V. 2D Cantilever Beam End Deflection 2
Find the deflection and moments for plate-bending finite element due to a pressure load.
Problem
A simple cantilever plate is divided into 12 4-noded finite elements. A uniform pressure load is applied and the maximum deflection at the tip of the cantilever and the maximum bending at the support are calculated.
Plate thickness = 25 mm
Uniform pressure= 5 N/mm2
Plate length = 6 spaces at 50 mm = 300 mm
Plate width = 2 space at 50 mm = 100 mm
Finite element mesh of cantilevered plate.
Comparison
Result Type | Hand Calculation | STAAD.Pro | Difference |
---|---|---|---|
δmax (mm) | 18.51 | 18.159 | 1.9% |
Mmax (kN·m) | 22.50 | 22.50 | none |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\04 Plates Shells\2D Cantilever Beam End Deflection 2.STD is typically installed with the program.
STAAD SPACE : DEFLECTION OF A CANTILEVER PLATE UNDER UNIFORM PRESSURE
START JOB INFORMATION
ENGINEER DATE 14-Sep-18
END JOB INFORMATION
*
* DEFLECTION OF A CANTILEVER PLATE UNDER UNIFORM PRESSURE.
* COMPARISON WITH ESTABLISHED FORMULA (WL^3/8EI)
*
UNIT MMS KN
JOINT COORDINATES
1 0 0 0; 2 50 0 0; 3 100 0 0; 4 150 0 0; 5 200 0 0; 6 250 0 0;
7 300 0 0; 8 0 50 0; 9 50 50 0; 10 100 50 0; 11 150 50 0; 12 200 50 0;
13 250 50 0; 14 300 50 0; 15 0 100 0; 16 50 100 0; 17 100 100 0;
18 150 100 0; 19 200 100 0; 20 250 100 0; 21 300 100 0;
ELEMENT INCIDENCES SHELL
1 1 2 9 8; 2 2 3 10 9; 3 3 4 11 10; 4 4 5 12 11; 5 5 6 13 12;
6 6 7 14 13; 7 8 9 16 15; 8 9 10 17 16; 9 10 11 18 17; 10 11 12 19 18;
11 12 13 20 19; 12 13 14 21 20;
ELEMENT PROPERTY
1 TO 12 THICKNESS 25
UNIT METER KN
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 2.1e+08
POISSON 0.3
END DEFINE MATERIAL
UNIT MMS KN
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 8 15 FIXED
UNIT MMS NEWTON
LOAD 1 5N/SQ.MM. UNIFORM LOAD
ELEMENT LOAD
1 TO 12 PR 5
PERFORM ANALYSIS
PRINT JOINT DISPLACEMENTS LIST 14
UNIT METER KN
PRINT SUPPORT REACTION
FINISH
STAAD Output
JOINT DISPLACEMENT (CM RADIANS) STRUCTURE TYPE = SPACE ------------------ JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 14 1 0.0000 0.0000 1.8159 0.0000 -0.0813 0.0000 ************** END OF LATEST ANALYSIS RESULT ************** 38. UNIT METER KN 39. PRINT SUPPORT REACTION SUPPORT REACTION : DEFLECTION OF A CANTILEVER PLATE UNDER UNIFORM PRESSUR -- PAGE NO. 4 SUPPORT REACTIONS -UNIT KN METE STRUCTURE TYPE = SPACE ----------------- JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 1 1 0.00 0.00 -18.91 -1.54 5.47 0.00 8 1 0.00 0.00 -112.19 0.00 11.56 0.00 15 1 0.00 0.00 -18.91 1.54 5.47 0.00