V. IS 1893 2015 Response Spectrum
Calculate the base shear and its distribution along the height for the response spectrum method in the IS 1893 (Part4): 2015 specification.
Details
Beam and column dimensions: 500 mm × 500 mm
Material: concrete
The structure is modelled in STAAD.Pro considering the following:- Seismic zone factor, Z = 0.16 (
ZONE 0.16
) - Importance factor, I = 1.5 (
I 1.5
) - Response reduction factor, R = 5 (
RF 5
) - Soil site condition = Soft (
SOIL TYPE 3
) - Minimum factor of total weight for base shear (
RSMIN 2.75
)
Validation
Mode | Frequency (cyc/sec) | Time Period (sec) |
---|---|---|
1 | 0.229 | 4.3681 |
2 | 0.625 | 1.59884 |
3 | 0.854 | 1.17043 |
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 |
1 | 2nd Floor/Joints 5 & 6 | 0.866 | 0 | 0 | 0 | 0 | 0 |
1 | 1st Floor/Joints 2 & 3 | 0.5 | 0 | 0 | 0 | 0 | 0 |
2 | Roof/Joints 7 & 8 | -1 | 0 | 0 | 0 | 0 | 0 |
2 | 2nd Floor/Joints 5 & 6 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 1st Floor/Joints 2 & 3 | 1 | 0 | 0 | 0 | 0 | 0 |
3 | Roof/Joints 7 & 8 | 1 | 0 | 0 | 0 | 0 | 0 |
3 | 2nd Floor/Joints 5 & 6 | -0.866 | 0 | 0 | 0 | 0 | 0 |
3 | 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 × ϕ2 | ϕ | Wi × ϕ | Wi × ϕ2 | ϕ | Wi × ϕ | Wi × ϕ2 | ||
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 | -0.866 | -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 | 245.18 | 183.00 | 147.11 | 49.035 | 147.105 | 13.138 | 147.11 |
Mode 1 | Mode 2 | Mode 3 | |
---|---|---|---|
Modal Weight, Mk × g | |||
Modal Weight Participation (In %) | |||
Mode Participation Factor,Pk |
Direction factor =
Mode 1 | Mode 2 | Mode 3 | |
---|---|---|---|
Sa/g | |||
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 | 0.560 | 0.560 | -1 | -0.410 | -0.410 | 1 | 0.150 | 0.150 | 0.71 |
2nd Floor | 98.07 | 0.866 | 0.970 | 1.530 | 0 | 0 | -0.410 | -0.866 | -0.260 | -0.110 | 1.59 |
1st Floor | 98.07 | 0.5 | 0.560 | 2.089 | 1 | 0.820 | 0.410 | 0.5 | 0.150 | 0.040 | 2.13 |
Total SRSS Shear | 2.13 |
Minimum base shear per Table 2:
2.75 × 245.18 / 100 = 6.74
kN
The multiplying factor (ratio of minimum base shear to total SRSS base shear): 6.47 / 2.13 = 3.17
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Story shear, roof (kN) | 0.71 | 0.71 | none | |
Story shear, 2nd (kN) | 1.59 | 1.59 | none | |
Story shear, 1st (kN) | 2.13 | 2.13 | none | |
Base shear (kN) | 2.13 | 2.13 | none | |
Minimum base shear (kN) | 6.74 | 6.7423 | negligible | |
Multiplying factor | 3.17 | 3.1668 | negligible |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\06 Loading\IS 1893\IS 1893 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 4e-06 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 IS1893 2015-P4 X 0.024 DAMP 0.05 RSMIN 2.75
SOIL TYPE 3
PERFORM ANALYSIS PRINT ALL
PRINT MODE SHAPES
PRINT ANALYSIS RESULTS
FINISH
STAAD.Pro Output
CALCULATED FREQUENCIES FOR LOAD CASE 1
MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC)
1 0.229 4.36810
2 0.625 1.59884
3 0.854 1.17043
***NOTE: Response Spectrum Analysis for IS1893 (Part-4): 2015 should be carried
out with P-Delta Analysis as per 10.3
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 -3.177131E-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 0.38232 0.0092 0.0000 0.0000
2 1.04451 0.0251 0.0000 0.0000
3 1.42683 0.0342 0.0000 0.0000
STAAD SPACE -- PAGE NO. 6
PEAK STORY SHEAR
STORY LEVEL IN METE PEAK STORY SHEAR IN KN
----- ------------- --------------------------------------------------
X Y Z
3 9.00 0.71 0.00 0.00
2 6.00 1.59 0.00 0.00
1 3.00 2.13 0.00 0.00
BASE 0.00 2.13 0.00 0.00
RESPONSE SPECTRUM VALUES - UNITS ( METE SECOND )
------------------------
DIRECTIONAL VALUES: SCALE FACTOR = 1.00
X = 0.02 Y = 0.00 Z = 0.00 DAMPING FACTOR = 0.050
PERIOD VS. ACCELERATION
4.3681 3.7492
1.5988 10.2431
1.1704 13.9924
MODE ACCELERATION-G DAMPING
---- -------------- -------
1 0.38232 0.05000
2 1.04451 0.05000
3 1.42683 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 4.368 2.09 0.00 0.00 0.00 0.00 -12.53
2 1.599 0.41 0.00 0.00 0.00 0.00 1.23
3 1.170 0.04 0.00 0.00 0.00 0.00 -0.24
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 2.09 0.00 0.00
2 6.67 0.00 0.00 99.521 0.000 0.000 0.41 0.00 0.00
3 0.48 0.00 0.00 100.000 0.000 0.000 0.04 0.00 0.00
---------------------------
TOTAL SRSS SHEAR 2.13 0.00 0.00
TOTAL 10PCT SHEAR 2.13 0.00 0.00
TOTAL ABS SHEAR 2.54 0.00 0.00
TOTAL CSM SHEAR 2.13 0.00 0.00
Minimum Base Shear Per Table 2 IS1893 2015 Part-4: 6.7423 KN
NOTE : THE BASE SHEAR (VB) FROM RESPONSE SPECTRUM IS LESS THAN THE
MINIMUM BASE SHEAR PER TABLE 2. MULTIPLYING FACTOR IS 3.1668