# V. IBC 2006 Static Seismic

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

## 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 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 = CT × hnx = 0.016 × 52.490.9 = 0.565,

Since SD1 = 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, Tused = 0.791

Csx = SDS/(Rx/I) = 1.21067 / (3/1) = 0.404

$C s x lower limit = | 0.01 0.5 × S 1 R x / I = 0.5 × 0.673 3 / 1 = 0.112 max ⁡$

Csx upper limit = SD1 / (Tused × (Rx/I)) = 0.673 / (0.791 × (3/1)) = 0.2835

Csx used = 0.2835

Seismic Base Shear V = Cs × W = 0.2835 × (200 × 4) = 226.8 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. k = 1.1455.

Story Level Wi hi Wi × hi 1.1455 (Wi × hi 1.1455 )/∑(Wi × hi 1.1455) Fx
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
Vx 226.8

## Comparison

Table 1. Comparison of results
Story shear, Fx (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, Vx (kN) 226.8 226.69 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\IBC\IBC 2006 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 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
PRINT ANALYSIS RESULTS
FINISH


   ************************************************************
*  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