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.
Calculations
Validation
Natural frequency and time period information and mode shapes obtained from STAAD 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 ×ϕ | Wi ×ϕ 2 | ϕ | Wi ×ϕ | Wi ×ϕ 2 | ϕ | Wi x ϕ | Wi ×ϕ | ||
| Roof | 49.04 | 1 | 49.04 | 49.04 | -1 | -49.04 | 49.04 | 1 | 49.04 | 49.04 |
| 2nd Floor | 98.07 | 0.86603 | 84.93 | 73.55 | 0 | 0 | 0 | -0.86603 | -84.93 | 73.55 |
| 1st Floor | 98.07 | 0.5 | 49.04 | 24.52 | 1 | 98.07 | 98.07 | 0.5 | 49.04 | 24.52 |
| Summation | 245.175 | 183.0 | 147.11 | 49.04 | 147.11 | 13.14 | 147.11 | |||
| Modal Weight Mk × g | 227.7 | 16.345 | 1.173 | |||||||
| Modal Weight Participation (In %) | 92.85 | 6.667 | 0.4786 | |||||||
| Mode Participation Factor, ∏ = ∑Wi×ϕ / ∑ Wi×ϕ 2 | 1.244 | 0.3333 | 0.0893 | |||||||
| Mode 1 | Mode 2 | Mode 3 | |
|---|---|---|---|
| Time Period T | 0.30014 | 0.10986 | 0.08042 |
| Spectrum Data | Obtain from NRC_Calculation.xlsx within worksheet named RS Values | ||
| Formula | Linearly Interpolate acceleration values between 0.3 sec & 0.36 sec to obtain acceleration value for 0.30014 sec. | Linearly Interpolate acceleration values between 0.06 sec & 0.12 sec to obtain acceleration value for 0.10986 sec. | Linearly Interpolate acceleration values between 0.06 sec & 0.12 sec to obtain acceleration value for 0.08042 sec. |
| Sa | 1.50 | 1.40 | 1.10 |
| Horizontal Seismic Coefficient Cs = (Sa × Direction Factor) = Sa × 0.5 | 1.25 | 1.20 | 1.05 |
| 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 | |||
| 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 | ||||||||||
Results
| Parameter | STAAD.Pro | Reference | Difference | Comments |
|---|---|---|---|---|
| Base shear (kN) | 285.25 | 285.25 | none |
Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2026\Samples \Verification Models\06 Loading\NRC\NRC 2005 Response Spectrum.STD is typically installed with the program.
STAAD
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
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