V. IBC 2006 Static Seismic

Calculation of base shear and its distribution along the height for equivalent lateral force method in IBC 2006.

Details

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 2006 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 = hn = 16m = 52.49 ft, Ta = C_T × hn^x = 0.016 × 52.49^0.9 = 0.565,

Since S_D1 = 0.673 > 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, T_used = 0.791

Cs_x = S_DS/(R_x/I) = 1.21067 / (3/1) = 0.404

Cs_x upper limit = S_D1 / (T_used × (Rx/I)) = 0.673 / (0.791 × (3/1)) = 0.2835

Cs_x used = 0.2835

Seismic Base Shear V = Cs × W = 0.2835 × (200 × 4) = 226.8 kN

Lateral seismic force Fx = C_vx × V

C_vx: W_x × h_x ^k / ∑ W_i × h_i ^k

Since T_used = 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. k = 1.1455.

Story Level	W_i	h_i	W_i × h_i ^1.1455	(W_i × h_i ^1.1455 )/∑(W_i × h_i ^1.1455)	F_x
Roof	200	16	4,792.1	0.4210	95.51
3rd	200	12	3,446.6	0.3028	68.69
2nd	200	8	2,166.0	0.1903	43.17
1st	200	4	979.0	0.0860	19.52
Summation	800		11,383.7	1
V_x	226.8

Results

Table 1. Comparison of results
Parameter		Hand Calculation	STAAD.Pro	Difference
Story shear, F_x (kN)	1st	19.52	19.505	negligible
	2nd	43.17	43.153	negligible
	3rd	68.69	68.667	negligible
	roof	95.51	95.474	negligible
Base shear, V_x (kN)		226.8	226.69	negligible

Input

The file C:\Users\Public\Public Documents\STAAD.Pro 2026\Samples \Verification Models\06 Loading\IBC\IBC 2006 Static Seismic.STD is typically installed with the program.

STAAD

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 2006
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

Output

   ************************************************************
   *  IBC 2006 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 =  0.112 UPPER =  0.283               *
   *  LOAD FACTOR          =  1.000                           *
   *  DESIGN BASE SHEAR    =  1.000 X  0.283 X       800.00   *
   *                       =       226.69  KN                 * 
   ************************************************************
    JOINT            LATERAL          TORSIONAL            LOAD -    1
                     LOAD (KN  )      MOMENT (KN  -METE) FACTOR -   1.000
    -----            -------          ---------
       2     FX        4.874    MY        0.000
       3     FX        4.874    MY        0.000
       8     FX        4.874    MY        0.000
       9     FX        4.874    MY        0.000
                 -----------        -----------
          TOTAL =     19.495              0.000 AT LEVEL     4.000 METE 
       5     FX       10.783    MY        0.000
       6     FX       10.783    MY        0.000
      11     FX       10.783    MY        0.000
      12     FX       10.783    MY        0.000
                 -----------        -----------
          TOTAL =     43.133              0.000 AT LEVEL     8.000 METE 
      13     FX       17.159    MY        0.000
      14     FX       17.159    MY        0.000
      15     FX       17.159    MY        0.000
      16     FX       17.159    MY        0.000
                 -----------        -----------
          TOTAL =     68.635              0.000 AT LEVEL    12.000 METE 
      17     FX       23.857    MY        0.000
      18     FX       23.857    MY        0.000
      19     FX       23.857    MY        0.000
      20     FX       23.857    MY        0.000
                 -----------        -----------
          TOTAL =     95.430              0.000 AT LEVEL    16.000 METE