088
2 27.083 0.03692
3 36.996 0.02703
Table 2. Mode shapes
Mode Story Level/Joint Numbers X-Trans Y-Trans Z-Trans X-Rot Y-Rot Z-Rot
1 Roof/Joint 4 0 1 0 0 0 0
2nd Floor/Joint 3 0 0.86603 0 0 0 0
1st Floor/Joint 2 0 0.5 0 0 0 0
2 Roof/Joint 4 0 -1 0 0 0 0
2nd Floor/Joint 3 0 0 0 0 0 0
1st Floor/Joint 2 0 1 0 0 0 0
3 Roof/Joint 4 0 1 0 0 0 0
2nd Floor/Joint 3 0 -0.86603 0 0 0 0
1st Floor/Joint 2 0 0.5 0 0 0 0

Validation

Story Level Weight Wi (kN) Mode 1 Mode 2 Mode 3
ϕ Wi × ϕ Wi × ϕ2 ϕ Wi × ϕ Wi × ϕ2 ϕ Wi × ϕ Wi × ϕ2
Roof 49.035 1 49.035 49.035 -1 -49.035 49.035 1 49.035 49.035
2nd Floor 98.07 0.8660 84.932 73.553 0 0 0 -0.8660 -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 - 183.002 147.106 - 49.035 147.105 - 13.138 147.106
Modal Weight Mk × g 227.7 16.35 1.173
Modal Weight Participation (In %) 92.85 6.667 0.479
Mode Participation Factor Pk ∑Wi x ϕ / ∑ Wi x ϕ2 1.244 0.333 0.089
Table 3. Design vertical acceleration spectrum value calculation
Mode 1 Mode 2 Mode 3
Time period(sec) 0.1009 0.0369 0.0270
Sa/g 2.5 2.5 2.5
Ak (2/3 × Z/2 × I/R × Sa/g) 0.072 0.072 0.072
Table 4. Base shear calculation
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 Vi ϕ Qi Vi ϕQi Vi ϕ
Roof 49.035 1 4.392 4.392 -1 -1.177 -1.177 1 0.315 0.315 4.56
2nd Floor 98.07 0.8660 7.607 12.0 0 0 -1.177 -0.8660 -0.546 -0.231 12.06
1st Floor 98.07 0.5 4.392 16.39 1 2.354 1.177 0.5 0.315 0.084 16.43
Base shear 16.43

Results

Table 5. Comparison of results
Result Type Reference STAAD.Pro Difference Comments
Base shear (kN) 16.43 16.43 none  

STAAD.Pro Input File

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\IS 1893\2016\IS 1893 2016 Response Spectrum Vertical.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 3 0 0; 2 3 3 0; 3 3 6 0; 4 3 9 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4;
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 2 3 PRIS YD 0.2 ZD 0.1
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORTS
1 FIXED
DEFINE REFERENCE LOADS
LOAD R1 LOADTYPE Mass  TITLE REF LOAD CASE 1
JOINT LOAD
4 FY 49.035
2 3 FY 98.07
END DEFINE REFERENCE LOADS
LOAD 1 LOADTYPE NONE  TITLE RS_Y
SPECTRUM SRSS IS1893 2016 Y 0.0432 DAMP 0.05
SOIL TYPE 1
PERFORM ANALYSIS PRINT ALL
PRINT MODE SHAPES
PRINT ANALYSIS RESULTS
FINISH

STAAD.Pro Output

               CALCULATED FREQUENCIES FOR LOAD CASE       1
       MODE            FREQUENCY(CYCLES/SEC)         PERIOD(SEC)
         1                       9.913                  0.10088
         2                      27.083                  0.03692
         3                      36.996                  0.02703
 1893 RESPONSE SPECTRUM LOAD     1 
     RESPONSE LOAD CASE      1
            MODAL WEIGHT (MODAL MASS TIMES g) IN KN           GENERALIZED
      MODE           X             Y             Z              WEIGHT
         1       0.000000E+00  2.276565E+02  0.000000E+00    1.471050E+02
         2       0.000000E+00  1.634500E+01  0.000000E+00    1.471050E+02
         3       0.000000E+00  1.173519E+00  0.000000E+00    1.471050E+02
     SRSS          MODAL COMBINATION METHOD USED.
     DYNAMIC WEIGHT X Y Z   0.000000E+00  2.451750E+02  0.000000E+00 KN  
     MISSING WEIGHT X Y Z   0.000000E+00 -3.177129E-06  0.000000E+00 KN  
       MODAL WEIGHT X Y Z   0.000000E+00  2.451750E+02  0.000000E+00 KN  
   ***NOTE: IT IS RECOMMENDED TO DEFINE FLOOR LEVELS USING "FLOOR HEIGHT" INPUT.
     RESPONSE LOAD CASE     1
        MODE    SPECTRAL ACCELERATION       DESIGN   SEISMIC   COEFFICIENT
        ----    ---------------------     ------------------------------
                                              X           Y           Z
          1           2.50000                0.0000      0.0720      0.0000
          2           2.50000                0.0000      0.0720      0.0000
          3           2.50000                0.0000      0.0720      0.0000
      STAAD SPACE                                              -- PAGE NO.    5
 PEAK STORY SHEAR 
        STORY           LEVEL IN METE                    PEAK STORY SHEAR IN  KN  
        -----           -------------           -------------------------------------------------- 
                                                  X                  Y                  Z
        BASE                  0.00               0.00              16.43               0.00
   RESPONSE SPECTRUM VALUES - UNITS ( METE SECOND )
   ------------------------
           DIRECTIONAL VALUES:                 SCALE FACTOR =    1.00
    X =  0.00   Y =  0.04   Z =  0.00          DAMPING FACTOR = 0.050
           PERIOD  VS.  ACCELERATION
           0.1009          24.5166
           0.0369          24.5166
           0.0270          24.5166
           MODE                 ACCELERATION-G     DAMPING
           ----                 --------------     -------
              1                      2.50000       0.05000
              2                      2.50000       0.05000
              3                      2.50000       0.05000
 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      0.101        0.00       16.39        0.00        0.00        0.00       49.17
      2      0.037        0.00        1.18        0.00        0.00        0.00        3.53
      3      0.027        0.00        0.08        0.00        0.00        0.00        0.25
      STAAD SPACE                                              -- PAGE NO.    6
 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    0.00 92.85  0.00    0.000   92.855    0.000      0.00    16.39     0.00
   2    0.00  6.67  0.00    0.000   99.521    0.000      0.00     1.18     0.00
   3    0.00  0.48  0.00    0.000  100.000    0.000      0.00     0.08     0.00
                                                    ---------------------------
                                  TOTAL SRSS  SHEAR      0.00    16.43     0.00
                                  TOTAL 10PCT SHEAR      0.00    16.43     0.00
                                  TOTAL ABS   SHEAR      0.00    17.65     0.00
                                  TOTAL CSM   SHEAR      0.00    16.43     0.00
   ** NOTE: IS-1893:2016 PARAMETERS ARE MISSING.
   DESIGN BASE SHEAR FROM RESPONSE SPECTRUM METHOD CANNOT BE COMPARED WITH
   BASE SHEAR CALCULATED USING EMPIRICAL FORMULA FOR FUNDAMENTAL PERIOD.
   ************ END OF DATA FROM INTERNAL STORAGE ************
    39. PRINT MODE SHAPES
  MODE     SHAPES                     
      STAAD SPACE                                              -- PAGE NO.    7
   MODE SHAPES
   -----------
  JOINT  MODE   X-TRANS   Y-TRANS   Z-TRANS    X-ROTAN    Y-ROTAN    Z-ROTAN
     1     1    0.00000   0.00000   0.00000  0.000E+00  0.000E+00  0.000E+00
     2     1    0.00000   0.50000   0.00000  0.000E+00  0.000E+00  0.000E+00
     3     1    0.00000   0.86603   0.00000  0.000E+00  0.000E+00  0.000E+00
     4     1    0.00000   1.00000   0.00000  0.000E+00  0.000E+00  0.000E+00
   MODE SHAPES
   -----------
  JOINT  MODE   X-TRANS   Y-TRANS   Z-TRANS    X-ROTAN    Y-ROTAN    Z-ROTAN
     1     2    0.00000   0.00000   0.00000  0.000E+00  0.000E+00  0.000E+00
     2     2    0.00000   1.00000   0.00000  0.000E+00  0.000E+00  0.000E+00
     3     2    0.00000   0.00000   0.00000  0.000E+00  0.000E+00  0.000E+00
     4     2    0.00000  -1.00000   0.00000  0.000E+00  0.000E+00  0.000E+00
   MODE SHAPES
   -----------
  JOINT  MODE   X-TRANS   Y-TRANS   Z-TRANS    X-ROTAN    Y-ROTAN    Z-ROTAN
     1     3    0.00000   0.00000   0.00000  0.000E+00  0.000E+00  0.000E+00
     2     3    0.00000   0.50000   0.00000  0.000E+00  0.000E+00  0.000E+00
     3     3    0.00000  -0.86603   0.00000  0.000E+00  0.000E+00  0.000E+00
     4     3    0.00000   1.00000   0.00000  0.000E+00  0.000E+00  0.000E+00
    40. PRINT ANALYSIS RESULTS
  ANALYSIS RESULTS                    
      STAAD SPACE                                              -- PAGE NO.    8
   JOINT DISPLACEMENT (CM   RADIANS)    STRUCTURE TYPE = SPACE
   ------------------
 JOINT  LOAD   X-TRANS   Y-TRANS   Z-TRANS   X-ROTAN   Y-ROTAN   Z-ROTAN
      1    1     0.0000    0.0000    0.0000    0.0000    0.0000    0.0000
      2    1     0.0000    0.0114    0.0000    0.0000    0.0000    0.0000
      3    1     0.0000    0.0196    0.0000    0.0000    0.0000    0.0000
      4    1     0.0000    0.0227    0.0000    0.0000    0.0000    0.0000
      STAAD SPACE                                              -- PAGE NO.    9
   SUPPORT REACTIONS -UNIT KN   METE    STRUCTURE TYPE = SPACE
   -----------------
 JOINT  LOAD   FORCE-X   FORCE-Y   FORCE-Z     MOM-X     MOM-Y     MOM Z
      1    1      0.00     16.43      0.00      0.00      0.00      0.00
      STAAD SPACE                                              -- PAGE NO.   10
   MEMBER END FORCES    STRUCTURE TYPE = SPACE
   -----------------
   ALL UNITS ARE -- KN   METE     (LOCAL )
  MEMBER  LOAD  JT     AXIAL   SHEAR-Y  SHEAR-Z   TORSION     MOM-Y      MOM-Z
      1    1     1     16.43      0.00     0.00      0.00      0.00       0.00
                 2     16.43      0.00     0.00      0.00      0.00       0.00
      2    1     2     12.06      0.00     0.00      0.00      0.00       0.00
                 3     12.06      0.00     0.00      0.00      0.00       0.00
      3    1     3      4.56      0.00     0.00      0.00      0.00       0.00
                 4      4.56      0.00     0.00      0.00      0.00       0.00
   ************** END OF LATEST ANALYSIS RESULT **************