V. IS 1893 2002 Response Spectrum
Calculation of base shear and its distribution along the height for response spectrum method in IS 1893 (Part 1) : 2002.
Problem
A three story building is modelled in
STAAD.Pro considering the following:
- Seismic zone factor, Z = 0.36
- Importance factor, I = 1
- Response reduction factor, R = 5
- Soil site conditions = Hard
The generated model is subjected to a response spectrum load along global X direction. The base shear and its distribution along height reported by STAAD.Pro is verified against hand calculation.
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 | 24.518 |
| Summation | 245.175 | 183.00 | 147.11 | 49.035 | 147.105 | 13.138 | 147.106 | |||
| Modal Weight Mk × g | 227.66 | 16.345 | 1.173 | |||||||
| Modal Weight Participation (In %) | 92.85 | 6.667 | 0.479 | |||||||
| Mode Participation Factor Pk ∑Wi × ϕ / ∑ Wi × ϕ 2 | 1.244 | 0.3333 | 0.0893 | |||||||
| Mode 1 | Mode 2 | Mode 3 | |
|---|---|---|---|
| Sa/g | 2.5 (time period < 0.4 s) | 2.5 (time period < 0.4 s) | 2.2063 (1 + 15 × 0.08042 as time period < 0.1 s) |
| Ak (Z/2 × I/R × Sa/g) | 0.09
(0.36/2 × 1/5 × 2.5) |
0.09
(0.36/2 × 1/5 × 2.5) |
0.0794 (0.36/2 × 1/5 × 2.2063) |
| 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 (Ak × ϕ × Pk × Wi) | Vi (∑Qi) | ϕ | Qi (Ak × ϕ × Pk × Wi) | Vi (∑Qi) | ϕ | Qi (Ak × ϕ × Pk × Wi) | Vi (∑Qi) | |||
| Roof | 49.035 | 1 | 5.490 | 5.490 | -1 | -1.471 | -1.471 | 1 | 0.3478 | 0.3478 | 5.69 |
| 2nd Floor | 98.07 | 0.86603 | 9.509 | 15.0 | 0 | 0 | -1.471 | -0.86603 | -0.6025 | -0.2546 | 15.073 |
| 1st Floor | 98.07 | 0.5 | 5.490 | 20.49 | 1 | 2.942 | 1.471 | 0.5 | 0.3478 | 0.0932 | 20.542 |
| Base Shear | 20.54 | ||||||||||
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\IS 1893\IS 1893 2002 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 1893 X 0.036 ACC DAMP 0.05
SOIL TYPE 1
PERFORM ANALYSIS PRINT ALL
PRINT MODE SHAPES
PRINT ANALYSIS RESULTS
FINISH
STAAD Output
1893 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 RESPONSE LOAD CASE 1 MODE SPECTRAL ACCELERATION DESIGN SEISMIC COEFFICIENT ---- --------------------- ------------------------------ X Y Z 1 2.50000 0.0900 0.0000 0.0000 2 2.50000 0.0900 0.0000 0.0000 3 2.20632 0.0794 0.0000 0.0000 STAAD SPACE -- PAGE NO. 6 PEAK STORY SHEAR STORY LEVEL IN METE PEAK STORY SHEAR IN KN ----- ------------- ------------------------- X Z 3 9.00 5.69 0.00 2 6.00 15.07 0.00 1 3.00 20.54 0.00 BASE 0.00 20.54 0.00 RESPONSE SPECTRUM VALUES - UNITS ( METE SECOND ) ------------------------ DIRECTIONAL VALUES: SCALE FACTOR = 1.00 X = 0.04 Y = 0.00 Z = 0.00 DAMPING FACTOR = 0.050 PERIOD VS. ACCELERATION 0.3001 24.5166 0.1099 24.5166 0.0804 21.6366 MODE ACCELERATION-G DAMPING ---- -------------- ------- 1 2.50000 0.05000 2 2.50000 0.05000 3 2.20632 0.05000 STAAD SPACE -- PAGE NO. 7 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 20.49 0.00 0.00 0.00 0.00 -122.93 2 0.110 1.47 0.00 0.00 0.00 0.00 4.41 3 0.080 0.09 0.00 0.00 0.00 0.00 -0.56 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 20.49 0.00 0.00 2 6.67 0.00 0.00 99.521 0.000 0.000 1.47 0.00 0.00 3 0.48 0.00 0.00 100.000 0.000 0.000 0.09 0.00 0.00 --------------------------- TOTAL SRSS SHEAR 20.54 0.00 0.00 TOTAL 10PCT SHEAR 20.54 0.00 0.00 TOTAL ABS SHEAR 22.05 0.00 0.00 TOTAL CSM SHEAR 20.54 0.00 0.00