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 | ϕQi | 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 | |||||||||||
STAAD.Pro Input File
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\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