V. IBC 2006 Response Spectrum
Calculation of Base Shear for Response Spectrum Method in IBC 2006.
Details
- Location: Corona, CA (ZIP 92887)
- Short period acceleration, Ss = 1.8157
- One second acceleration: S1 = 0.67269
- Site class D
- Response modification factor, R = 3
- Importance factor, I = 1.0
- Fa = 1.0
- Fv = 1.5
- TL = 12
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 | 0.627 | 1.59501 |
| 2 | 1.713 | 0.58381 |
| 3 | 2.340 | 0.42738 |
| 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 = 1.8157 × 1 = 1.8157
Sm1 = S1 × Fv = 0.67269 × 1.5 = 1.0090
Sds = 2/3 × Sms = 2/3 × 1.8157 = 1.2104
Sd1 = 2/3 × Sm1 = 2/3 × 1.0090 = 0.6727
T0 = 0.2 × (Sd1/Sds) = 0.2 × (0.6727 / 1.2104) = 0.1111
Ts = Sd1/Sds = 0.6727 / 1.2104 = 0.5557
| Mode 1 | Mode 2 | Mode 3 | |
|---|---|---|---|
| Time Period T | 1.5950 (T s≤ T ≤ T l ) | 0.5838 (T s≤ T ≤ T l ) | 0.4274 (T 0≤ T ≤ T s ) |
| Formula | Sa = Sd1 / T | Sa = Sd1 / T | Sa = Sds |
| Sa | 0.4217 | 1.1522 | 1.2104 |
| Cs = Sa/(Rx/I) | 0.141 | 0.384 | 0.403 |
| 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 | 8.575 | 8.575 | -1 | -6.278 | -6.278 | 1 | 1.767 | 1.767 | 10.77 |
| 2nd Floor | 98.07 | 0.86603 | 14.85 | 23.43 | 0 | 0 | -6.278 | -0.86603 | -3.061 | -1.294 | 24.29 |
| 1st Floor | 98.07 | 0.5 | 8.575 | 32.00 | 1 | 12.56 | 6.278 | 0.5 | 1.767 | 0.473 | 32.62 |
| Base Shear, V | 32.62 | ||||||||||
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\IBC\IBC 2006 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 0.00003 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 2006 X 0.333 ACC DAMP 0.05 LIN
ZIP 92887 SITE CLASS D FA 1.000 FV 1.500 TL 12.000
PERFORM ANALYSIS PRINT ALL
PRINT MODE SHAPES
PRINT ANALYSIS RESULTS
FINISH
STAAD Output
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 31.97 0.00 0.00 2 6.67 0.00 0.00 99.521 0.000 0.000 6.27 0.00 0.00 3 0.48 0.00 0.00 100.000 0.000 0.000 0.47 0.00 0.00 --------------------------- TOTAL SRSS SHEAR 32.59 0.00 0.00 TOTAL 10PCT SHEAR 32.59 0.00 0.00 TOTAL ABS SHEAR 38.72 0.00 0.00