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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

Structure to be modelled:
  • height = 3× 5m = 15m
  • plan dimension X = 5m
  • plan dimension Z = 5m
Input parameters:
  • 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)

Story Level Wi hi Wi × hi (Wi × hi)/∑(Wi × hi) Fx Fz
Roof 200 15 3,000 0.5 9.469 9.469
2nd 200 10 2,000 0. 333 6.313 6.313
1st 200 5 1,000 1.667 3.156 3.156
Summation 600 6,000
V 18.938 18.938

Comparison

Table 1. Comparison of results
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\2010\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