V. IBC 2015 Response Spectrum
Calculation of Base Shear for Response Spectrum Method in IBC 2015.
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)
| 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 = 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 |
| 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 | ||||||||||
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\IBC\IBC 2015 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 2015 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