V. Cantilever Tube Stresses and Deflection
To find deflections and element stresses due to loads at the free end of a Cantilever beam of tubular section. The beam is modeled using plate/shell elements.
Reference
Timoshenko, S., Strength of Materials, Part I, Elementary Theory and Problems, 2nd Edition, Van Nostrand Company, 1940.
Problem
A cantilever beam is made of a tubular section. Using plate/shell elements calculate the deflection at the free end and axial stress at the center of the beam for the following free end loads:
| P = 1,000 lb |
| Mx = 2,000 in·lb |
| My = 2,500 in·lb |
| V = 1,000 lb |
Average deflection for nodes 11, 22, 33, 44, 55, 66, 77, 88, 99 and 10 due to load case 3 (My):
d = [4(0.07431) + 4(0.07384) + 2(0.07374)]/10 = 0.074008
Average deflection for nodes 11, 22, 33, 44, 55, 66, 77, 88, 99 and 10 due to load case 4 (V):
d = [4(-0.41123) + 4(-0.41124) + 2(-0.41057)]/10 = 0.41110
Average bending stress for nodes 76, 86, 126, and 136 due to load case 3 (My):
σ = 4(5551.52)/4 = 5551.52 psi
Average bending stress for nodes 71, 81, 121, and 131 due to load case 4 (V):
σ = 4(42074.63)/4 = 42074.63 psi
Comparison
| Result Type | Theory | STAAD.Pro | Difference | |
|---|---|---|---|---|
| Free end deflection due to axial load, P (in) | Nodes 11, 44, 66, 99 | 0.004 | 0.00410 | 2.5% |
| Nodes 22,33, 55, 77, 88, 110 | 0.004 | 0.00401 | negligible | |
| Axial stress at the middle of the beam due to axial load, P (psi) | Elements 46, 66, 96, 116 | 2,000 | 2,000.02 | negligible |
| Elements 56, 106 | 2,000 | 1,991.57 | negligible | |
| Elements 76, 86, 126, 136 | 2,000 | 2,004,19 | negligible | |
| In plane shear stress at the free end due to torque, Mx (psi) | Elements 50,70,100,120 | 3,333 | 3,333.55 | negligible |
| Elements 60, 110 | 3,333 | 3,325.54 | negligible | |
| Elements 80,90,130,140 | 3,333 | 3,342.23 | negligible | |
| Avg. free end deflection at the center due to moment, My (in) | 0.0741 | 0.074008 | negligible | |
| Avg. free end bending stress at the center due to moment, My (psi) | 5,647 | 5,551.52 | 1.7% | |
| Avg. free end deflection at the center due to shear, V (in) | 0.4152 | -0.41110 | 1.0% | |
| Avg. free end bending stress at the center due to shear, V (psi) | 42,913 | 42,074.63 | 2.0% | |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\04 Plates Shells\Cantilever Tube Stresses and Deflection.STD is typically installed with the program.
STAAD SPACE :A CANTILEVER BEAM OF TUBULAR SECTION
START JOB INFORMATION
ENGINEER DATE 14-Sep-18
END JOB INFORMATION
*
* REFERENCES: 1. TIMOSHENKO, S., STRENGTH OF MATERIALS, PART 1,
* 2ND EDITION, D. VAN NOSTRAND COMPANY, 1940
* 2. SEELEY, F. B., AND SMITH, J.O., ADVANCED MECHANICS
* OF MATERIALS, 2ND EDITION, JOHN WILEY AND SONS, 1955
*
UNIT INCHES POUND
JOINT COORDINATES
1 0 0 0; 2 2 0 0; 3 4 0 0; 4 6 0 0; 5 8 0 0; 6 10 0 0; 7 12 0 0;
8 14 0 0; 9 16 0 0; 10 18 0 0; 11 20 0 0; 12 0 1 0; 13 2 1 0; 14 4 1 0;
15 6 1 0; 16 8 1 0; 17 10 1 0; 18 12 1 0; 19 14 1 0; 20 16 1 0;
21 18 1 0; 22 20 1 0; 23 0 2 0; 24 2 2 0; 25 4 2 0; 26 6 2 0; 27 8 2 0;
28 10 2 0; 29 12 2 0; 30 14 2 0; 31 16 2 0; 32 18 2 0; 33 20 2 0;
34 0 3 0; 35 2 3 0; 36 4 3 0; 37 6 3 0; 38 8 3 0; 39 10 3 0; 40 12 3 0;
41 14 3 0; 42 16 3 0; 43 18 3 0; 44 20 3 0; 45 0 3 1; 46 2 3 1;
47 4 3 1; 48 6 3 1; 49 8 3 1; 50 10 3 1; 51 12 3 1; 52 14 3 1;
53 16 3 1; 54 18 3 1; 55 20 3 1; 56 0 3 2; 57 2 3 2; 58 4 3 2; 59 6 3 2;
60 8 3 2; 61 10 3 2; 62 12 3 2; 63 14 3 2; 64 16 3 2; 65 18 3 2;
66 20 3 2; 67 0 2 2; 68 2 2 2; 69 4 2 2; 70 6 2 2; 71 8 2 2; 72 10 2 2;
73 12 2 2; 74 14 2 2; 75 16 2 2; 76 18 2 2; 77 20 2 2; 78 0 1 2;
79 2 1 2; 80 4 1 2; 81 6 1 2; 82 8 1 2; 83 10 1 2; 84 12 1 2; 85 14 1 2;
86 16 1 2; 87 18 1 2; 88 20 1 2; 89 0 0 2; 90 2 0 2; 91 4 0 2; 92 6 0 2;
93 8 0 2; 94 10 0 2; 95 12 0 2; 96 14 0 2; 97 16 0 2; 98 18 0 2;
99 20 0 2; 100 0 0 1; 101 2 0 1; 102 4 0 1; 103 6 0 1; 104 8 0 1;
105 10 0 1; 106 12 0 1; 107 14 0 1; 108 16 0 1; 109 18 0 1; 110 20 0 1;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 4 5; 5 5 6; 6 6 7; 7 7 8; 8 8 9; 9 9 10;
10 10 11; 11 34 35; 12 35 36; 13 36 37; 14 37 38; 15 38 39; 16 39 40;
17 40 41; 18 41 42; 19 42 43; 20 43 44; 21 56 57; 22 57 58; 23 58 59;
24 59 60; 25 60 61; 26 61 62; 27 62 63; 28 63 64; 29 64 65; 30 65 66;
31 89 90; 32 90 91; 33 91 92; 34 92 93; 35 93 94; 36 94 95; 37 95 96;
38 96 97; 39 97 98; 40 98 99;
ELEMENT INCIDENCES SHELL
41 1 2 13 12; 42 2 3 14 13; 43 3 4 15 14; 44 4 5 16 15; 45 5 6 17 16;
46 6 7 18 17; 47 7 8 19 18; 48 8 9 20 19; 49 9 10 21 20; 50 10 11 22 21;
51 12 13 24 23; 52 13 14 25 24; 53 14 15 26 25; 54 15 16 27 26;
55 16 17 28 27; 56 17 18 29 28; 57 18 19 30 29; 58 19 20 31 30;
59 20 21 32 31; 60 21 22 33 32; 61 23 24 35 34; 62 24 25 36 35;
63 25 26 37 36; 64 26 27 38 37; 65 27 28 39 38; 66 28 29 40 39;
67 29 30 41 40; 68 30 31 42 41; 69 31 32 43 42; 70 32 33 44 43;
71 34 35 46 45; 72 35 36 47 46; 73 36 37 48 47; 74 37 38 49 48;
75 38 39 50 49; 76 39 40 51 50; 77 40 41 52 51; 78 41 42 53 52;
79 42 43 54 53; 80 43 44 55 54; 81 45 46 57 56; 82 46 47 58 57;
83 47 48 59 58; 84 48 49 60 59; 85 49 50 61 60; 86 50 51 62 61;
87 51 52 63 62; 88 52 53 64 63; 89 53 54 65 64; 90 54 55 66 65;
91 56 57 68 67; 92 57 58 69 68; 93 58 59 70 69; 94 59 60 71 70;
95 60 61 72 71; 96 61 62 73 72; 97 62 63 74 73; 98 63 64 75 74;
99 64 65 76 75; 100 65 66 77 76; 101 67 68 79 78; 102 68 69 80 79;
103 69 70 81 80; 104 70 71 82 81; 105 71 72 83 82; 106 72 73 84 83;
107 73 74 85 84; 108 74 75 86 85; 109 75 76 87 86; 110 76 77 88 87;
111 78 79 90 89; 112 79 80 91 90; 113 80 81 92 91; 114 81 82 93 92;
115 82 83 94 93; 116 83 84 95 94; 117 84 85 96 95; 118 85 86 97 96;
119 86 87 98 97; 120 87 88 99 98; 121 89 90 101 100; 122 90 91 102 101;
123 91 92 103 102; 124 92 93 104 103; 125 93 94 105 104;
126 94 95 106 105; 127 95 96 107 106; 128 96 97 108 107;
129 97 98 109 108; 130 98 99 110 109; 131 100 101 2 1; 132 101 102 3 2;
133 102 103 4 3; 134 103 104 5 4; 135 104 105 6 5; 136 105 106 7 6;
137 106 107 8 7; 138 107 108 9 8; 139 108 109 10 9; 140 109 110 11 10;
MEMBER TRUSS
1 TO 40
MEMBER PROPERTY AMERICAN
1 TO 40 PRIS AX 0.0005
ELEMENT PROPERTY
41 TO 140 THICKNESS 0.05
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 1000
POISSON 0.599866
ISOTROPIC MATERIAL2
E 1e+07
POISSON 0.33
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 MEMB 1 TO 40
MATERIAL MATERIAL2 MEMB 41 TO 140
SUPPORTS
1 12 23 34 45 56 67 78 89 100 FIXED
LOAD 1 AXIAL LOAD
JOINT LOAD
11 22 33 44 55 66 77 88 99 110 FX 100
LOAD 2 TORQUE
JOINT LOAD
11 FY 80.43 FZ -86.21
22 33 FY 169.44
44 FY 80.43 FZ 86.21
55 FZ 162.23
66 FY -80.43 FZ 86.21
77 88 FY -169.44
99 FY -80.43 FZ -86.21
110 FZ -162.23
LOAD 3 END MOMENT
JOINT LOAD
44 55 66 FX -258.6
33 77 FX -86.3
22 88 FX 86.3
11 99 110 FX 258.6
LOAD 4 SHEAR
JOINT LOAD
11 44 66 99 FY -66
22 33 77 88 FY -184
PERFORM ANALYSIS
LOAD LIST 1 TO 4
PRINT JOINT DISPLACEMENTS LIST 11 22 33 44 55 66 77 88 99 110
LOAD LIST 1
PRINT ELEMENT STRESSES LIST 46 56 66 76 86 96 106 116 126 136
LOAD LIST 2
PRINT ELEMENT STRESSES LIST 50 60 70 80 90 100 110 120 130 140
LOAD LIST 3
PRINT ELEMENT STRESSES LIST 45 46 55 56 65 66 75 76 85 86 95 96 105 -
106 115 116 125 126 135 136
LOAD LIST 4
PRINT ELEMENT STRESSES LIST 41 51 61 71 81 91 101 111 121 131
FINISH
STAAD Output
JOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = SPACE ------------------ JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 11 1 0.00410 0.00024 0.00020 -0.00005 -0.00082 0.00093 2 -0.00035 0.01443 -0.02268 0.01498 0.00067 0.00001 3 0.01142 0.07431 0.00056 0.00039 -0.00233 0.00846 4 -0.04451 -0.41123 -0.00026 -0.00119 0.00184 -0.02863 22 1 0.00401 0.00004 -0.00001 -0.00010 0.00013 0.00012 2 -0.00011 0.01446 -0.00757 0.01505 0.00058 0.00007 3 0.00371 0.07384 0.00015 -0.00031 0.00034 0.00638 4 -0.01476 -0.41124 -0.00036 0.00050 -0.00013 -0.02764 33 1 0.00401 -0.00004 -0.00001 0.00010 0.00013 -0.00012 2 0.00011 0.01446 0.00757 0.01505 -0.00058 0.00007 3 -0.00371 0.07384 -0.00015 -0.00031 -0.00034 0.00638 4 0.01476 -0.41124 0.00036 0.00050 0.00013 -0.02764 44 1 0.00410 -0.00024 0.00020 0.00005 -0.00082 -0.00093 2 0.00035 0.01443 0.02268 0.01498 -0.00067 0.00001 3 -0.01142 0.07431 -0.00056 0.00039 0.00233 0.00846 4 0.04451 -0.41123 0.00026 -0.00119 -0.00184 -0.02863 55 1 0.00401 -0.00011 0.00000 0.00000 0.00000 0.00027 2 0.00000 0.00000 0.02265 0.01404 -0.00059 0.00000 3 -0.01111 0.07374 0.00000 0.00000 0.00000 0.00696 4 0.04414 -0.41057 0.00000 0.00000 0.00000 -0.03079 66 1 0.00410 -0.00024 -0.00020 -0.00005 0.00082 -0.00093 2 -0.00035 -0.01443 0.02268 0.01498 -0.00067 -0.00001 3 -0.01142 0.07431 0.00056 -0.00039 -0.00233 0.00846 4 0.04451 -0.41123 -0.00026 0.00119 0.00184 -0.02863 77 1 0.00401 -0.00004 0.00001 -0.00010 -0.00013 -0.00012 2 -0.00011 -0.01446 0.00757 0.01505 -0.00058 -0.00007 3 -0.00371 0.07384 0.00015 0.00031 0.00034 0.00638 4 0.01476 -0.41124 -0.00036 -0.00050 -0.00013 -0.02764 88 1 0.00401 0.00004 0.00001 0.00010 -0.00013 0.00012 2 0.00011 -0.01446 -0.00757 0.01505 0.00058 -0.00007 3 0.00371 0.07384 -0.00015 0.00031 -0.00034 0.00638 4 -0.01476 -0.41124 0.00036 -0.00050 0.00013 -0.02764 99 1 0.00410 0.00024 -0.00020 0.00005 0.00082 0.00093 2 0.00035 -0.01443 -0.02268 0.01498 0.00067 -0.00001 3 0.01142 0.07431 -0.00056 -0.00039 0.00233 0.00846 4 -0.04451 -0.41123 0.00026 0.00119 -0.00184 -0.02863 110 1 0.00401 0.00011 0.00000 0.00000 0.00000 -0.00027 2 0.00000 0.00000 -0.02265 0.01404 0.00059 0.00000 3 0.01111 0.07374 0.00000 0.00000 0.00000 0.00696 4 -0.04414 -0.41057 0.00000 0.00000 0.00000 -0.03079 :A CANTILEVER BEAM OF TUBULAR SECTION -- PAGE NO. 6 ************** END OF LATEST ANALYSIS RESULT ************** 108. LOAD LIST 1 109. PRINT ELEMENT STRESSES LIST 46 56 66 76 86 96 106 116 126 136 ELEMENT STRESSES LIST 46 :A CANTILEVER BEAM OF TUBULAR SECTION -- PAGE NO. 7 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 46 1 0.02 0.00 0.00 0.00 -0.00 1998.93 1998.62 2000.02 2.49 -0.24 2000.58 1999.46 TOP : SMAX= 2000.58 SMIN= 3.31 TMAX= 998.64 ANGLE= -0.0 BOTT: SMAX= 1999.46 SMIN= 1.67 TMAX= 998.89 ANGLE= 0.0 56 1 -0.01 0.00 -0.00 0.00 -0.00 1994.35 1994.87 1991.57 -6.07 -0.00 1997.15 1998.13 TOP : SMAX= 1991.55 SMIN= -5.60 TMAX= 998.57 ANGLE= -0.0 BOTT: SMAX= 1991.59 SMIN= -6.53 TMAX= 999.06 ANGLE= 0.0 66 1 0.02 -0.00 0.00 0.00 0.00 1998.93 1998.62 2000.02 2.49 0.24 2000.58 1999.46 TOP : SMAX= 2000.58 SMIN= 3.31 TMAX= 998.64 ANGLE= 0.0 BOTT: SMAX= 1999.46 SMIN= 1.67 TMAX= 998.89 ANGLE= -0.0 76 1 -0.04 0.00 -0.00 -0.00 0.00 2003.32 2003.71 2004.19 1.36 -0.81 2003.44 2004.95 TOP : SMAX= 2003.44 SMIN= 0.24 TMAX= 1001.60 ANGLE= 0.0 BOTT: SMAX= 2004.95 SMIN= 2.48 TMAX= 1001.24 ANGLE= -0.1 86 1 -0.04 -0.00 -0.00 -0.00 -0.00 2003.32 2003.71 2004.19 1.36 0.81 2003.44 2004.95 TOP : SMAX= 2003.44 SMIN= 0.24 TMAX= 1001.60 ANGLE= -0.0 BOTT: SMAX= 2004.95 SMIN= 2.48 TMAX= 1001.24 ANGLE= 0.1 96 1 0.02 0.00 0.00 0.00 -0.00 1998.93 1998.62 2000.02 2.49 -0.24 2000.58 1999.46 TOP : SMAX= 2000.58 SMIN= 3.31 TMAX= 998.64 ANGLE= -0.0 BOTT: SMAX= 1999.46 SMIN= 1.67 TMAX= 998.89 ANGLE= 0.0 106 1 -0.01 0.00 -0.00 0.00 -0.00 1994.35 1994.87 1991.57 -6.07 0.00 1997.15 1998.13 TOP : SMAX= 1991.55 SMIN= -5.60 TMAX= 998.57 ANGLE= -0.0 BOTT: SMAX= 1991.59 SMIN= -6.53 TMAX= 999.06 ANGLE= 0.0 116 1 0.02 -0.00 0.00 0.00 0.00 1998.93 1998.62 2000.02 2.49 0.24 2000.58 1999.46 TOP : SMAX= 2000.58 SMIN= 3.31 TMAX= 998.64 ANGLE= 0.0 BOTT: SMAX= 1999.46 SMIN= 1.67 TMAX= 998.89 ANGLE= -0.0 :A CANTILEVER BEAM OF TUBULAR SECTION -- PAGE NO. 8 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 126 1 -0.04 0.00 -0.00 -0.00 0.00 2003.32 2003.71 2004.19 1.36 -0.81 2003.44 2004.95 TOP : SMAX= 2003.44 SMIN= 0.24 TMAX= 1001.60 ANGLE= 0.0 BOTT: SMAX= 2004.95 SMIN= 2.48 TMAX= 1001.24 ANGLE= -0.1 136 1 -0.04 -0.00 -0.00 -0.00 -0.00 2003.32 2003.71 2004.19 1.36 0.81 2003.44 2004.95 TOP : SMAX= 2003.44 SMIN= 0.24 TMAX= 1001.60 ANGLE= -0.0 BOTT: SMAX= 2004.95 SMIN= 2.48 TMAX= 1001.24 ANGLE= 0.1 **** MAXIMUM STRESSES AMONG SELECTED PLATES AND CASES **** MAXIMUM MINIMUM MAXIMUM MAXIMUM MAXIMUM PRINCIPAL PRINCIPAL SHEAR VONMISES TRESCA STRESS STRESS STRESS STRESS STRESS 2.004949E+03 -6.534180E+00 1.001600E+03 2.003712E+03 2.004949E+03 PLATE NO. 76 56 76 76 76 CASE NO. 1 1 1 1 1 ********************END OF ELEMENT FORCES******************** 110. LOAD LIST 2 111. PRINT ELEMENT STRESSES LIST 50 60 70 80 90 100 110 120 130 140 ELEMENT STRESSES LIST 50 :A CANTILEVER BEAM OF TUBULAR SECTION -- PAGE NO. 9 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 50 2 -2.88 1.41 -0.01 -0.02 -0.03 5636.28 5911.95 -0.36 18.30 3333.55 6508.14 6826.34 TOP : SMAX= 3227.82 SMIN= -3280.32 TMAX= 3254.07 ANGLE= 44.9 BOTT: SMAX= 3457.36 SMIN= -3368.98 TMAX= 3413.17 ANGLE= 45.2 60 2 0.00 1.42 0.00 -0.00 -0.08 5445.08 6074.93 0.00 -0.00 3325.54 6287.44 7014.73 TOP : SMAX= 3143.72 SMIN= -3143.72 TMAX= 3143.72 ANGLE= 90.0 BOTT: SMAX= 3507.36 SMIN= -3507.36 TMAX= 3507.36 ANGLE= 90.0 70 2 2.88 1.41 0.01 0.02 -0.03 5636.28 5911.95 0.36 -18.30 3333.55 6508.14 6826.34 TOP : SMAX= 3280.32 SMIN= -3227.82 TMAX= 3254.07 ANGLE= 45.1 BOTT: SMAX= 3368.98 SMIN= -3457.36 TMAX= 3413.17 ANGLE= 44.8 80 2 -3.78 -1.42 0.02 0.06 -0.03 5674.31 5906.56 1.32 -11.09 3342.23 6551.26 6819.29 TOP : SMAX= 3367.91 SMIN= -3183.35 TMAX= 3275.63 ANGLE= 45.4 BOTT: SMAX= 3307.60 SMIN= -3511.69 TMAX= 3409.64 ANGLE= 44.5 90 2 3.78 -1.42 -0.02 -0.06 -0.03 5674.31 5906.56 -1.32 11.09 3342.23 6551.26 6819.29 TOP : SMAX= 3183.35 SMIN= -3367.91 TMAX= 3275.63 ANGLE= 44.6 BOTT: SMAX= 3511.69 SMIN= -3307.60 TMAX= 3409.64 ANGLE= 45.5 100 2 -2.88 1.41 -0.01 -0.02 -0.03 5636.28 5911.95 -0.36 18.30 3333.55 6508.14 6826.34 TOP : SMAX= 3227.82 SMIN= -3280.32 TMAX= 3254.07 ANGLE= 44.9 BOTT: SMAX= 3457.36 SMIN= -3368.98 TMAX= 3413.17 ANGLE= 45.2 110 2 0.00 1.42 -0.00 -0.00 -0.08 5445.08 6074.93 -0.00 0.00 3325.54 6287.44 7014.73 TOP : SMAX= 3143.72 SMIN= -3143.72 TMAX= 3143.72 ANGLE= 90.0 BOTT: SMAX= 3507.36 SMIN= -3507.36 TMAX= 3507.36 ANGLE= 90.0 120 2 2.88 1.41 0.01 0.02 -0.03 5636.28 5911.95 0.36 -18.30 3333.55 6508.14 6826.34 TOP : SMAX= 3280.32 SMIN= -3227.82 TMAX= 3254.07 ANGLE= 45.1 BOTT: SMAX= 3368.98 SMIN= -3457.36 TMAX= 3413.17 ANGLE= 44.8 :A CANTILEVER BEAM OF TUBULAR SECTION -- PAGE NO. 10 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 130 2 -3.78 -1.42 0.02 0.06 -0.03 5674.31 5906.56 1.32 -11.09 3342.23 6551.26 6819.29 TOP : SMAX= 3367.91 SMIN= -3183.35 TMAX= 3275.63 ANGLE= 45.4 BOTT: SMAX= 3307.60 SMIN= -3511.69 TMAX= 3409.64 ANGLE= 44.5 140 2 3.78 -1.42 -0.02 -0.06 -0.03 5674.31 5906.56 -1.32 11.09 3342.23 6551.26 6819.29 TOP : SMAX= 3183.35 SMIN= -3367.91 TMAX= 3275.63 ANGLE= 44.6 BOTT: SMAX= 3511.69 SMIN= -3307.60 TMAX= 3409.64 ANGLE= 45.5 **** MAXIMUM STRESSES AMONG SELECTED PLATES AND CASES **** MAXIMUM MINIMUM MAXIMUM MAXIMUM MAXIMUM PRINCIPAL PRINCIPAL SHEAR VONMISES TRESCA STRESS STRESS STRESS STRESS STRESS 3.511688E+03 -3.511688E+03 3.507364E+03 6.074933E+03 7.014728E+03 PLATE NO. 90 80 60 60 60 CASE NO. 2 2 2 2 2 ********************END OF ELEMENT FORCES******************** 112. LOAD LIST 3 113. PRINT ELEMENT STRESSES LIST 45 46 55 56 65 66 75 76 85 86 95 96 105 - ELEMENT STRESSES LIST 45 114. 106 115 116 125 126 135 136 :A CANTILEVER BEAM OF TUBULAR SECTION -- PAGE NO. 11 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 45 3 -0.02 0.01 -0.00 -0.00 0.00 3703.79 3702.75 3703.80 1.06 -0.17 3704.34 3704.36 TOP : SMAX= 3703.23 SMIN= -1.11 TMAX= 1852.17 ANGLE= 0.0 BOTT: SMAX= 3704.36 SMIN= 3.23 TMAX= 1850.57 ANGLE= -0.0 46 3 0.03 0.03 -0.00 -0.00 -0.00 3704.99 3703.08 3709.20 10.35 -1.86 3709.14 3709.27 TOP : SMAX= 3709.14 SMIN= 8.31 TMAX= 1850.41 ANGLE= -0.0 BOTT: SMAX= 3709.27 SMIN= 12.39 TMAX= 1848.44 ANGLE= -0.0 55 3 0.00 0.02 0.00 -0.00 -0.00 2.87 1.59 -0.00 0.00 -1.29 3.32 1.83 TOP : SMAX= 1.66 SMIN= -1.66 TMAX= 1.66 ANGLE= 90.0 BOTT: SMAX= 0.92 SMIN= -0.92 TMAX= 0.92 ANGLE= 90.0 56 3 0.00 0.03 0.00 -0.00 0.00 4.19 1.52 -0.00 0.00 1.65 4.83 1.75 TOP : SMAX= 2.42 SMIN= -2.42 TMAX= 2.42 ANGLE= 90.0 BOTT: SMAX= 0.88 SMIN= -0.88 TMAX= 0.88 ANGLE= 90.0 65 3 0.02 0.01 0.00 0.00 0.00 3703.79 3702.75 -3703.80 -1.06 -0.17 3704.34 3704.36 TOP : SMAX= 1.11 SMIN= -3703.23 TMAX= 1852.17 ANGLE= 90.0 BOTT: SMAX= -3.23 SMIN= -3704.36 TMAX= 1850.57 ANGLE=-90.0 66 3 -0.03 0.03 0.00 0.00 -0.00 3704.99 3703.08 -3709.20 -10.35 -1.86 3709.14 3709.27 TOP : SMAX= -8.31 SMIN= -3709.14 TMAX= 1850.41 ANGLE=-90.0 BOTT: SMAX= -12.39 SMIN= -3709.27 TMAX= 1848.44 ANGLE=-90.0 75 3 -0.81 -0.01 0.04 -0.00 0.01 5463.48 5646.25 -5554.57 0.18 1.31 5464.40 5647.48 TOP : SMAX= -1.84 SMIN= -5464.40 TMAX= 2731.28 ANGLE= 89.7 BOTT: SMAX= 2.48 SMIN= -5645.01 TMAX= 2823.74 ANGLE=-89.7 76 3 -1.04 -0.03 0.04 -0.00 0.01 5459.11 5640.90 -5551.52 -3.75 4.91 5462.11 5641.41 TOP : SMAX= -6.00 SMIN= -5462.11 TMAX= 2728.05 ANGLE= 89.6 BOTT: SMAX= -1.02 SMIN= -5641.41 TMAX= 2820.19 ANGLE=-89.7 :A CANTILEVER BEAM OF TUBULAR SECTION -- PAGE NO. 12 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 85 3 -0.81 0.01 0.04 -0.00 -0.01 5463.48 5646.25 -5554.57 0.18 -1.31 5464.40 5647.48 TOP : SMAX= -1.84 SMIN= -5464.40 TMAX= 2731.28 ANGLE=-89.7 BOTT: SMAX= 2.48 SMIN= -5645.01 TMAX= 2823.74 ANGLE= 89.7 86 3 -1.04 0.03 0.04 -0.00 -0.01 5459.11 5640.90 -5551.52 -3.75 -4.91 5462.11 5641.41 TOP : SMAX= -6.00 SMIN= -5462.11 TMAX= 2728.05 ANGLE=-89.6 BOTT: SMAX= -1.02 SMIN= -5641.41 TMAX= 2820.19 ANGLE= 89.7 95 3 0.02 -0.01 0.00 0.00 -0.00 3703.79 3702.75 -3703.80 -1.06 0.17 3704.34 3704.36 TOP : SMAX= 1.11 SMIN= -3703.23 TMAX= 1852.17 ANGLE=-90.0 BOTT: SMAX= -3.23 SMIN= -3704.36 TMAX= 1850.57 ANGLE= 90.0 96 3 -0.03 -0.03 0.00 0.00 0.00 3704.99 3703.08 -3709.20 -10.35 1.86 3709.14 3709.27 TOP : SMAX= -8.31 SMIN= -3709.14 TMAX= 1850.41 ANGLE= 90.0 BOTT: SMAX= -12.39 SMIN= -3709.27 TMAX= 1848.44 ANGLE= 90.0 105 3 -0.00 -0.02 -0.00 -0.00 0.00 2.87 1.59 0.00 0.00 1.29 3.32 1.83 TOP : SMAX= 1.66 SMIN= -1.66 TMAX= 1.66 ANGLE= 90.0 BOTT: SMAX= 0.92 SMIN= -0.92 TMAX= 0.92 ANGLE= 90.0 106 3 -0.00 -0.03 -0.00 -0.00 -0.00 4.19 1.52 0.00 0.00 -1.65 4.83 1.75 TOP : SMAX= 2.42 SMIN= -2.42 TMAX= 2.42 ANGLE= 90.0 BOTT: SMAX= 0.88 SMIN= -0.88 TMAX= 0.88 ANGLE= 90.0 115 3 -0.02 -0.01 -0.00 -0.00 -0.00 3703.79 3702.75 3703.80 1.06 0.17 3704.34 3704.36 TOP : SMAX= 3703.23 SMIN= -1.11 TMAX= 1852.17 ANGLE= -0.0 BOTT: SMAX= 3704.36 SMIN= 3.23 TMAX= 1850.57 ANGLE= 0.0 116 3 0.03 -0.03 -0.00 -0.00 0.00 3704.99 3703.08 3709.20 10.35 1.86 3709.14 3709.27 TOP : SMAX= 3709.14 SMIN= 8.31 TMAX= 1850.41 ANGLE= 0.0 BOTT: SMAX= 3709.27 SMIN= 12.39 TMAX= 1848.44 ANGLE= 0.0 :A CANTILEVER BEAM OF TUBULAR SECTION -- PAGE NO. 13 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 125 3 0.81 0.01 -0.04 0.00 -0.01 5463.48 5646.25 5554.57 -0.18 -1.31 5464.40 5647.48 TOP : SMAX= 5464.40 SMIN= 1.84 TMAX= 2731.28 ANGLE= -0.3 BOTT: SMAX= 5645.01 SMIN= -2.48 TMAX= 2823.74 ANGLE= 0.3 126 3 1.04 0.03 -0.04 0.00 -0.01 5459.11 5640.90 5551.52 3.75 -4.91 5462.11 5641.41 TOP : SMAX= 5462.11 SMIN= 6.00 TMAX= 2728.05 ANGLE= -0.4 BOTT: SMAX= 5641.41 SMIN= 1.02 TMAX= 2820.19 ANGLE= 0.3 135 3 0.81 -0.01 -0.04 0.00 0.01 5463.48 5646.25 5554.57 -0.18 1.31 5464.40 5647.48 TOP : SMAX= 5464.40 SMIN= 1.84 TMAX= 2731.28 ANGLE= 0.3 BOTT: SMAX= 5645.01 SMIN= -2.48 TMAX= 2823.74 ANGLE= -0.3 136 3 1.04 -0.03 -0.04 0.00 0.01 5459.11 5640.90 5551.52 3.75 4.91 5462.11 5641.41 TOP : SMAX= 5462.11 SMIN= 6.00 TMAX= 2728.05 ANGLE= 0.4 BOTT: SMAX= 5641.41 SMIN= 1.02 TMAX= 2820.19 ANGLE= -0.3 **** MAXIMUM STRESSES AMONG SELECTED PLATES AND CASES **** MAXIMUM MINIMUM MAXIMUM MAXIMUM MAXIMUM PRINCIPAL PRINCIPAL SHEAR VONMISES TRESCA STRESS STRESS STRESS STRESS STRESS 5.645007E+03 -5.645007E+03 2.823742E+03 5.646246E+03 5.647484E+03 PLATE NO. 125 75 75 75 75 CASE NO. 3 3 3 3 3 ********************END OF ELEMENT FORCES******************** 115. LOAD LIST 4 116. PRINT ELEMENT STRESSES LIST 41 51 61 71 81 91 101 111 121 131 ELEMENT STRESSES LIST 41 :A CANTILEVER BEAM OF TUBULAR SECTION -- PAGE NO. 14 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 41 4 -14.20 10.26 -0.04 -0.03 0.01 28183.86 28061.26 -28424.34 -2007.57 -3462.32 28963.74 28777.50 TOP : SMAX= -1630.57 SMIN= -28963.74 TMAX= 13666.59 ANGLE=-82.7 BOTT: SMAX= -1492.00 SMIN= -28777.50 TMAX= 13642.75 ANGLE=-82.6 51 4 -0.00 -1.14 0.00 0.00 -0.02 5356.82 5150.93 -0.00 -0.00 -3033.32 6185.52 5947.78 TOP : SMAX= 3092.76 SMIN= -3092.76 TMAX= 3092.76 ANGLE= 90.0 BOTT: SMAX= 2973.89 SMIN= -2973.89 TMAX= 2973.89 ANGLE= 90.0 61 4 14.20 10.26 0.04 0.03 0.01 28183.86 28061.26 28424.34 2007.57 -3462.32 28963.74 28777.50 TOP : SMAX= 28963.74 SMIN= 1630.57 TMAX= 13666.59 ANGLE= -7.3 BOTT: SMAX= 28777.50 SMIN= 1492.00 TMAX= 13642.75 ANGLE= -7.4 71 4 21.02 -14.62 -0.33 -0.06 -0.06 39671.99 41111.66 42074.63 3650.80 692.96 41300.99 42874.24 TOP : SMAX= 41300.99 SMIN= 3488.38 TMAX= 18906.30 ANGLE= 0.8 BOTT: SMAX= 42874.24 SMIN= 3787.25 TMAX= 19543.49 ANGLE= 1.2 81 4 21.02 14.62 -0.33 -0.06 0.06 39671.99 41111.66 42074.63 3650.80 -692.96 41300.99 42874.24 TOP : SMAX= 41300.99 SMIN= 3488.38 TMAX= 18906.30 ANGLE= -0.8 BOTT: SMAX= 42874.24 SMIN= 3787.25 TMAX= 19543.49 ANGLE= -1.2 91 4 14.20 -10.26 0.04 0.03 -0.01 28183.86 28061.26 28424.34 2007.57 3462.32 28963.74 28777.50 TOP : SMAX= 28963.74 SMIN= 1630.57 TMAX= 13666.59 ANGLE= 7.3 BOTT: SMAX= 28777.50 SMIN= 1492.00 TMAX= 13642.75 ANGLE= 7.4 101 4 0.00 1.14 -0.00 -0.00 0.02 5356.82 5150.93 0.00 0.00 3033.32 6185.52 5947.78 TOP : SMAX= 3092.76 SMIN= -3092.76 TMAX= 3092.76 ANGLE= 90.0 BOTT: SMAX= 2973.89 SMIN= -2973.89 TMAX= 2973.89 ANGLE= 90.0 111 4 -14.20 -10.26 -0.04 -0.03 -0.01 28183.86 28061.26 -28424.34 -2007.57 3462.32 28963.74 28777.50 TOP : SMAX= -1630.57 SMIN= -28963.74 TMAX= 13666.59 ANGLE= 82.7 BOTT: SMAX= -1492.00 SMIN= -28777.50 TMAX= 13642.75 ANGLE= 82.6 :A CANTILEVER BEAM OF TUBULAR SECTION -- PAGE NO. 15 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 121 4 -21.02 14.62 0.33 0.06 0.06 39671.99 41111.66 -42074.63 -3650.80 -692.96 41300.99 42874.24 TOP : SMAX= -3488.38 SMIN= -41300.99 TMAX= 18906.30 ANGLE=-89.2 BOTT: SMAX= -3787.25 SMIN= -42874.24 TMAX= 19543.49 ANGLE=-88.8 131 4 -21.02 -14.62 0.33 0.06 -0.06 39671.99 41111.66 -42074.63 -3650.80 692.96 41300.99 42874.24 TOP : SMAX= -3488.38 SMIN= -41300.99 TMAX= 18906.30 ANGLE= 89.2 BOTT: SMAX= -3787.25 SMIN= -42874.24 TMAX= 19543.49 ANGLE= 88.8 **** MAXIMUM STRESSES AMONG SELECTED PLATES AND CASES **** MAXIMUM MINIMUM MAXIMUM MAXIMUM MAXIMUM PRINCIPAL PRINCIPAL SHEAR VONMISES TRESCA STRESS STRESS STRESS STRESS STRESS 4.287424E+04 -4.287424E+04 1.954349E+04 4.111166E+04 4.287424E+04 PLATE NO. 71 121 71 71 71 CASE NO. 4 4 4 4 4 ********************END OF ELEMENT FORCES********************