# EX. UK-19 Inclined Supports

This example demonstrates the usage of inclined supports. The word INCLINED refers to the fact that the restraints at a joint where such a support is specified are along a user-specified axis system instead of along the default directions of the global axis system. STAAD.Pro offers a few different methods for assigning inclined supports, and we examine those in this example.

This problem is installed with the program by default to C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\Sample Models\UK\UK-19 Inclined Supports.STD when you install the program.

### Example Problem No. 19

Actual input is shown in bold lettering followed by explanation.

```    STAAD SPACE
INPUT WIDTH 79
```

Every input has to start with the term STAAD. The word SPACE signifies that the structure is a space frame structure (3-D) and the geometry is defined through X, Y, and Z coordinates.

```    UNIT METER KN
```

Defines the input units for the data that follows.

```    JOINT COORDINATES
1 0 5 0; 2 10 5 10; 3 20 5 20; 4 30 5 30; 5 5 0 5; 6 25 0 25;
```

Joint number followed by X, Y and Z coordinates are provided above.

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

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

```    UNIT MMS KN
MEMBER PROPERTY AMERICAN
4 5 PRIS YD 800
1 TO 3 PRIS YD 750 ZD 500
```

Properties for all members of the model are provided using the PRISMATIC option (abbreviated to PRIS here). YD and ZD stand for depth and width. If ZD is not provided, a circular shape with diameter = YD is assumed for that cross section. All properties required for the analysis, such as, Area, Moments of Inertia, etc. are calculated automatically from these dimensions unless these are explicitly defined. The values are provided in MMS unit.

```    DEFINE MATERIAL START
ISOTROPIC CONCRETE
E 21.72
POISSON 0.17
DENSITY 2.35615e-008
ALPHA 5e-006
DAMP 0.05
G 9.281
TYPE CONCRETE
STRENGTH FCU 0.0275
END DEFINE MATERIAL
CONSTANTS
MATERIAL CONCRETE ALL
```

Material constants like E (modulus of elasticity) and Poisson’s ratio are specified following the command CONSTANTS.

```    UNIT METER KN
SUPPORTS
5 INCLINED REF 10 5 10 FIXED BUT MX MY MZ KFX 30000
6 INCLINED REFJT 3 FIXED BUT MX MY MZ KFX 30000
1 PINNED
4 INCLINED 1 0 1 FIXED BUT FX MX MY MZ
```

We assign supports (restraints) at 4 nodes - 5, 6, 1 and 4. For 3 of those, namely, 5, 6 and 4, the node number is followed by the keyword INCLINED, signifying that an INCLINED support is defined there. For the remaining one - node 1 - that keyword is missing. Hence, the support at node 1 is a global direction support.

The most important aspect of inclined supports is their axis system. Each node where an inclined support is defined has its own distinct local X, local Y and local Z axes. In order to define the axis system, we first have to define a datum point. The support node and the datum point together help define the axis system.

Three different methods are shown in the above 3 instances for defining the datum point.

• At node 5, notice the keyword REF followed by the numbers (10,5,10). This means that the datum point associated with node 5 is one which has the global coordinates of (10m, 5m, 10m). Coincidentally, this happens to be node 2.
• At node 6, the keyword REFJT is used followed by the number 3. This means that the datum point for support node 6 is the joint number 3 of the model. The coordinates of the datum point are hence those of node 3, namely, (20m, 5m and 20m).
• At node 4, the word INCLINED is merely followed by 3 numbers (1,0,1). In the absence of the words REF and REFJT, the program sets the datum point to be the following. It takes the coordinates of node 4, which are (30m,5m,30m) and adds to them, the 3 numbers which comes after the word INCLINED. Thus, the datum point becomes (31m, 5m and 31m).

Once the datum point is established, the local axis system is defined as follows. Local X is a straight line (vector) pointing from the support node towards the datum point. Local Z is the vector obtained by the cross product of local X and the global Y axis (unless the SET Z UP command is used in which case one would use global Z instead of global Y and that would yield local Y). Local Y is the vector resulting from the cross product of local Z and local X. The right hand rule must be used when performing these cross products.

Notice the unique nature of these datum points. The one for node 5 tells us that a line connecting nodes 5 to 2 is the local X axis, and is hence along the axis of member 4. By defining a KFX spring at that one, we are saying that the lower end of member 4 can move along its axis like the piston of a car engine. Think of a pile bored into rock with a certain amount of freedom to expand and contract axially.

The same is true for the support at the bottom of member 5. The local X axis of that support is along the axis of member 5. That also happens to be the case for the supported end of member 3. The line going from node 4 to the datum point (31,5,31) happens to be coincident with the axis of the member, or the traffic direction. The expression FIXED BUT FX MX MY MZ for that support indicates that it is free to translate along local X, suggesting that it is an expansion joint - free to expand or contract along the axis of member 3.

Since MX, MY, and MZ are all released at these supports, no moment will be resisted by these supports.

```    LOAD 1 DEAD LOAD
SELFWEIGHT Y -1.2
1 TO 3 UNI GY -6
1 1.0 2 1.0
PERFORM ANALYSIS PRINT STATICS CHECK
```

Three load cases followed by the instruction for the type of analysis are specified. The PRINT STATICS CHECK option will instruct the program to produce a report consisting of total applied load versus total reactions from the supports for each primary load case.

```    PRINT SUPPORT REACTION
```

By default, support reactions are printed in the global axis directions. The above command is an instruction for such a report.

```    SET INCLINED REACTION
PRINT SUPPORT REACTION
```

Just earlier, we saw how to obtain support reactions in the global axis system. What if we need them in the inclined axis system? The SET INCLINED REACTION is a switch for that purpose. It tells the program that reactions should be reported in the inclined axis system instead of the global axis system. This has to be followed by the PRINT SUPPORT REACTIONS command.

```    PRINT MEMBER FORCES
PRINT JOINT DISP
FINISH
```

Member forces are reported in the local axis system of the members. Joint displacements at all joints are reported in the global axis system. Following this, the STAAD run is terminated.

## Input File

``````STAAD SPACE
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 5 0; 2 10 5 10; 3 20 5 20; 4 30 5 30; 5 5 0 5; 6 25 0 25;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 5 2; 5 6 3;
UNIT MMS KN
MEMBER PROPERTY AMERICAN
4 5 PRIS YD 800
1 TO 3 PRIS YD 750 ZD 500
DEFINE MATERIAL START
ISOTROPIC CONCRETE
E 21.0
POISSON 0.17
DENSITY 2.36158e-008
ALPHA 5e-006
DAMP 0.05
G 9.25
TYPE CONCRETE
STRENGTH FCU 0.0275
END DEFINE MATERIAL
CONSTANTS
MATERIAL CONCRETE ALL
UNIT METER KN
SUPPORTS
5 INC REF 10 5 10 FIXED BUT MX MY MZ KFX 30000
6 INC REFJT 3 FIXED BUT MX MY MZ KFX 30000
1 PINNED
4 INC 1 0 1 FIXED BUT FX MX MY MZ
SELFWEIGHT Y -1.2
1 TO 3 UNI GY -6
1 1.0 2 1.0
PERFORM ANALYSIS PRINT STATICS CHECK
PRINT SUPPORT REACTION
SET INCLINED REACTION
PRINT SUPPORT REACTION
PRINT MEMBER FORCES
PRINT JOINT DISP
FINISH
``````

```                                                                  PAGE NO.    1
****************************************************
*                                                  *
*           Version  22.04.00.**                   *
*           Proprietary Program of                 *
*           Bentley Systems, Inc.                  *
*           Date=    APR 21, 2020                  *
*           Time=    15:40:41                      *
*                                                  *
*  Licensed to: Bentley Systems Inc                *
****************************************************
INPUT FILE: UK-19 Inclined Supports.STD
2. INPUT WIDTH 79
3. UNIT METER KN
4. JOINT COORDINATES
5. 1 0 5 0; 2 10 5 10; 3 20 5 20; 4 30 5 30; 5 5 0 5; 6 25 0 25
6. MEMBER INCIDENCES
7. 1 1 2; 2 2 3; 3 3 4; 4 5 2; 5 6 3
8. UNIT MMS KN
9. MEMBER PROPERTY AMERICAN
10. 4 5 PRIS YD 800
11. 1 TO 3 PRIS YD 750 ZD 500
12. DEFINE MATERIAL START
13. ISOTROPIC CONCRETE
14. E 21.0
15. POISSON 0.17
16. DENSITY 2.36158E-008
17. ALPHA 5E-006
18. DAMP 0.05
19. G 9.25
20. TYPE CONCRETE
21. STRENGTH FCU 0.0275
22. END DEFINE MATERIAL
23. CONSTANTS
24. MATERIAL CONCRETE ALL
25. UNIT METER KN
26. SUPPORTS
27. 5 INC REF 10 5 10 FIXED BUT MX MY MZ KFX 30000
28. 6 INC REFJT 3 FIXED BUT MX MY MZ KFX 30000
29. 1 PINNED
30. 4 INC 1 0 1 FIXED BUT FX MX MY MZ
32. SELFWEIGHT Y -1.2
35. 1 TO 3 UNI GY -6
37. 1 1.0 2 1.0
38. PERFORM ANALYSIS PRINT STATICS CHECK
STAAD SPACE                                              -- PAGE NO.    2
P R O B L E M   S T A T I S T I C S
-----------------------------------
NUMBER OF JOINTS          6  NUMBER OF MEMBERS       5
NUMBER OF PLATES          0  NUMBER OF SOLIDS        0
NUMBER OF SURFACES        0  NUMBER OF SUPPORTS      4
Using 64-bit analysis engine.
SOLVER USED IS THE IN-CORE ADVANCED MATH SOLVER
TOTAL      PRIMARY LOAD CASES =     2, TOTAL DEGREES OF FREEDOM =      27
TOTAL LOAD COMBINATION  CASES =     1  SO FAR.
STAAD SPACE                                              -- PAGE NO.    3
STATIC LOAD/REACTION/EQUILIBRIUM SUMMARY FOR CASE NO.     1
CENTER OF FORCE BASED ON Y FORCES ONLY (METE).
(FORCES IN NON-GLOBAL DIRECTIONS WILL INVALIDATE RESULTS)
X =  0.150000000E+02
Y =  0.411580006E+01
Z =  0.150000000E+02
SUMMATION FORCE-X =           0.00
SUMMATION FORCE-Y =        -697.60
SUMMATION FORCE-Z =           0.00
SUMMATION OF MOMENTS AROUND THE ORIGIN-
MX=       10463.94  MY=           0.00  MZ=      -10463.94
SUMMATION FORCE-X =          -0.00
SUMMATION FORCE-Y =         697.60
SUMMATION FORCE-Z =          -0.00
SUMMATION OF MOMENTS AROUND THE ORIGIN-
MX=      -10463.94  MY=          -0.00  MZ=       10463.94
MAXIMUMS    AT NODE
X = -8.02030E-01       5
Y = -2.50768E+00       3
Z = -8.02030E-01       5
RX= -2.71938E-03       4
RY=  8.02194E-18       1
RZ=  2.71938E-03       4
STATIC LOAD/REACTION/EQUILIBRIUM SUMMARY FOR CASE NO.     2
CENTER OF FORCE BASED ON Y FORCES ONLY (METE).
(FORCES IN NON-GLOBAL DIRECTIONS WILL INVALIDATE RESULTS)
X =  0.149999999E+02
Y =  0.500000017E+01
Z =  0.149999999E+02
STAAD SPACE                                              -- PAGE NO.    4
SUMMATION FORCE-X =           0.00
SUMMATION FORCE-Y =        -254.56
SUMMATION FORCE-Z =           0.00
SUMMATION OF MOMENTS AROUND THE ORIGIN-
MX=        3818.38  MY=           0.00  MZ=       -3818.38
SUMMATION FORCE-X =          -0.00
SUMMATION FORCE-Y =         254.56
SUMMATION FORCE-Z =          -0.00
SUMMATION OF MOMENTS AROUND THE ORIGIN-
MX=       -3818.38  MY=          -0.00  MZ=        3818.38
MAXIMUMS    AT NODE
X = -2.97766E-01       5
Y = -9.34280E-01       3
Z = -2.97766E-01       5
RX= -1.21481E-03       4
RY= -3.94177E-18       4
RZ=  1.21481E-03       4
************ END OF DATA FROM INTERNAL STORAGE ************
39. PRINT SUPPORT REACTION
SUPPORT  REACTION
STAAD SPACE                                              -- PAGE NO.    5
SUPPORT REACTIONS -UNIT KN   METE    STRUCTURE TYPE = SPACE
-----------------
JOINT  LOAD   FORCE-X   FORCE-Y   FORCE-Z     MOM-X     MOM-Y     MOM Z
5    1    216.27    289.28    216.27      0.00      0.00      0.00
2     86.61     94.78     86.61      0.00      0.00      0.00
3    302.88    384.06    302.88      0.00      0.00      0.00
6    1   -213.07    287.50   -213.07      0.00      0.00      0.00
2    -85.33     94.06    -85.33      0.00      0.00      0.00
3   -298.40    381.56   -298.40      0.00      0.00      0.00
1    1     -3.20     60.34     -3.20      0.00      0.00      0.00
2     -1.28     32.84     -1.28      0.00      0.00      0.00
3     -4.48     93.18     -4.48      0.00      0.00      0.00
4    1      0.00     60.47      0.00      0.00      0.00      0.00
2      0.00     32.89      0.00      0.00      0.00      0.00
3      0.00     93.36      0.00      0.00      0.00      0.00
************** END OF LATEST ANALYSIS RESULT **************
40. SET INCLINED REACTION
41. PRINT SUPPORT REACTION
SUPPORT  REACTION
STAAD SPACE                                              -- PAGE NO.    6
SUPPORT REACTIONS -UNIT KN   METE    STRUCTURE TYPE = SPACE
-----------------
JOINT  LOAD   FORCE-X   FORCE-Y   FORCE-Z     MOM-X     MOM-Y     MOM Z
5    1    416.75     59.61      0.00      0.00      0.00      0.00
2    154.72      6.67      0.00      0.00      0.00      0.00
3    571.47     66.28      0.00      0.00      0.00      0.00
6    1    412.02     60.77      0.00      0.00      0.00      0.00
2    152.83      7.13      0.00      0.00      0.00      0.00
3    564.85     67.90      0.00      0.00      0.00      0.00
1    1     -3.20     60.34     -3.20      0.00      0.00      0.00
2     -1.28     32.84     -1.28      0.00      0.00      0.00
3     -4.48     93.18     -4.48      0.00      0.00      0.00
4    1      0.00     60.47      0.00      0.00      0.00      0.00
2      0.00     32.89      0.00      0.00      0.00      0.00
3      0.00     93.36      0.00      0.00      0.00      0.00
************** END OF LATEST ANALYSIS RESULT **************
42. PRINT MEMBER FORCES
MEMBER   FORCES
STAAD SPACE                                              -- PAGE NO.    7
MEMBER END FORCES    STRUCTURE TYPE = SPACE
-----------------
ALL UNITS ARE -- KN   METE     (LOCAL )
MEMBER  LOAD  JT     AXIAL   SHEAR-Y  SHEAR-Z   TORSION     MOM-Y      MOM-Z
1    1     1     -4.52     60.34     0.00      0.00     -0.00      -0.00
2      4.52     89.95    -0.00      0.00     -0.00    -209.31
2     1     -1.81     32.84     0.00     -0.00     -0.00       0.00
2      1.81     52.02    -0.00      0.00     -0.00    -135.62
3     1     -6.33     93.18     0.00     -0.00     -0.00      -0.00
2      6.33    141.96    -0.00      0.00     -0.00    -344.93
2    1     2    301.33     75.98    -0.00      0.00      0.00     129.19
3   -301.33     74.31     0.00     -0.00     -0.00    -117.44
2     2    120.67     42.76    -0.00      0.00      0.00      77.86
3   -120.67     42.09     0.00     -0.00     -0.00     -73.16
3     2    422.00    118.73    -0.00      0.00      0.00     207.05
3   -422.00    116.41     0.00     -0.00     -0.00    -190.59
3    1     3      0.00     89.82    -0.00      0.00      0.00     207.54
4      0.00     60.47     0.00      0.00      0.00       0.00
2     3      0.00     51.97    -0.00     -0.00      0.00     134.91
4     -0.00     32.89     0.00      0.00      0.00       0.00
3     3      0.00    141.79    -0.00     -0.00      0.00     342.45
4     -0.00     93.36     0.00      0.00      0.00       0.00
4    1     5    416.75     59.61     0.00     -0.00      0.00      -0.00
2   -345.52     41.11    -0.00      0.00     -0.00      80.12
2     5    154.72      6.67     0.00      0.00      0.00       0.00
2   -154.72     -6.67    -0.00      0.00      0.00      57.76
3     5    571.47     66.28     0.00     -0.00      0.00       0.00
2   -500.25     34.44    -0.00      0.00     -0.00     137.88
5    1     6    412.02     60.77     0.00     -0.00     -0.00      -0.00
3   -340.80     39.96    -0.00      0.00     -0.00      90.10
2     6    152.83      7.13     0.00     -0.00     -0.00       0.00
3   -152.83     -7.13    -0.00      0.00     -0.00      61.75
3     6    564.85     67.90     0.00     -0.00     -0.00       0.00
3   -493.63     32.83    -0.00      0.00     -0.00     151.86
************** END OF LATEST ANALYSIS RESULT **************
43. PRINT JOINT DISP
STAAD SPACE                                              -- PAGE NO.    8
JOINT    DISP
STAAD SPACE                                              -- PAGE NO.    9
JOINT DISPLACEMENT (CM   RADIANS)    STRUCTURE TYPE = SPACE
------------------
JOINT  LOAD   X-TRANS   Y-TRANS   Z-TRANS   X-ROTAN   Y-ROTAN   Z-ROTAN
1    1     0.0000    0.0000    0.0000    0.0027    0.0000   -0.0027
2     0.0000    0.0000    0.0000    0.0012    0.0000   -0.0012
3     0.0000    0.0000    0.0000    0.0039    0.0000   -0.0039
2    1     0.0006   -2.4614    0.0006    0.0007    0.0000   -0.0007
2     0.0002   -0.9157    0.0002    0.0003    0.0000   -0.0003
3     0.0008   -3.3771    0.0008    0.0011    0.0000   -0.0011
3    1    -0.0377   -2.5077   -0.0377   -0.0007    0.0000    0.0007
2    -0.0151   -0.9343   -0.0151   -0.0003    0.0000    0.0003
3    -0.0528   -3.4420   -0.0528   -0.0011    0.0000    0.0011
4    1    -0.0377    0.0000   -0.0377   -0.0027    0.0000    0.0027
2    -0.0151    0.0000   -0.0151   -0.0012    0.0000    0.0012
3    -0.0528    0.0000   -0.0528   -0.0039    0.0000    0.0039
5    1    -0.8020   -0.8020   -0.8020    0.0024    0.0000   -0.0024
2    -0.2978   -0.2978   -0.2978    0.0007    0.0000   -0.0007
3    -1.0998   -1.0998   -1.0998    0.0031    0.0000   -0.0031
6    1     0.7929   -0.7929    0.7929   -0.0024    0.0000    0.0024
2     0.2941   -0.2941    0.2941   -0.0008    0.0000    0.0008
3     1.0871   -1.0871    1.0871   -0.0032    0.0000    0.0032
************** END OF LATEST ANALYSIS RESULT **************
44. FINISH
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= APR 21,2020   TIME= 15:40:42 ****
STAAD SPACE                                              -- PAGE NO.   10
************************************************************