V. IS 1893 2016 Response Spectrum Vertical
Calculation of base shear for vertical motion of oscillation by response spectrum method in IS 1893 : 2016 (Part 1).
Details
The structure is modelled in STAAD.Pro considering the following:
- Seismic zone factor, Z = 0.36
- Importance factor, I = 1.2
- Response reduction factor, R = 5
- Soil site conditions = Hard
The dimension of the columns is 0.2m x 0.1 m and material is concrete
The generated model is subjected to a response spectrum load along global Y direction.
Natural frequencies / time period and mode shapes are obtained from the STAAD.Pro output file.
Mode | Frequency (cyc/sec) | Time Period (sec) |
---|---|---|
1 | 9.913 | 0.10088 |
2 | 27.083 | 0.03692 |
3 | 36.996 | 0.02703 |
Mode | Story Level/Joint Numbers | X-Trans | Y-Trans | Z-Trans | X-Rot | Y-Rot | Z-Rot |
---|---|---|---|---|---|---|---|
1 | Roof/Joint 4 | 0 | 1 | 0 | 0 | 0 | 0 |
2nd Floor/Joint 3 | 0 | 0.86603 | 0 | 0 | 0 | 0 | |
1st Floor/Joint 2 | 0 | 0.5 | 0 | 0 | 0 | 0 | |
2 | Roof/Joint 4 | 0 | -1 | 0 | 0 | 0 | 0 |
2nd Floor/Joint 3 | 0 | 0 | 0 | 0 | 0 | 0 | |
1st Floor/Joint 2 | 0 | 1 | 0 | 0 | 0 | 0 | |
3 | Roof/Joint 4 | 0 | 1 | 0 | 0 | 0 | 0 |
2nd Floor/Joint 3 | 0 | -0.86603 | 0 | 0 | 0 | 0 | |
1st Floor/Joint 2 | 0 | 0.5 | 0 | 0 | 0 | 0 |
Validation
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 | 0.8660 | 84.932 | 73.553 | 0 | 0 | 0 | -0.8660 | -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 | - | 183.002 | 147.106 | - | 49.035 | 147.105 | - | 13.138 | 147.106 |
Modal Weight Mk × g | 227.7 | 16.35 | 1.173 | |||||||
Modal Weight Participation (In %) | 92.85 | 6.667 | 0.479 | |||||||
Mode Participation Factor Pk ∑Wi x ϕ / ∑ Wi x ϕ2 | 1.244 | 0.333 | 0.089 |
Mode 1 | Mode 2 | Mode 3 | |
---|---|---|---|
Time period(sec) | 0.1009 | 0.0369 | 0.0270 |
Sa/g | 2.5 | 2.5 | 2.5 |
Ak (2/3 × Z/2 × I/R × Sa/g) | 0.072 | 0.072 | 0.072 |
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 | Vi | ϕ | Qi | Vi | ϕ Qi | Vi | ϕ | ||||
Roof | 49.035 | 1 | 4.392 | 4.392 | -1 | -1.177 | -1.177 | 1 | 0.315 | 0.315 | 4.56 | |
2nd Floor | 98.07 | 0.8660 | 7.607 | 12.0 | 0 | 0 | -1.177 | -0.8660 | -0.546 | -0.231 | 12.06 | |
1st Floor | 98.07 | 0.5 | 4.392 | 16.39 | 1 | 2.354 | 1.177 | 0.5 | 0.315 | 0.084 | 16.43 | |
Base shear | 16.43 |
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Base shear (kN) | 16.43 | 16.43 | none |
STAAD.Pro Input File
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\06 Loading\IS 1893\IS 1893 2016 Response Spectrum Vertical.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 3 0 0; 2 3 3 0; 3 3 6 0; 4 3 9 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4;
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 2 3 PRIS YD 0.2 ZD 0.1
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORTS
1 FIXED
DEFINE REFERENCE LOADS
LOAD R1 LOADTYPE Mass TITLE REF LOAD CASE 1
JOINT LOAD
4 FY 49.035
2 3 FY 98.07
END DEFINE REFERENCE LOADS
LOAD 1 LOADTYPE NONE TITLE RS_Y
SPECTRUM SRSS IS1893 2016 Y 0.0432 DAMP 0.05
SOIL TYPE 1
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 9.913 0.10088
2 27.083 0.03692
3 36.996 0.02703
1893 RESPONSE SPECTRUM LOAD 1
RESPONSE LOAD CASE 1
MODAL WEIGHT (MODAL MASS TIMES g) IN KN GENERALIZED
MODE X Y Z WEIGHT
1 0.000000E+00 2.276565E+02 0.000000E+00 1.471050E+02
2 0.000000E+00 1.634500E+01 0.000000E+00 1.471050E+02
3 0.000000E+00 1.173519E+00 0.000000E+00 1.471050E+02
SRSS MODAL COMBINATION METHOD USED.
DYNAMIC WEIGHT X Y Z 0.000000E+00 2.451750E+02 0.000000E+00 KN
MISSING WEIGHT X Y Z 0.000000E+00 -3.177129E-06 0.000000E+00 KN
MODAL WEIGHT X Y Z 0.000000E+00 2.451750E+02 0.000000E+00 KN
***NOTE: IT IS RECOMMENDED TO DEFINE FLOOR LEVELS USING "FLOOR HEIGHT" INPUT.
RESPONSE LOAD CASE 1
MODE SPECTRAL ACCELERATION DESIGN SEISMIC COEFFICIENT
---- --------------------- ------------------------------
X Y Z
1 2.50000 0.0000 0.0720 0.0000
2 2.50000 0.0000 0.0720 0.0000
3 2.50000 0.0000 0.0720 0.0000
STAAD SPACE -- PAGE NO. 5
PEAK STORY SHEAR
STORY LEVEL IN METE PEAK STORY SHEAR IN KN
----- ------------- --------------------------------------------------
X Y Z
BASE 0.00 0.00 16.43 0.00
RESPONSE SPECTRUM VALUES - UNITS ( METE SECOND )
------------------------
DIRECTIONAL VALUES: SCALE FACTOR = 1.00
X = 0.00 Y = 0.04 Z = 0.00 DAMPING FACTOR = 0.050
PERIOD VS. ACCELERATION
0.1009 24.5166
0.0369 24.5166
0.0270 24.5166
MODE ACCELERATION-G DAMPING
---- -------------- -------
1 2.50000 0.05000
2 2.50000 0.05000
3 2.50000 0.05000
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 0.101 0.00 16.39 0.00 0.00 0.00 49.17
2 0.037 0.00 1.18 0.00 0.00 0.00 3.53
3 0.027 0.00 0.08 0.00 0.00 0.00 0.25
STAAD SPACE -- PAGE NO. 6
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 0.00 92.85 0.00 0.000 92.855 0.000 0.00 16.39 0.00
2 0.00 6.67 0.00 0.000 99.521 0.000 0.00 1.18 0.00
3 0.00 0.48 0.00 0.000 100.000 0.000 0.00 0.08 0.00
---------------------------
TOTAL SRSS SHEAR 0.00 16.43 0.00
TOTAL 10PCT SHEAR 0.00 16.43 0.00
TOTAL ABS SHEAR 0.00 17.65 0.00
TOTAL CSM SHEAR 0.00 16.43 0.00
** NOTE: IS-1893:2016 PARAMETERS ARE MISSING.
DESIGN BASE SHEAR FROM RESPONSE SPECTRUM METHOD CANNOT BE COMPARED WITH
BASE SHEAR CALCULATED USING EMPIRICAL FORMULA FOR FUNDAMENTAL PERIOD.
**WARNING: At least 1 horizontal RS load should be defined before vertical RS load# 1
Refer Clause 7.7.3b or Help. Program will take dynamic scale factor as 1.0
************ END OF DATA FROM INTERNAL STORAGE ************
39. PRINT MODE SHAPES
MODE SHAPES
STAAD SPACE -- PAGE NO. 7
MODE SHAPES
-----------
JOINT MODE X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN
1 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00
2 1 0.00000 0.50000 0.00000 0.000E+00 0.000E+00 0.000E+00
3 1 0.00000 0.86603 0.00000 0.000E+00 0.000E+00 0.000E+00
4 1 0.00000 1.00000 0.00000 0.000E+00 0.000E+00 0.000E+00
MODE SHAPES
-----------
JOINT MODE X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN
1 2 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00
2 2 0.00000 1.00000 0.00000 0.000E+00 0.000E+00 0.000E+00
3 2 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00
4 2 0.00000 -1.00000 0.00000 0.000E+00 0.000E+00 0.000E+00
MODE SHAPES
-----------
JOINT MODE X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN
1 3 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00
2 3 0.00000 0.50000 0.00000 0.000E+00 0.000E+00 0.000E+00
3 3 0.00000 -0.86603 0.00000 0.000E+00 0.000E+00 0.000E+00
4 3 0.00000 1.00000 0.00000 0.000E+00 0.000E+00 0.000E+00
40. PRINT ANALYSIS RESULTS
ANALYSIS RESULTS
STAAD SPACE -- PAGE NO. 8
JOINT DISPLACEMENT (CM RADIANS) STRUCTURE TYPE = SPACE
------------------
JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN
1 1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
2 1 0.0000 0.0114 0.0000 0.0000 0.0000 0.0000
3 1 0.0000 0.0196 0.0000 0.0000 0.0000 0.0000
4 1 0.0000 0.0227 0.0000 0.0000 0.0000 0.0000
STAAD SPACE -- PAGE NO. 9
SUPPORT REACTIONS -UNIT KN METE STRUCTURE TYPE = SPACE
-----------------
JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z
1 1 0.00 16.43 0.00 0.00 0.00 0.00
STAAD SPACE -- PAGE NO. 10
MEMBER END FORCES STRUCTURE TYPE = SPACE
-----------------
ALL UNITS ARE -- KN METE (LOCAL )
MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z
1 1 1 16.43 0.00 0.00 0.00 0.00 0.00
2 16.43 0.00 0.00 0.00 0.00 0.00
2 1 2 12.06 0.00 0.00 0.00 0.00 0.00
3 12.06 0.00 0.00 0.00 0.00 0.00
3 1 3 4.56 0.00 0.00 0.00 0.00 0.00
4 4.56 0.00 0.00 0.00 0.00 0.00