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V. IBC 2012 Response Spectrum

Calculation of Base Shear for Response Spectrum Method in IBC 2012.

Details

A three story buiding is modelled in STAAD.Pro considering the following:
  • Location: Corona, CA (ZIP 92887)
  • Short period acceleration, Ss = 2.24658
  • One second acceleration: S1 = 0.817039
  • Site class E
  • Response modification factor, R = 3
  • Importance factor, I = 1.0
  • Fa = 0.9
  • Fv = 2.4
  • TL = 8

The generated model is subjected to a Response Spectrum Load along global X direction. The base shear reported by STAAD.Pro is verified against hand calculation.

Validation

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 24.5175
Summation 245.175 183.00 147.11 49.035 147.105 13.138 147.106
Modal Weight Mk × g 227.66 16.35 1.173
Modal Weight Participation (In %) 92.85 6.667 0.479
Mode Participation Factor ∏ ∑Wi × ϕ / ∑ Wi × ϕ 2 1.244 0.333 0.0893

Horizontal Acceleration Spectrum Value Calculation.

Sms = Ss × Fa = 2.24658 × 0.9 = 2.022

Sm1 = S1 × Fv = 0.817039 × 2.4 = 1.961

Sds = 2/3 × Sms = 2/3 × 2.022 = 1.348

Sd1 = 2/3 × Sm1 = 2/3 × 1.961 = 1.307

T0 = 0.2 × (Sd1/Sds) = 0.2 × (1.307 / 1.348) = 0.1940

Ts = Sd1/Sds = 1.307 / 1.348 = 0.9698

Mode 1 Mode 2 Mode 3
Time Period T 0.30014 (T 0≤ T ≤ T s ) 0.10986 (T < T 0 ) 0.08042 (T < T 0 )
Formula Sa = Sds Sa = Sds × (0.4 + 0.6 × (T/T 0 ) ) Sa= Sds × (0.4 + 0.6 × (T/T 0 ) )
Sa 1.348 0.997 0.875
Cs = Sa/(Rx/I) 0.449 0.332 0.292
Table 4. Base Shear Calculation and its Distribution Across Height
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 (Cs × ϕ × ∏ × Wi) Vi (∑Qi) ϕ Qi (Cs × ϕ × ∏ × Wi) Vi (∑Qi) ϕ Qi (Cs × ϕ × ∏ × Wi) Vi (∑Qi)
Roof 49.035 1 27.408 27.408 -1 -5.433 -5.433 1 1.277 1.277 27.971
2nd Floor 98.07 0.86603 47.473 74.881 0 0 -5.433 -0.86603 -2.211 -0.9346 75.084
1st Floor 98.07 0.5 27.408 102.29 1 10.867 5.433 0.5 1.277 0.3421 102.43
Base Shear, V 102.43

Comparison

Table 5. Comparison of results
Parameter STAAD.Pro Reference Difference Comments
Base shear (kN) 102.43 102.33 negligible

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\IBC\2012\IBC 2012 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 IBC 2012 X 0.333 ACC DAMP 0.05 LIN
ZIP 92887 SITE CLASS E FA 0.900 FV 2.400 TL 8.000
PERFORM ANALYSIS PRINT ALL
PRINT MODE SHAPES
PRINT ANALYSIS RESULTS
FINISH

STAAD Output

               CALCULATED FREQUENCIES FOR LOAD CASE       1
       MODE            FREQUENCY(CYCLES/SEC)         PERIOD(SEC)
         1                       3.332                  0.30014
         2                       9.103                  0.10986
         3                      12.435                  0.08042
  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  
           MODE                 ACCELERATION-G     DAMPING
           ----                 --------------     -------
              1                      1.34795       0.05000
              2                      0.99725       0.05000
              3                      0.87451       0.05000
      STAAD SPACE                                              -- PAGE NO.   15
 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      102.19        0.00        0.00        0.00        0.00     -613.12
      2      0.110        5.43        0.00        0.00        0.00        0.00       16.28
      3      0.080        0.34        0.00        0.00        0.00        0.00       -2.05
 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    102.19     0.00     0.00
   2    6.67  0.00  0.00   99.521    0.000    0.000      5.43     0.00     0.00
   3    0.48  0.00  0.00  100.000    0.000    0.000      0.34     0.00     0.00
                                                    ---------------------------
                                  TOTAL SRSS  SHEAR    102.33     0.00     0.00
                                  TOTAL 10PCT SHEAR    102.33     0.00     0.00
                                  TOTAL ABS   SHEAR    107.96     0.00     0.00