# V. IS 1893 2002 Static Seismic

Calculation of base shear and its distribution along the height for equivalent static method in IS 1893 (Part 1) : 2002

## Problem

A reinforced concrete frame structure is 4 bays at 4m ea. by 3 bays at 4m ea. in plan. The structure is 3 stories at 3m ea.

The structure is modelled in STAAD.Pro considering the following:
• Seismic zone factor, Z = 0.36 (ZONE 0.36)
• Importance factor, I = 1 (I 1)
• Response reduction factor, R = 5 (RF 5)
• Soil site condition = Hard (SS 1)
• Structure type is a reinforced concrete frame (ST 1)

The seismic weight for each floor is assumed as 100 kN applied as joint weight to nodes 39, 60, & 80. Seismic Loads as per IS 1893 (Part 1) : 2002 specifications are generated along two horizontal directions global X & global Z. The base shear and its distribution along height reported by STAAD.Pro is verified against hand calculation.

Height = 3 × 3 = 9m

Tax = 0.075h0.75 = 0.075 × (90.75) = 0.39 sec

Taz = 0.075h0.75 = 0.075 × (90.75) = 0.39 sec

[Sa/g]x = [Sa/g]z = 2.5 (As time period < 0.4 sec)

Ahx = (Z/2) × (I/R) × [Sa/g]x = 0.36/2 × 1/5 × 2.5 =0.09

Ahz = (Z/2) × (I/R) × [Sa/g]z = 0.36/2 × 1/5 × 2.5 =0.09

VB = Ah × W

VBx = Ahx × W = 0.09 × (3 × 100) = 27 kN

VBz = Ahz × W = 0.09 × (3 × 100) = 27 kN

Story Level Wi hi Wi × hi 2 (Wi × hi 2 )/∑(Wi × hi 2 ) Qx Qz
Roof 100 9 8,100 0.643 17.357 17.357
2nd 100 6 3,600 0.286 7.714 7.714
1st 100 3 900 0.0714 1.929 1.929
Summation 300 12,600
Vb h 27 27

## Comparison

Table 1. Comparison of results
Story shear X, Z (kN) roof 1.929, 1.929 1.929, 1.929 none
2nd 7.714, 7.714 7.714, 7.714 none
1st 17.357, 17.357 17.357, 17.357 none
Base Shear (kN) VBx 27 27.000 none
VBz 27 27.000 none

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\IS 1893\IS 1893 2002 Static Seismic.STD is typically installed with the program.

``````STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 26-Jun-18
END JOB INFORMATION
INPUT WIDTH 79
*SET STAR 0
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 3 0; 3 4 3 0; 4 4 0 0; 5 0 0 4; 6 0 3 4; 7 4 3 4; 8 4 0 4;
9 8 3 0; 10 8 0 0; 11 8 3 4; 12 8 0 4; 13 12 3 0; 14 12 0 0; 15 12 3 4;
16 12 0 4; 17 16 3 0; 18 16 0 0; 19 16 3 4; 20 16 0 4; 21 0 0 8; 22 0 3 8;
23 4 3 8; 24 4 0 8; 25 8 3 8; 26 8 0 8; 27 12 3 8; 28 12 0 8; 29 16 3 8;
30 16 0 8; 31 0 0 12; 32 0 3 12; 33 4 3 12; 34 4 0 12; 35 8 3 12; 36 8 0 12;
37 12 3 12; 38 12 0 12; 39 16 3 12; 40 16 0 12; 41 0 6 0; 42 4 6 0; 43 0 6 4;
44 4 6 4; 45 8 6 0; 46 8 6 4; 47 12 6 0; 48 12 6 4; 49 16 6 0; 50 16 6 4;
51 0 6 8; 52 4 6 8; 53 8 6 8; 54 12 6 8; 55 16 6 8; 56 0 6 12; 57 4 6 12;
58 8 6 12; 59 12 6 12; 60 16 6 12; 61 0 9 0; 62 4 9 0; 63 0 9 4; 64 4 9 4;
65 8 9 0; 66 8 9 4; 67 12 9 0; 68 12 9 4; 69 16 9 0; 70 16 9 4;
71 0 9 8; 72 4 9 8; 73 8 9 8; 74 12 9 8; 75 16 9 8; 76 0 9 12;
77 4 9 12; 78 8 9 12; 79 12 9 12; 80 16 9 12;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 2 6; 5 3 7; 6 5 6; 7 6 7; 8 7 8; 9 3 9; 10 7 11;
11 9 10; 12 9 11; 13 11 12; 14 9 13; 15 11 15; 16 13 14; 17 13 15; 18 15 16;
19 13 17; 20 15 19; 21 17 18; 22 17 19; 23 19 20; 24 6 22; 25 7 23; 26 11 25;
27 15 27; 28 19 29; 29 21 22; 30 22 23; 31 23 24; 32 23 25; 33 25 26; 34 25 27;
35 27 28; 36 27 29; 37 29 30; 38 22 32; 39 23 33; 40 25 35; 41 27 37; 42 29 39;
43 31 32; 44 32 33; 45 33 34; 46 33 35; 47 35 36; 48 35 37; 49 37 38; 50 37 39;
51 39 40; 52 2 41; 53 3 42; 54 6 43; 55 7 44; 56 9 45; 57 11 46; 58 13 47;
59 15 48; 60 17 49; 61 19 50; 62 22 51; 63 23 52; 64 25 53; 65 27 54; 66 29 55;
67 32 56; 68 33 57; 69 35 58; 70 37 59; 71 39 60; 72 41 42; 73 41 43; 74 42 44;
75 43 44; 76 42 45; 77 44 46; 78 45 46; 79 45 47; 80 46 48; 81 47 48; 82 47 49;
83 48 50; 84 49 50; 85 43 51; 86 44 52; 87 46 53; 88 48 54; 89 50 55; 90 51 52;
91 52 53; 92 53 54; 93 54 55; 94 51 56; 95 52 57; 96 53 58; 97 54 59; 98 55 60;
99 56 57; 100 57 58; 101 58 59; 102 59 60; 103 41 61; 104 42 62; 105 43 63;
106 44 64; 107 45 65; 108 46 66; 109 47 67; 110 48 68; 111 49 69; 112 50 70;
113 51 71; 114 52 72; 115 53 73; 116 54 74; 117 55 75; 118 56 76; 119 57 77;
120 58 78; 121 59 79; 122 60 80; 123 61 62; 124 61 63; 125 62 64; 126 63 64;
127 62 65; 128 64 66; 129 65 66; 130 65 67; 131 66 68; 132 67 68; 133 67 69;
134 68 70; 135 69 70; 136 63 71; 137 64 72; 138 66 73; 139 68 74; 140 70 75;
141 71 72; 142 72 73; 143 73 74; 144 74 75; 145 71 76; 146 72 77; 147 73 78;
148 74 79; 149 75 80; 150 76 77; 151 77 78; 152 78 79; 153 79 80;
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 TO 153 PRIS YD 0.5 ZD 0.5
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORTS
1 4 5 8 10 12 14 16 18 20 21 24 26 28 30 31 34 36 38 40 FIXED
*ZONE 0.36 RF 5 I 1.2 SS 1 ST 1 DM 0.05 HT 9 DX 16 DZ 12
ZONE 0.36 RF 5 I 1 SS 1 ST 1 DM 0.05
*ZONE 0.36 RF 5 I 1.2 SS 2 ST 1 DM 0.05 HT 9 DX 16 DZ 12
*ZONE 0.36 RF 5 I 1.2 SS 2 ST 1 DM 0.05
*ZONE 0.36 RF 5 I 1.2 SS 3 ST 1 DM 0.05 HT 9 DX 16 DZ 12
*ZONE 0.36 RF 5 I 1.2 SS 3 ST 1 DM 0.05
JOINT WEIGHT
39 60 80 WEIGHT 100
PRINT ANALYSIS RESULTS
FINISH
``````

```   *********************************************************
* UNITS - KN    METE                                    *
* SA/G PER 1893=    2.500, LOAD FACTOR= 1.000           *
* VB PER 1893=    0.0900 X      300.00=      27.00 KN   *
*                                                       *
*********************************************************
*********************************************************
* UNITS - KN    METE                                    *
* SA/G PER 1893=    2.500, LOAD FACTOR= 1.000           *
* VB PER 1893=    0.0900 X      300.00=      27.00 KN   *
*                                                       *
*********************************************************
JOINT            LATERAL          TORSIONAL            LOAD -    1
LOAD (KN  )      MOMENT (KN  -METE) FACTOR -   1.000
-----            -------          ---------
39     FX        1.929    MY        0.000
-----------        -----------
TOTAL =      1.929              0.000 AT LEVEL     3.000 METE
VB PER 1893 =     27.000 KN
60     FX        7.714    MY        0.000
-----------        -----------
TOTAL =      7.714              0.000 AT LEVEL     6.000 METE
VB PER 1893 =     27.000 KN
80     FX       17.357    MY        0.000
-----------        -----------
TOTAL =     17.357              0.000 AT LEVEL     9.000 METE
VB PER 1893 =     27.000 KN
STAAD SPACE                                              -- PAGE NO.    5
JOINT            LATERAL          TORSIONAL            LOAD -    2
LOAD (KN  )      MOMENT (KN  -METE) FACTOR -   1.000
-----            -------          ---------
39     FZ        1.929    MY        0.000
-----------        -----------
TOTAL =      1.929              0.000 AT LEVEL     3.000 METE
VB PER 1893 =     27.000 KN
60     FZ        7.714    MY        0.000
-----------        -----------
TOTAL =      7.714              0.000 AT LEVEL     6.000 METE
VB PER 1893 =     27.000 KN
80     FZ       17.357    MY        0.000
-----------        -----------
TOTAL =     17.357              0.000 AT LEVEL     9.000 METE
VB PER 1893 =     27.000 KN
```