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V. IBC 2015 Static Seismic

Calculation of base shear and its distribution along the height for equivalent lateral force method in IBC 2015.

Problem

Structure to be modelled:
  • height = 4× 4m = 16m
  • plan dimension X = 4m
  • plan dimension Z = 5m
Input parameters:
  • Location: Corona, CA, USA (ZIP 92877)
  • Site class D (SCLASS 4)
  • Long-period transition time = 12s (TL 12)
  • Importance factor = 1.0 (I 1.0)
  • Response modification factor X = 3 (RX 3)
  • Response modification factor Z = 4 (RZ 4)

The seismic weight for each floor is assumed as 200 KN applied as joint weight of 50KN to nodes 2 3 5 6 8 9 11 To 20. Seismic Load as per IBC 2015 specifications are generated along horizontal direction global X. The base shear and its distribution along height reported by STAAD.Pro is verified against hand calculation.

Calculations

ZIP = 92887; Ss = 2.247 & S1 = 0.817

For Site Class D, Fa = 1 (Ss > 1.25) and Fv = 1.5 (S1 > 0.5)

SMS = Ss × Fa = 2.247, SM1 = S1 × Fv = 1.2255

SDS = 2/3 × SMS = 1.498, SD1 = 2/3 × SM1 = 0.817

For concrete moment resisting frames Ct = 0.0466 in metric system & x = 0.9

Height = ha = 16m, Ta = Ct × hax = 0.0466 × 160.9 = 0.565,

Since SD1 = 0.817 > 0.4, Cu = 1.4

Cu × Ta = 1.4 × 0.565 = 0.791

T (from output file) = 1.286, Cu × Ta = 0.791 < 1.286, Tused = 0.791

Csx = SDS/(Rx/I) = 1.498 / (3/1) = 0.49933

Csx lower limit = 0.044 × SDS × I & 0.5 × S1 / (Rx/I),

Csx lower limit = 0.044 × 1.498 × 1 & 0.5 × 0.817 / (3/1)

Csx lower limit = 0.065912 & 0.136166

Csx upper limit = SD1 / (Tused × (Rx/I)) as Tused < TL

Csx upper limit = 0.817 / (0.791 × (3/1)) = 0.34429

Csx used = 0.34429

Seismic Base Shear V = Cs × W = 0.34429 × (200 × 4) = 275.432 KN

Lateral seismic force Fx = Cvx × V where Cvx = Wx × hxk / ∑ Wi × hik

Since Tused = 0.791 sec > 0.5 Sec distribution of Base Shear along story levels would have the value of exponent k linearly interpolated between 1 (less than equal to 0.5 sec) and 2 (greater than equal to 2.5 sec) i.e. power = 1.1455.

Story Level Wi hi Wi × hi 1.1455 (Wi × hi 1.1455 )/∑(Wi × hi 1.1455) Fx
Roof 200 16 4,790.2 0.4209 115.941
3rd 200 12 3,445.3 0.3028 83.391
2nd 200 8 2,165.3 0.1903 52.409
1st 200 4 978.79 0.0860 23.691
Summation 800 11,379.6 1
Vx 275.432

Comparison

Table 1. Comparison of results
Parameter Hand Calculation STAAD.Pro Difference Comments
Story shear, Fx (kN) 1st 23.691 23.697 Negligible  
2nd 52.409 52.389 Negligible
3rd 83.391 83.364 Negligible
roof 115.941 115.908 Negligible
Base shear, Vx (kN) 275.432 275.34 Negligible  

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\IBC\2015\IBC 2015 Static Seismic.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 18-May-15
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 4 0; 3 4 4 0; 4 4 0 0; 5 0 8 0; 6 4 8 0; 7 0 0 5; 8 0 4 5;
9 4 4 5; 10 4 0 5; 11 0 8 5; 12 4 8 5; 13 0 12 0; 14 4 12 0; 15 0 12 5;
16 4 12 5; 17 0 16 0; 18 4 16 0; 19 0 16 5; 20 4 16 5;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 2 5; 5 5 6; 6 6 3; 7 2 8; 8 3 9; 9 5 11; 10 6 12;
11 7 8; 12 8 9; 13 9 10; 14 8 11; 15 11 12; 16 12 9; 17 5 13; 18 6 14;
19 11 15; 20 12 16; 21 13 14; 22 13 15; 23 14 16; 24 15 16; 25 13 17; 26 14 18;
27 15 19; 28 16 20; 29 17 18; 30 17 19; 31 18 20; 32 19 20;
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 3 4 6 11 13 14 16 TO 20 25 TO 28 PRIS YD 0.3 ZD 0.3
2 5 7 TO 10 12 15 21 TO 24 29 TO 32 PRIS YD 0.3 ZD 0.25
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORTS
1 4 7 10 FIXED
DEFINE IBC 2015
*DEFINE IBC 2012
ZIP 92887 I 1 RX 3 RZ 4 SCLASS 4 TL 12
JOINT WEIGHT
2 3 5 6 8 9 11 TO 20 WEIGHT 50
*SELFWEIGHT 1
*MEMBER WEIGHT
*2 5 7 TO 10 12 15 UNI 10
LOAD 1 LOADTYPE Seismic  TITLE EL-X DIR
IBC LOAD X 1
PERFORM ANALYSIS PRINT LOAD DATA
PRINT ANALYSIS RESULTS
FINISH

STAAD Output

   ************************************************************
   *  IBC 2015 SEISMIC LOAD ALONG X  :                        *
   *     CT =  0.047 Cu =  1.400 x =  0.9000                  *
   *  TIME PERIODS :                                          *
   *     Ta =  0.565 T =  1.286 Tuser = 0.000                 *
   *  TIME PERIOD USED (T) =  0.791                           *
   *  Cs LIMITS : LOWER =  0.136 UPPER =  0.344               *
   *  LOAD FACTOR          =  1.000                           *
   *  DESIGN BASE SHEAR    =  1.000 X  0.344 X       800.00   *
   *                       =       275.34  KN                 *
   ************************************************************
    JOINT            LATERAL          TORSIONAL            LOAD -    1
                     LOAD (KN  )      MOMENT (KN  -METE) FACTOR -   1.000
    -----            -------          ---------
       2     FX        5.920    MY        0.000
       3     FX        5.920    MY        0.000
       8     FX        5.920    MY        0.000
       9     FX        5.920    MY        0.000
                 -----------        -----------
          TOTAL =     23.679              0.000 AT LEVEL     4.000 METE
       5     FX       13.097    MY        0.000
       6     FX       13.097    MY        0.000
      11     FX       13.097    MY        0.000
      12     FX       13.097    MY        0.000
                 -----------        -----------
          TOTAL =     52.389              0.000 AT LEVEL     8.000 METE
      13     FX       20.841    MY        0.000
      14     FX       20.841    MY        0.000
      15     FX       20.841    MY        0.000
      16     FX       20.841    MY        0.000
                 -----------        -----------
          TOTAL =     83.364              0.000 AT LEVEL    12.000 METE
      17     FX       28.977    MY        0.000
      18     FX       28.977    MY        0.000
      19     FX       28.977    MY        0.000
      20     FX       28.977    MY        0.000
                 -----------        -----------
          TOTAL =    115.908              0.000 AT LEVEL    16.000 METE