# V. IS 1893 2016 GL Calculation

Calculation of the base shear and its distribution along the height using the static method for Global X, Global Z, Global Y directions using IS 1893:2016 (Part 1).

## Details

The following structure is modelled.

Seismic zone factor, Z 0.16 Z 0.16
Importance factor, I 1 I 1
Response reduce factor, R 3 (OMRF) RF 3
Soil site condition Hard soil SS 1
Structure type Steel moment-resisting frame building ST 3

Total height of the building is 100 ft

Dimension of each floor slab is 20 ft × 10 ft

Floor to floor height for super structure is 10 ft

Floor to floor height for sub structure is 5 ft

GL is located at -2 ft (Y co-ordinate)

Depth of Foundation (DT) is (20-2) = 18 ft = 5.4864 m

All the analytical members are W shaped steel beam (W12X190)

Supports are fixed

The generated model is subjected to joint weight(100kip). The base shear and its distribution along the height is calculated in Global X, Global Z, Global Y direction.

## Verification

Design horizontal acceleration coefficient value calculation for above GL and below GL for Global X(Ah), Global Z(Ah), Global Y(Av) direction.

Table 1. Calculated values for hard soil
Value X Z Y
Time Period (s) 1.103 1.103
Sa/g 0.907

(1/T, 0.4s < t < 4s)

0.907

(1/T, 0.4s < t < 4s)

2.5
Ah or Av 0.02418 0.02418 0.04445
Ah or Av 30 m 0.01209 0.01209 0.0222
Reduced Ah or Av 0.02197 0.02197 0.04038

Base shear calculation and its distribution along the height for above GL and below GL for Global X, Global Z, Global Y direction and Vbmin calculation

Table 2. Vertical distribution of forces above GL
Story Level in ft from base. Wi

(kip)

hi

(m from GL)

Wi× hi2 (Wi × hi2)/∑(Wi × hi2) Qx

(kip)

Qz

(kip)

Qy

(kip)

100 400 24.9936 2,689,600 0.3074 26.761 26.761 49.179
90 400 21.9456 2,073,600 0.2370 20.632 20.632 37.916
80 400 18.8976 1,537,600 0.1757 15.299 15.299 28.115
70 400 15.8496 1,081,600 0.1236 10.762 10.762 19.777
60 400 12.8016 705,600 0.0806 7.021 7.021 12.902
50 400 9.7536 409,600 0.0468 4.075 4.075 7.489
40 400 6.7056 193,600 0.0221 1.926 1.926 3.540
30 400 3.6576 57,600 0.0066 0.573 0.573 1.053
20 400 0.6096 1,600 0.0002 0.016 0.016 0.029
Summation 3,600 8,750,400 1 87.064 87.064 160
Vbh 87.064 87.064 160
Vbmin 39.6 39.6
Table 3. Vertical distribution of forces below GL
Below ground level (ft) Wi

(kip)

hi

(m below GL)

Wi× hi2 (Wi × hi2)/∑(Wi × hi2) Qx

(kip)

Qz

(kip)

Qy

(kip)

10 400 3.048 40,000 0.8 14.063 14.063 25.843
5 400 1.524 10,000 0.2 3.516 3.516 6.461
Summation 800 50,000 17.579 17.579 32.304
Vbh 17.579 17.579 32.304
Vbmin 8.8 8.8

## Results

Table 4. Comparison of results
Qi(X) Qi(Z) Qi(Y) Qi(X) Qi(Z) Qi(Y)
Above GL Story shear (kip) 26.761 26.761 49.179 26.761 26.761 49.179 none
20.632 20.632 37.916 20.632 20.632 37.916 none
15.299 15.299 28.115 15.299 15.299 28.115 none
10.762 10.762 19.777 10.762 10.762 19.777 none
7.021 7.021 12.902 7.021 7.021 12.902 none
4.075 4.075 7.489 4.075 4.075 7.489 none
1.926 1.926 3.540 1.962 1.962 3.54 none
0.573 0.573 1.053 0.573 0.573 1.053 none
0.016 0.016 0.029 0.016 0.016 0.029 none
Base Shear (kip) 87.064 87.064 160 87.064 87.064 160 none
Below GL Story Shear (kip) 14.063 14.063 25.843 14.063 14.063 25.843 none
3.516 3.516 6.461 3.516 3.516 6.461 none
Base Shear (kip) 17.579 17.579 32.304 17.579 17.579 32.304 none

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\IS 1893\IS 1893 2016 GL Calculation.STD is typically installed with the program.

``````STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 16-Aug-18
END JOB INFORMATION
UNIT FEET KIP
JOINT COORDINATES
1 0 -20 0; 2 0 -10 0; 3 20 -20 0; 4 20 -10 0; 5 0 0 0; 6 20 0 0;
7 0 -10 10; 8 20 -10 10; 9 0 0 10; 10 20 0 10; 11 0 -20 10;
12 20 -20 10; 13 0 10 0; 14 20 10 0; 15 0 10 10; 16 20 10 10; 17 0 20 0;
18 20 20 0; 19 0 20 10; 20 20 20 10; 21 0 30 0; 22 20 30 0; 23 0 30 10;
24 20 30 10; 25 0 40 0; 26 20 40 0; 27 0 40 10; 28 20 40 10; 29 0 50 0;
30 20 50 0; 31 0 50 10; 32 20 50 10; 33 0 60 0; 34 20 60 0; 35 0 60 10;
36 20 60 10; 37 0 70 0; 38 20 70 0; 39 0 70 10; 40 20 70 10; 41 0 80 0;
42 20 80 0; 43 0 80 10; 44 20 80 10; 45 0 -15 10; 46 0 -15 0;
47 20 -15 10; 48 20 -15 0;
MEMBER INCIDENCES
1 1 46; 2 3 48; 3 2 5; 4 4 6; 5 2 4; 6 5 6; 7 2 7; 8 4 8; 9 5 9;
10 6 10; 11 11 45; 12 12 47; 13 7 9; 14 8 10; 15 7 8; 16 9 10; 17 5 13;
18 6 14; 19 13 14; 20 13 15; 21 14 16; 22 9 15; 23 10 16; 24 15 16;
25 13 17; 26 14 18; 27 17 18; 28 17 19; 29 18 20; 30 15 19; 31 16 20;
32 19 20; 33 17 21; 34 18 22; 35 21 22; 36 21 23; 37 22 24; 38 19 23;
39 20 24; 40 23 24; 41 21 25; 42 22 26; 43 25 26; 44 25 27; 45 26 28;
46 23 27; 47 24 28; 48 27 28; 49 25 29; 50 26 30; 51 29 30; 52 29 31;
53 30 32; 54 27 31; 55 28 32; 56 31 32; 57 29 33; 58 30 34; 59 33 34;
60 31 35; 61 32 36; 62 35 36; 63 33 37; 64 34 38; 65 37 38; 66 35 39;
67 36 40; 68 39 40; 69 33 35; 70 34 36; 71 37 39; 72 38 40; 73 37 41;
74 38 42; 75 41 42; 76 39 43; 77 40 44; 78 43 44; 79 41 43; 80 42 44;
81 45 7; 82 46 2; 83 47 8; 84 48 4; 85 45 47; 86 47 48; 87 48 46;
88 46 45;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 4.176e+06
POISSON 0.3
DENSITY 0.489024
ALPHA 6.5e-06
DAMP 0.03
TYPE STEEL
STRENGTH FY 5184 FU 8352 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TO 88 TABLE ST W12X190
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 3 11 12 FIXED
ZONE 0.16 RF 3 I 1 SS 1 ST 3 GL -2
JOINT WEIGHT
2 4 TO 10 13 TO 48 WEIGHT 100
FINISH
``````

```   ***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 X
--ABOVE GROUND LEVEL
*********************************************************
* UNITS - KIP   FEET                                    *
* SA/G PER 1893=    0.907, LOAD FACTOR= 1.000           *
* VB PER 1893=    0.0242 X     3600.00=      87.06 KIP  *
* VB Act Based on Clause 7.2.1 =       87.06 KIP        *
* VB Min based on Clause 7.2.2 =       39.60 KIP        *
*                                                       *
*********************************************************
--BELOW GROUND LEVEL
*********************************************************
* UNITS - KIP   FEET                                    *
* SA/G PER 1893=    0.907, LOAD FACTOR= 1.000           *
* FACTOR V  PER 1893 AT GL=    0.0242 X    800.00       *
* FACTOR V  PER 1893 AT 30 M=    0.0121 X    800.00     *
*      FACTOR V  PER 1893=    0.0220 X    800.00        *
* VB Min based on Clause 7.2.2 =        8.80 KIP        *
*                                                       *
*********************************************************
--WEIGHT AND BASE SHEAR SUMMERY
Units:KIP   FEET
|------------------------------------------------------------------------------|
| Category |   Weight   |     Ah     | VB Calculated | VB Minimum |  VB Final  |
|------------------------------------------------------------------------------|
| Above GL |  3600.00000|   0.0241846|      87.06450 |    39.60000|    87.06450|
|------------------------------------------------------------------------------|
| Below GL |   800.00000|   0.0219731|      17.57852 |     8.80000|    17.57852|
|------------------------------------------------------------------------------|
***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
--ABOVE GROUND LEVEL
*********************************************************
* UNITS - KIP   FEET                                    *
* SA/G PER 1893=    0.907, LOAD FACTOR= 1.000           *
* VB PER 1893=    0.0242 X     3600.00=      87.06 KIP  *
* VB Act Based on Clause 7.2.1 =       87.06 KIP        *
* VB Min based on Clause 7.2.2 =       39.60 KIP        *
*                                                       *
*********************************************************
--BELOW GROUND LEVEL
*********************************************************
* UNITS - KIP   FEET                                    *
* SA/G PER 1893=    0.907, LOAD FACTOR= 1.000           *
* FACTOR V  PER 1893 AT GL=    0.0242 X    800.00       *
* FACTOR V  PER 1893 AT 30 M=    0.0121 X    800.00     *
*      FACTOR V  PER 1893=    0.0220 X    800.00        *
* VB Min based on Clause 7.2.2 =        8.80 KIP        *
*                                                       *
*********************************************************
--WEIGHT AND BASE SHEAR SUMMERY
Units:KIP   FEET
|------------------------------------------------------------------------------|
| Category |   Weight   |     Ah     | VB Calculated | VB Minimum |  VB Final  |
|------------------------------------------------------------------------------|
| Above GL |  3600.00000|   0.0241846|      87.06450 |    39.60000|    87.06450|
|------------------------------------------------------------------------------|
| Below GL |   800.00000|   0.0219731|      17.57852 |     8.80000|    17.57852|
|------------------------------------------------------------------------------|
***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
--ABOVE GROUND LEVEL
*********************************************************
* UNITS - KIP   FEET                                    *
* 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=    0.0444 X     3600.00=     160.00 KIP  *
*                                                       *
*********************************************************
--BELOW GROUND LEVEL
*********************************************************
* UNITS - KIP   FEET                                    *
* Calculation of SA/G for Y  based on Clause 6.4.6       *
* SA/G PER 1893=    2.500, LOAD FACTOR= 1.000           *
* FACTOR V  PER 1893 AT GL=    0.0444 X    800.00       *
* FACTOR V  PER 1893 AT 30 M=    0.0223 X    800.00     *
*      FACTOR V  PER 1893=    0.0404 X    800.00        *
*                                                       *
*********************************************************
--WEIGHT AND BASE SHEAR SUMMERY
Units:KIP   FEET
|------------------------------------------------------------------------------|
| Category |   Weight   |     Ah     | VB Calculated | VB Minimum |  VB Final  |
|------------------------------------------------------------------------------|
| Above GL |  3600.00000|   0.0444444|     160.00002 |     0.00000|   160.00002|
|------------------------------------------------------------------------------|
| Below GL |   800.00000|   0.0403805|      32.30436 |     0.00000|    32.30436|
|------------------------------------------------------------------------------|
STAAD SPACE                                              -- PAGE NO.    4
JOINT            LATERAL          TORSIONAL            LOAD -    1
LOAD (KIP )      MOMENT (KIP -FEET) FACTOR -   1.000
-----            -------          ---------
45     FX        0.879    MY        0.000
46     FX        0.879    MY        0.000
47     FX        0.879    MY        0.000
48     FX        0.879    MY        0.000
-----------        -----------
TOTAL =      3.516              0.000 AT LEVEL   -15.000 FEET
VB PER 1893 =     17.579 KIP
2     FX        3.516    MY        0.000
4     FX        3.516    MY        0.000
7     FX        3.516    MY        0.000
8     FX        3.516    MY        0.000
-----------        -----------
TOTAL =     14.063              0.000 AT LEVEL   -10.000 FEET
VB PER 1893 =     17.579 KIP
5     FX        0.004    MY        0.000
6     FX        0.004    MY        0.000
9     FX        0.004    MY        0.000
10     FX        0.004    MY        0.000
-----------        -----------
TOTAL =      0.016              0.000 AT LEVEL     0.000 FEET
VB PER 1893 =     87.064 KIP
13     FX        0.143    MY        0.000
14     FX        0.143    MY        0.000
15     FX        0.143    MY        0.000
16     FX        0.143    MY        0.000
-----------        -----------
TOTAL =      0.573              0.000 AT LEVEL    10.000 FEET
VB PER 1893 =     87.064 KIP
17     FX        0.482    MY        0.000
18     FX        0.482    MY        0.000
19     FX        0.482    MY        0.000
20     FX        0.482    MY        0.000
-----------        -----------
TOTAL =      1.926              0.000 AT LEVEL    20.000 FEET
VB PER 1893 =     87.064 KIP
21     FX        1.019    MY        0.000
22     FX        1.019    MY        0.000
23     FX        1.019    MY        0.000
24     FX        1.019    MY        0.000
-----------        -----------
TOTAL =      4.075              0.000 AT LEVEL    30.000 FEET
VB PER 1893 =     87.064 KIP
25     FX        1.755    MY        0.000
26     FX        1.755    MY        0.000
27     FX        1.755    MY        0.000
28     FX        1.755    MY        0.000
STAAD SPACE                                              -- PAGE NO.    5
-----------        -----------
TOTAL =      7.021              0.000 AT LEVEL    40.000 FEET
VB PER 1893 =     87.064 KIP
29     FX        2.690    MY        0.000
30     FX        2.690    MY        0.000
31     FX        2.690    MY        0.000
32     FX        2.690    MY        0.000
-----------        -----------
TOTAL =     10.762              0.000 AT LEVEL    50.000 FEET
VB PER 1893 =     87.064 KIP
33     FX        3.825    MY        0.000
34     FX        3.825    MY        0.000
35     FX        3.825    MY        0.000
36     FX        3.825    MY        0.000
-----------        -----------
TOTAL =     15.299              0.000 AT LEVEL    60.000 FEET
VB PER 1893 =     87.064 KIP
37     FX        5.158    MY        0.000
38     FX        5.158    MY        0.000
39     FX        5.158    MY        0.000
40     FX        5.158    MY        0.000
-----------        -----------
TOTAL =     20.632              0.000 AT LEVEL    70.000 FEET
VB PER 1893 =     87.064 KIP
41     FX        6.690    MY        0.000
42     FX        6.690    MY        0.000
43     FX        6.690    MY        0.000
44     FX        6.690    MY        0.000
-----------        -----------
TOTAL =     26.761              0.000 AT LEVEL    80.000 FEET
VB PER 1893 =     87.064 KIP
JOINT            LATERAL          TORSIONAL            LOAD -    2
LOAD (KIP )      MOMENT (KIP -FEET) FACTOR -   1.000
-----            -------          ---------
45     FZ        0.879    MY        0.000
46     FZ        0.879    MY        0.000
47     FZ        0.879    MY        0.000
48     FZ        0.879    MY        0.000
-----------        -----------
TOTAL =      3.516              0.000 AT LEVEL   -15.000 FEET
VB PER 1893 =     17.579 KIP
2     FZ        3.516    MY        0.000
4     FZ        3.516    MY        0.000
7     FZ        3.516    MY        0.000
8     FZ        3.516    MY        0.000
STAAD SPACE                                              -- PAGE NO.    6
-----------        -----------
TOTAL =     14.063              0.000 AT LEVEL   -10.000 FEET
VB PER 1893 =     17.579 KIP
5     FZ        0.004    MY        0.000
6     FZ        0.004    MY        0.000
9     FZ        0.004    MY        0.000
10     FZ        0.004    MY        0.000
-----------        -----------
TOTAL =      0.016              0.000 AT LEVEL     0.000 FEET
VB PER 1893 =     87.064 KIP
13     FZ        0.143    MY        0.000
14     FZ        0.143    MY        0.000
15     FZ        0.143    MY        0.000
16     FZ        0.143    MY        0.000
-----------        -----------
TOTAL =      0.573              0.000 AT LEVEL    10.000 FEET
VB PER 1893 =     87.064 KIP
17     FZ        0.482    MY        0.000
18     FZ        0.482    MY        0.000
19     FZ        0.482    MY        0.000
20     FZ        0.482    MY        0.000
-----------        -----------
TOTAL =      1.926              0.000 AT LEVEL    20.000 FEET
VB PER 1893 =     87.064 KIP
21     FZ        1.019    MY        0.000
22     FZ        1.019    MY        0.000
23     FZ        1.019    MY        0.000
24     FZ        1.019    MY        0.000
-----------        -----------
TOTAL =      4.075              0.000 AT LEVEL    30.000 FEET
VB PER 1893 =     87.064 KIP
25     FZ        1.755    MY        0.000
26     FZ        1.755    MY        0.000
27     FZ        1.755    MY        0.000
28     FZ        1.755    MY        0.000
-----------        -----------
TOTAL =      7.021              0.000 AT LEVEL    40.000 FEET
VB PER 1893 =     87.064 KIP
29     FZ        2.690    MY        0.000
30     FZ        2.690    MY        0.000
31     FZ        2.690    MY        0.000
32     FZ        2.690    MY        0.000
-----------        -----------
TOTAL =     10.762              0.000 AT LEVEL    50.000 FEET
VB PER 1893 =     87.064 KIP
33     FZ        3.825    MY        0.000
34     FZ        3.825    MY        0.000
35     FZ        3.825    MY        0.000
36     FZ        3.825    MY        0.000
STAAD SPACE                                              -- PAGE NO.    7
-----------        -----------
TOTAL =     15.299              0.000 AT LEVEL    60.000 FEET
VB PER 1893 =     87.064 KIP
37     FZ        5.158    MY        0.000
38     FZ        5.158    MY        0.000
39     FZ        5.158    MY        0.000
40     FZ        5.158    MY        0.000
-----------        -----------
TOTAL =     20.632              0.000 AT LEVEL    70.000 FEET
VB PER 1893 =     87.064 KIP
41     FZ        6.690    MY        0.000
42     FZ        6.690    MY        0.000
43     FZ        6.690    MY        0.000
44     FZ        6.690    MY        0.000
-----------        -----------
TOTAL =     26.761              0.000 AT LEVEL    80.000 FEET
VB PER 1893 =     87.064 KIP
JOINT            LATERAL          TORSIONAL            LOAD -    3
LOAD (KIP )      MOMENT (KIP -FEET) FACTOR -   1.000
-----            -------          ---------
45     FY        1.615    MY        0.000
46     FY        1.615    MY        0.000
47     FY        1.615    MY        0.000
48     FY        1.615    MY        0.000
-----------        -----------
TOTAL =      6.461              0.000 AT LEVEL   -15.000 FEET
VB PER 1893 =     32.304 KIP
2     FY        6.461    MY        0.000
4     FY        6.461    MY        0.000
7     FY        6.461    MY        0.000
8     FY        6.461    MY        0.000
-----------        -----------
TOTAL =     25.843              0.000 AT LEVEL   -10.000 FEET
VB PER 1893 =     32.304 KIP
5     FY        0.007    MY        0.000
6     FY        0.007    MY        0.000
9     FY        0.007    MY        0.000
10     FY        0.007    MY        0.000
-----------        -----------
TOTAL =      0.029              0.000 AT LEVEL     0.000 FEET
VB PER 1893 =    160.000 KIP
13     FY        0.263    MY        0.000
14     FY        0.263    MY        0.000
15     FY        0.263    MY        0.000
16     FY        0.263    MY        0.000
STAAD SPACE                                              -- PAGE NO.    8
-----------        -----------
TOTAL =      1.053              0.000 AT LEVEL    10.000 FEET
VB PER 1893 =    160.000 KIP
17     FY        0.885    MY        0.000
18     FY        0.885    MY        0.000
19     FY        0.885    MY        0.000
20     FY        0.885    MY        0.000
-----------        -----------
TOTAL =      3.540              0.000 AT LEVEL    20.000 FEET
VB PER 1893 =    160.000 KIP
21     FY        1.872    MY        0.000
22     FY        1.872    MY        0.000
23     FY        1.872    MY        0.000
24     FY        1.872    MY        0.000
-----------        -----------
TOTAL =      7.489              0.000 AT LEVEL    30.000 FEET
VB PER 1893 =    160.000 KIP
25     FY        3.225    MY        0.000
26     FY        3.225    MY        0.000
27     FY        3.225    MY        0.000
28     FY        3.225    MY        0.000
-----------        -----------
TOTAL =     12.902              0.000 AT LEVEL    40.000 FEET
VB PER 1893 =    160.000 KIP
29     FY        4.944    MY        0.000
30     FY        4.944    MY        0.000
31     FY        4.944    MY        0.000
32     FY        4.944    MY        0.000
-----------        -----------
TOTAL =     19.777              0.000 AT LEVEL    50.000 FEET
VB PER 1893 =    160.000 KIP
33     FY        7.029    MY        0.000
34     FY        7.029    MY        0.000
35     FY        7.029    MY        0.000
36     FY        7.029    MY        0.000
-----------        -----------
TOTAL =     28.115              0.000 AT LEVEL    60.000 FEET
VB PER 1893 =    160.000 KIP
37     FY        9.479    MY        0.000
38     FY        9.479    MY        0.000
39     FY        9.479    MY        0.000
40     FY        9.479    MY        0.000
-----------        -----------
TOTAL =     37.916              0.000 AT LEVEL    70.000 FEET
VB PER 1893 =    160.000 KIP
41     FY       12.295    MY        0.000
42     FY       12.295    MY        0.000
43     FY       12.295    MY        0.000
44     FY       12.295    MY        0.000
STAAD SPACE                                              -- PAGE NO.    9
-----------        -----------
TOTAL =     49.179              0.000 AT LEVEL    80.000 FEET
VB PER 1893 =    160.000 KIP
```