V. IBC 2018 Response Spectrum
Calculation of Base Shear for Response Spectrum Method in IBC 2018.
Details
A three story building is modelled in STAAD.Pro considering the following:
- Location: Corona, CA (
ZIP 92887
) - Short period acceleration, Ss = 1.996
- One second acceleration: S1 = 0.7
- Site class A
- Response modification factor, R = 3
- Importance factor, I = 1.0
- Fa = 0.8
- Fv = 0.8
- 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)
Mode | Frequency (cyc/sec) | Time Period (sec) |
---|---|---|
1 | 3.332 | 0.30014 |
2 | 9.103 | 0.10986 |
3 | 12.435 | 0.08042 |
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 |
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 = 1.996 × 0.8 =
1.597
Sm1 = S1 × Fv = 0.7 × 0.8 =
0.56
Sds = 2/3 × Sms = 2/3 × 1.597 = 1.065
Sd1 = 2/3 × Sm1 = 2/3 × 0.56 × 0.373
T0 = 0.2 × (Sd1/Sds) = 0.2 × (0.373 /
1.065) = 0.070
Ts = Sd1/Sds = 0.373 / 1.065 =
0.350
Mode 1 | Mode 2 | Mode 3 | |
---|---|---|---|
Time Period T | 0.30014 (T 0≤ T ≤ T s ) | 0.10986 (T 0≤ T ≤ T s ) | 0.08042 (T 0≤ T ≤ T s ) |
Formula | Sa = Sds | Sa = Sds | Sa = Sds |
Sa | 1.065 | 1.065 | 1.065 |
Cs = Sa/(Rx/I) | 0.355 | 0.355 | 0.355 |
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 | 21.646 | 21.646 | -1 | -5.80 | -5.80 | 1 | 1.554 | 1.554 | 22.463 |
2nd Floor | 98.07 | 0.86603 | 37.491 | 59.137 | 0 | 0 | -5.80 | -0.86603 | -2.692 | -1.138 | 59.432 |
1st Floor | 98.07 | 0.5 | 21.646 | 80.783 | 1 | 11.60 | 5.80 | 0.5 | 1.554 | 0.416 | 80.992 |
Base Shear, V | 80.992 |
Comparison
Parameter | STAAD.Pro | Reference | Difference | Comments |
---|---|---|---|---|
Base shear (kN) | 80.91 | 80.992 | negligible |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\06 Loading\IBC\IBC 2018 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 2018 X 0.333 ACC DAMP 0.05 LIN
ZIP 92887 SITE CLASS A FA 0.800 FV 0.800 TL 8.000
*SS 1.996 S1 0.7 SITE CLASS A FA 0.8 FV 0.8 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 1.06453 0.05000
2 1.06453 0.05000
3 1.06453 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 80.70 0.00 0.00 0.00 0.00 -484.21
2 0.110 5.79 0.00 0.00 0.00 0.00 17.38
3 0.080 0.42 0.00 0.00 0.00 0.00 -2.50
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 80.70 0.00 0.00
2 6.67 0.00 0.00 99.521 0.000 0.000 5.79 0.00 0.00
3 0.48 0.00 0.00 100.000 0.000 0.000 0.42 0.00 0.00
---------------------------
TOTAL SRSS SHEAR 80.91 0.00 0.00
TOTAL 10PCT SHEAR 80.91 0.00 0.00
TOTAL ABS SHEAR 86.91 0.00 0.00