V. NRC 2005 Response Spectrum
Calculation of Base Shear for Response Spectrum Method in NBCC/NRC 2005.
Details
Example 4.7(1) is modeled in STAAD.Pro.
The generated model is subjected to a Response Spectrum Load along global X direction. Time-Acceleration pairs for the spectrum data can be seen in supporting excel file NRC_Calculation.xlsx within worksheet named RS Values. The direction factor along global X direction is assumed as 0.5. The base shear reported by STAAD.Pro is verified against hand calculation.
Validation
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 x ϕ | Wi x ϕ 2 | ϕ | Wi x ϕ | Wi x ϕ 2 | ϕ | Wi x ϕ | Wi x 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 | 147.11 | 13.138 | 147.11 | |||
| Modal Weight Mk x g | 227.7 | 16.345 | 1.173 | |||||||
| Modal Weight Participation (In %) | 92.85 | 6.667 | 0.4786 | |||||||
| Mode Participation Factor ∏ ∑Wi x ϕ / ∑ Wi x ϕ 2 | 1.244 | 0.3333 | 0.0893 | |||||||
| 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 (Cs x ϕ x ∏ x Wi) | Vi (∑Qi) | ϕ | Qi (Cs x ϕ x ∏ x Wi) | Vi (∑Qi) | ϕ | Qi (Cs x ϕ x ∏ x Wi) | Vi (∑Qi) | |||
| Roof | 49.035 | 1 | 76.25 | 76.25 | -1 | -19.60 | -19.60 | 1 | 4.608 | 4.608 | 78.86 |
| 2nd Floor | 98.07 | 0.86603 | 132.1 | 208.3 | 0 | 0 | -19.60 | -0.86603 | -7.981 | -3.373 | 209.27 |
| 1st Floor | 98.07 | 0.5 | 76.25 | 284.6 | 1 | 39.21 | 19.60 | 0.5 | 4.608 | 1.235 | 285.25 |
| Base Shear V | 285.25 | ||||||||||
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\NRC\NRC 2005 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 NRC 2005 X 0.5 ACC DAMP 0.05 LIN
0 9.80665; 0.06 18.6326; 0.12 24.5166; 0.18 24.5166; 0.24 24.5166; 0.3 24.5166;
0.36 24.5166; 0.42 23.3492; 0.48 20.4305; 0.54 18.1605; 0.6 16.3444;
0.66 14.8586; 0.72 13.6203; 0.78 12.5726; 0.84 11.6746; 0.9 10.8963;
0.96 10.2153; 1.02 9.61436; 1.08 9.08023; 1.14 8.60233; 1.2 8.17221;
1.26 7.78306; 1.32 7.42928; 1.38 7.10627; 1.44 6.81018; 1.5 6.53777;
1.56 6.28632; 1.62 6.05349; 1.68 5.83729; 1.74 5.63601; 1.8 5.44814;
1.86 5.2724; 1.92 5.10763; 1.98 4.95286; 2.04 4.80718; 2.1 4.66984;
2.16 4.54012; 2.22 4.41741; 2.28 4.30116; 2.34 4.19088; 2.4 4.08611;
2.46 3.98645; 2.52 3.89153; 2.58 3.80103; 2.64 3.71464; 2.7 3.63209;
2.76 3.55314; 2.82 3.47754; 2.88 3.40509; 2.94 3.3356; 3 3.26889; 3.06 3.20479;
3.12 3.14316; 3.18 3.08385; 3.24 3.02675; 3.3 2.97171; 3.36 2.91865;
3.42 2.86744; 3.48 2.818; 3.54 2.77024; 3.6 2.72407; 3.66 2.67941; 3.72 2.6362;
3.78 2.59435; 3.84 2.55382; 3.9 2.51453; 3.96 2.47643; 4.02 2.45166;
4.08 2.45166; 4.14 2.45166; 4.2 2.45166; 4.26 2.45166; 4.32 2.45166;
4.38 2.45166; 4.44 2.45166; 4.5 2.45166; 4.56 2.45166; 4.62 2.45166;
4.68 2.45166; 4.74 2.45166; 4.8 2.45166; 4.86 2.45166; 4.92 2.45166;
4.98 2.45166; 5.04 2.45166; 5.1 2.45166; 5.16 2.45166; 5.22 2.45166;
5.28 2.45166; 5.34 2.45166; 5.4 2.45166; 5.46 2.45166; 5.52 2.45166;
5.58 2.45166; 5.64 2.45166; 5.7 2.45166; 5.76 2.45166; 5.82 2.45166;
5.88 2.45166; 5.94 2.45166;
PERFORM ANALYSIS PRINT ALL
PRINT MODE SHAPES
PRINT ANALYSIS RESULTS
FINISH
STAAD Output
CALCULATED FREQUENCIES FOR LOAD CASE 1 MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) 1 3.332 0.30014 2 9.103 0.10986 3 12.435 0.08042 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 MODE ACCELERATION-G DAMPING ---- -------------- ------- 1 2.50000 0.05000 2 2.39857 0.05000 3 2.10421 0.05000 STAAD SPACE -- PAGE NO. 8 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 0.300 284.57 0.00 0.00 0.00 0.00 -1707.42 2 0.110 19.60 0.00 0.00 0.00 0.00 58.81 3 0.080 1.23 0.00 0.00 0.00 0.00 -7.41 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 0.000 284.57 0.00 0.00 2 6.67 0.00 0.00 99.521 0.000 0.000 19.60 0.00 0.00 3 0.48 0.00 0.00 100.000 0.000 0.000 1.23 0.00 0.00 --------------------------- TOTAL SRSS SHEAR 285.25 0.00 0.00 TOTAL 10PCT SHEAR 285.25 0.00 0.00 TOTAL ABS SHEAR 305.41 0.00 0.00