V. NRC 2010 Static Seismic
Calculation of base shear and its distribution along the height for equivalent static force method in NBCC/NRC 2010.
Problem
- height = 3× 5m = 15m
- plan dimension X = 5m
- plan dimension Z = 5m
- Seismic acceleration values Sa(0.2) = 0.28, Sa(0.5) = 0.17, Sa(1.0) = 0.11, and Sa(2) = 0.063 (SA1 0.28, SA2 0.17, SA3 0.11, SA4 0.063)
- Importance factor = 1.3 (I 1.3)
- Site class C (SCL 3)
- Higher mode factor X = 1 (MVX 1)
- Higher mode factor Z = 1 (MVZ 1)
- Ductility-related force modification factor X = 5 (RDX 5)
- Ductility-related force modification factor Z = 5 (RDZ 5)
- Overstrength-related force modification factor X = 5 (ROX 1.5)
- Overstrength-related force modification factor Z = 5 (ROZ 1.5)
- Moment resisting frames in both X and Z directions (STX 1, STZ 1)
- Provisions to be checked for member strength (MD 1)
The seismic weight for each floor is assumed as 200 kN applied as joint weight of 50kN to nodes 2 3 6 7 9 To 16. Seismic Load as per NBCC/NRC 2010 specifications are generated along horizontal direction global X and global Z. The base shear and its distribution along height reported by STAAD.Pro is verified against hand calculation.
Tax = 0.075×(hn)0.75 (for concrete moment frames) = 0.075 × 150.75 = 0.57 sec
Taz = 0.075×(hn)0.75 (for concrete moment frames) = 0.075 × 150.75 = 0.57 sec
Tcx (Rayleigh method from output file) = 0.467, Tcz (Rayleigh method from output file) = 0.467
1.5 × Tax = 0.86 > Tcx so Taused = Tcx = 0.467
1.5 × Taz = 0.86 > Tcz so Taused = Tcz = 0.467
Fa = 1 (For Site Class = C and Sa(0.2) = 0.28)
Fv = 1 (For Site Class = C and Sa(1.0) = 0.11)
S(0.2) = Fa × Sa(0.2) = 1 × 0.28 = 0.28
S(0.5) = smaller of Fv × Sa(0.5) and Fa × Sa(0.2) = smaller of 1 x 0.17 and 1 × 0.28 = 0.17
S(Taused)x = S(Taused)z = 0.17 + ((0.28-0.17)/(0.5-0.2) × (0.5-0.467)) = 0.1821
Vx = S(Taused)x × MVX × I × W / RDX × ROX = 0.1821 × 1 × 1.3 × (200x3) / 5 × 1.5 = 18.9384 kN
Min Base Shear = S(2.0) × MVX × I × W / (RDX × ROX) = 0.063 × 1 x 1.3 × (200x3) / 5 × 1.5 = 6.552 kN
Max Base Shear = 2/3 × S(0.2) × I × W / (RDX × ROX) = 2/3 × 0.28 x 1.3 × (200x3) / 5 × 1.5 = 19.413 kN
Vx > Min Base Shear & Vx < Max Base Shear, Vx = 18.9384 kN
Vz = S(Taused)z × MVZ × I × W / RDZ × ROZ = 0.1821 × 1 × 1.3 × (200x3) / 5 × 1.5 = 18.9384 kN
Min Base Shear = S(2.0) × MVZ × I × W / (RDZ × ROZ) = 0.063 × 1 x 1.3 × (200x3) / 5 × 1.5 = 6.552 kN
Max Base Shear = 2/3 × S(0.2) × I × W / (RDZ × ROZ) = 2/3 × 0.28 x 1.3 × (200x3) / 5 × 1.5 = 19.413 kN
Vz > Min Base Shear & Vz < Max Base Shear, Vz = 18.9384 kN
Since fundamental lateral period < 0.7 sec Ft = 0, calculated Base Shear is distributed along the height as under:
Fx = (V - 0) × (Wx × hx / ∑ Wi × hi) = (V) × (Wx × hx / ∑ Wi × hi)
Comparison
| Parameter | Hand Calculation | STAAD.Pro | Difference | Comments | |
|---|---|---|---|---|---|
| Story shear (kN) | X, 1st | 3.156 | 3.159 | Negligible | |
| Z, 1st | 3.156 | 3.159 | Negligible | ||
| X, 2nd | 6.313 | 6.318 | Negligible | ||
| Z, 2nd | 6.313 | 6.318 | Negligible | ||
| X, roof | 9.469 | 9.477 | Negligible | ||
| Z, roof | 9.469 | 9.477 | Negligible | ||
| Base shear (kN) | Vx | 18.938 | 18.955 | Negligible | |
| Vz | 18.938 | 18.955 | Negligible | ||
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\NRC\NRC 2010 Static Seismic.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 25-Aug-18
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 5 0; 3 5 5 0; 4 5 0 0; 5 0 0 5; 6 0 5 5; 7 5 5 5; 8 5 0 5;
9 0 10 0; 10 5 10 0; 11 0 10 5; 12 5 10 5; 13 0 15 0; 14 5 15 0; 15 0 15 5;
16 5 15 5;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 2 6; 5 3 7; 6 5 6; 7 6 7; 8 7 8; 9 2 9; 10 3 10;
11 6 11; 12 7 12; 13 9 10; 14 9 11; 15 10 12; 16 11 12; 17 9 13; 18 10 14;
19 11 15; 20 12 16; 21 13 14; 22 13 15; 23 14 16; 24 15 16;
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
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TO 24 PRIS YD 0.5 ZD 0.5
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORTS
1 4 5 8 FIXED
DEFINE NRC 2010 LOAD
SA1 0.28 SA2 0.17 SA3 0.11 SA4 0.063 I 1.3 SCL 3 MVX 1 MVZ 1 RDX 5 RDZ 5 ROX -
1.5 ROZ 1.5 STX 1 STZ 1 MD 1
JOINT WEIGHT
2 3 6 7 9 To 16 WEIGHT 50
LOAD 1 LOADTYPE None TITLE STATIC_X
NRC LOAD X 1
LOAD 2 LOADTYPE None TITLE STATIC_Z
NRC LOAD Z 1
PERFORM ANALYSIS PRINT LOAD DATA
PRINT ANALYSIS RESULTS
SECTION 0 0.25 0.5 0.75 1 ALL
PRINT MEMBER SECTION FORCES ALL
FINISH
STAAD Output
***************************************************************************** * * * EQUIV. SEISMIC LOADS AS PER NATIONAL BUILDING CODE OF CANADA 2010 ALONG X * * CT = 0.075 Ta = 0.572 SEC. Tc = 0.467 SEC. * * T USED = 0.467 SEC. DESIGN SPECTRAL ACCELERATION = 0.182258 * * EQUIVALENT LATERAL SEISMIC FORCE (ELASTIC RESPONSE) * * = 0.032 X 600.000 = 18.955 KN * * DESIGN BASE SHEAR = 1.000 X 18.955 * * = 18.955 KN * * * ***************************************************************************** ***************************************************************************** * * * EQUIV. SEISMIC LOADS AS PER NATIONAL BUILDING CODE OF CANADA 2010 ALONG Z * * CT = 0.075 Ta = 0.572 SEC. Tc = 0.467 SEC. * * T USED = 0.467 SEC. DESIGN SPECTRAL ACCELERATION = 0.182258 * * EQUIVALENT LATERAL SEISMIC FORCE (ELASTIC RESPONSE) * * = 0.032 X 600.000 = 18.955 KN * * DESIGN BASE SHEAR = 1.000 X 18.955 * * = 18.955 KN * * * ***************************************************************************** JOINT LATERAL TORSIONAL LOAD - 1 LOAD (KN ) MOMENT (KN -METE) FACTOR - 1.000 ----- ------- --------- 2 FX 0.790 MY 0.000 3 FX 0.790 MY 0.000 6 FX 0.790 MY 0.000 7 FX 0.790 MY 0.000 ----------- ----------- TOTAL = 3.159 0.000 AT LEVEL 5.000 METE 9 FX 1.580 MY 0.000 10 FX 1.580 MY 0.000 11 FX 1.580 MY 0.000 12 FX 1.580 MY 0.000 STAAD SPACE -- PAGE NO. 4 ----------- ----------- TOTAL = 6.318 0.000 AT LEVEL 10.000 METE 13 FX 2.369 MY 0.000 14 FX 2.369 MY 0.000 15 FX 2.369 MY 0.000 16 FX 2.369 MY 0.000 ----------- ----------- TOTAL = 9.477 0.000 AT LEVEL 15.000 METE JOINT LATERAL TORSIONAL LOAD - 2 LOAD (KN ) MOMENT (KN -METE) FACTOR - 1.000 ----- ------- --------- 2 FZ 0.790 MY 0.000 3 FZ 0.790 MY 0.000 6 FZ 0.790 MY 0.000 7 FZ 0.790 MY 0.000 ----------- ----------- TOTAL = 3.159 0.000 AT LEVEL 5.000 METE 9 FZ 1.580 MY 0.000 10 FZ 1.580 MY 0.000 11 FZ 1.580 MY 0.000 12 FZ 1.580 MY 0.000 ----------- ----------- TOTAL = 6.318 0.000 AT LEVEL 10.000 METE 13 FZ 2.369 MY 0.000 14 FZ 2.369 MY 0.000 15 FZ 2.369 MY 0.000 16 FZ 2.369 MY 0.000 ----------- ----------- TOTAL = 9.477 0.000 AT LEVEL 15.000 METE