V. GB 50011 2010 Response Spectrum
Calculation of base shear and for response spectrum method in GB 50011-2010.
Details
- Classification of seismic design = Group 2
- Design seismic intensity = 8
- Site class = II
- Damping = 3.5%
The seismic weight of 420 kN applied as a joint weight of 70 kN to the joints at each floor (joints 2, 3, 4, 6,7, and 8); or 140 kN at each story above ground.
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 | 1.114 | 0.897 |
2 | 3.122 | 0.320 |
3 | 4.512 | 0.222 |
Mode | Story Level/Joint Numbers | X-Trans | Y-Trans | Z-Trans | X-Rot | Y-Rot | Z-Rot |
---|---|---|---|---|---|---|---|
1 | Roof/Joints 4 & 8 | 1 | 0 | 0 | 0 | 0 | 0 |
2nd Floor/Joints 3 & 7 | 0.802 | 0 | 0 | 0 | 0 | 0 | |
1st Floor/Joints 2 & 6 | 0.445 | 0 | 0 | 0 | 0 | 0 | |
2 | Roof/Joints 4 & 8 | -0.802 | 0 | 0 | 0 | 0 | 0 |
2nd Floor/Joints 3 & 7 | 0 .445 | 0 | 0 | 0 | 0 | 0 | |
1st Floor/Joints 2 & 6 | 1 | 0 | 0 | 0 | 0 | 0 | |
3 | Roof/Joints 4 & 8 | -0.445 | 0 | 0 | 0 | 0 | 0 |
2nd Floor/Joints 3 & 7 | 1 | 0 | 0 | 0 | 0 | 0 | |
1st Floor/Joints 2 & 6 | -0.802 | 0 | 0 | 0 | 0 | 0 |
Horizontal Acceleration Spectrum Value
The max value of horizontal seismic influence, ɑmax = 0.16.
The characteristic period, Tg = 0.4s.
The damping ratio, ζ = 0.035.
The power index of the curvilinear decrease section:
The damping adjustment factor is determined as:
Mode 1 | Mode 2 | Mode 3 | |
---|---|---|---|
Time Period T |
0.897 (Tg<T<5Tg) |
0.320 (0.1<T < Tg) |
0.222 (0.1<T < Tg) |
Formula | |||
Seismic Coefficient a | 0.0839 | 0.1776 | 0.1776 |
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 | 140 | 1 | 140 | 140 | -0.802 | -112.3 | 90.05 | -0.445 | -62.3 | 27.72 |
2nd Floor | 140 | 0.802 | 112.3 | 90.05 | 0.445 | 62.3 | 27.72 | 1 | 140 | 140 |
1st Floor | 140 | 0.445 | 62.3 | 27.72 | 1 | 140 | 140 | -0.802 | -112.3 | 90.05 |
Summation | 420 | 314.6 | 257.77 | 90.02 | 257.77 | -34.58 | 257.77 | |||
Mode Participation Factor Pk ∑Wi × ϕ / ∑ Wi × ϕ 2 | 1.22 | 0.349 | -0.134 | |||||||
Seismic Coefficient ɑ | 0.0839 | 0.1776 | 0.1776 | |||||||
Horizontal seismic action | Roof | 14.33 | -6.959 | 1.483 | ||||||
2nd Floor | 11.49 | 3.862 | -3.332 | |||||||
1st Floor | 6.377 | 8.678 | 2.672 | |||||||
Base shear | 32.197 | 5.581 | 0.823 |
Summation by SRSS:
Comparison
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\06 Loading\GB 50011\GB 50011 2010 Response Spectrum.std is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 18-May-15
END JOB INFORMATION
INPUT WIDTH 79
SET SHEAR
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 5.00001 0; 3 0 10 0; 4 0 15 0; 5 5.00001 0 0; 6 5.00001 5.00001 0;
7 5.00001 10 0; 8 5.00001 15 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 5 6; 5 6 7; 6 7 8; 7 2 6; 8 3 7; 9 4 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
ISOTROPIC STEEL
E 2.05e+08
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-05
DAMP 0.03
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY
1 TO 6 UPTABLE 1 COLLUMN
7 TO 9 UPTABLE 2 BEAM
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORTS
1 5 FIXED
DEFINE REFERENCE LOADS
LOAD R1 LOADTYPE Mass TITLE MASS
JOINT LOAD
2 TO 4 6 TO 8 FX 70
END DEFINE REFERENCE LOADS
FLOOR DIAPHRAGM
DIA 1 TYPE RIG HEI 5
DIA 2 TYPE RIG HEI 10
DIA 3 TYPE RIG HEI 15
LOAD 1 LOADTYPE Seismic-H TITLE EL-X DIR
SPECTRUM CQC GB50011 2010 X 1 ALPHA DAMP 0.035 LOGARITHMIC INTENSITY 8 -
FREQUENT GROUP 2 SCLASS 2
PERFORM ANALYSIS
FINISH
STAAD Output
GB50011 RESPONSE SPECTRUM LOAD 1 GB50011 RESPONSE LOAD CASE 1 MODAL WEIGHT (MODAL MASS TIMES g) IN KN GENERALIZED MODE X Y Z WEIGHT 1 3.839138E+02 0.000000E+00 0.000000E+00 2.577637E+02 2 3.144839E+01 0.000000E+00 0.000000E+00 2.577634E+02 3 4.638204E+00 0.000000E+00 0.000000E+00 2.577630E+02 CQC MODAL COMBINATION METHOD USED. DYNAMIC WEIGHT X Y Z 4.200000E+02 0.000000E+00 0.000000E+00 KN MISSING WEIGHT X Y Z 4.013087E-04 0.000000E+00 0.000000E+00 KN MODAL WEIGHT X Y Z 4.200004E+02 0.000000E+00 0.000000E+00 KN MODE ACCELERATION-G DAMPING ---- -------------- ------- 1 0.08383 0.03500 2 0.17765 0.03500 3 0.17765 0.03500 STAAD SPACE -- PAGE NO. 5 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 0.897 32.18 0.00 0.00 0.00 0.00 -361.56 2 0.320 5.59 0.00 0.00 0.00 0.00 22.40 3 0.222 0.82 0.00 0.00 0.00 0.00 -2.29 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 91.41 0.00 0.00 91.408 0.000 0.000 32.18 0.00 0.00 2 7.49 0.00 0.00 98.896 0.000 0.000 5.59 0.00 0.00 3 1.10 0.00 0.00 100.000 0.000 0.000 0.82 0.00 0.00 --------------------------- TOTAL CQC SHEAR 32.68 0.00 0.00