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V. IS 1893 2016 Static Seismic

Calculation of base shear and its distribution along the height for equivalent static method in IS 1893 (Part 1) : 2016

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 = 1.2 (I 1.2)
  • 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) : 2016 specifications are generated along two horizontal directions global X & global Z and also along vertical direction global Y. 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)

[Sa/g]y = 2.5 (constant)

Ahx = (Z/2) × (I/R) × [Sa/g]x = 0.36/2 × 1.2/5 × 2.5 =0.108

Ahz = (Z/2) × (I/R) × [Sa/g]z = 0.36/2 × 1.2/5 × 2.5 =0.108

Av = (2/3) × (Z/2) × (I/R) × [Sa/g]y = 2/3 × 0.36/2 × 1.2/5 × 2.5 = 0.072

VB = Ah × W or Av × W

VBx = Ahx × W = 0.108 × (3 × 100) = 32.4 kN

VBminx = 2.4% of W = 2.4 × (3 × 100) / 100 = 7.2 kN

VBx > VBminx

VBz = Ahz × W = 0.108 × (3 × 100) = 32.4 kN

VBminz = 2.4% of W = 2.4 × (3 × 100) / 100 = 7.2 kN

VBz > VBminz

VBy = Av × W = 0.072 × (3 × 100) = 21.6 kN

Story Level Wi hi Wi × hi 2 (Wi × hi 2 )/∑(Wi × hi 2 ) Qx Qz Qy
Roof 100 9 8,100 0.6429 20.83 20.83 13.886
2nd 100 6 3,600 0.2857 9.257 9.257 6.171
1st 100 3 900 0.0714 2.314 2.314 1.543
Summation 300 12,600
Vb h 32.4 32.4
Vbv 21.6
Vb h(min) 7.2 7.2

Comparison

Table 1. Comparison of results
Parameter Hand Calculation STAAD.Pro Difference Comments
Story shear X, Z, Y (kN) Roof 2.314, 2.314, 1.543 2.314, 2.314, 1.543 none  
2nd 9.257, 9.257, 6.171 9.257, 9.257, 6.171 none  
1st 20.829, 20.829, 13.886 20.829, 20.829, 13.886 none
Base shear (kN) VBx 32.4 32.4 none
VBz 32.4 32.4 none
VBy 21.6 21.6 none
Min base shear (kN) VBx 7.2 7.2 none
VBz 7.2 7.2 none

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\IS 1893\2016\IS 1893 2016 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
*DEFINE 1893 LOAD
DEFINE IS1893 2016 LOAD
*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 1.2 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
LOAD 1 LOADTYPE Seismic  TITLE SS_(+X)
1893 LOAD X 1
LOAD 2 LOADTYPE Seismic  TITLE SS_(+Z)
1893 LOAD Z 1
LOAD 3 LOADTYPE Seismic  TITLE SS_(+Y)
1893 LOAD Y 1
PERFORM ANALYSIS PRINT LOAD DATA
PRINT ANALYSIS RESULTS
FINISH

STAAD Output

 BASE SHEAR AND TIME PERIOD IN X    
   *********************************************************
   * UNITS - KN    METE                                    *
   * TIME PERIOD FOR X 1893 LOADING =    0.38971 SEC       *
   * SA/G PER 1893=    2.500, LOAD FACTOR= 1.000           *
   * VB PER 1893=    0.1080 X      300.00=      32.40 KN   *
   * VB Act Based on Clause 7.2.1 =       32.40 KN         *
   * VB Min based on Clause 7.2.2 =        7.20 KN         *
   *                                                       *
   *********************************************************
   ***NOTE: Equivalent Static Analysis should preferably be performed for regular
structures with approximate natural time period less than 0.4s and regular
structures with height less than 15m in Seismic Zone II. Ref Cl.6.4.3 and 7.6
 BASE SHEAR AND TIME PERIOD IN Z    
   *********************************************************
   * UNITS - KN    METE                                    *
   * TIME PERIOD FOR Z 1893 LOADING =    0.38971 SEC       *
   * SA/G PER 1893=    2.500, LOAD FACTOR= 1.000           *
   * VB PER 1893=    0.1080 X      300.00=      32.40 KN   *
   * VB Act Based on Clause 7.2.1 =       32.40 KN         *
   * VB Min based on Clause 7.2.2 =        7.20 KN         *
   *                                                       *
   *********************************************************
   ***NOTE: Equivalent Static Analysis should preferably be performed for regular
structures with approximate natural time period less than 0.4s and regular
structures with height less than 15m in Seismic Zone II. Ref Cl.6.4.3 and 7.6
 BASE SHEAR AND TIME PERIOD IN Y    
   *********************************************************
   * UNITS - KN    METE                                    *
   * Calculation of SA/G for Y  based on Clause 6.4.6      *
   * SA/G PER 1893=    2.500, LOAD FACTOR= 1.000           *
   * VB PER 1893=    0.0720 X      300.00=      21.60 KN   *
   *                                                       *
   *********************************************************
      STAAD SPACE                                              -- PAGE NO.    5
    JOINT            LATERAL          TORSIONAL            LOAD -    1
                     LOAD (KN  )      MOMENT (KN  -METE) FACTOR -   1.000
    -----            -------          ---------
      39     FX        2.314    MY        0.000
                 -----------        -----------
          TOTAL =      2.314              0.000 AT LEVEL     3.000 METE
    VB PER 1893 =     32.400 KN  
      60     FX        9.257    MY        0.000
                 -----------        -----------
          TOTAL =      9.257              0.000 AT LEVEL     6.000 METE
    VB PER 1893 =     32.400 KN  
      80     FX       20.829    MY        0.000
                 -----------        -----------
          TOTAL =     20.829              0.000 AT LEVEL     9.000 METE
    VB PER 1893 =     32.400 KN  
    JOINT            LATERAL          TORSIONAL            LOAD -    2
                     LOAD (KN  )      MOMENT (KN  -METE) FACTOR -   1.000
    -----            -------          ---------
      39     FZ        2.314    MY        0.000
                 -----------        -----------
          TOTAL =      2.314              0.000 AT LEVEL     3.000 METE
    VB PER 1893 =     32.400 KN  
      60     FZ        9.257    MY        0.000
                 -----------        -----------
          TOTAL =      9.257              0.000 AT LEVEL     6.000 METE
    VB PER 1893 =     32.400 KN  
      80     FZ       20.829    MY        0.000
                 -----------        -----------
          TOTAL =     20.829              0.000 AT LEVEL     9.000 METE
    VB PER 1893 =     32.400 KN  
    JOINT            LATERAL          TORSIONAL            LOAD -    3
                     LOAD (KN  )      MOMENT (KN  -METE) FACTOR -   1.000
    -----            -------          ---------
      39     FY        1.543    MY        0.000
                 -----------        -----------
          TOTAL =      1.543              0.000 AT LEVEL     3.000 METE
    VB PER 1893 =     21.600 KN  
      60     FY        6.171    MY        0.000
                 -----------        -----------
          TOTAL =      6.171              0.000 AT LEVEL     6.000 METE
    VB PER 1893 =     21.600 KN  
      80     FY       13.886    MY        0.000
      STAAD SPACE                                              -- PAGE NO.    6
                 -----------        -----------
          TOTAL =     13.886              0.000 AT LEVEL     9.000 METE
    VB PER 1893 =     21.600 KN