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, C_T = 0.0731
Near source factor, N_a = 1.5
Near source factor, N_v = 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:

Height = hn = 16m, Ta = C_T × hn^x = 0.0731 × 16^0.75 = 0.585,
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

V_{Upper 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

V_{lower limit} = {}_{\max}{| \begin{array}{l} 0.11 \times C_{a} \times I \times W = 0.11 \times 0.6 \times 1 \times (200 \times 4) = 0.066 \times 800 = 52.8 kN \\ 0.8 \times Z \times N_{v} \times I / R \times W = 0.8 \times 0.4 \times 2 \times 1 / 3.5 \times (200 \times 4) \\ = 0.1829 \times 800 = 146.3 kN \end{array}}

Hence Design Base Shear V = 342.88 kN

Lateral seismic force Fx = (W_x × h_x / ∑ W_i × h_i) × (V - F_t)

Since T = 0.585 < 0.7 sec, F_t = 0

Story Level	W_i	h_i	W_i × h_i	(W_i × h_i )/∑(W_i × h_i )	F_x
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
V_x	342.88

Comparison

Table 1. Comparison of results
Parameter		Hand Calculation	STAAD.Pro	Difference
Story shear, F_x (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, V_x (kN)		342.88	342.86	negligible

STAAD Input

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
DEFINE UBC LOAD
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
LOAD 1 LOADTYPE Seismic  TITLE EL-X DIR
UBC LOAD X 1
PERFORM ANALYSIS PRINT LOAD DATA
PRINT ANALYSIS RESULTS
FINISH

STAAD Output

   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