# EX. UK-10 Finite Element Model for a Rectangular Tank

A tank structure is modeled with four-noded plate elements. Water pressure from inside is used as loading for the tank. Reinforcement calculations have been done for some elements.

This problem is installed with the program by default to C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\Sample Models\UK\UK-10 Finite Element Model for a Rectangular Tank.STD when you install the program.

### Deflected Shape

Actual input is shown in bold lettering followed by explanation.

```    STAAD SPACE FINITE ELEMENT MODEL OF TANK
* STRUCTURE
```

Every input has to start with the term STAAD. The word SPACE signifies that the structure is a space frame (3-D) structure.

```    UNITS METER KNS
```

Defines the input units for the data that follows.

```    JOINT COORDINATES
1 0. 0. 0. 5 0. 6. 0.
REPEAT 4 1.5. 0. 0.
REPEAT 4 0. 0. 1.5.
REPEAT 4 -1.5. 0. 0.
REPEAT 3 0. 0. –1.5.
81 1.5. 0. 1.5. 83 1.5. 0. 4.5.
REPEAT 2 1.5. 0. 0.
```

Joint number followed by X, Y and Z coordinates are provided above. The REPEAT command generates joint coordinates by repeating the pattern of the previous line of joint coordinates. The number following the REPEAT command is the number of repetitions to be carried out. This is followed by X, Y and Z coordinate increments. See TR.11 ジョイント座標の設定 .

```    ELEMENT INCIDENCES
1 1 2 7 6 TO 4 1 1
REPEAT 14 4 5
61 76 77 2 1 TO 64 1 1
65 1 6 81 76
66 76 81 82 71
67 71 82 83 66
68 66 83 56 61
69 6 11 84 81
70 81 84 85 82
71 82 85 86 83
72 83 86 51 56
73 11 16 87 84
74 84 87 88 85
75 85 88 89 86
76 86 89 46 51
77 16 21 26 87
78 87 26 31 88
79 88 31 36 89
80 89 36 41 46
```

Element connectivities are input as above by providing the element number followed by joint numbers defining the element. The REPEAT command generates element incidences by repeating the pattern of the previous line of element nodes. The number following the REPEAT command is the number of repetitions to be carried out and that is followed by element and joint number increments. See TR.12 メンバー生成の設定 .

```    UNIT MMS
ELEMENT PROPERTIES
1 TO 80 TH 200.0
```

Element properties are provided by specifying that the elements are 200.0 mm THick.

```    DEFINE MATERIAL START
ISOTROPIC CONCRETE
E 21.0
POISSON 0.17
DENSITY 2.4e-008
ALPHA 5e-006
DAMP 0.05
G 9.25
TYPE CONCRETE
STRENGTH FCU 0.028
END DEFINE MATERIAL
CONSTANTS
MATERIAL CONCRETE ALL```

The DEFINE MATERIAL command is used to specify material properties and the CONSTANT is used to assign the material to all members.

```    SUPPORT
1 TO 76 BY 5 81 TO 89 PINNED
```

Pinned supports are specified at the joints listed above. No moments will be carried by these supports. The expression 1 TO 76 BY 5 means 1, 6, 11, etc. up to 76.

```    UNIT METER
4 TO 64 BY 4 PR 50.0
3 TO 63 BY 4 PR 100.0
2 TO 62 BY 4 PR 150.0
1 TO 61 BY 4 PR 200.0
```

Load case 1 is initiated. It consists of element loads in the form of uniform pressure(indicated by PR)  acting along the local z-axis.

```    PERFORM ANALYSIS
```

This command instructs the program to proceed with the analysis.

```    UNIT MMS
PRINT JOINT DISPLACEMENTS LIST 5 25 45 65
PRINT ELEM FORCE LIST 9 TO 16
```

Joint displacements for a selected set of nodes and element corner forces for some elements are written in the output file as a result of the above commands. The forces printed are in the global directions at the nodes of the elements. The LIST option restricts the print output to that for the joints/elements listed.

```    START CONCRETE DESIGN
```

The above command initiates concrete design.

```    CODE BRITISH
DESIGN SLAB 9 12
```

Slabs (i.e., elements) 9 and 12 will be designed and the reinforcement requirements obtained. In STAAD, elements are typically designed for the moments MX and MY at the centroid of the element.

```    END CONCRETE DESIGN
```

Terminates the concrete design operation.

`    FINISH`

This command terminates the STAAD run.

## Input File

``````STAAD SPACE FINITE ELEMENT MODEL OF TANK STRUCTURE
UNIT METER KNS
JOINT COORDINATES
1 0.0 0.0 0.0 5 0.0 6.0 0.0
REPEAT 4  1.5  0.0  0.0
REPEAT 4  0.0  0.0  1.5
REPEAT 4 -1.5  0.0  0.0
REPEAT 3  0.0  0.0 -1.5
81 1.5 0.0 1.5 83 1.5 0.0 4.5
REPEAT 2  1.5  0.0  0.0
ELEMENT INCIDENCES
1 1 2 7 6 TO 4 1 1
REPEAT 14 4 5
61 76 77 2 1 TO 64 1 1
65 1 6 81 76
66 76 81 82 71
67 71 82 83 66
68 66 83 56 61
69 6 11 84 81
70 81 84 85 82
71 82 85 86 83
72 83 86 51 56
73 11 16 87 84
74 84 87 88 85
75 85 88 89 86
76 86 89 46 51
77 16 21 26 87
78 87 26 31 88
79 88 31 36 89
80 89 36 41 46
UNIT MMS
ELEMENT PROPERTIES
1 TO 80 TH 200.0
DEFINE MATERIAL START
ISOTROPIC CONCRETE
E 21.0
POISSON 0.17
DENSITY 2.4e-008
ALPHA 5e-006
DAMP 0.05
G 9.25
TYPE CONCRETE
STRENGTH FCU 0.028
END DEFINE MATERIAL
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORT
1 TO 76 BY 5 81 TO 89 PINNED
UNIT METER
4 TO 64 BY 4 PR 50.0
3 TO 63 BY 4 PR 100.0
2 TO 62 BY 4 PR 150.0
1 TO 61 BY 4 PR 200.0
PERFORM ANALYSIS
UNIT MMS
PRINT JOINT DISPLACEMENTS LIST 5 25 45 65
PRINT ELEM FORCE LIST 9 TO 16
START CONCRETE DESIGN
CODE BS8007
DESIGN SLAB 9 12
END CONCRETE DESIGN
FINISH
``````

```                                                                  PAGE NO.    1
****************************************************
*                                                  *
*           Version  22.08.00.***                  *
*           Proprietary Program of                 *
*           Bentley Systems, Inc.                  *
*           Date=    OCT 19, 2021                  *
*           Time=    17:53:26                      *
*                                                  *
*  Licensed to: Bentley Systems Inc                *
****************************************************
1. STAAD SPACE FINITE ELEMENT MODEL OF TANK STRUCTURE
INPUT FILE: UK-10 Finite Element Model for a Rectangular Tank.STD
2. UNIT METER KNS
3. JOINT COORDINATES
4. 1 0.0 0.0 0.0 5 0.0 6.0 0.0
5. REPEAT 4  1.5  0.0  0.0
6. REPEAT 4  0.0  0.0  1.5
7. REPEAT 4 -1.5  0.0  0.0
8. REPEAT 3  0.0  0.0 -1.5
9. 81 1.5 0.0 1.5 83 1.5 0.0 4.5
10. REPEAT 2  1.5  0.0  0.0
11. ELEMENT INCIDENCES
12. 1 1 2 7 6 TO 4 1 1
13. REPEAT 14 4 5
14. 61 76 77 2 1 TO 64 1 1
15. 65 1 6 81 76
16. 66 76 81 82 71
17. 67 71 82 83 66
18. 68 66 83 56 61
19. 69 6 11 84 81
20. 70 81 84 85 82
21. 71 82 85 86 83
22. 72 83 86 51 56
23. 73 11 16 87 84
24. 74 84 87 88 85
25. 75 85 88 89 86
26. 76 86 89 46 51
27. 77 16 21 26 87
28. 78 87 26 31 88
29. 79 88 31 36 89
30. 80 89 36 41 46
31. UNIT MMS
32. ELEMENT PROPERTIES
33. 1 TO 80 TH 200.0
34. DEFINE MATERIAL START
35. ISOTROPIC CONCRETE
36. E 21.0
37. POISSON 0.17
38. DENSITY 2.4E-008
FINITE ELEMENT MODEL OF TANK STRUCTURE                   -- PAGE NO.    2
39. ALPHA 5E-006
40. DAMP 0.05
41. G 9.25
42. TYPE CONCRETE
43. STRENGTH FCU 0.028
44. END DEFINE MATERIAL
45. CONSTANTS
46. MATERIAL CONCRETE ALL
47. SUPPORT
48. 1 TO 76 BY 5 81 TO 89 PINNED
49. UNIT METER
52. 4 TO 64 BY 4 PR 50.0
53. 3 TO 63 BY 4 PR 100.0
54. 2 TO 62 BY 4 PR 150.0
55. 1 TO 61 BY 4 PR 200.0
56. PERFORM ANALYSIS
P R O B L E M   S T A T I S T I C S
-----------------------------------
NUMBER OF JOINTS         89  NUMBER OF MEMBERS       0
NUMBER OF PLATES         80  NUMBER OF SOLIDS        0
NUMBER OF SURFACES        0  NUMBER OF SUPPORTS     25
Using 64-bit analysis engine.
SOLVER USED IS THE IN-CORE ADVANCED MATH SOLVER
TOTAL      PRIMARY LOAD CASES =     1, TOTAL DEGREES OF FREEDOM =     459
TOTAL LOAD COMBINATION  CASES =     0  SO FAR.
57. UNIT MMS
58. PRINT JOINT DISPLACEMENTS LIST 5 25 45 65
JOINT    DISPLACE LIST     5
FINITE ELEMENT MODEL OF TANK STRUCTURE                   -- PAGE NO.    3
JOINT DISPLACEMENT (CM   RADIANS)    STRUCTURE TYPE = SPACE
------------------
JOINT  LOAD   X-TRANS   Y-TRANS   Z-TRANS   X-ROTAN   Y-ROTAN   Z-ROTAN
5    1    -0.0103    0.0007   -0.0103    0.0002    0.0000   -0.0002
25    1     0.0103    0.0007   -0.0103    0.0002    0.0000    0.0002
45    1     0.0103    0.0007    0.0103   -0.0002    0.0000    0.0002
65    1    -0.0103    0.0007    0.0103   -0.0002    0.0000   -0.0002
************** END OF LATEST ANALYSIS RESULT **************
59. PRINT ELEM FORCE LIST 9 TO 16
ELEM     FORCE    LIST     9
FINITE ELEMENT MODEL OF TANK STRUCTURE                   -- PAGE NO.    4
ELEMENT FORCES    FORCE,LENGTH UNITS= KNS  MMS
--------------
GLOBAL CORNER FORCES
JOINT     FX          FY          FZ          MX          MY          MZ
ELE.NO.      9 FOR LOAD CASE     1
11 -8.8840E+01 -5.4966E+01  2.9486E+02  1.3176E+05 -4.1177E+04  1.0696E+04
12 -8.2763E+01 -6.0241E+00 -4.4118E+01  7.9554E+04  5.9496E+04 -1.6817E+04
17  1.4375E+02  4.7401E+01 -5.6234E+01  1.2776E+05 -1.1029E+05  2.1861E+04
16  2.7850E+01  1.3590E+01  2.5550E+02  1.4896E+05  5.3365E+04 -1.5740E+04
ELE.NO.     10 FOR LOAD CASE     1
12 -1.8729E+02  6.0241E+00  4.4118E+01 -7.9554E+04  1.0833E+05  4.7435E+04
13 -1.9921E+02 -3.6766E+01  2.0250E+01  6.9592E+04  1.0234E+05 -5.8037E+04
18  2.2995E+02 -1.3963E+01  1.1488E+02  5.8552E+04 -5.3896E+04  6.1870E+04
17  1.5655E+02  4.4705E+01  1.5825E+02  1.8395E+03 -2.0026E+02 -5.1268E+04
ELE.NO.     11 FOR LOAD CASE     1
13 -2.1146E+02  3.6766E+01 -2.0250E+01 -6.9592E+04  1.2194E+05  5.7366E+04
14 -2.3180E+02 -1.4769E+01  3.2094E+01  2.6339E+04  1.0470E+05 -6.4752E+04
19  2.0981E+02 -3.2909E+01  1.4009E+02 -1.5592E+04 -2.4195E+04  6.5369E+04
18  2.3345E+02  1.0912E+01  7.3067E+01 -3.0678E+04 -5.1461E+04 -5.7982E+04
ELE.NO.     12 FOR LOAD CASE     1
14 -1.7545E+02  1.4769E+01 -3.2094E+01 -2.6339E+04  1.0553E+05  4.3931E+04
15 -1.7917E+02 -1.7164E-07 -5.3352E-07  5.4335E-04  9.5913E+04 -4.9179E+04
20  1.6440E+02 -2.5971E+00  9.3630E+01 -2.8746E+04 -2.4521E+04  4.5374E+04
19  1.9022E+02 -1.2172E+01  5.0964E+01 -9.8543E+02 -4.4410E+04 -4.0126E+04
ELE.NO.     13 FOR LOAD CASE     1
16 -1.0576E+02 -8.2837E+01  9.5266E+01 -1.4733E+04  2.7047E+04  1.5133E+04
17 -3.2926E+01 -6.8334E+01  3.5521E+01 -8.9147E+03 -4.0371E+03 -2.4466E+04
22  1.8410E+02  2.6957E+01  1.9413E+02 -1.6851E+04  6.2037E+04  2.9884E+04
21 -4.5408E+01  1.2421E+02  1.2508E+02  3.3522E+04  5.6274E+04 -2.0551E+04
ELE.NO.     14 FOR LOAD CASE     1
17 -2.6737E+02 -2.3772E+01 -1.3754E+02 -1.2068E+05  1.1453E+05  5.3873E+04
18 -2.5271E+02 -5.3156E+00 -6.4895E+01  3.2784E+04  5.0765E+04 -5.2692E+04
23  2.8179E+02  5.6045E+01  3.1168E+02 -8.0772E+04  2.0347E+05  6.3464E+04
22  2.3828E+02 -2.6957E+01  2.2825E+02  5.1613E+04  1.8801E+05 -6.4645E+04
ELE.NO.     15 FOR LOAD CASE     1
18 -2.1070E+02  8.3668E+00 -1.2305E+02 -6.0658E+04  5.4592E+04  4.8803E+04
19 -2.3137E+02  2.9518E+01 -9.1935E+01  4.3694E+04  4.6686E+04 -5.2443E+04
24  1.9349E+02  1.8160E+01  2.2130E+02 -7.1791E+04  1.9591E+05  4.9794E+04
23  2.4858E+02 -5.6045E+01  2.1869E+02  6.3463E+04  1.9404E+05 -4.6155E+04
ELE.NO.     16 FOR LOAD CASE     1
19 -1.6865E+02  1.5563E+01 -9.9117E+01 -2.7116E+04  2.1920E+04  2.7200E+04
20 -1.6440E+02  2.5971E+00 -9.3630E+01  2.8746E+04  2.4521E+04 -4.5374E+04
25  1.4624E+02 -1.1240E-06  1.4624E+02 -5.5416E+04  1.6204E+05  5.5416E+04
24  1.8681E+02 -1.8160E+01  1.5900E+02  5.9238E+04  1.6501E+05 -3.7241E+04
60. START CONCRETE DESIGN
FINITE ELEMENT MODEL OF TANK STRUCTURE                   -- PAGE NO.    5
CONCRETE DESIGN
61. CODE BS8007
PROGRAM CODE REVISION V1.0_8007_87/1
62. DESIGN SLAB 9 12
FINITE ELEMENT MODEL OF TANK STRUCTURE                   -- PAGE NO.    6
--------------------------------------------------------------------------
|  ELEMENT  DESIGN  TO  BS8007  AND  BS8110              ELEMENT NO.     9 |
|--------------------------------------------------------------------------|
|            A >                         e           f             g       |
|    l--------|---------k    Top___________________________________        |
|    |                  |      | o_______o_______o_______o_______o |       |
|    |        ! y       |      |        outer bars // to  x        | My    |
|    |        |         |      | o-------o-------o-------o-------o |       |
|    |       z+ --> x   |    Bot-----------------------------------        |
|    |                  |                 Section A-A                      |
|    |                  |                                                  |
|    i--------|---------j    Depth=200 mm  Width=1000 mm  Cover=20 mm      |
|            A >                                                           |
|--------------------------------------------------------------------------|
| Ultimate Limit State |  12 mm Bars    |  16 mm Bars     |  20 mm Bars    |
| Max.Momnt. kNm/m  Lo |C/C  AS R. AS P.|C/C  AS R.  AS P.|C/C  AS R. AS P.|
|----------------------|---|------|-----|---|------|------|---|------|-----|
| Mx Top =   0.0     0 |200|  259 | 565 |200|  259 | 1065 |200|  259 |1572 |
| Mx Bot = -24.5     1 |200|  367 | 565 |200|  372 | 1065 |200|  376 |1572 |
| My Top =  25.1     1 |200|  404 | 565 |200|  420 | 1065 |200|  437 |1572 |
| My Bot =   0.0     0 |200|  259 | 565 |200|  259 | 1065 |200|  259 |1572 |
--------------------------------------------------------------------------
--------------------------------------------------------------------------
|  SERVICEABILITY    LIMIT    STATE                     ELEMENT NO.     9  |
|--------------------------------------------------------------------------|
| Longitudinal  Moments  Mx   kNm/m  | Transverse    Moments   My   kNm/m  |
| Flexural      Crack    Width   mm  | Flexural      Crack     Width   mm  |
|------------------------------------|-------------------------------------|
| Top=  0.0  L.   0 Bot= -24.5 L.   1| Top= 25.1  L.   1 Bot=   0.0 L.   0 |
|------------------------------------|-------------------------------------|
| 12 | 16 | 20 |  @  | 12 | 16 |  20 | 12  | 16 | 20 |  @  | 12 | 16 | 20  |
|----|----|----|-----|----|----|-----|-----|----|----|-----|----|----|-----|
|0.00|0.00|0.00|  e  |0.08|0.04|0.03 | 0.17|0.12|0.12|  e  |0.00|0.00|0.00 |
|0.00|0.00|0.00|  f  |0.20|0.11|0.08 | 0.27|0.17|0.15|  f  |0.00|0.00|0.00 |
|0.00|0.00|0.00|  g  |0.10|0.06|0.05 | 0.13|0.08|0.08|  g  |0.00|0.00|0.00 |
|--------------------------------------------------------------------------|
|  Thermal   Crack   Width   Calculations  Based  On   Wmax=Smax*R*T1*Alfa |
|--------------------------------------------------------------------------|
| Surface Type : Suspended    Constuction type : 1     Temp. Range = 30 C  |
|--------------------------------------------------------------------------|
| Surface  Zones & ROWcrit | 8 mm bars |10 mm Bars |12 mm Bars |16 mm Bars |
| Top  : 100  mm  350  mm2 |-----------|-----------|-----------|-----------|
| Bot. : 100  mm  350  mm2 | Top | Bot.| Top | Bot.| Top | Bot.| Top | Bot.|
|--------------------------|-----|-----|-----|-----|-----|-----|-----|-----|
| Smax                  mm | 765 | 765 | 957 | 957 |1148 |1148 |1531 |1531 |
| Wmax                  mm |0.14 |0.14 |0.17 |0.17 |0.21 |0.21 |0.28 |0.28 |
| Sp. For  Wmax = 0.20  mm | 208 | 208 | 260 | 260 | 312 | 312 | 416 | 416 |
--------------------------------------------------------------------------
FINITE ELEMENT MODEL OF TANK STRUCTURE                   -- PAGE NO.    7
--------------------------------------------------------------------------
|  ELEMENT  DESIGN  TO  BS8007  AND  BS8110              ELEMENT NO.    12 |
|--------------------------------------------------------------------------|
|            A >                         e           f             g       |
|    l--------|---------k    Top___________________________________        |
|    |                  |      | o_______o_______o_______o_______o |       |
|    |        ! y       |      |        outer bars // to  x        | My    |
|    |        |         |      | o-------o-------o-------o-------o |       |
|    |       z+ --> x   |    Bot-----------------------------------        |
|    |                  |                 Section A-A                      |
|    |                  |                                                  |
|    i--------|---------j    Depth=200 mm  Width=1000 mm  Cover=20 mm      |
|            A >                                                           |
|--------------------------------------------------------------------------|
| Ultimate Limit State |  12 mm Bars    |  16 mm Bars     |  20 mm Bars    |
| Max.Momnt. kNm/m  Lo |C/C  AS R. AS P.|C/C  AS R.  AS P.|C/C  AS R. AS P.|
|----------------------|---|------|-----|---|------|------|---|------|-----|
| Mx Top =   0.0     0 |200|  259 | 565 |200|  259 | 1065 |200|  259 |1572 |
| Mx Bot =  -0.5     1 |200|  259 | 565 |200|  259 | 1065 |200|  259 |1572 |
| My Top =  90.1     1 |***| 1621 | 565 |100| 1712 | 2011 |150| 1816 |2094 |
| My Bot =   0.0     0 |200|  259 | 565 |200|  259 | 1065 |200|  259 |1572 |
--------------------------------------------------------------------------
--------------------------------------------------------------------------
|  SERVICEABILITY    LIMIT    STATE                     ELEMENT NO.    12  |
|--------------------------------------------------------------------------|
| Longitudinal  Moments  Mx   kNm/m  | Transverse    Moments   My   kNm/m  |
| Flexural      Crack    Width   mm  | Flexural      Crack     Width   mm  |
|------------------------------------|-------------------------------------|
| Top=  0.0  L.   0 Bot=  -0.5 L.   1| Top= 90.1  L.   1 Bot=   0.0 L.   0 |
|------------------------------------|-------------------------------------|
| 12 | 16 | 20 |  @  | 12 | 16 |  20 | 12  | 16 | 20 |  @  | 12 | 16 | 20  |
|----|----|----|-----|----|----|-----|-----|----|----|-----|----|----|-----|
|0.00|0.00|0.00|  e  |-.03|-.02|-.01 | 0.76|0.30|0.40|  e  |0.00|0.00|0.00 |
|0.00|0.00|0.00|  f  |-.08|-.04|-.02 | 1.75|0.32|0.44|  f  |0.00|0.00|0.00 |
|0.00|0.00|0.00|  g  |-.04|-.02|-.01 | 0.56|0.20|0.25|  g  |0.00|0.00|0.00 |
|--------------------------------------------------------------------------|
|  Thermal   Crack   Width   Calculations  Based  On   Wmax=Smax*R*T1*Alfa |
|--------------------------------------------------------------------------|
| Surface Type : Suspended    Constuction type : 1     Temp. Range = 30 C  |
|--------------------------------------------------------------------------|
| Surface  Zones & ROWcrit | 8 mm bars |10 mm Bars |12 mm Bars |16 mm Bars |
| Top  : 100  mm  350  mm2 |-----------|-----------|-----------|-----------|
| Bot. : 100  mm  350  mm2 | Top | Bot.| Top | Bot.| Top | Bot.| Top | Bot.|
|--------------------------|-----|-----|-----|-----|-----|-----|-----|-----|
| Smax                  mm | 765 | 765 | 957 | 957 |1148 |1148 |1531 |1531 |
| Wmax                  mm |0.14 |0.14 |0.17 |0.17 |0.21 |0.21 |0.28 |0.28 |
| Sp. For  Wmax = 0.20  mm | 208 | 208 | 260 | 260 | 312 | 312 | 416 | 416 |
--------------------------------------------------------------------------
***************************END OF ELEMENT DESIGN**************************
63. END CONCRETE DESIGN
64. FINISH
FINITE ELEMENT MODEL OF TANK STRUCTURE                   -- PAGE NO.    8
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= OCT 19,2021   TIME= 17:53:27 ****
************************************************************