V. EN 1998-1-2004 Response Spectrum
Calculation of base shear for response spectrum method per EN 1998-1-2004.
Details
- Type 1
- Ground type A
- Soil factor, S = 1
- Lower limit of period, TB = 0.15 sec
- Upper limit of period, TC = 0.4 sec
- Value defining the beginning of constant displacement response range, TD = 2 sec
- Damping: 5%
- Design ground acceleration, ag = 0.981 m/sec2
- Damping correction factor, η = 1
- Behavior factor, q = 3
- Lower bound factor for horizontal design spectrum, β = 0.2
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 × ϕ | Wi × ϕ 2 | ϕ | Wi × ϕ | Wi × ϕ 2 | ϕ | Wi × ϕ | Wi × 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 | 24.5175 |
Summation | 245.175 | 183.00 | 147.11 | 49.035 | 147.105 | 13.138 | 147.106 | |||
Modal Weight Mk × g | 227.66 | 16.35 | 1.173 | |||||||
Modal Weight Participation (In %) | 92.86 | 6.667 | 0.479 | |||||||
Mode Participation Factor ∏ ∑Wi × ϕ / ∑ Wi × ϕ 2 | 1.244 | 0.333 | 0.089 |
Mode 1 | Mode 2 | Mode 3 | |
---|---|---|---|
Time Period T | 0.30014 | 0.10986 | 0.08042 |
Design response spectrum Sd(T): |
As TB≤ T≤ TC ,hence-
ag x S x (2.5/q)
= 0.981 x 1 x (2.5/3)
= 0.8175 |
As 0 ≤ T≤ TB ,hence-
ag x S x [(2/3) + (T/TB) x {(2.5/q)-(2/3)}]
= 0.981 x 1 x [(2/3) + (0.10986/0.15) x {(2.5/3)-(2/3)}]
= 0.7737 |
As 0 ≤ T≤ TB ,hence-
ag x S x [(2/3) + (T/TB) x {(2.5/q)-(2/3)}]
= 0.981 x 1 x [(2/3) + (0.08042/0.15) x {(2.5/3)-(2/3)}]
= 0.7417
|
Sd/g = | 0.083 | 0.079 | 0.076 |
Design lateral force at each floor in each mode, Qi = Pk × si × (Sd/g) × Wi
Story Level | Weight Wi (KN) | Mode 1 | Mode 2 | Mode 3 | Story Shear due to all modes i.e. SRSS of all modes | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|
si | Qi | Vi | si | Qi | Vi | si | Qi | Vi | |||
Roof | 49.035 | 1 | 5.08 | 5.08 | -1 | -1.29 | -1.29 | 1 | 0.33 | 0.33 | 5.25 |
2nd Floor | 98.070 | 0.86603 | 8.80 | 13.89 | 0 | 0.00 | -1.29 | -0.86603 | -0.57 | -0.24 | 13.95 |
1st Floor | 98.070 | 0.5 | 5.08 | 18.97 | 1 | 2.58 | 1.29 | 0.5 | 0.33 | 0.09 | 19.02 |
Base Shear, V | 19.02 |
Comparison
Parameter | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Base shear (kN) | 19.02 | 19.02 | none |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\06 Loading\EN 1998-1-2004\EN 1998-1-2004 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 EURO 2004 DESIGN RS1 X 1 ACC DAMP 0.05
SOIL TYPE A ALPHA 0.1 Q 3
PERFORM ANALYSIS PRINT ALL
PRINT MODE SHAPES
PRINT ANALYSIS RESULTS
FINISH
STAAD Output
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 18.97 0.00 0.00 0.00 0.00 -113.83
2 0.110 1.29 0.00 0.00 0.00 0.00 3.87
3 0.080 0.09 0.00 0.00 0.00 0.00 -0.53
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 18.97 0.00 0.00
2 6.67 0.00 0.00 99.521 0.000 0.000 1.29 0.00 0.00
3 0.48 0.00 0.00 100.000 0.000 0.000 0.09 0.00 0.00
---------------------------
TOTAL SRSS SHEAR 19.02 0.00 0.00
TOTAL 10PCT SHEAR 19.02 0.00 0.00
TOTAL ABS SHEAR 20.35 0.00 0.00