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EX. US-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\US\US-13 Section Displacements for a Frame.STD when you install the program.

Example Problem No. 13

Where:

  • L1 = 15 ft, L2 =20 ft
  • P = 5.0 k
  • w = 3.0 k/ft

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 KIP FEET

Defines the input units for the data that follows.

    JOINT COORDINATES
    1  0.  0.  ;  2  0.  15.  ;  3  20.  15.  ;  4  20.  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 AMERICAN
    1  3  TABLE  ST  W8X18
    2  TABLE  ST  W12X26

Properties for all members are assigned from the American AISC steel table. The word ST stands for standard single section.

    UNIT INCHES
    DEFINE MATERIAL START
    ISOTROPIC STEEL
    E 29000.0
    POISSON 0.3
    DENSITY 283e-006
    ALPHA 6e-006
    DAMP 0.03
    TYPE STEEL
    STRENGTH FY 36 FU 58 RY 1.5 RT 1.2
    END DEFINE MATERIAL
    CONSTANT
    MATERIAL STEEL ALL

The input units are changed from FT to INCH. 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 FT
    LOADING 1 DEAD + LIVE + WIND

Load case 1 is initiated followed by an optional title.

    JOINT LOAD
    2 FX 5.

Load 1 contains a joint load of 5 kips at node 2. FX indicates that the load is a force in the global X direction.

    MEMBER LOAD
    2 UNI GY -3.0

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 KIP FEET
JOINT COORDINATES
1 0. 0. ; 2 0. 15. ; 3 20. 15. ; 4 20. 0.
MEMBER INCIDENCE
1 1 2 ; 2 2 3 ; 3 3 4
MEMBER PROPERTY AMERICAN
1 3 TABLE ST W8X18
2 TABLE ST W12X26
UNIT INCHES
DEFINE MATERIAL START
ISOTROPIC STEEL
E 29000.0
POISSON 0.3
DENSITY 283e-006
ALPHA 6e-006
DAMP 0.03
TYPE STEEL
STRENGTH FY 36 FU 58 RY 1.5 RT 1.2
END DEFINE MATERIAL
CONSTANT
MATERIAL STEEL ALL
SUPPORT
1 FIXED ; 4 PINNED
UNIT FT
LOADING 1 DEAD + LIVE + WIND
JOINT LOAD
2 FX 5.
MEMBER LOAD
2 UNI GY -3.0
PERFORM ANALYSIS
PRINT MEMBER FORCES
*
* FOLLOWING PRINT COMMAMND WILL PRINT DISPLACEMENTS
* OF THE MEMBERS CONSIDERING EVERY TWELVETH INTERMEDIATE
* POINTS (THAT IS TOTAL 13 POINTS). THESE DISPLACEMENTS
* ARE MEASURED IN GLOBAL X Y Z COORDINATE SYSTEM AND
* THE VALUES ARE FROM ORIGINAL COORDINATES (THAT IS
* UNDEFLECTED) OF CORRESPONDING TWELVETH POINTS.
*
* MAX LOCAL DISPLACEMENT IS ALSO PRINTED. THE LOCATION
* OF THE 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

STAAD Output File

                                                                  PAGE NO.    1
             ****************************************************        
             *                                                  *        
             *           STAAD.Pro CONNECT Edition              *        
             *           Version  22.04.00.**                   *        
             *           Proprietary Program of                 *        
             *           Bentley Systems, Inc.                  *        
             *           Date=    APR 21, 2020                  *        
             *           Time=    15:41:45                      *        
             *                                                  *        
             *  Licensed to: Bentley Systems Inc                *        
             ****************************************************        
     1. STAAD PLANE TEST FOR SECTION DISPLACEMENT
INPUT FILE: US-13 Section Displacements for a Frame.STD
     2. UNIT KIP FEET
     3. JOINT COORDINATES
     4. 1 0. 0. ; 2 0. 15. ; 3 20. 15. ; 4 20. 0.
     5. MEMBER INCIDENCE
     6. 1 1 2 ; 2 2 3 ; 3 3 4
     7. MEMBER PROPERTY AMERICAN
     8. 1 3 TABLE ST W8X18
     9. 2 TABLE ST W12X26
    10. UNIT INCHES
    11. DEFINE MATERIAL START
    12. ISOTROPIC STEEL
    13. E 29000.0
    14. POISSON 0.3
    15. DENSITY 283E-006
    16. ALPHA 6E-006
    17. DAMP 0.03
    18. TYPE STEEL
    19. STRENGTH FY 36 FU 58 RY 1.5 RT 1.2
    20. END DEFINE MATERIAL
    21. CONSTANT
    22. MATERIAL STEEL ALL
    23. SUPPORT
    24. 1 FIXED ; 4 PINNED
    25. UNIT FT
    26. LOADING 1 DEAD + LIVE + WIND
    27. JOINT LOAD
    28. 2 FX 5.
    29. MEMBER LOAD
    30. 2 UNI GY -3.0
    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 -- KIP  FEET     (LOCAL )
  MEMBER  LOAD  JT     AXIAL   SHEAR-Y  SHEAR-Z   TORSION     MOM-Y      MOM-Z
      1    1     1     27.37      0.97     0.00      0.00      0.00      22.49
                 2    -27.37     -0.97     0.00      0.00      0.00      -7.88
      2    1     2      4.03     27.37     0.00      0.00      0.00       7.88
                 3     -4.03     32.63     0.00      0.00      0.00     -60.39
      3    1     3     32.63      4.03     0.00      0.00      0.00      60.39
                 4    -32.63     -4.03     0.00      0.00      0.00       0.00
   ************** END OF LATEST ANALYSIS RESULT **************
    33. *
    34. * FOLLOWING PRINT COMMAMND WILL PRINT DISPLACEMENTS
    35. * OF THE MEMBERS CONSIDERING EVERY TWELVETH INTERMEDIATE
    36. * POINTS (THAT IS TOTAL 13 POINTS). THESE DISPLACEMENTS
    37. * ARE MEASURED IN GLOBAL X Y Z COORDINATE SYSTEM AND
    38. * THE VALUES ARE FROM ORIGINAL COORDINATES (THAT IS
    39. * UNDEFLECTED) OF CORRESPONDING TWELVETH POINTS.
    40. *
    41. * MAX LOCAL DISPLACEMENT IS ALSO PRINTED. THE LOCATION
    42. * OF THE MAXIMUM INTERMEDIATE DISPLACEMENT IS DETERMINED.
    43. * THIS VALUE IS MEASURED FROM ABOVE LOCATION TO THE STRAIGHT
    44. * LINE JOINING START AND END JOINTS OF THE DEFLECTED MEMBER.
    45. *
    46. PRINT SECTION DISPLACEMENT
  SECTION  DISPLACE                   
      TEST FOR SECTION DISPLACEMENT                            -- PAGE NO.    4
     MEMBER SECTION DISPLACEMENTS
     ----------------------------
     UNITS ARE - INCH
     MEMB  LOAD     GLOBAL X,Y,Z DISPL FROM START TO END JOINTS AT 1/12TH PTS
       1     1       0.0000    0.0000    0.0000    0.0173   -0.0027    0.0000
                     0.0666   -0.0054    0.0000    0.1461   -0.0081    0.0000
                     0.2539   -0.0108    0.0000    0.3882   -0.0135    0.0000
                     0.5472   -0.0162    0.0000    0.7290   -0.0188    0.0000
                     0.9318   -0.0215    0.0000    1.1538   -0.0242    0.0000
                     1.3931   -0.0269    0.0000    1.6480   -0.0296    0.0000
                     1.9165   -0.0323    0.0000
     MAX LOCAL  DISP =    0.41112   AT      90.00  LOAD    1   L/DISP=    437
       2     1       1.9165   -0.0323    0.0000    1.9162   -0.3903    0.0000
                     1.9158   -0.7221    0.0000    1.9154   -1.0010    0.0000
                     1.9151   -1.2067    0.0000    1.9147   -1.3260    0.0000
                     1.9144   -1.3523    0.0000    1.9140   -1.2856    0.0000
                     1.9136   -1.1331    0.0000    1.9133   -0.9082    0.0000
                     1.9129   -0.6316    0.0000    1.9125   -0.3303    0.0000
                     1.9122   -0.0385    0.0000
     MAX LOCAL  DISP =    1.31688   AT     120.00  LOAD    1   L/DISP=    182
       3     1       1.9122   -0.0385    0.0000    2.0720   -0.0353    0.0000
                     2.1486   -0.0321    0.0000    2.1495   -0.0289    0.0000
                     2.0822   -0.0257    0.0000    1.9544   -0.0225    0.0000
                     1.7736   -0.0192    0.0000    1.5474   -0.0160    0.0000
                     1.2833   -0.0128    0.0000    0.9890   -0.0096    0.0000
                     0.6719   -0.0064    0.0000    0.3398   -0.0032    0.0000
                     0.0000    0.0000    0.0000
     MAX LOCAL  DISP =    0.83895   AT      75.00  LOAD    1   L/DISP=    214
         ************ END OF SECT DISPL RESULTS ***********
    47. FINISH
      TEST FOR SECTION DISPLACEMENT                            -- PAGE NO.    5
             *********** END OF THE STAAD.Pro RUN ***********         
               **** DATE= APR 21,2020   TIME= 15:41:45 ****
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