# EX. UK-13 Section Displacements for a Frame

Calculation of displacements at intermediate points of members of a plane frame is demonstrated 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-13 Section Displacements for a Frame.STD when you install the program.

### Example Problem No. 13

Where:

• L1 = 4.5 m, L2 = 6.0 m
• P = 25 kN
• w = 45 kN/m

The dashed line represents the deflected shape of the structure. The shape is generated on the basis of displacements at the ends plus several intermediate points of the members.

Actual input is shown in bold lettering followed by explanation.

```    STAAD PLANE TEST FOR SECTION DISPLACEMENT
```

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 ; 2 0. 4.5 ; 3 6 4.5 ; 4 6 0.
```

Joint number followed by X and Y coordinates are provided above. Since this is a plane structure, the Z coordinates need not be provided.

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

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

```    MEMBER PROPERTY BRITISH
1 3 TABLE ST UC203X203X46
2 TABLE ST UB305X165X40
```

Member properties are specified from the British steel table. The word ST stands for standard single section.

```    UNIT MMS
DEFINE MATERIAL START
ISOTROPIC STEEL
E 210
POISSON 0.3
DENSITY 7.6977e-008
ALPHA 6e-006
DAMP 0.03
TYPE STEEL
STRENGTH FY 0.25 FU 0.4 RY 1.5 RT 1.2
END DEFINE MATERIAL
CONSTANTS
MATERIAL STEEL ALL
```

The length unit is changed from METER to MMS. The DEFINE MATERIAL command is used to specify material properties and the CONSTANT is used to assign the material to all members.

```    SUPPORT
1 FIXED ; 4 PINNED
```

A fixed support is specified at Joint 1 and a pinned support at Joint 4.

```    UNIT METER
```

Load case 1 is initiated followed by an optional title.

```    JOINT LOAD
2 FX 25.0
```

Load 1 contains a joint load of 25KN at node 2. FX indicates that the load is a force in the global X direction.

```    MEMBER LOAD
2 UNI GY -45.0
```

Load 1 contains a member load also. GY indicates that the load is in the global Y direction. The word UNI stands for uniformly distributed load.

```    PERFORM ANALYSIS
```

This command instructs the program to proceed with the analysis.

```    PRINT MEMBER FORCES
```

The above PRINT command is self-explanatory.

```    *
* FOLLOWING PRINT COMMAND WILL PRINT
* DISPLACEMENTS OF THE MEMBERS
* CONSIDERING EVERY TWELFTH INTERMEDIATE
* POINT (THAT IS TOTAL OF 13 POINTS). THESE
* DISPLACEMENTS ARE MEASURED IN GLOBAL X
* Y Z COORDINATE SYSTEM AND THE VALUES
* ARE FROM ORIGINAL COORDINATES (UNDEFLECTED
* POSITION) OF CORRESPONDING TWELFTH
* POINTS.
*
* MAX LOCAL DISPLACEMENT IS ALSO PRINTED.
* THE LOCATION OF MAXIMUM INTERMEDIATE
* DISPLACEMENT IS DETERMINED. THIS VALUE IS
* MEASURED FROM ABOVE LOCATION TO THE
* STRAIGHT LINE JOINING START AND END
* JOINTS OF THE DEFLECTED MEMBER.
*
PRINT SECTION DISPLACEMENT
```

Above PRINT command is explained in the comment lines above.

```    FINISH
```

This command terminates the STAAD run.

## Input File

``````STAAD PLANE TEST FOR SECTION DISPLACEMENT
UNIT METER KNS
JOINT COORDINATES
1 0.0 0.0 ; 2 0.0 4.5 ; 3 6.0 4.5 ; 4 6.0 0.0
MEMBER INCIDENCE
1 1 2 ; 2 2 3 ; 3 3 4
MEMBER PROPERTY BRITISH
1 3 TABLE ST UC203X203X46
2 TABLE ST UB305X165X40
UNIT MMS
DEFINE MATERIAL START
ISOTROPIC STEEL
E 210.0
POISSON 0.3
DENSITY 7.6977e-008
ALPHA 6e-006
DAMP 0.03
TYPE STEEL
STRENGTH FY 0.25 FU 0.4 RY 1.5 RT 1.2
END DEFINE MATERIAL
CONSTANTS
MATERIAL STEEL ALL
SUPPORT
1 FIXED ; 4 PINNED
UNIT METER
2 FX 25.0
2 UNI GY -45.0
PERFORM ANALYSIS
PRINT MEMBER FORCES
*
* FOLLOWING PRINT COMMAND WILL PRINT
* DISPLACEMENTS OF THE MEMBERS CONSIDERING EVERY
* TWELFTH INTERMEDIATE POINT (THAT IS TOTAL OF 13 POINTS).
* THESE DISPLACEMENTS ARE MEASURED IN GLOBAL X Y Z
* COORDINATE SYSTEM AND THE VALUES ARE FROM
* ORIGINAL COORDINATES (UNDEFLECTED POSITION)
* OF THE CORRESPONDING TWELFTH POINTS.
*
* MAX LOCAL DISPLACEMENT IS ALSO PRINTED. THE
* LOCATION OF MAXIMUM INTERMEDIATE DISPLACEMENT
* IS DETERMINED. THIS VALUE IS MEASURED FROM ABOVE
* LOCATION TO THE STRAIGHT LINE JOINING START AND
* END JOINTS OF THE DEFLECTED MEMBER.
*
PRINT SECTION DISPLACEMENT
FINISH
``````

```                                                                  PAGE NO.    1
****************************************************
*                                                  *
*           Version  22.08.00.***                  *
*           Proprietary Program of                 *
*           Bentley Systems, Inc.                  *
*           Date=    OCT 19, 2021                  *
*           Time=    17:53:34                      *
*                                                  *
*  Licensed to: Bentley Systems Inc                *
****************************************************
1. STAAD PLANE TEST FOR SECTION DISPLACEMENT
INPUT FILE: UK-13 Section Displacements for a Frame.STD
2. UNIT METER KNS
3. JOINT COORDINATES
4. 1 0.0 0.0 ; 2 0.0 4.5 ; 3 6.0 4.5 ; 4 6.0 0.0
5. MEMBER INCIDENCE
6. 1 1 2 ; 2 2 3 ; 3 3 4
7. MEMBER PROPERTY BRITISH
8. 1 3 TABLE ST UC203X203X46
9. 2 TABLE ST UB305X165X40
10. UNIT MMS
11. DEFINE MATERIAL START
12. ISOTROPIC STEEL
13. E 210.0
14. POISSON 0.3
15. DENSITY 7.6977E-008
16. ALPHA 6E-006
17. DAMP 0.03
18. TYPE STEEL
19. STRENGTH FY 0.25 FU 0.4 RY 1.5 RT 1.2
20. END DEFINE MATERIAL
21. CONSTANTS
22. MATERIAL STEEL ALL
23. SUPPORT
24. 1 FIXED ; 4 PINNED
25. UNIT METER
28. 2 FX 25.0
30. 2 UNI GY -45.0
31. PERFORM ANALYSIS
TEST FOR SECTION DISPLACEMENT                            -- PAGE NO.    2
P R O B L E M   S T A T I S T I C S
-----------------------------------
NUMBER OF JOINTS          4  NUMBER OF MEMBERS       3
NUMBER OF PLATES          0  NUMBER OF SOLIDS        0
NUMBER OF SURFACES        0  NUMBER OF SUPPORTS      2
Using 64-bit analysis engine.
SOLVER USED IS THE IN-CORE ADVANCED MATH SOLVER
TOTAL      PRIMARY LOAD CASES =     1, TOTAL DEGREES OF FREEDOM =       7
TOTAL LOAD COMBINATION  CASES =     0  SO FAR.
32. PRINT MEMBER FORCES
MEMBER   FORCES
TEST FOR SECTION DISPLACEMENT                            -- PAGE NO.    3
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    121.84      1.65     0.00      0.00      0.00      33.54
2   -121.84     -1.65     0.00      0.00      0.00     -26.10
2    1     2     23.35    121.84     0.00      0.00      0.00      26.10
3    -23.35    148.16     0.00      0.00      0.00    -105.06
3    1     3    148.16     23.35     0.00      0.00      0.00     105.06
4   -148.16    -23.35     0.00      0.00      0.00      -0.00
************** END OF LATEST ANALYSIS RESULT **************
33. *
34. * FOLLOWING PRINT COMMAND WILL PRINT
35. * DISPLACEMENTS OF THE MEMBERS CONSIDERING EVERY
36. * TWELFTH INTERMEDIATE POINT (THAT IS TOTAL OF 13 POINTS).
37. * THESE DISPLACEMENTS ARE MEASURED IN GLOBAL X Y Z
38. * COORDINATE SYSTEM AND THE VALUES ARE FROM
39. * ORIGINAL COORDINATES (UNDEFLECTED POSITION)
40. * OF THE CORRESPONDING TWELFTH POINTS.
41. *
42. * MAX LOCAL DISPLACEMENT IS ALSO PRINTED. THE
43. * LOCATION OF MAXIMUM INTERMEDIATE DISPLACEMENT
44. * IS DETERMINED. THIS VALUE IS MEASURED FROM ABOVE
45. * LOCATION TO THE STRAIGHT LINE JOINING START AND
46. * END JOINTS OF THE DEFLECTED MEMBER.
47. *
48. PRINT SECTION DISPLACEMENT
SECTION  DISPLACE
TEST FOR SECTION DISPLACEMENT                            -- PAGE NO.    4
MEMBER SECTION DISPLACEMENTS
----------------------------
UNITS ARE - CM
MEMB  LOAD     GLOBAL X,Y,Z DISPL FROM START TO END JOINTS AT 1/12TH PTS
1     1       0.0000    0.0000    0.0000    0.0249   -0.0037    0.0000
0.0981   -0.0074    0.0000    0.2187   -0.0111    0.0000
0.3856   -0.0148    0.0000    0.5981   -0.0185    0.0000
0.8552   -0.0222    0.0000    1.1560   -0.0260    0.0000
1.4996   -0.0297    0.0000    1.8850   -0.0334    0.0000
2.3115   -0.0371    0.0000    2.7780   -0.0408    0.0000
3.2836   -0.0445    0.0000
MAX LOCAL  DISP =    0.78662   AT     225.00  LOAD    1   L/DISP=    572
2     1       3.2836   -0.0445    0.0000    3.2825   -0.7367    0.0000
3.2814   -1.3907    0.0000    3.2804   -1.9447    0.0000
3.2793   -2.3529    0.0000    3.2782   -2.5850    0.0000
3.2771   -2.6266    0.0000    3.2760   -2.4791    0.0000
3.2749   -2.1595    0.0000    3.2739   -1.7007    0.0000
3.2728   -1.1514    0.0000    3.2717   -0.5758    0.0000
3.2706   -0.0541    0.0000
MAX LOCAL  DISP =    2.57728   AT     300.00  LOAD    1   L/DISP=    232
3     1       3.2706   -0.0541    0.0000    3.5390   -0.0496    0.0000
3.6663   -0.0451    0.0000    3.6653   -0.0406    0.0000
3.5488   -0.0361    0.0000    3.3297   -0.0316    0.0000
3.0208   -0.0271    0.0000    2.6349   -0.0225    0.0000
2.1849   -0.0180    0.0000    1.6836   -0.0135    0.0000
1.1438   -0.0090    0.0000    0.5783   -0.0045    0.0000
0.0000    0.0000    0.0000
MAX LOCAL  DISP =    1.42182   AT     187.50  LOAD    1   L/DISP=    316
************ END OF SECT DISPL RESULTS ***********
49. FINISH
TEST FOR SECTION DISPLACEMENT                            -- PAGE NO.    5
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= OCT 19,2021   TIME= 17:53:34 ****
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