# V. IBC 2000 Static Seismic

Calculation of base shear and its distribution along the height for equivalent lateral force method in IBC 2000.

## Problem

Structure to be modelled:
• height = 4× 4m = 16m
• plan dimension X = 4m
• plan dimension Z = 5m

Input parameters:
• Short period acceleration, SDS = 0.06 (SDS 0.06)
• 1-Second period acceleration, SD1 = 1.36 (SD1 1.36)
• Site class D (SCLASS 4)
• Building period coefficient = 0.073 (CT 0.073)
• 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 2000 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

Height = hn = 16m, Ta = CT × hnx = 0.073 × 160.75 = 0.584,

Since SD1 = 1.36 > 0.4, Cu = 1.2

Cu × Ta = 1.2 × 0.584 = 0.701

T (from output file) = 1.286, Cu × Ta = 0.701 < 1.286, Tused = 0.701

Csx = SDS/(Rx/I) = 0.06 / (3/1) = 0.02

$Csx lower limit = |0.044×SDS×I=0.044×0.06×1=0.002640.5×S1Rx/I=0.5×1.33/1=0.2167max⁡$

Csx upper limit = SD1 / (Tused × (Rx/I)) = 1.36 / (0.701 × (3/1)) = 0.6469

Csx used = 0.2167

Seismic Base Shear V = Cs × W = 0.2167 × (200 × 4) = 173.3 kN

Lateral seismic force Fx = Cvx × V

where
 Cvx = Wx × hxk / ∑ Wi × hik

Since Tused = 0.701 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 = 1.1004.

Story Level Wi hi Wi × hi 1.1004 (Wi × hi 1.1004 )/∑(Wi × hi 1.1004) Fx
Roof 200 16 4,227.1 0.4145 71.85
3rd 200 12 3,080.1 0.3020 52.35
2nd 200 8 1,971.5 0.1933 33.51
1st 200 4 919.5 0.0902 15.63
Summation 800 10,198.2 1
Vx 173.33

## Comparison

Table 1. Comparison of results
Story shear, Fx (kN) 1st 15.63 15.628 Negligible
2nd 33.51 33.508 Negligible
3rd 52.35 52.351 Negligible
roof 71.85 71.846 Negligible
Base shear, Vx (kN) 173.33 173.33 Negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\IBC\IBC 2000 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 2000
SDS 0.06 SD1 1.36 S1 1.3 IE 1 RX 3 RZ 4 SCLASS 4 CT 0.073
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 2000 SEISMIC LOAD ALONG X  :                        *
*     CT =  0.073 Cu =  1.200                              *
*  TIME PERIODS :                                          *
*     Ta =  0.584 T =  1.286 Tuser = 0.000                 *
*  TIME PERIOD USED (T) =  0.701                           *
*  LOAD FACTOR          =  1.000                           *
*  DESIGN BASE SHEAR    =  1.000 X  0.217 X       800.00   *
*                       =       173.33  KN                 *
************************************************************
JOINT            LATERAL          TORSIONAL            LOAD -    1
LOAD (KN  )      MOMENT (KN  -METE) FACTOR -   1.000
-----            -------          ---------
2     FX        3.907    MY        0.000
3     FX        3.907    MY        0.000
8     FX        3.907    MY        0.000
9     FX        3.907    MY        0.000
-----------        -----------
TOTAL =     15.628              0.000 AT LEVEL     4.000 METE
5     FX        8.377    MY        0.000
6     FX        8.377    MY        0.000
11     FX        8.377    MY        0.000
12     FX        8.377    MY        0.000
-----------        -----------
TOTAL =     33.508              0.000 AT LEVEL     8.000 METE
13     FX       13.088    MY        0.000
14     FX       13.088    MY        0.000
15     FX       13.088    MY        0.000
16     FX       13.088    MY        0.000
-----------        -----------
TOTAL =     52.351              0.000 AT LEVEL    12.000 METE
17     FX       17.962    MY        0.000
18     FX       17.962    MY        0.000
19     FX       17.962    MY        0.000
20     FX       17.962    MY        0.000
-----------        -----------
TOTAL =     71.846              0.000 AT LEVEL    16.000 METE