# V. UBC 1997 Static Seismic

Calculation of base shear and its distribution along the height for equivalent lateral force method in UBC 1997.

## Problem

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

Input parameters:
• Zone = 0.4
• Importance factor = 1.0
• Response modification factor X = 3.5
• Response modification factor Z = 3.5
• Site type = 3
• Building period coefficient, CT = 0.0731
• Near source factor, Na = 1.5
• Near source factor, Nv = 2

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 UBC 1997 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

Structure period calculation:

1. Height = hn = 16m, Ta = CT × hnx = 0.0731 × 160.75 = 0.585,
2. Tb (from output file) = 1.286

Since Zone = 0.4 & Tb > 1.3 x Ta; T = Ta = 0.585

For STYP = 3 & Zone = 0.4; Ca = 0.4 x NA = 0.4 x 1.5 = 0.6

For STYP = 3 & Zone = 0.4; Cv = 0.56 x NV = 0.56 x 2 = 1.12

Design base shear calculation:

V = Cv/R x I/T x W = 1.12/3.5 x 1/0.585 x (200 x 4) = 0.547 x 800 = 437.6 kN

VUpper Limit = (2.5 x Ca x I)/R x W = (2.5 x 0.6 x 1)/3.5 x (200 x 4) = 0.4286 x 800 = 342.88 kN

Hence Design Base Shear V = 342.88 kN

Lateral seismic force Fx = (Wx × hx / ∑ Wi × hi) × (V - Ft)

Since T = 0.585 < 0.7 sec, Ft = 0
Story Level Wi hi Wi × hi (Wi × hi )/∑(Wi × hi ) Fx
Roof 200 16 3,200 0.4 137.15
3rd 200 12 2,400 0.3 102.86
2nd 200 8 1,600 0.2 68.58
1st 200 4 800 0.1 34.29
Summation 800 8,000 1
Vx 342.88

## Comparison

Table 1. Comparison of results
Story shear, Fx (kN) 1st 34.29 34.286 negligible
2nd 68.58 68.571 negligible
3rd 102.86 102.857 negligible
roof 137.15 137.143 negligible
Base shear, Vx (kN) 342.88 342.86 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\UBC\UBC 1997 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
ZONE 0.4 I 1 RWX 3.5 RWZ 3.5 STYP 3 CT 0.0731 NA 1.5 NV 2
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


   LOADING     1  LOADTYPE SEISMIC  TITLE EL-X DIR
-----------
***********************************************************
*                                                         *
*  X  DIRECTION : Ta =  0.585 Tb =  1.286 Tuser =  0.000  *
*  T =  0.585, LOAD FACTOR =  1.000                       *
* UBC TYPE = 97                                           *
* UBC FACTOR V = 0.4286 x        800.00 =     342.86 KN   *
*                                                         *
***********************************************************
JOINT            LATERAL          TORSIONAL            LOAD -    1
LOAD (KN  )      MOMENT (KN  -METE) FACTOR -   1.000
-----            -------          ---------
2     FX        8.571    MY        0.000
3     FX        8.571    MY        0.000
8     FX        8.571    MY        0.000
9     FX        8.571    MY        0.000
-----------        -----------
TOTAL =     34.286              0.000 AT LEVEL     4.000 METE
5     FX       17.143    MY        0.000
6     FX       17.143    MY        0.000
11     FX       17.143    MY        0.000
12     FX       17.143    MY        0.000
-----------        -----------
TOTAL =     68.571              0.000 AT LEVEL     8.000 METE
13     FX       25.714    MY        0.000
14     FX       25.714    MY        0.000
15     FX       25.714    MY        0.000
16     FX       25.714    MY        0.000
-----------        -----------
TOTAL =    102.857              0.000 AT LEVEL    12.000 METE
17     FX       34.286    MY        0.000
18     FX       34.286    MY        0.000
19     FX       34.286    MY        0.000
20     FX       34.286    MY        0.000
-----------        -----------
TOTAL =    137.143              0.000 AT LEVEL    16.000 METE