# EX. UK-3 Soil Springs for Portal Frame

A portal frame type steel structure is sitting on concrete footings. The soil is to be considered as an elastic foundation. The value of soil subgrade reaction is known from which spring constants are calculated by multiplying the subgrade reaction by the tributary area of each modeled spring.

This problem is installed with the program by default to C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\Sample Models\UK\UK-3 Soil Springs for Portal Frame.STD when you install the program.

### Example Problem No. 3

Where:

• B = 6 m, H = 3 m, F1 = 1.2 m, F2 = 2.4 m
• P = 20 KN, w = 4.5 KN/m
• Soil Subgrade Reaction = 41,666.67 KN/m3
Table 1. Spring constant calculation
Springs of Joints Spring Constant

1, 5, 10, & 14 (Edges)

2.4 x 0.3 x 41,666.67

= 30,000 KN/m

2, 3, 4, 11, 12, & 13 (Interior)

2.4 x 0.6 x 41,666.67

= 60,000 KN/m

Actual input is shown in bold lettering followed by explanation.

`    STAAD PLANE PORTAL ON FOOTING FOUNDATION`

Every input has to start with the term STAAD. The term PLANE signifies that the structure is a plane frame structure and the geometry is defined through X and Y axes.

`    UNIT METER KNS`

Defines the input units for the data that follows.

```    JOINT COORDINATES
1 0.0 0.0 0.0 5 2.4 0.0 0.0
6 1.2 3.0 0.0 ; 7 1.2 6.0 0.0
8 7.2 6.0 0.0 ; 9 7.2 3.0 0.0
10 6.0 0.0 0.0 14 8.4 0.0 0.0```

Joint number followed by X, Y and Z coordinates are provided above. Since this is a plane structure, the Z coordinates are given as all zeros.

Note: Semicolons (;) are used as line separators to allow for input of multiple sets of data on one line.
```    MEMBER INCIDENCES
1 1 2 4
5 3 6 ; 6 6 7
7 7 8 ; 8 6 9
9 8 9 ; 10 9 12
11 10 11 14```

Defines the members by the joints to which they are connected.

```    MEMBER PROPERTIES BRITISH
1 4 11 14 PRIS YD 0.30 ZD 2.40
2 3 12 13 PRIS YD 0.60 ZD  2.40
5 6 9 10 TABLE ST JO254X203
7 8 TA ST UB305X165X40```

The first two lines define member properties as prismatic (PRIS) followed by depth (YD) and width (ZD) values. The program will calculate the properties necessary to perform the analysis. See G.6.1 Prismatic Properties for additional information. Member properties for the remaining members are chosen from the British steel table. The term ST stands for standard single section.

```    UNIT MMS
* E FOR STEEL IS 210 (KN/sq.mm.) AND FOR CONCRETE 21 (KN/sq.mm.)
DEFINE MATERIAL START
ISOTROPIC STEEL
E 210
POISSON 0.3
DENSITY 76.977e-009
ALPHA 6e-006
DAMP 0.03
TYPE STEEL
STRENGTH FY 0.24821 FU 0.399894 RY 1.5 RT 1.2
ISOTROPIC CONCRETE
E 21
POISSON 0.17
DENSITY 23.534e-009
ALPHA 5e-006
DAMP 0.05
G 9.25
TYPE CONCRETE
STRENGTH FCU 0.0275
END DEFINE MATERIAL
CONSTANTS
MATERIAL CONCRETE MEMB 1 TO 4 11 TO 14
MATERIAL STEEL MEMB 5 TO 10```

The CONSTANT command initiates input for material constants like modulus of elasticity, Density, and Poisson's ratio. The length unit is changed from METER to MM to facilitate the input in familiar units.

Note: Any line beginning with anĀ asterisk (* character) is treated as a comment line.
```    SUPPORTS
2 TO 4 11 TO 13 FIXED BUT MZ KFY 60
1 5 10 14 FIXED BUT MZ KFY 30```

The supports for the structure are specified above. The first set of joints are supports restrained in all directions except global moment-z (MZ). Also, a spring having a spring constant of 60 KN/mm is provided in the global Y direction at these nodes. The second set is similar to the former except for a different value of the spring constant.

`    UNIT METER`
` LOADING 1 DEAD AND WIND LOAD COMBINED`

Load case 1 is initiated followed by a title.

` SELF Y -1.0`

The selfweight of the structure is specified as acting in the global Y direction with a -1.0 factor.

Since global Y is vertically upwards, the -1.0 factor indicates that this load will act downwards.

```    JOINT LOAD
6 7 FX 20.0```

Load 1 contains joint loads also. FX indicates that the load is a force in the global X direction.

```    MEMBER LOAD
7 8 UNI GY -45.0```

Load 1 contains member loads also. GY indicates that the load acts in the global Y direction. The term UNI stands for uniformly distributed load, and is applied on members 7 and 8, acting downwards.

`    PERFORM ANALYSIS `

This command instructs the program to proceed with the analysis.

`    PRINT ANALYSIS RESULTS`

The above PRINT command instructs the program to print analysis results which include joint displacements, member forces and support reactions.

`    FINISH`

This command terminates the STAAD run.

## Input File

``````STAAD PLANE PORTAL ON FOOTING FOUNDATION
UNIT METER KNS
JOINT COORDINATES
1 0.0 0.0 0.0 5 2.4 0.0 0.0
6 1.2 3.0 0.0 ; 7 1.2 6.0 0.0
8 7.2 6.0 0.0 ; 9 7.2 3.0 0.0
10 6.0 0.0 0.0 14 8.4 0.0 0.0
MEMBER INCIDENCES
1 1 2 4
5 3 6 ; 6 6 7
7 7 8 ; 8 6 9
9 8 9 ; 10 9 12
11 10 11 14
MEMBER PROPERTIES BRITISH
1 4 11 14 PRIS YD 0.30 ZD 2.40
2 3 12 13 PRIS YD 0.60 ZD 2.40
5 6 9 10 TABLE ST JO254X203
7 8 TA ST UB305X165X40
UNIT MMS
* E FOR STEEL IS 210 (KN/sq.mm.) AND FOR CONCRETE 21 (KN/sq.mm.)
DEFINE MATERIAL START
ISOTROPIC STEEL
E 210
POISSON 0.3
DENSITY 76.977e-009
ALPHA 6e-006
DAMP 0.03
TYPE STEEL
STRENGTH FY 0.24821 FU 0.399894 RY 1.5 RT 1.2
ISOTROPIC CONCRETE
E 21
POISSON 0.17
DENSITY 23.534e-009
ALPHA 5e-006
DAMP 0.05
G 9.25
TYPE CONCRETE
STRENGTH FCU 0.0275
END DEFINE MATERIAL
CONSTANTS
MATERIAL CONCRETE MEMB 1 TO 4 11 TO 14
MATERIAL STEEL MEMB 5 TO 10
SUPPORTS
2 TO 4 11 TO 13 FIXED BUT MZ KFY 60
1 5 10 14 FIXED BUT MZ KFY 30
UNIT METER
SELF Y -1.0
6 7 FX 20.0
7 8 UNI GY -45.0
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
FINISH
``````

```                                                                  PAGE NO.    1
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*                                                  *
*           Version  22.04.00.**                   *
*           Proprietary Program of                 *
*           Bentley Systems, Inc.                  *
*           Date=    APR 21, 2020                  *
*           Time=    15:41:14                      *
*                                                  *
*  Licensed to: Bentley Systems Inc                *
****************************************************
1. STAAD PLANE PORTAL ON FOOTING FOUNDATION
INPUT FILE: UK-3 Soil Springs for Portal Frame.STD
2. UNIT METER KNS
3. JOINT COORDINATES
4. 1 0.0 0.0 0.0 5 2.4 0.0 0.0
5. 6 1.2 3.0 0.0 ; 7 1.2 6.0 0.0
6. 8 7.2 6.0 0.0 ; 9 7.2 3.0 0.0
7. 10 6.0 0.0 0.0 14 8.4 0.0 0.0
8. MEMBER INCIDENCES
9. 1 1 2 4
10. 5 3 6 ; 6 6 7
11. 7 7 8 ; 8 6 9
12. 9 8 9 ; 10 9 12
13. 11 10 11 14
14. MEMBER PROPERTIES BRITISH
15. 1 4 11 14 PRIS YD 0.30 ZD 2.40
16. 2 3 12 13 PRIS YD 0.60 ZD 2.40
17. 5 6 9 10 TABLE ST JO254X203
18. 7 8 TA ST UB305X165X40
19. UNIT MMS
20. * E FOR STEEL IS 210 (KN/SQ.MM.) AND FOR CONCRETE 21 (KN/SQ.MM.)
21. DEFINE MATERIAL START
22. ISOTROPIC STEEL
23. E 210
24. POISSON 0.3
25. DENSITY 76.977E-009
26. ALPHA 6E-006
27. DAMP 0.03
28. TYPE STEEL
29. STRENGTH FY 0.24821 FU 0.399894 RY 1.5 RT 1.2
30. ISOTROPIC CONCRETE
31. E 21
32. POISSON 0.17
33. DENSITY 23.534E-009
34. ALPHA 5E-006
35. DAMP 0.05
36. G 9.25
37. TYPE CONCRETE
38. STRENGTH FCU 0.0275
PORTAL ON FOOTING FOUNDATION                             -- PAGE NO.    2
39. END DEFINE MATERIAL
40. CONSTANTS
41. MATERIAL CONCRETE MEMB 1 TO 4 11 TO 14
42. MATERIAL STEEL MEMB 5 TO 10
43. SUPPORTS
44. 2 TO 4 11 TO 13 FIXED BUT MZ KFY 60
45. 1 5 10 14 FIXED BUT MZ KFY 30
46. UNIT METER
48. SELF Y -1.0
50. 6 7 FX 20.0
52. 7 8 UNI GY -45.0
53. PERFORM ANALYSIS
P R O B L E M   S T A T I S T I C S
-----------------------------------
NUMBER OF JOINTS         14  NUMBER OF MEMBERS      14
NUMBER OF PLATES          0  NUMBER OF SOLIDS        0
NUMBER OF SURFACES        0  NUMBER OF SUPPORTS     10
Using 64-bit analysis engine.
SOLVER USED IS THE IN-CORE ADVANCED MATH SOLVER
TOTAL      PRIMARY LOAD CASES =     1, TOTAL DEGREES OF FREEDOM =      32
TOTAL LOAD COMBINATION  CASES =     0  SO FAR.
54. PRINT ANALYSIS RESULTS
ANALYSIS RESULTS
PORTAL ON FOOTING FOUNDATION                             -- PAGE NO.    3
JOINT DISPLACEMENT (CM   RADIANS)    STRUCTURE TYPE = PLANE
------------------
JOINT  LOAD   X-TRANS   Y-TRANS   Z-TRANS   X-ROTAN   Y-ROTAN   Z-ROTAN
1    1     0.0000   -0.1075    0.0000    0.0000    0.0000   -0.0003
2    1     0.0000   -0.1232    0.0000    0.0000    0.0000   -0.0002
3    1     0.0000   -0.1367    0.0000    0.0000    0.0000   -0.0002
4    1     0.0000   -0.1466    0.0000    0.0000    0.0000   -0.0002
5    1     0.0000   -0.1531    0.0000    0.0000    0.0000   -0.0001
6    1     0.5036   -0.1720    0.0000    0.0000    0.0000   -0.0032
7    1     1.0714   -0.1898    0.0000    0.0000    0.0000   -0.0045
8    1     1.0286   -0.2097    0.0000    0.0000    0.0000    0.0022
9    1     0.5240   -0.1901    0.0000    0.0000    0.0000   -0.0003
10    1     0.0000   -0.0897    0.0000    0.0000    0.0000   -0.0005
11    1     0.0000   -0.1210    0.0000    0.0000    0.0000   -0.0005
12    1     0.0000   -0.1504    0.0000    0.0000    0.0000   -0.0005
13    1     0.0000   -0.1759    0.0000    0.0000    0.0000   -0.0004
14    1     0.0000   -0.1969    0.0000    0.0000    0.0000   -0.0003
PORTAL ON FOOTING FOUNDATION                             -- PAGE NO.    4
SUPPORT REACTIONS -UNIT KNS  METE    STRUCTURE TYPE = PLANE
-----------------
JOINT  LOAD   FORCE-X   FORCE-Y   FORCE-Z     MOM-X     MOM-Y     MOM Z
2    1      0.00     73.95      0.00      0.00      0.00      0.00
3    1      0.09     82.00      0.00      0.00      0.00      0.00
4    1      0.00     87.96      0.00      0.00      0.00      0.00
11    1      0.00     72.58      0.00      0.00      0.00      0.00
12    1    -40.09     90.24      0.00      0.00      0.00      0.00
13    1      0.00    105.56      0.00      0.00      0.00      0.00
1    1      0.00     32.25      0.00      0.00      0.00      0.00
5    1      0.00     45.92      0.00      0.00      0.00      0.00
10    1      0.00     26.90      0.00      0.00      0.00      0.00
14    1      0.00     59.07      0.00      0.00      0.00      0.00
PORTAL ON FOOTING FOUNDATION                             -- PAGE NO.    5
MEMBER END FORCES    STRUCTURE TYPE = PLANE
-----------------
ALL UNITS ARE -- KNS  METE     (LOCAL )
MEMBER  LOAD  JT     AXIAL   SHEAR-Y  SHEAR-Z   TORSION     MOM-Y      MOM-Z
1    1     1      0.00     32.25     0.00      0.00      0.00       0.00
2      0.00    -22.08     0.00      0.00      0.00      16.30
2    1     2      0.00     96.03     0.00      0.00      0.00     -16.30
3      0.00    -75.70     0.00      0.00      0.00      67.82
3    1     3      0.00   -103.39     0.00      0.00      0.00     -92.63
4      0.00    123.72     0.00      0.00      0.00      24.50
4    1     4      0.00    -35.76     0.00      0.00      0.00     -24.50
5      0.00     45.92     0.00      0.00      0.00       0.00
5    1     3    261.09     -0.09     0.00      0.00      0.00      24.82
6   -258.66      0.09     0.00      0.00      0.00     -25.09
6    1     6    132.10    -56.74     0.00      0.00      0.00     -73.59
7   -129.67     56.74     0.00      0.00      0.00     -96.64
7    1     7     76.74    129.67     0.00      0.00      0.00      96.64
8    -76.74    142.70     0.00      0.00      0.00    -135.72
8    1     6    -36.65    126.57     0.00      0.00      0.00      98.68
9     36.65    145.80     0.00      0.00      0.00    -156.40
9    1     8    142.70     76.74     0.00      0.00      0.00     135.72
9   -145.12    -76.74     0.00      0.00      0.00      94.51
10    1     9    290.93     40.09     0.00      0.00      0.00      61.89
12   -293.35    -40.09     0.00      0.00      0.00      58.38
11    1    10      0.00     26.90     0.00      0.00      0.00      -0.00
11      0.00    -16.74     0.00      0.00      0.00      13.09
12    1    11      0.00     89.32     0.00      0.00      0.00     -13.09
12      0.00    -68.99     0.00      0.00      0.00      60.58
13    1    12      0.00   -134.13     0.00      0.00      0.00    -118.97
13      0.00    154.46     0.00      0.00      0.00      32.39
14    1    13      0.00    -48.90     0.00      0.00      0.00     -32.39
14      0.00     59.07     0.00      0.00      0.00       0.00
PORTAL ON FOOTING FOUNDATION                             -- PAGE NO.    6
************** END OF LATEST ANALYSIS RESULT **************
55. FINISH
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= APR 21,2020   TIME= 15:41:15 ****
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