V. 2D Portal Reactions Sidesway 1

To find the displacements at the nodes of a frame due to movements of supports.

Reference

C.K. Wang, Intermediate Structural Analysis, International Student Edition, 1983, McGraw Hill, Section 2.11, p47.

Problem

Calculate the deflections at node B and support D.

Frame subject to imposed displacements

Load Cases:

Vertical displacement of 1 cm at Node A
Vertical displacement of 1 cm at Node B

Comparison

Table 1. Comparison of results
Result Type		Theory	STAAD.Pro	Difference	Comment
Load Case 1	Horizontal displacement at node B (cm)	1.25	-1.25	none	Different orientation of positive axis results in different sign.
	Rotation at node B	0.001667	0.0017	none
	Horizontal displacement at node D (cm)	0.4167	-0.4167	none	Different orientation of positive axis results in different sign.
Load Case 2	Horizontal displacement at node B (cm)	1.25	1.25	none
	Rotation at node B	0.001667	0.0017	none
	Horizontal displacement at node D (cm)	0.4167	0.4167	none

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\03 Frames\2D Portal Reactions Sidesway 1.STD is typically installed with the program.

STAAD PLANE DEFLECTIONS DUE TO MOVEMENT OF SUPPORTS
START JOB INFORMATION
ENGINEER DATE 17-Sep-18
END JOB INFORMATION
*
* REFERENCE: INTERMEDIATE STRUCTURAL ANALYSIS, C.K.WANG
*     INTERNATIONAL STUDENT EDITION, 1983, MCGRAW HILL
*     SECTION 2.11, PAGE 47
*
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 7.5 0; 3 6 7.5 0; 4 6 2.5 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4;
UNIT CM KN
MEMBER PROPERTY AMERICAN
1 3 PRIS AX 2400 IZ 720000
2 PRIS AX 4800 IZ 1.44e+06
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 2171.84
POISSON 0.17
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 PINNED
4 FIXED BUT FX MZ
LOAD 1
SUPPORT DISPLACEMENT LOAD
1 FY -1
LOAD 2
SUPPORT DISPLACEMENT LOAD
4 FY -1
PERFORM ANALYSIS
LOAD LIST 1
PRINT JOINT DISPLACEMENTS
LOAD LIST 2
PRINT JOINT DISPLACEMENTS
FINISH

STAAD Output

   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   -1.0000    0.0000    0.0000    0.0000    0.0017
      2    1    -1.2500   -1.0000    0.0000    0.0000    0.0000    0.0017 
      3    1    -1.2500    0.0000    0.0000    0.0000    0.0000    0.0017
      4    1    -0.4167    0.0000    0.0000    0.0000    0.0000    0.0017 
   ************** END OF LATEST ANALYSIS RESULT **************
    38. LOAD LIST 2
    39. PRINT JOINT DISPLACEMENTS
  JOINT    DISPLACE                   
      DEFLECTIONS DUE TO MOVEMENT OF SUPPORTS                  -- PAGE NO.    4 
   JOINT DISPLACEMENT (CM   RADIANS)    STRUCTURE TYPE = PLANE
   ------------------
 JOINT  LOAD   X-TRANS   Y-TRANS   Z-TRANS   X-ROTAN   Y-ROTAN   Z-ROTAN
      1    2     0.0000    0.0000    0.0000    0.0000    0.0000   -0.0017
      2    2     1.2500    0.0000    0.0000    0.0000    0.0000   -0.0017 
      3    2     1.2500   -1.0000    0.0000    0.0000    0.0000   -0.0017
      4    2     0.4167   -1.0000    0.0000    0.0000    0.0000   -0.0017