V. IBC 2003 Static Seismic

Calculation of base shear and its distribution along the height for equivalent lateral force method in IBC 2003.

Problem

Structure to be modelled:

height = 4× 4m = 16m
plan dimension X = 4m
plan dimension Z = 5m

Input parameters:

Short period acceleration, S_DS = 1.21067 (SDS 1.21067)
1-Second period acceleration, S_D1 = 0.673 (SD1 0.673)
Site class D (SCLASS 4)
Importance factor = 1.0 (I 1.0)
Response modification factor X = 3 (RX 3)

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 2003 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

For concrete moment-resisting frames, C_T = 0.016 and 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

{C s}_{x} lower limit = {}_{\max}{| \begin{array}{l} 0.044 \times S_{D S} \times I = 0.044 \times 1.21067 \times 1 = 0.0533 \\ \frac{0.5 \times S_{1}}{R_{x} / I} = \frac{0.5 \times 0.673}{3 / 1} = 0.112 \end{array}}

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

where

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 = 1.1457.

Story Level	W_i	h_i	W_i × h_i^1.1457	(W_i × h_i ^1.1457 )/∑(W_i × h_i ^1.1457)	F_x
Roof	200	16	4,792.1	0.4210	95.47
3rd	200	12	3,446.6	0.3028	68.67
2nd	200	8	2,166.0	0.1903	43.15
1st	200	4	979.0	0.0860	19.51
Summation	800		11,383.7	1
V_x	226.8

Comparison

Table 1. Comparison of results
Parameter		Hand Calculation	STAAD.Pro	Difference
Story shear, F_x (kN)	1st	19.51	19.505	negligible
	2nd	43.15	43.153	negligible
	3rd	68.67	68.667	negligible
	roof	95.47	95.474	negligible
Base shear, V_x (kN)		226.8	226.8	none

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\IBC\IBC 2003 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 2003
SDS 1.21067 SD1 0.673 S1 0.673 IE 1 RX 3 RZ 4 SCLASS 4
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 2003 SEISMIC LOAD ALONG X  :                        *
   *     CT =  0.016 Cu =  1.400                              *
   *  TIME PERIODS :                                          *
   *     Ta =  0.565 T =  1.286 Tuser = 0.000                 *
   *  TIME PERIOD USED (T) =  0.791                           *
   *  LOAD FACTOR          =  1.000                           *
   *  DESIGN BASE SHEAR    =  1.000 X  0.283 X       800.00   *
   *                       =       226.80  KN                 *
   ************************************************************
    JOINT            LATERAL          TORSIONAL            LOAD -    1
                     LOAD (KN  )      MOMENT (KN  -METE) FACTOR -   1.000
    -----            -------          ---------
       2     FX        4.876    MY        0.000
       3     FX        4.876    MY        0.000
       8     FX        4.876    MY        0.000
       9     FX        4.876    MY        0.000
                 -----------        -----------
          TOTAL =     19.505              0.000 AT LEVEL     4.000 METE
       5     FX       10.788    MY        0.000
       6     FX       10.788    MY        0.000
      11     FX       10.788    MY        0.000
      12     FX       10.788    MY        0.000
                 -----------        -----------
          TOTAL =     43.153              0.000 AT LEVEL     8.000 METE
      13     FX       17.167    MY        0.000
      14     FX       17.167    MY        0.000
      15     FX       17.167    MY        0.000
      16     FX       17.167    MY        0.000
                 -----------        -----------
          TOTAL =     68.667              0.000 AT LEVEL    12.000 METE
      17     FX       23.869    MY        0.000
      18     FX       23.869    MY        0.000
      19     FX       23.869    MY        0.000
      20     FX       23.869    MY        0.000
                 -----------        -----------
          TOTAL =     95.474              0.000 AT LEVEL    16.000 METE