# 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

### Element numbers at a) the middle section and b) the free end

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

Table 1. Comparison of results
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%

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
11 22 33 44 55 66 77 88 99 110 FX 100
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
44 55 66 FX -258.6
33 77 FX -86.3
22 88 FX 86.3
11 99 110 FX 258.6
11 44 66 99 FY -66
22 33 77 88 FY -184
PERFORM ANALYSIS
PRINT JOINT DISPLACEMENTS LIST 11 22 33 44 55 66 77 88 99 110
PRINT ELEMENT STRESSES LIST 46 56 66 76 86 96 106 116 126 136
PRINT ELEMENT STRESSES LIST 50 60 70 80 90 100 110 120 130 140
PRINT ELEMENT STRESSES LIST 45 46 55 56 65 66 75 76 85 86 95 96 105 -
106 115 116 125 126 135 136
PRINT ELEMENT STRESSES LIST 41 51 61 71 81 91 101 111 121 131
FINISH
``````

```   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 **************
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********************
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********************
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********************
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********************
```