A thick cylindrical plate supported along 2 radial edges. Find the radial displacement, radial stress, tangential stress and longitudinal stress at inner surface due to a unit pressure applied at the inner surface.
Reference
MacNeal, R.H. and Harder, R.C., A Proposed Standard Set of Problems to Test Finite Element Accuracy, Finite Element in Analysis and Design 1, 1985.
Problem
Loading is unit pressure at inner radius
Semi-circular plate finite element model
Comparison
Table 1. Comparison of results
Result Type |
Theory |
STAAD.Pro
|
Difference |
Radial deflection (10-3 in) |
4.582 |
4.650a
|
1.5% |
Radial stress (psi) |
-1.00 |
-0.95b
|
5.0% |
Tangential stress (psi) |
1.25 |
1.26b
|
0.8% |
Longitudinal stress (psi) |
0.075 |
0.080 |
7.0% |
- Radial displacements are measured along FY at node 102 and FX at node 101.
- On element 82, at node 102, SX is tangential stress, SY is radial stress.
STAAD Output
JOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = SPACE
------------------
JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN
101 2 0.00465 0.00000 0.00000 0.00000 0.00000 0.00000
102 2 0.00000 0.00465 0.00000 0.00000 0.00000 0.00000
107 2 0.00357 0.00299 0.00000 0.00000 0.00000 0.00000
************** END OF LATEST ANALYSIS RESULT **************
97. LOAD LIST 1
98. PRINT ELEMENT JOINT STRESSES LIST 82 83 89 90
ELEMENT JOINT STRESSES LIST
:A THICK WALLED CYLINDER PLATE SUPPORTED ALONG 2 RADIAL -- PAGE NO. 5
ELEMENT STRESSES FORCE,LENGTH UNITS= POUN INCH
----------------
STRESS = FORCE/UNIT WIDTH/THICK, MOMENT = FORCE-LENGTH/UNIT WIDTH
ELEMENT LOAD SQX SQY MX MY MXY
VONT VONB SX SY SXY
TRESCAT TRESCAB
82 1 0.00 0.00 0.00 0.00 0.00
1.81 1.81 1.17 -0.91 0.00
2.08 2.08
TOP : SMAX= 1.17 SMIN= -0.91 TMAX= 1.04 ANGLE= 0.0
BOTT: SMAX= 1.17 SMIN= -0.91 TMAX= 1.04 ANGLE= 0.0
JOINT 0.00 0.00 0.00 0.00 0.00
92 1.69 1.69 1.07 -0.88 -0.08
TOP : SMAX= 1.07 SMIN= -0.88 TMAX= 0.98 ANGLE= -2.3
BOTT: SMAX= 1.07 SMIN= -0.88 TMAX= 0.98 ANGLE= -2.3
JOINT 0.00 0.00 0.00 0.00 0.00
93 1.69 1.69 1.07 -0.88 0.08
TOP : SMAX= 1.07 SMIN= -0.88 TMAX= 0.98 ANGLE= 2.3
BOTT: SMAX= 1.07 SMIN= -0.88 TMAX= 0.98 ANGLE= 2.3
JOINT 0.00 0.00 0.00 0.00 0.00
103 1.93 1.93 1.26 -0.95 0.08
TOP : SMAX= 1.26 SMIN= -0.95 TMAX= 1.11 ANGLE= 2.1
BOTT: SMAX= 1.26 SMIN= -0.95 TMAX= 1.11 ANGLE= 2.1
JOINT 0.00 0.00 0.00 0.00 0.00
102 1.93 1.93 1.26 -0.95 -0.08
TOP : SMAX= 1.26 SMIN= -0.95 TMAX= 1.11 ANGLE= -2.0
BOTT: SMAX= 1.26 SMIN= -0.95 TMAX= 1.11 ANGLE= -2.0
83 1 0.00 0.00 0.00 0.00 0.00
1.81 1.81 1.17 -0.92 -0.00
2.08 2.08
TOP : SMAX= 1.17 SMIN= -0.92 TMAX= 1.04 ANGLE= -0.0
BOTT: SMAX= 1.17 SMIN= -0.92 TMAX= 1.04 ANGLE= -0.0
JOINT 0.00 0.00 0.00 0.00 0.00
93 1.69 1.69 1.07 -0.88 -0.08
TOP : SMAX= 1.07 SMIN= -0.88 TMAX= 0.98 ANGLE= -2.3
BOTT: SMAX= 1.07 SMIN= -0.88 TMAX= 0.98 ANGLE= -2.3
JOINT 0.00 0.00 0.00 0.00 0.00
94 1.69 1.69 1.06 -0.88 0.08
TOP : SMAX= 1.07 SMIN= -0.88 TMAX= 0.98 ANGLE= 2.3
BOTT: SMAX= 1.07 SMIN= -0.88 TMAX= 0.98 ANGLE= 2.3
JOINT 0.00 0.00 0.00 0.00 0.00
104 1.93 1.93 1.26 -0.95 0.08
TOP : SMAX= 1.26 SMIN= -0.96 TMAX= 1.11 ANGLE= 2.1
BOTT: SMAX= 1.26 SMIN= -0.96 TMAX= 1.11 ANGLE= 2.1
JOINT 0.00 0.00 0.00 0.00 0.00
103 1.93 1.93 1.26 -0.95 -0.08
TOP : SMAX= 1.26 SMIN= -0.96 TMAX= 1.11 ANGLE= -2.1
BOTT: SMAX= 1.26 SMIN= -0.96 TMAX= 1.11 ANGLE= -2.1
89 1 0.00 0.00 0.00 0.00 0.00
1.81 1.81 1.17 -0.92 0.00
2.08 2.08
TOP : SMAX= 1.17 SMIN= -0.92 TMAX= 1.04 ANGLE= 0.0
BOTT: SMAX= 1.17 SMIN= -0.92 TMAX= 1.04 ANGLE= 0.0
:A THICK WALLED CYLINDER PLATE SUPPORTED ALONG 2 RADIAL -- PAGE NO. 6
ELEMENT STRESSES FORCE,LENGTH UNITS= POUN INCH
----------------
STRESS = FORCE/UNIT WIDTH/THICK, MOMENT = FORCE-LENGTH/UNIT WIDTH
ELEMENT LOAD SQX SQY MX MY MXY
VONT VONB SX SY SXY
TRESCAT TRESCAB
JOINT 0.00 0.00 0.00 0.00 0.00
99 1.69 1.69 1.06 -0.88 -0.08
TOP : SMAX= 1.07 SMIN= -0.88 TMAX= 0.98 ANGLE= -2.3
BOTT: SMAX= 1.07 SMIN= -0.88 TMAX= 0.98 ANGLE= -2.3
JOINT 0.00 0.00 0.00 0.00 0.00
100 1.69 1.69 1.07 -0.88 0.08
TOP : SMAX= 1.07 SMIN= -0.88 TMAX= 0.98 ANGLE= 2.3
BOTT: SMAX= 1.07 SMIN= -0.88 TMAX= 0.98 ANGLE= 2.3
JOINT 0.00 0.00 0.00 0.00 0.00
110 1.93 1.93 1.26 -0.95 0.08
TOP : SMAX= 1.26 SMIN= -0.96 TMAX= 1.11 ANGLE= 2.1
BOTT: SMAX= 1.26 SMIN= -0.96 TMAX= 1.11 ANGLE= 2.1
JOINT 0.00 0.00 0.00 0.00 0.00
109 1.93 1.93 1.26 -0.95 -0.08
TOP : SMAX= 1.26 SMIN= -0.96 TMAX= 1.11 ANGLE= -2.1
BOTT: SMAX= 1.26 SMIN= -0.96 TMAX= 1.11 ANGLE= -2.1
90 1 0.00 0.00 0.00 0.00 0.00
1.81 1.81 1.17 -0.91 -0.00
2.08 2.08
TOP : SMAX= 1.17 SMIN= -0.91 TMAX= 1.04 ANGLE= -0.0
BOTT: SMAX= 1.17 SMIN= -0.91 TMAX= 1.04 ANGLE= -0.0
JOINT 0.00 0.00 0.00 0.00 0.00
100 1.69 1.69 1.07 -0.88 -0.08
TOP : SMAX= 1.07 SMIN= -0.88 TMAX= 0.98 ANGLE= -2.3
BOTT: SMAX= 1.07 SMIN= -0.88 TMAX= 0.98 ANGLE= -2.3
JOINT 0.00 0.00 0.00 0.00 0.00
91 1.69 1.69 1.07 -0.88 0.08
TOP : SMAX= 1.07 SMIN= -0.88 TMAX= 0.98 ANGLE= 2.3
BOTT: SMAX= 1.07 SMIN= -0.88 TMAX= 0.98 ANGLE= 2.3
JOINT 0.00 0.00 0.00 0.00 0.00
101 1.93 1.93 1.26 -0.95 0.08
TOP : SMAX= 1.26 SMIN= -0.95 TMAX= 1.11 ANGLE= 2.0
BOTT: SMAX= 1.26 SMIN= -0.95 TMAX= 1.11 ANGLE= 2.0
JOINT 0.00 0.00 0.00 0.00 0.00
110 1.93 1.93 1.26 -0.95 -0.08
TOP : SMAX= 1.26 SMIN= -0.95 TMAX= 1.11 ANGLE= -2.1
BOTT: SMAX= 1.26 SMIN= -0.95 TMAX= 1.11 ANGLE= -2.1
:A THICK WALLED CYLINDER PLATE SUPPORTED ALONG 2 RADIAL -- PAGE NO. 7
**** MAXIMUM STRESSES AMONG SELECTED PLATES AND CASES ****
MAXIMUM MINIMUM MAXIMUM MAXIMUM MAXIMUM
PRINCIPAL PRINCIPAL SHEAR VONMISES TRESCA
STRESS STRESS STRESS STRESS STRESS
1.263807E+00 -9.557953E-01 1.109365E+00 1.807750E+00 2.082330E+00
PLATE NO. 82 83 82 89 89
CASE NO. 1 1 1 1 1