V. 2D Curved Beam Maximum Stress
Using plate/shell elements, find maximum bending stress due to a force couple on a curved cantilever beam.
References
Timoshenko, S., Strength of Materials, Part I, 3rd Edition, Van Nostrand Co., 1956.
Details
Find the maximum bending stress
E = 3,000.0 ksi.
Poisson’s ratio = 0.3.
t = 1.0 in.
P = 100 lbs
Results
| Result Type | Theory | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| Plate Corner Stress at Node 41 (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 |
Input
Tip: 您可以直接将此内容复制并粘贴到 .std 文件中，以在 STAAD.Pro 中运行。
The file C:\Users\Public\Public Documents\STAAD.Pro 2026\Samples \Verification Models\04 Plates Shells\2D Curved Beam Maximum Stress.STD is typically installed with the program.
STAAD
STAAD SPACE :CURVED BEAM WITH PLATE ELEMENTS
START JOB INFORMATION
ENGINEER DATE 14-Sep-18
END JOB INFORMATION
*
* REFERENCE: TIMOSHENKO, S., "STENGTH OF MATERIALS, PART I, ELEMENTARY
* THEORY AND PROBLEMS", 3RD EDITION, D. VAN NOSTRAND CO.,
* INC., NEW YORK, 1956.
*
UNIT INCHES POUND
JOINT COORDINATES
1 4.5 0 0; 2 0 4.5 0; 3 0.781 4.432 0; 4 1.539 4.229 0; 5 2.25 3.897 0;
6 2.893 3.447 0; 7 3.447 2.893 0; 8 3.897 2.25 0; 9 4.229 1.539 0;
10 4.432 0.781 0; 11 4.25 0 0; 12 0 4.25 0; 13 0.738 4.185 0;
14 1.454 3.994 0; 15 2.125 3.681 0; 16 2.732 3.256 0; 17 3.256 2.732 0;
18 3.681 2.125 0; 19 3.994 1.454 0; 20 4.185 0.738 0; 21 4 0 0;
22 0 4 0; 23 0.695 3.939 0; 24 1.368 3.759 0; 25 2 3.464 0;
26 2.571 3.064 0; 27 3.064 2.571 0; 28 3.464 2 0; 29 3.759 1.368 0;
30 3.939 0.695 0; 31 3.75 0 0; 32 0 3.75 0; 33 0.651 3.693 0;
34 1.283 3.524 0; 35 1.875 3.248 0; 36 2.41 2.873 0; 37 2.873 2.41 0;
38 3.248 1.875 0; 39 3.524 1.283 0; 40 3.693 0.651 0; 41 3.5 0 0;
42 0 3.5 0; 43 0.608 3.447 0; 44 1.197 3.289 0; 45 1.75 3.031 0;
46 2.25 2.681 0; 47 2.681 2.25 0; 48 3.031 1.75 0; 49 3.289 1.197 0;
50 3.447 0.608 0;
ELEMENT INCIDENCES SHELL
1 2 3 13 12; 2 3 4 14 13; 3 4 5 15 14; 4 5 6 16 15; 5 6 7 17 16;
6 7 8 18 17; 7 8 9 19 18; 8 9 10 20 19; 9 10 1 11 20; 10 12 13 23 22;
11 13 14 24 23; 12 14 15 25 24; 13 15 16 26 25; 14 16 17 27 26;
15 17 18 28 27; 16 18 19 29 28; 17 19 20 30 29; 18 20 11 21 30;
19 22 23 33 32; 20 23 24 34 33; 21 24 25 35 34; 22 25 26 36 35;
23 26 27 37 36; 24 27 28 38 37; 25 28 29 39 38; 26 29 30 40 39;
27 30 21 31 40; 28 32 33 43 42; 29 33 34 44 43; 30 34 35 45 44;
31 35 36 46 45; 32 36 37 47 46; 33 37 38 48 47; 34 38 39 49 48;
35 39 40 50 49; 36 40 31 41 50;
ELEMENT PROPERTY
1 TO 36 THICKNESS 1
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 3e+07
POISSON 0.3
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 11 21 31 41 FIXED
LOAD 1 100 IN-IB
JOINT LOAD
2 FX 100
42 FX -100
PERFORM ANALYSIS
PRINT SUPPORT REACTION
PRINT ELEMENT JOINT STRESSES LIST 9 36
FINISHOutput
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