Using plate/shell elements, find maximum bending stress
due to a force couple on a curved cantilever beam.
Reference
Timoshenko, S.,
Strength of Materials, Part I, 3rd Edition, Van
Nostrand Co., 1956.
Problem
Find the maximum bending stress
Cantilevered, curved
plate with coupling load at free end
Comparison
Table 1. Comparison of results
Result Type
|
Theory
|
STAAD.Pro
|
Difference
|
Comments
|
Inside stress (psi)
|
655.0
|
636.02
|
2.9%
|
The result from the Beam theory is
compared with the result from a Finite Element Model output, hence the
difference in results.
|
Outside stress (psi)
|
555.0
|
556.73
|
negligible
|
|
STAAD Output
SUPPORT REACTIONS -UNIT POUN INCH STRUCTURE TYPE = SPACE
-----------------
JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z
1 1 -15.30 61.91 0.00 0.00 0.00 -2.09
11 1 3.80 69.53 0.00 0.00 0.00 0.72
21 1 12.47 5.36 0.00 0.00 0.00 1.21
31 1 11.58 -66.95 0.00 0.00 0.00 1.75
41 1 -12.55 -69.85 0.00 0.00 0.00 -1.59
************** END OF LATEST ANALYSIS RESULT **************
52. PRINT ELEMENT JOINT STRESSES LIST 9 36
ELEMENT JOINT STRESSES LIST
:CURVED BEAM WITH PLATE ELEMENTS -- PAGE NO. 4
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
9 1 0.00 0.00 0.00 0.00 0.00
432.15 432.15 -433.11 -2.49 8.94
433.30 433.30
TOP : SMAX= -2.31 SMIN= -433.30 TMAX= 215.50 ANGLE= 88.8
BOTT: SMAX= -2.31 SMIN= -433.30 TMAX= 215.50 ANGLE= 88.8
JOINT 0.00 0.00 0.00 0.00 0.00
10 592.15 592.15 -560.35 58.12 15.37
TOP : SMAX= 58.50 SMIN= -560.73 TMAX= 309.62 ANGLE= 88.6
BOTT: SMAX= 58.50 SMIN= -560.73 TMAX= 309.62 ANGLE= 88.6
JOINT 0.00 0.00 0.00 0.00 0.00
1 527.90 527.90 -556.47 -63.65 11.40
TOP : SMAX= -63.39 SMIN= -556.73 TMAX= 246.67 ANGLE= 88.7
BOTT: SMAX= -63.39 SMIN= -556.73 TMAX= 246.67 ANGLE= 88.7
JOINT 0.00 0.00 0.00 0.00 0.00
11 285.05 285.05 -310.91 -64.85 13.47
TOP : SMAX= -64.11 SMIN= -311.65 TMAX= 123.77 ANGLE= 86.9
BOTT: SMAX= -64.11 SMIN= -311.65 TMAX= 123.77 ANGLE= 86.9
JOINT 0.00 0.00 0.00 0.00 0.00
20 351.99 351.99 -318.48 58.96 8.48
TOP : SMAX= 59.15 SMIN= -318.67 TMAX= 188.91 ANGLE= 88.7
BOTT: SMAX= 59.15 SMIN= -318.67 TMAX= 188.91 ANGLE= 88.7
36 1 0.00 0.00 0.00 0.00 0.00
457.10 457.10 473.43 34.66 2.24
473.44 473.44
TOP : SMAX= 473.44 SMIN= 34.64 TMAX= 219.40 ANGLE= 0.3
BOTT: SMAX= 473.44 SMIN= 34.64 TMAX= 219.40 ANGLE= 0.3
JOINT 0.00 0.00 0.00 0.00 0.00
40 314.58 314.58 298.80 -24.94 -23.18
TOP : SMAX= 300.45 SMIN= -26.59 TMAX= 163.52 ANGLE= -4.1
BOTT: SMAX= 300.45 SMIN= -26.59 TMAX= 163.52 ANGLE= -4.1
JOINT 0.00 0.00 0.00 0.00 0.00
31 247.25 247.25 282.26 108.74 10.51
TOP : SMAX= 282.90 SMIN= 108.11 TMAX= 87.39 ANGLE= 3.5
BOTT: SMAX= 282.90 SMIN= 108.11 TMAX= 87.39 ANGLE= 3.5
JOINT 0.00 0.00 0.00 0.00 0.00
41 594.55 594.55 634.80 95.42 25.72
TOP : SMAX= 636.02 SMIN= 94.20 TMAX= 270.91 ANGLE= 2.7
BOTT: SMAX= 636.02 SMIN= 94.20 TMAX= 270.91 ANGLE= 2.7
JOINT 0.00 0.00 0.00 0.00 0.00
50 680.99 680.99 656.97 -43.84 -21.63
TOP : SMAX= 657.64 SMIN= -44.51 TMAX= 351.08 ANGLE= -1.8
BOTT: SMAX= 657.64 SMIN= -44.51 TMAX= 351.08 ANGLE= -1.8
:CURVED BEAM WITH PLATE ELEMENTS -- PAGE NO. 5
**** MAXIMUM STRESSES AMONG SELECTED PLATES AND CASES ****
MAXIMUM MINIMUM MAXIMUM MAXIMUM MAXIMUM
PRINCIPAL PRINCIPAL SHEAR VONMISES TRESCA
STRESS STRESS STRESS STRESS STRESS
6.576412E+02 -5.607280E+02 3.510752E+02 4.571006E+02 4.734368E+02
PLATE NO. 36 9 36 36 36
CASE NO. 1 1 1 1 1