Mohr Circle Plot: Mohr Plots of Up To 4 Stress States With A Failure Envelope and Tensile Cutoff Case 1 Case 2 Case 3
Mohr Circle Plot: Mohr Plots of Up To 4 Stress States With A Failure Envelope and Tensile Cutoff Case 1 Case 2 Case 3
Mohr Circle Plot: Mohr Plots of Up To 4 Stress States With A Failure Envelope and Tensile Cutoff Case 1 Case 2 Case 3
failure?
failure?
failure?
two- normal shear two- normal shear two- normal shear
theta traction traction theta traction traction theta traction traction
1 2.50019 0.021816 No 1 2.000228 0.026179 No 1 1.500267 0.030542 No
2 2.500761 0.043624 No 2 2.000914 0.052349 No 2 1.501066 0.061074 No
3 2.501713 0.06542 No 3 2.002056 0.078504 No 3 1.502398 0.091588 No
4 2.503045 0.087196 No 4 Mohr circle plot
2.003654 0.104635 No 4 1.504263 0.122074 No
5 2.504757 0.108945 No 5 2.005708 0.130734 No 5 1.506659 0.152523 No
6 2.506848 0.130661 No 6 2.008217 0.156793 No 6 1.509587 0.182925 No
7 2.509317 0.152337 No 7 2.011181 0.182804 No 7 1.513044 0.213271 No
8 2.5121654 0.173966 No 8 2.014598 0.20876 No 8 1.517031 0.243553 No
9 2.51539 0.195543 No 9 2.018467 0.234652 No 9 1.521545 0.27376 No
10 2.51899
3.5 0.21706 No 10 2.022788 0.260472 No 10 1.526586 0.303884 No
11 2.522966 0.238511 No 11 2.027559 0.286213 No 11 1.532152 0.333916 No
12 2.5273153 0.25989 No 12 2.032779 0.311868 No 12 1.538242 0.363845 No
13 2.532037 0.281189 No 13 2.038445 0.337427 No 13 1.544852 0.393664
case 1No
shear stress traction
failure?
two- normal shear normal shear normal shear
theta traction traction tracton tracton tracton tracton
1 1.000305 0.034905 No -0.668333 0.164138 -0.7 0.004862
2 1.001218 0.069799 No -0.636667 0.18242 -0.7 0.009724
3 Explanation:
1.002741 ThisNo
0.104672 sheet plots
-0.605up 0.200703
to 4 Mohr circles -0.7 0.014585
4 representing
1.004872 0.139513 No4 stress states (in 2D)
-0.573333 0.218986 simultaneously,
-0.7 each
0.019447
labeled as case 1 through case 4 on the plot. A failure
5 1.007611 0.174311 No -0.541667 0.237269 -0.7 0.024309
envelope and a tensile cut off are also plotted. Input values
6 1.010956
are in the0.209057
outlinedNo boxes -0.51
- simply0.255551
change the default-0.7 values
0.029171
7 1.014908
to those0.243739
you desire.No They-0.478333
should0.273834 -0.7 units.
all be in the same 0.034033
8 Make sure that
1.019464 0.278346 No sigma 1 is always greater
-0.446667 0.292117 than sigma
-0.7 3 0.038895
9 (sigma 10.312869
1.024623 and 3 referring
No to the two0.3104
-0.415 principal stress-0.7being0.043756
plotted.
10 1.030384 0.347296 No -0.383333 0.328682 -0.7 0.048618
11 1.036746
You can 0.381618 No
use this sheet -0.351667
to model stress0.346965 -0.7
state evolution 0.05348
that
12 1.043705
leads to 0.415823 Noto model
failure (i.e. -0.32loading
0.365248 -0.7of the
paths). If one 0.058342
case 1 13 circles 'touches'
1.05126 0.449902 theNo failure envelope
-0.288333 or tensile cutoff
0.383531 -0.7 then0.063204
failure should occur. In this particular sheet what is
Case 2 14 1.059409 0.483844 No -0.256667 0.401813 -0.7 0.068066
modeled is pristine failure. Note the fourth column for each
case 3 15 1.068148
of the for0.517638 No cases
stress state -0.225(each 0.420096 -0.7
marked by a differently 0.072927
case 4 16 1.077477
colored 0.551275 No
block of cells). -0.193333
It marks the 0.438379
cases where-0.7 0.077789
the shear
Failure envelope
17 stress exceeds
1.08739 0.584743the Nofailure criteria0.456662
-0.161667 and slip would-0.7 be 0.082651
Tensile cutoff 18 expected with
1.097887 0.618034 No the word yes (otherwise
-0.13 0.474944 no is returned
-0.7 and
0.087513
the slip surface should be stable). You may have to move
19 1.108963
the plot 0.651136 No
or this explanation-0.098333
box to 0.493227
see the values-0.7 in this0.092375
20 1.120615
column. 0.68404 No -0.066667 0.51151 -0.7 0.097237
21 1.132839 0.716736 No -0.035 0.529793 -0.7 0.102098
22 You can easily
1.145632 0.749213 No modify this sheet to
-0.003333 0.548075 add additional cases.
-0.7 0.10696
23 Depending on
1.15899 0.781462 No the input values the
0.028333 0.566358x and y axis may
-0.7 not be
0.111822
scaled the same and so the circles will plot as ellipses. You
24 1.172909
can simply0.813473 No grab the
click on, 0.06corner0.584641
and resize the-0.7plot0.116684
until
25 1.187384 0.845237 No 0.091667
the Mohr circles look like circles. 0.602924 -0.7 0.121546
26 H.D.Maher 9/12
1.202412 0.876742 No 0.123333 0.621207 -0.7 0.126408
27 1.217987 0.907981 No 0.155 0.639489 -0.7 0.131269
28 1.234105 0.938943 No 0.186667 0.657772 -0.7 0.136131
29 1.250761 0.969619 No 0.218333 0.676055 -0.7 0.140993
30 1.267949 1 No 0.25 0.694338 -0.7 0.145855
31 1.285665 1.030076 No 0.281667 0.71262
32 1.303904 1.059839 No 0.313333 0.730903
33 1.322659 1.089278 No 0.345 0.749186
34 1.341925 1.118386 No 0.376667 0.767469
35 1.361696 1.147153 No 0.408333 0.785751
36 1.381966 1.175571 No 0.44 0.804034
37 1.402729 1.20363 No 0.471667 0.822317
38 1.423978 1.231323 No 0.503333 0.8406
39 1.445708 1.258641 No 0.535 0.858882
40 1.467911 1.285575 No 0.566667 0.877165
41 1.490581 1.312118 No 0.598333 0.895448
42 1.51371 1.338261 No 0.63 0.913731
43 1.537293 1.363997 No 0.661667 0.932013
44 1.56132 1.389317 No 0.693333 0.950296
45 1.585786 1.414214 No 0.725 0.968579
46 1.610683 1.43868 No 0.756667 0.986862
47 1.636003 1.462707 No 0.788333 1.005144
48 1.661739 1.48629 No 0.82 1.023427
49 1.687882 1.509419 No 0.851667 1.04171
50 1.714425 1.532089 No 0.883333 1.059993
51 1.741359 1.554292 No 0.915 1.078275
52 1.768677 1.576022 Yes 0.946667 1.096558
53 1.79637 1.597271 Yes 0.978333 1.114841
54 1.824429 1.618034 Yes 1.01 1.133124
55 1.852847 1.638304 Yes 1.041667 1.151407
56 1.881614 1.658075 Yes 1.073333 1.169689
57 1.910722 1.677341 Yes 1.105 1.187972
58 1.940161 1.696096 Yes 1.136667 1.206255
59 1.969924 1.714335 Yes 1.168333 1.224538
60 2 1.732051 Yes 1.2 1.24282
61 2.030381 1.749239 Yes 1.231667 1.261103
62 2.061057 1.765895 Yes 1.263333 1.279386
63 2.092019 1.782013 Yes 1.295 1.297669
64 2.123258 1.797588 Yes 1.326667 1.315951
65 2.154763 1.812616 Yes 1.358333 1.334234
66 2.186527 1.827091 Yes 1.39 1.352517
67 2.218538 1.84101 Yes 1.421667 1.3708
68 2.250787 1.854368 Yes 1.453333 1.389082
69 2.283264 1.867161 No 1.485 1.407365
70 2.31596 1.879385 No 1.516667 1.425648
71 2.348864 1.891037 No 1.548333 1.443931
72 2.381966 1.902113 No 1.58 1.462213
73 2.415257 1.91261 No 1.611667 1.480496
74 2.448725 1.922523 No 1.643333 1.498779
75 2.482362 1.931852 No 1.675 1.517062
76 2.516156 1.940591 No 1.706667 1.535344
77 2.550098 1.94874 No 1.738333 1.553627
78 2.584177 1.956295 No 1.77 1.57191
79 2.618382 1.963254 No 1.801667 1.590193
80 2.652704 1.969616 No 1.833333 1.608475
81 2.687131 1.975377 No 1.865 1.626758
82 2.721654 1.980536 No 1.896667 1.645041
83 2.756261 1.985092 No 1.928333 1.663324
84 2.790943 1.989044 No 1.96 1.681607
85 2.825689 1.992389 No 1.991667 1.699889
86 2.860487 1.995128 No 2.023333 1.718172
87 2.895328 1.997259 No 2.055 1.736455
88 2.930201 1.998782 No 2.086667 1.754738
89 2.965095 1.999695 No 2.118333 1.77302
90 3 2 No 2.15 1.791303
91 3.034905 1.999695 No 2.181667 1.809586
92 3.069799 1.998782 No 2.213333 1.827869
93 3.104672 1.997259 No 2.245 1.846151
94 3.139513 1.995128 No 2.276667 1.864434
95 3.174311 1.992389 No 2.308333 1.882717
96 3.209057 1.989044 No 2.34 1.901
97 3.243739 1.985092 No 2.371667 1.919282
98 3.278346 1.980536 No 2.403333 1.937565
99 3.312869 1.975377 No 2.435 1.955848
100 3.347296 1.969616 No 2.466667 1.974131
101 3.381618 1.963254 No 2.498333 1.992413
102 3.415823 1.956295 No 2.53 2.010696
103 3.449902 1.94874 No 2.561667 2.028979
104 3.483844 1.940591 No 2.593333 2.047262
105 3.517638 1.931852 No 2.625 2.065544
106 3.551275 1.922523 No 2.656667 2.083827
107 3.584743 1.91261 No 2.688333 2.10211
108 3.618034 1.902113 No 2.72 2.120393
109 3.651136 1.891037 No 2.751667 2.138675
110 3.68404 1.879385 No 2.783333 2.156958
111 3.716736 1.867161 No 2.815 2.175241
112 3.749213 1.854368 No 2.846667 2.193524
113 3.781462 1.84101 No 2.878333 2.211807
114 3.813473 1.827091 No 2.91 2.230089
115 3.845237 1.812616 No 2.941667 2.248372
116 3.876742 1.797588 No 2.973333 2.266655
117 3.907981 1.782013 No 3.005 2.284938
118 3.938943 1.765895 No 3.036667 2.30322
119 3.969619 1.749239 No 3.068333 2.321503
120 4 1.732051 No 3.1 2.339786
121 4.030076 1.714335 No 3.131667 2.358069
122 4.059839 1.696096 No 3.163333 2.376351
123 4.089278 1.677341 No 3.195 2.394634
124 4.118386 1.658075 No 3.226667 2.412917
125 4.147153 1.638304 No 3.258333 2.4312
126 4.175571 1.618034 No 3.29 2.449482
127 4.20363 1.597271 No 3.321667 2.467765
128 4.231323 1.576022 No 3.353333 2.486048
129 4.258641 1.554292 No 3.385 2.504331
130 4.285575 1.532089 No 3.416667 2.522613
131 4.312118 1.509419 No 3.448333 2.540896
132 4.338261 1.48629 No 3.48 2.559179
133 4.363997 1.462707 No 3.511667 2.577462
134 4.389317 1.43868 No 3.543333 2.595744
135 4.414214 1.414214 No 3.575 2.614027
136 4.43868 1.389317 No 3.606667 2.63231
137 4.462707 1.363997 No 3.638333 2.650593
138 4.48629 1.338261 No 3.67 2.668875
139 4.509419 1.312118 No 3.701667 2.687158
140 4.532089 1.285575 No 3.733333 2.705441
141 4.554292 1.258641 No 3.765 2.723724
142 4.576022 1.231323 No 3.796667 2.742007
143 4.597271 1.20363 No 3.828333 2.760289
144 4.618034 1.175571 No 3.86 2.778572
145 4.638304 1.147153 No 3.891667 2.796855
146 4.658075 1.118386 No 3.923333 2.815138
147 4.677341 1.089278 No 3.955 2.83342
148 4.696096 1.059839 No 3.986667 2.851703
149 4.714335 1.030076 No 4.018333 2.869986
150 4.732051 1 No 4.05 2.888269
151 4.749239 0.969619 No 4.081667 2.906551
152 4.765895 0.938943 No 4.113333 2.924834
153 4.782013 0.907981 No 4.145 2.943117
154 4.797588 0.876742 No 4.176667 2.9614
155 4.812616 0.845237 No 4.208333 2.979682
156 4.827091 0.813473 No 4.24 2.997965
157 4.84101 0.781462 No 4.271667 3.016248
158 4.854368 0.749213 No 4.303333 3.034531
159 4.867161 0.716736 No 4.335 3.052813
160 4.879385 0.68404 No 4.366667 3.071096
161 4.891037 0.651136 No 4.398333 3.089379
162 4.902113 0.618034 No 4.43 3.107662
163 4.91261 0.584743 No 4.461667 3.125944
164 4.922523 0.551275 No 4.493333 3.144227
165 4.931852 0.517638 No 4.525 3.16251
166 4.940591 0.483844 No 4.556667 3.180793
167 4.94874 0.449902 No 4.588333 3.199075
168 4.956295 0.415823 No 4.62 3.217358
169 4.963254 0.381618 No 4.651667 3.235641
170 4.969616 0.347296 No 4.683333 3.253924
171 4.975377 0.312869 No 4.715 3.272207
172 4.980536 0.278346 No 4.746667 3.290489
173 4.985092 0.243739 No 4.778333 3.308772
174 4.989044 0.209057 No 4.81 3.327055
175 4.992389 0.174311 No 4.841667 3.345338
176 4.995128 0.139513 No 4.873333 3.36362
177 4.997259 0.104672 No 4.905 3.381903
178 4.998782 0.069799 No 4.936667 3.400186
179 4.999695 0.034905 No 4.968333 3.418469
180 5 2.449E-16 No 5 3.436751