V. UBC 1994 Static Seismic

Calculation of base shear and its distribution along the height for equivalent lateral force method in UBC 1994.

Problem

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

Input parameters:
• Zone = 0.4
• Site coefficient, S = 1
• Building period coefficient, CT = 0.0731
• Importance factor = 1.0 (I 1.0)
• Response modification factor X = 3 (RX 3)
• Response modification factor Z = 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 UBC 1994 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

Tused = 0.585

C = 1.25× S /(T2/3) = 1.25 × 1 / (0.5852/3) = 1.787

Design base shear calculation:

V = (Z × I × C / Rwx) × W= (0.4 × 1 × 1.787 / 3 ) × (200 × 4) = 0.2383 × 800 = 190.62 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 76.25
3rd 200 12 2,400 0.3 57.19
2nd 200 8 1,600 0.2 38.12
1st 200 4 800 0.1 19.06
Summation 800 8,000 1
Vx 190.62

Comparison

Table 1. Comparison of results
Story shear, Fx (kN) 1st 19.06 19.062 negligible
2nd 38.12 38.124 negligible
3rd 57.19 57.200 negligible
roof 76.25 76.267 negligible
Base shear, Vx (kN) 190.62 190.67 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\UBC\UBC 1994 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 RWZ 3 CT 0.0731 S 1
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  *
*  C =   1.7875, LOAD FACTOR =  1.000                     *
* UBC TYPE = 94                                           *
* UBC FACTOR V = 0.2383 x        800.00 =     190.67 KN   *
*                                                         *
***********************************************************
JOINT            LATERAL          TORSIONAL            LOAD -    1
LOAD (KN  )      MOMENT (KN  -METE) FACTOR -   1.000
-----            -------          ---------
2     FX        4.767    MY        0.000
3     FX        4.767    MY        0.000
8     FX        4.767    MY        0.000
9     FX        4.767    MY        0.000
-----------        -----------
TOTAL =     19.067              0.000 AT LEVEL     4.000 METE
5     FX        9.533    MY        0.000
6     FX        9.533    MY        0.000
11     FX        9.533    MY        0.000
12     FX        9.533    MY        0.000
-----------        -----------
TOTAL =     38.133              0.000 AT LEVEL     8.000 METE
13     FX       14.300    MY        0.000
14     FX       14.300    MY        0.000
15     FX       14.300    MY        0.000
16     FX       14.300    MY        0.000
-----------        -----------
TOTAL =     57.200              0.000 AT LEVEL    12.000 METE
17     FX       19.067    MY        0.000
18     FX       19.067    MY        0.000
19     FX       19.067    MY        0.000
20     FX       19.067    MY        0.000
-----------        -----------
TOTAL =     76.267              0.000 AT LEVEL    16.000 METE
```