CE-475: Pavement Design & Evaluation
ASSIGNMENT-3 (Part-2) Spring- 2017
Submitted By: Fahmid Tousif; ID: 16141630;
[email protected] 2-8-2017
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Problem5.3:
Determine the curling stresses during the day at points A, B, and C of a finite slab shown in Figure P5 .3a using one-quarter of the slab. The slab has a thickness of 8 in. and is subjected to a temperature gradient of 3°F per inch of slab. The modulus of subgrade reaction is 50 pci.
Solution:
In this problem, the solution was done for t he curling only as there is no loading condition mentioned. Problem Input:
Length of the slab= 20 ft & width of the slab= 12 ft No. of grids in X direction= 9 No. of grids in Y direction= 6 No. of nodes in X axis of symmetry= 9 No. of nodes in Y axis of symmetry= 6 T (thickness of each slab layer= 8 in. PR (Poisson's ratio of each slab layer). = 0.15 (for concret e) YM (Young's modulus of each slab layer) = 4e6 Temperature difference = -(3*8)=-24 SUBMOD (subgrade modulus of liquid foundation)= 50 pci The analysis along with the Lgraph has been presented below:
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Lgraph:
Kenslab Output:
INPUT FILE NAME -C:\KENPAVE\CE 475\classwork kenslab\Problem-5.3-book-Fahmid.T kenslab\Problem-5.3-book-Fahmid.TXT XT
NUMBER OF PROBLEMS PROBLEMS TO BE SOLVED SOLVED = 1
TITLE -problem 5.3 of book Fahmid 1
TYPE OF FOUNDATION (NFOUND)
=
0
TYPE OF DAMAGE ANALYSIS (NDAMA)
=
NUMBER OF PERIODS PER YEAR (NPY)
0
=
1
NUMBER OF LOAD GROUPS (NLG)
=
1
TOTAL NUMBER OF SLABS (NSLAB)
=
1
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TOTAL NUMBER OF JOINTS (NJOINT)
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=
0
ARRANGEMENT OF SLABS SLAB NO. NODES (NX) NO. NODES (NY) JOINT NO. AT FOUR SIDES (JONO) NO. IN X DIRECTION IN Y DIRECTION 1
9
6
0
0
0
LEFT RIGHT BOTTOM TOP 0
NUMBER OF LAYERS (NLAYER)-------------------------------------= 1 NODAL NUMBER USED TO CHECK CONVERGENCE (NNCK)-----------------= 1 NUMBER OF NODES NOT IN CONTACT (NOTCON)-----------------------= 0 NUMBER OF GAPS (NGAP)-----------------------------------------= 0 NUMBER OF POINTS FOR PRINTOUT (NPRINT)------------------------= 0 CODE FOR INPUT OF GAPS OR PRECOMPRESSIONS (INPUT)- -----------= 0 BOND BETWEEN TWO LAYERS (NBOND)-------------------------------= 0 CONDITION OF WARPING (NTEMP)----------------------------------= 1 CODE INDICATING WHETHER SLAB WEIGHT IS CONSIDERED (NWT)-------= 0 MAX NO. OF CYCLES FOR CHECKING CONTACT (NCYCLE)---------------= 1 NUMBER OF ADDITIONAL THICKNESSES FOR SLAB LAYER 1 (NAT1)------= 0 NUMBER OF ADDITIONAL THICKNESSES FOR SLAB LAYER 2 (NAT2)------= 0 NUMBER OF POINTS ON X AXIS OF SYMMETRY (NSX)------------------= 9 NUMBER OF POINTS ON Y AXIS OF SYMMETRY (NSY)------------------= 6 MORE DETAILED PRINTOUT FOR EACH CONTACT CYCLE (MDPO)----------= 0 TOLERANCE FOR ITERATIONS (DEL)--------------------------------= 0.001 MAXIMUM ALLOWABLE VERTICAL DISPLACEMENT (FMAX)----------------= 1 DIFFERENCE IN TEMP. BETWEEN TOP AND BOTTOM OF SLAB (TEMP)-----= -24 COEFFICIENT OF THERMAL EXPANSION (CT)-------------------------= 0.000005
SYSTEM OF UNITS (NUNIT)---------------------------------------= 0 (Length in in., force in lb, stress in psi, unit weigh in pcf
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subgrade and dowel K value in pci, and temperature in F)
FOR SLAB NO. 1 COORDINATES OF FINITE ELEMENT GRID ARE: X = 0 12 28 44 60 76 92 108 120 Y = 0 12 28 44 60 72
LAYER
THICKNESS (T)
NO. 1
POISSON'S
RATIO (PR) 8.00000
YOUNG'S
MODULUS (YM)
0.15000
4.000E+06
No. OF LOADED AREAS (NUDL) FOR EACH LOAD GROUP ARE: 0 NO. OF NODAL FORCES (NCNF) AND MOMENTS (NCMX AND NCMY) ARE: 0 0 0
NODES ON X AXIS OF SYMMETRY (NODSX) ARE: 6 12 18 24 30 36 42 48 54
NODES ON Y AXIS OF SYMMETRY (NODSY) ARE: 49 50 51 52 53 54
FOUNDATION ADJUSTMENT FACTOR (FSAF) FOR EACH PERIOD ARE: 1
NUMBER OF ADDITIONAL SUBGRADE MODULI (NAS) TO BE READ IN-----= 0 SUBGRADE MODULUS (SUBMOD)------------------------------------= 50
NODAL COORDINATES (XN AND YN) OF INDIVIDUAL SLAB ARE: 1
0.000
0.000
2
4
0.000
44.000
5
0.000
7
12.000
0.000
8
12.000 12.000
10 12.000 44.000 11 13 28.000
0.000
12.000
0.000
28.000
6
0.000
72.000
9
12.000 28.000
12.000 60.000 12 12.000 72.000
0.000 14 28.000
16 28.000 44.000 17
60.000
3
12.000 15 28.000
28.000
28.000 60.000 18 28.000 72.000
Tousif_Hw3_Feb8_2017
19 44.000
0.000 20 44.000
22 44.000 44.000 23 25 60.000
31 76.000
37 92.000
12.000 27 60.000
12.000 33 76.000
76.000 60.000 36
0.000 38 92.000
40 92.000 44.000 41
28.000
28.000
60.000 60.000 30 60.000 72.000
0.000 32 76.000
34 76.000 44.000 35
12.000 21 44.000
44.000 60.000 24 44.000 72.000
0.000 26 60.000
28 60.000 44.000 29
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28.000
76.000
12.000 39 92.000
72.000 28.000
92.000 60.000 42 92.000 72.000
43 108.000
0.000 44 108.000
46 108.000
44.000 47 108.000
49 120.000
0.000 50 120.000
52 120.000
44.000 53 120.000
12.000 45 108.000 60.000 48 108.000 12.000 51 120.000 60.000 54 120.000
28.000 72.000 28.000 72.000
AMOUNT OF INITIAL CURLING AND GAP (CURL) AT THE NODES IS 1 -0.14688 2 -0.13500 3 -0.12252 4 -0.11388 5 -0.10908 6 -0.10800 7 -0.12636 8 -0.11448 9 -0.10200 10 -0.09336 11 -0.08856 12 -0.08748 13 -0.10236 14 -0.09048 15 -0.07800 16 -0.06936 17 -0.06456 18 -0.06348 19 -0.08220 20 -0.07032 21 -0.05784 22 -0.04920 23 -0.04440 24 -0.04332 25 -0.06588 26 -0.05400 27 -0.04152 28 -0.03288 29 -0.02808 30 -0.02700 31 -0.05340 32 -0.04152 33 -0.02904 34 -0.02040 35 -0.01560 36 -0.01452 37 -0.04476 38 -0.03288 39 -0.02040 40 -0.01176 41 -0.00696 42 -0.00588 43 -0.03996 44 -0.02808 45 -0.01560 46 -0.00696 47 -0.00216 48 -0.00108 49 -0.03888 50 -0.02700 51 -0.01452 52 -0.00588 53 -0.00108 54 0.00000
HALF BAND WIDTH (NB) = 24
PERIOD 1 LOAD GROUP 1 AND CYCLE NO. 1
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DEFLECTIONS OF SLABS (F) ARE: (DOWNWARD POSITIVE) 1 0.05083
2 0.04046
3 0.02995
4 0.02299
5 0.01926
6 0.01843
7 0.04041
8 0.03001 9 0.01946 10 0.01245
11 0.00869 12 0.00786 13 0.02975 14 0.01928 15 0.00866 16 0.00162 17 -0.00217 18 -0.00301 19 0.02232 20 0.01176 21 0.00107 22 -0.00601 23 -0.00982 24 -0.01066 25 0.01748 26 0.00682 27 -0.00395 28 -0.01107 29 -0.01489 30 -0.01574 31 0.01455 32 0.00379 33 -0.00706 34 -0.01422 35 -0.01805 36 -0.01890 37 0.01293 38 0.00209 39 -0.00881 40 -0.01600 41 -0.01985 42 -0.02070 43 0.01218 44 0.00130 45 -0.00964 46 -0.01685 47 -0.02070 48 -0.02155 49 0.01203 50 0.00114 51 -0.00981 52 -0.01702 53 -0.02088 54 -0.02173
NODAL NUMBER AND REACTIVE PRESSURE (SUBR) ARE: (COMPRESSION POSITIVE) 1
2.541
2
2.023
3
1.498
4
1.150
6
0.922
7
2.020
8
1.501
9
0.973 10
0.393 13
5
0.963 0.623
11
0.434 12
1.487 14
0.964 15
0.433
16
0.081 17 -0.109 18 -0.150 19
1.116 20
0.588
21
0.054 22 -0.301 23
-0.491 24 -0.533 25
0.874
26
0.341 27
-0.198 28
-0.554 29
-0.787
31
0.727 32
0.189 33
-0.353 34 -0.711 35 -0.903
36 -0.945 37
0.647 38
0.105 39
-0.440 40 -0.800
41 -0.992 42 -1.035 43
0.609 44
0.065 45
-0.482
46 -0.842 47 -1.035 48
-1.078 49
0.602 50
0.057
-0.745 30
51 -0.490 52 -0.851 53 -1.044 54 -1.087
SUM OF FORCES (FOSUM) = 0.0 SUM OF REACTIONS (SUBSUM) = -1.3
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NODE
LAYER
STRESS X
STRESS Y
STRESS XY
MAX.SHEAR
MAJOR
MINOR
1
1
0
0
0
0
0
0
2
1
0
0.378
0
0.189
0.378
0
3
1
0
-17.867
0
8.934
0
-17.867
4
1
0
-39.355
0
19.678
0
-39.355
5
1
0
-54.299
0
27.15
0
-54.299
6
1
0
-57.865
0
28.933
0
-57.865
7
1
-3.948
0
0
1.974
0
-3.948
8
1
-7.004
-1.606
3.531
4.444
0.139
-8.749
9
1
-9.549
-19.089
2.883
5.573
-8.746
-19.892
10
1
-11.428
-39.979
2.144
14.436
-11.268
-40.14
11
1
-12.498
-54.612
1.056
21.083
-12.472
-54.638
12
1
-12.724
-58.18
0
22.728
-12.724
-58.18
13
1
-35.619
0
0
17.809
0
-35.619
14
1
-37.955
-3.996
4.764
17.635
-3.341
-38.61
15
1
-41.638
-22.782
2.7
9.807
-22.403
-42.017
16
1
-44.775
-43.961
1.5
1.554
-42.814
-45.922
17
1
-46.679
-58.58
0.604
5.981
-46.648
-58.61
18
1
-47.112
-62.085
0
7.487
-47.112
-62.085
19
1
-78.33
0
0
39.165
0
-78.33
20
1
-79.819
-6.36
5.715
37.171
-5.918
-80.26
21
1
-83.401
-27.051
2.931
28.327
-26.899
-83.553
22
1
-86.851
-49.116
1.388
18.919
-49.065
-86.902
23
1
-89.075
-64.09
0.494
12.502
-64.081
-89.085
24
1
-67.676
0
10.962
-67.676
0
0
60.899
0
-89.6 121.798
-8.444
5.805
57.336
-8.149
-31.007
2.982
47.415
-30.913
-54.156
1.371
37.464
-54.131
1
-89.6 121.798 122.526 125.649 129.034 131.329
-69.655
0.468
30.84
-69.651
-122.82 125.743 129.059 131.332
1
-131.87
-73.334
0
29.268
-73.334
-131.87
25 26 27 28 29 30
1 1 1 1
Tousif_Hw3_Feb8_2017
31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
159.505 159.631 162.292 165.471
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0
0
79.752
0
-10.101
5.028
74.934
-9.932
-34.244
2.633
64.078
-34.19
-58.375
1.225
53.562
-58.361
-167.7 168.242 187.576 187.219 189.546 192.542 194.691 195.209 203.759 203.192 205.274
-74.372
0.422
46.666
-74.37
-78.164
0
45.039
-78.164
0
0
93.788
0
-11.249
3.558
88.057
-11.177
-36.543
1.895
76.525
-36.52
-61.424
0.894
65.565
-61.418
-77.816
0.312
58.438
-77.815
-81.682
0
56.763
-81.682
0
0
101.879
0
-11.861
1.692
95.68
-11.846
-37.821
0.866
83.731
-37.816
-208.14 210.235
-63.145
0.409
72.499
-63.144
-79.774
0.14
65.231
-79.773
-83.683
0
63.529
-83.683
0
0
103.712
0
-11.977
0
97.457
-11.977
-38.097
0
85.367
-38.097
-63.531
0
74.072
-63.531
-80.213
0
66.773
-80.213
-84.139
0
65.065
-84.139
-210.74 207.423 206.891 -208.83 211.676 -213.76 214.269
159.505 -159.8 162.346 165.485 167.702 168.242 187.576 187.291 189.569 192.548 194.692 195.209 203.759 203.207 205.278 208.141 210.235 -210.74 207.423 206.891 -208.83 211.676 -213.76 214.269
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MAXIMUM STRESS (SMAX) IN LAYER 1 IS
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-214.269 ( NODE 54 )
MAXIMUM NEGATIVE STRESS IN X DIRECTION =
-214.3 ( NODE 54 )
MAXIMUM POSITIVE STRESS IN X DIRECTION =
0.0 ( NODE 0 )
MAXIMUM NEGATIVE STRESS IN Y DIRECTION =
-84.1 ( NODE 54 )
MAXIMUM POSITIVE STRESS IN Y DIRECTION =
0.4 ( NODE 2 )
Result: Location At point A At point B At point C
Curling Stresses (psi) 214.269 207.423 57.865
Node No. 54 49 6
Problem 5.4: Figure P5 .4a shows a concrete slab, 10 in. thick, supported by a subgrade with a modulus of subgrade reaction of 200 pci. A 12,000-lb dual-wheel load (each wheel 6000 lb) spaced at 14 in. on centers is applied at the corner of the slab. The contact pressure is 80 psi. Determine the maximum stress in the concrete.
Solution: In this problem, a dual wheel load has been applied in the corner of the infinite slab. Problem input: Here, since it is a dual wheel, there is 2 tires. Since the tire pressure q=QQ= 80 psi, Thus area, A= (6000/80)=75 in2 & L= = √(75/0.5227)=11.97855 in.
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So for the equivalent rectangular area length= 0.8712L=0.8712*11.97855 = 10.44 in. & width= 0.6L=0.6*11.97855 =7.19 in. No. of grids in X direction= 7 No. of grids in Y direction= 6 T (thickness of each slab layer= 10 in. PR (Poisson's ratio of each slab layer). = 0.15 (for concrete) YM (Young's modulus of each slab layer) = 4e6 NUDL (number of uniformly distributed load for each load group) = 2 ( as its dual wheel load and placed at the corner) SUBMOD (subgrade modulus of liquid foundation)= 200 pci The analysis along with the Lgraph has been presented below: Lgraph:
Kenslab Output:
INPUT FILE NAME -C:\KENPAVE\CE 475\classwork kenslab\Problem-5.4-book-Fahmid.TXT
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NUMBER OF PROBLEMS TO BE SOLVED = 1
TITLE -problem 5.4 of book Fahmid
TYPE OF FOUNDATION (NFOUND)
=
0
TYPE OF DAMAGE ANALYSIS (NDAMA)
=
NUMBER OF PERIODS PER YEAR (NPY)
0
=
1
NUMBER OF LOAD GROUPS (NLG)
=
1
TOTAL NUMBER OF SLABS (NSLAB)
=
1
TOTAL NUMBER OF JOINTS (NJOINT)
=
0
ARRANGEMENT OF SLABS SLAB NO. NODES (NX) NO. NODES (NY) JOINT NO. AT FOUR SIDES (JONO) NO. IN X DIRECTION IN Y DIRECTION 1
7
6
0
0
0
LEFT RIGHT BOTTOM TOP 0
NUMBER OF LAYERS (NLAYER)-------------------------------------= 1 NODAL NUMBER USED TO CHECK CONVERGENCE (NNCK)-----------------= 1 NUMBER OF NODES NOT IN CONTACT (NOTCON)-----------------------= 0 NUMBER OF GAPS (NGAP)-----------------------------------------= 0 NUMBER OF POINTS FOR PRINTOUT (NPRINT)------------------------= 0 CODE FOR INPUT OF GAPS OR PRECOMPRESSIONS (INPUT)- -----------= 0 BOND BETWEEN TWO LAYERS (NBOND)-------------------------------= 0 CONDITION OF WARPING (NTEMP)----------------------------------= 0 CODE INDICATING WHETHER SLAB WEIGHT IS CONSIDERED (NWT)-------= 0 MAX NO. OF CYCLES FOR CHECKING CONTACT (NCYCLE)---------------= 1 NUMBER OF ADDITIONAL THICKNESSES FOR SLAB LAYER 1 (NAT1)------= 0 NUMBER OF ADDITIONAL THICKNESSES FOR SLAB LAYER 2 (NAT2)------= 0 NUMBER OF POINTS ON X AXIS OF SYMMETRY (NSX)------------------= 0
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NUMBER OF POINTS ON Y AXIS OF SYMMETRY (NSY)------------------= 0 MORE DETAILED PRINTOUT FOR EACH CONTACT CYCLE (MDPO)----------= 0 TOLERANCE FOR ITERATIONS (DEL)--------------------------------= 0.001 MAXIMUM ALLOWABLE VERTICAL DISPLACEMENT (FMAX)----------------= 1
SYSTEM OF UNITS (NUNIT)---------------------------------------= 0 (Length in in., force in lb, stress in psi, unit weigh in pcf subgrade and dowel K value in pci, and temperature in F)
FOR SLAB NO. 1 COORDINATES OF FINITE ELEMENT GRID ARE: X = 0 12 24 36 54 78 120 Y = 0 17.6 36 54 78 120
LAYER
THICKNESS (T)
NO. 1
POISSON'S
RATIO (PR) 10.00000
YOUNG'S
MODULUS (YM)
0.15000
4.000E+06
No. OF LOADED AREAS (NUDL) FOR EACH LOAD GROUP ARE: 2 NO. OF NODAL FORCES (NCNF) AND MOMENTS (NCMX AND NCMY) ARE: 0 0 0
FOR LOAD GROUP NO. 1 LOADS ARE APPLIED AS FOLLOWS: SLAB NO.
X COORDINATES
Y COORDINATES
(LS) (XL1)
(XL2)
(YL1)
(YL2)
1
0.00000
10.44000
1
0.00000
10.44000 14.00500
0.00000
INTENSITY
(QQ) 7.19000
80.00000
21.19500 80.00000
FOUNDATION ADJUSTMENT FACTOR (FSAF) FOR EACH PERIOD ARE: 1
NUMBER OF ADDITIONAL SUBGRADE MODULI (NAS) TO BE READ IN-----= 0
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SUBGRADE MODULUS (SUBMOD)------------------------------------= 200
NODAL COORDINATES (XN AND YN) OF INDIVIDUAL SLAB ARE: 1
0.000
0.000
4
0.000
54.000 5
7
12.000
0.000
2
8
0.000
17.600
0.000
3
0.000
78.000 6
12.000 17.600
9
36.000
0.000 120.000 12.000 36.000
10 12.000 54.000 11 12.000 78.000 12 12.000 120.000 13 24.000
0.000 14 24.000
17.600 15 24.000 36.000
16 24.000 54.000 17 24.000 78.000 18 24.000 120.000 19 36.000
0.000 20 36.000
17.600 21 36.000
36.000
22 36.000 54.000 23 36.000 78.000 24 36.000 120.000 25 54.000
0.000 26 54.000
17.600 27 54.000
36.000
28 54.000 54.000 29 54.000 78.000 30 54.000 120.000 31 78.000
0.000 32 78.000
17.600 33 78.000
36.000
34 78.000 54.000 35 78.000 78.000 36 78.000 120.000 37 120.000
0.000 38 120.000
17.600 39 120.000
36.000
40 120.000 54.000 41 120.000 78.000 42 120.000 120.000
HALF BAND WIDTH (NB) = 24
PERIOD 1 LOAD GROUP 1 AND CYCLE NO. 1
DEFLECTIONS OF SLABS (F) ARE: (DOWNWARD POSITIVE) 1 0.04269
2 0.03416
3 0.02479
4 0.01687
5 0.00922
6 0.00130
7 0.03550
8 0.02799
9 0.02012 10 0.01346
11 0.00693 12 -0.00013 13 0.02839 14 0.02208 15 0.01564 16 0.01018 17 0.00472 18 -0.00143 19 0.02191 20 0.01676 21 0.01157 22 0.00719 23 0.00272 24 -0.00253 25 0.01397 26 0.01025 27 0.00656 28 0.00346 29 0.00024 30 -0.00378
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31 0.00667 32 0.00422 33 0.00183 34 -0.00013 35 -0.00218 36 -0.00492 37 -0.00056 38 -0.00203 39 -0.00328 40 -0.00418 41 -0.00506 42 -0.00643
NODAL NUMBER AND REACTIVE PRESSURE (SUBR) ARE: (COMPRESSION POSITIVE) 1
8.537
2
6.831
3
4.958
4
3.374
5
6
0.261
7
7.100
8
5.599
9
4.025 10
1.843 2.693
11
1.385 12
-0.026 13
5.678 14
4.416 15
3.127
16
2.035 17
0.944 18
-0.286 19
4.382 20
3.351
21
2.315 22
1.438 23
0.545 24
-0.505 25
2.795
26
2.050 27
1.312 28
0.691 29
0.048 30
-0.755
31
1.334 32
0.843 33
0.366 34 -0.027 35 -0.437
36 -0.984 37 -0.113 38 -0.405 39 -0.656 40 -0.837 41 -1.012 42 -1.286
SUM OF FORCES (FOSUM) = 12010.2
SUM OF REACTIONS (SUBSUM) = 12008.9
NODE LAYER STRESS X STRESS Y STRESS XY MAX.SHEAR 0.000
0.000
0.000
MAJOR
1
1
0.000
0.000
2
1
0.000
-72.750
0.000
36.375
0.000
3
1
0.000
100.449
0.000
50.224
100.449
0.000
4
1
0.000
124.274
0.000
62.137
124.274
0.000
5
1
0.000
103.260
0.000
51.630
103.260
0.000
6
1
0.000
0.000
0.000
0.000
0.000
0.000
7
1
-9.966
0.000
0.000
4.983
0.000
-9.966
8 1
25.731 -16.097 -104.601 106.672
9
37.469
1
81.237 -112.211
10
1
34.538
105.271
11
1
25.392
82.306
-84.774 -47.669
0.000 -72.750
111.489 -101.855
114.325 173.678 91.856 55.517
-54.972
161.760 -21.951 109.366
-1.668
MINOR
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12
1
20.366
0.000
0.000
10.183
20.366
0.000
13
1
97.520
0.000
0.000
48.760
97.520
0.000
14
1
91.012
17.465 -104.099
110.403
164.642
-56.165
15
1
71.277
67.274 -104.140
104.159
173.434
-34.884
16
1
55.985
87.424
-80.030
81.559
153.264
-9.855
17
1
40.666
66.362
-47.108
48.829 102.343
4.685
18
1
29.657
0.000
0.000
19
1
137.317
0.000
0.000
20
1
117.710
30.326
-90.734
21
1
91.428
58.321
-87.774
89.321
164.196
-14.447
22
1
67.895
70.091
-70.043
70.052
139.045
-1.059
23
1
47.044
52.274
-43.577
43.655
93.314
6.004
24
1
31.116
0.000
0.000
25
1
137.844
0.000
0.000
26
1
116.065
32.109
-67.032
27
1
90.473
46.955
-63.475
67.101 135.815
1.613
28
1
66.550
49.496
-52.448
53.137 111.160
4.886
29
1
43.144
34.472
-35.126
35.393
30
1
23.504
0.000
0.000
31
1
100.211
0.000
0.000
32
1
77.862
24.849
-38.085
33
1
59.051
33.744
34
1
42.433
35
1
36
14.828
29.657
68.659
137.317
100.706
0.000
174.724
15.558
31.116
68.922
137.844
79.091
0.000 -26.688
0.000 0.000
153.178
74.201
-5.004
3.415
11.752
23.504
50.106
100.211
0.000
46.401
97.756
4.954
-37.193
39.286
85.683
7.111
30.788
-32.312
32.833
69.443
3.778
25.287
17.864
-23.199
23.494
45.069
-1.919
1
5.389
0.000
0.000
2.695
5.389
0.000
37
1
0.000
0.000
0.000
0.000
0.000
0.000
38
1
0.000
18.830
0.000
9.415
39
1
0.000
21.829
0.000
10.914
40
1
0.000
15.017
0.000
7.509
18.830 21.829 15.017
0.000
0.000 0.000 0.000
Tousif_Hw3_Feb8_2017
P a g e | 16
41
1
0.000
0.118
0.000
0.059
0.118
0.000
42
1
0.000
0.000
0.000
0.000
0.000
0.000
MAXIMUM STRESS (SMAX) IN LAYER 1 IS
174.724 ( NODE 20 )
MAXIMUM NEGATIVE STRESS IN X DIRECTION =
-10.0 ( NODE 7 )
MAXIMUM POSITIVE STRESS IN X DIRECTION =
137.8 ( NODE 25 )
MAXIMUM NEGATIVE STRESS IN Y DIRECTION =
-72.8 ( NODE 2 )
MAXIMUM POSITIVE STRESS IN Y DIRECTION =
124.3 ( NODE 4 )
Result: Maximum Stress in Concrete (psi) 174.724
Node No.
20
Problem 5.5: The pavement and loading are the same as in Problem 5 .4, but the load is applied in the interior of an infinite slab, as shown in Figure P5 .5a. Determine the maximum stress in the slab using one-quarter of the slab.
Solution: In this problem, a dual wheel load has been applied in the interior of the infinite slab. Problem input: Here, since it is a dual wheel, there is 2 tires. Since the tire pressure q=QQ= 80 psi, Thus area, A= (6000/80)=75 in2 & L= = √(75/0.5227)=11.97855 in.
Tousif_Hw3_Feb8_2017
P a g e | 17
So for the equivalent rectangular area length= 0.8712L=0.8712*11.97855 = 10.44 in. & width= 0.6L=0.6*11.97855 =7.19 in. Here, the only difference is, by taking one quarter of the total slab, only wheel load will be applied and in that case the half of the length of the wheel in x direction=(10.44/2)in.=5.22in. will be applied. No. of grids in X direction= 7 No. of grids in Y direction= 7 No. of nodes in X axis of symmetry= 7 No. of nodes in Y axis of symmetry= 7 T (thickness of each slab layer= 10 in. PR (Poisson's ratio of each slab layer). = 0.15 (for c oncrete) YM (Young's modulus of each slab layer) = 4e6 NUDL (number of uniformly distributed load for each load group) = 1 SUBMOD (subgrade modulus of liquid foundation)= 200 pci Special Observation: The grid size in the far end of the mesh did not satisfy the aspect ratio, which was blocking the calculation, thus in the far e nd in x direction, the last two grids have been reduced to 83 and 117 randomly.
The analysis along with the Lgraph has been presented below: Lgraph:
Tousif_Hw3_Feb8_2017
P a g e | 18
Kenslab Output:
INPUT FILE NAME -C:\KENPAVE\CE 475\classwork kenslab\Problem-5.5-book-Fahmid.TXT
NUMBER OF PROBLEMS TO BE SOLVED = 1
TITLE -problem 5.5 of book Fahmid
TYPE OF FOUNDATION (NFOUND)
=
0
TYPE OF DAMAGE ANALYSIS (NDAMA)
=
NUMBER OF PERIODS PER YEAR (NPY)
0
=
1
NUMBER OF LOAD GROUPS (NLG)
=
1
TOTAL NUMBER OF SLABS (NSLAB)
=
1
TOTAL NUMBER OF JOINTS (NJOINT)
=
0
Tousif_Hw3_Feb8_2017
P a g e | 19
ARRANGEMENT OF SLABS SLAB NO. NODES (NX) NO. NODES (NY) JOINT NO. AT FOUR SIDES (JONO) NO. IN X DIRECTION IN Y DIRECTION 1
7
7
0
0
0
LEFT RIGHT BOTTOM TOP 0
NUMBER OF LAYERS (NLAYER)-------------------------------------= 1 NODAL NUMBER USED TO CHECK CONVERGENCE (NNCK)-----------------= 1 NUMBER OF NODES NOT IN CONTACT (NOTCON)-----------------------= 0 NUMBER OF GAPS (NGAP)-----------------------------------------= 0 NUMBER OF POINTS FOR PRINTOUT (NPRINT)------------------------= 0 CODE FOR INPUT OF GAPS OR PRECOMPRESSIONS (INPUT)- -----------= 0 BOND BETWEEN TWO LAYERS (NBOND)-------------------------------= 0 CONDITION OF WARPING (NTEMP)----------------------------------= 0 CODE INDICATING WHETHER SLAB WEIGHT IS CONSIDERED (NWT)-------= 0 MAX NO. OF CYCLES FOR CHECKING CONTACT (NCYCLE)---------------= 1 NUMBER OF ADDITIONAL THICKNESSES FOR SLAB LAYER 1 (NAT1)------= 0 NUMBER OF ADDITIONAL THICKNESSES FOR SLAB LAYER 2 (NAT2)------= 0 NUMBER OF POINTS ON X AXIS OF SYMMETRY (NSX)------------------= 7 NUMBER OF POINTS ON Y AXIS OF SYMMETRY (NSY)------------------= 7 MORE DETAILED PRINTOUT FOR EACH CONTACT CYCLE (MDPO)----------= 0 TOLERANCE FOR ITERATIONS (DEL)--------------------------------= 0.001 MAXIMUM ALLOWABLE VERTICAL DISPLACEMENT (FMAX)----------------= 1
SYSTEM OF UNITS (NUNIT)---------------------------------------= 0 (Length in in., force in lb, stress in psi, unit weigh in pcf subgrade and dowel K value in pci, and temperature in F)
FOR SLAB NO. 1 COORDINATES OF FINITE ELEMENT GRID ARE: X = 0 7 14 26 48 83 117
Tousif_Hw3_Feb8_2017
P a g e | 20
Y = 0 7 14 26 48 83 117
LAYER
THICKNESS (T)
NO. 1
POISSON'S
RATIO (PR) 10.00000
YOUNG'S
MODULUS (YM)
0.15000
4.000E+06
No. OF LOADED AREAS (NUDL) FOR EACH LOAD GROUP ARE: 1 NO. OF NODAL FORCES (NCNF) AND MOMENTS (NCMX AND NCMY) ARE: 0 0 0
FOR LOAD GROUP NO. 1 LOADS ARE APPLIED AS FOLLOWS: SLAB NO.
X COORDINATES
(LS) (XL1)
(XL2)
1
5.22000
0.00000
Y COORDINATES
(YL1)
(YL2)
3.40500
INTENSITY
(QQ)
10.59500
80.00000
NODES ON X AXIS OF SYMMETRY (NODSX) ARE: 1 8 15 22 29 36 43
NODES ON Y AXIS OF SYMMETRY (NODSY) ARE: 1 2 3 4 5 6 7
FOUNDATION ADJUSTMENT FACTOR (FSAF) FOR EACH PERIOD ARE: 1
NUMBER OF ADDITIONAL SUBGRADE MODULI (NAS) TO BE READ IN-----= 0 SUBGRADE MODULUS (SUBMOD)------------------------------------= 200
NODAL COORDINATES (XN AND YN) OF INDIVIDUAL SLAB ARE: 1
0.000
0.000
2
4
0.000
26.000
7
0.000 117.000 8
5
0.000 0.000 7.000
7.000
3
0.000
14.000
48.000
6
0.000
83.000
0.000
9
7.000
7.000
10
7.000
14.000 11
7.000
26.000 12
13
7.000
83.000 14
7.000 117.000 15
7.000 14.000
48.000 0.000
Tousif_Hw3_Feb8_2017
16 14.000
7.000 17 14.000
P a g e | 21
14.000 18 14.000
26.000
19 14.000 48.000 20 14.000 83.000 21 14.000 117.000 22
26.000
0.000 23
25 26.000 26.000 26
26.000
7.000 24
26.000
14.000
26.000 48.000 27 26.000
28 26.000 117.000 29 48.000
83.000
0.000 30 48.000
7.000
31 48.000 14.000 32
48.000 26.000 33 48.000 48.000
34 48.000 83.000 35
48.000 117.000 36
37 83.000
7.000 38 83.000
83.000
14.000 39 83.000
0.000 26.000
40 83.000 48.000 41 83.000 83.000 42 83.000 117.000 43 117.000
0.000 44 117.000
7.000 45 117.000
46 117.000
26.000 47 117.000
48.000 48 117.000
14.000 83.000
49 117.000 117.000
HALF BAND WIDTH (NB) = 27
PERIOD 1 LOAD GROUP 1 AND CYCLE NO. 1
DEFLECTIONS OF SLABS (F) ARE: (DOWNWARD POSITIVE) 1 0.00550
2 0.00540
6 0.00106 7 -0.00017
3 0.00510
4 0.00436
5 0.00289
8 0.00537 9 0.00528 10 0.00500
11 0.00430 12 0.00286 13 0.00105 14 -0.00018 15 0.00506 16 0.00498 17 0.00474 18 0.00412 19 0.00277 20 0.00101 21 -0.00019 22 0.00431 23 0.00425 24 0.00409 25 0.00361 26 0.00249 27 0.00091 28 -0.00022 29 0.00285 30 0.00282 31 0.00273 32 0.00246 33 0.00176 34 0.00061 35 -0.00032 36 0.00103 37 0.00102 38 0.00098 39 0.00089 40 0.00060 41 0.00000 42 -0.00061 43 -0.00020 44 -0.00020 45 -0.00021 46 -0.00023 47 -0.00033 48 -0.00062 49 -0.00103
Tousif_Hw3_Feb8_2017
P a g e | 22
NODAL NUMBER AND REACTIVE PRESSURE (SUBR) ARE: (COMPRESSION POSITIVE) 1
1.100
2
1.080
3
1.021
4
0.873
5
6
0.211
7
-0.035
8
1.075
9
1.056 10
0.578 1.001
11
0.860 12
0.572 13
0.209 14
-0.035 15
1.012
16
0.995 17
0.949 18
0.823 19
0.553 20
0.203
21
-0.037 22
0.862 23
0.851 24
0.817 25
0.722
26
0.498 27
0.183 28
-0.043 29
0.569 30
0.563
31
0.546 32
0.493 33
0.353 34
0.123 35
-0.064
36
0.205 37
0.203 38
0.197 39
0.178 40
0.120
41
0.000 42
-0.122 43
-0.039 44
-0.040 45
-0.041
46 -0.047 47 -0.067 48 -0.123 49 -0.205
SUM OF FORCES (FOSUM) = 3002.5
SUM OF REACTIONS (SUBSUM) = 3001.4
NODE LAYER STRESS X STRESS Y STRESS XY MAX.SHEAR -93.146
0.000
1
1 -126.618
2
1 -128.555 -111.422
3
1
-96.025
-57.202
0.000
19.411
-57.202 -96.025
4
1
-56.399
-13.890
0.000
21.254
-13.890 -56.399
5
1
-24.741
9.819
6
1
-7.469
9.636
0.000
8.553
9.636
-7.469
7
1
-2.508
0.000
0.000
1.254
0.000
-2.508
8
1
-92.633
-90.751
0.000
0.941
-90.751 -92.633
9
1
-87.625
-92.042
-8.205
8.497
-81.337
0.000
0.000
16.736
MAJOR
-93.146 -126.618
8.567 -111.422 -128.555
17.280
9.819
-24.741
-98.330
10
1
-76.365
-57.172
-14.068
17.030
-49.739
-83.798
11
1
-51.828
-15.366
-10.744
21.161
-12.435
-54.758
12
1
-23.750
9.480
13
1
-7.321
14
1
-2.495
-5.090
17.377
10.242
-24.512
9.520
-1.768
8.604
9.704
-7.504
0.000
0.000
1.248
0.000
-2.495
MINOR
Tousif_Hw3_Feb8_2017
P a g e | 23
15
1
-49.912
-77.005
0.000
16
1
-48.347
-70.582
-10.496
15.289
-44.175
-74.754
17
1
-47.225
-51.920
-17.673
17.828
-31.744
-67.401
18
1 -39.519
-17.864
-16.647
19.858
-8.833 -48.550
19
1
-21.009
20
1
-6.898
21
1
22
1
8.205
13.547
-49.912
-9.289
17.310
9.143
-3.390
8.708
9.830
-7.586
-2.539
0.000
0.000
1.269
0.000
-2.539
-12.892
-50.769
0.000
18.939
-12.892
23
1 -13.709
-47.343
-8.480
18.834
-11.693 -49.360
24
1 -15.040
-38.544
-14.861
18.946
-7.846 -45.738
25
1
-16.720
-18.616
-17.889
17.914
0.246
-35.582
26
1
-12.931
4.807
11.710
-19.834
27
1
-5.625
7.807
-5.610
8.751
9.842
-7.660
28
1
-2.614
0.000
0.000
1.307
0.000
-2.614
29
1
10.134
-23.228
30
1
9.714
31
1
32
-13.042
15.772
10.908
-77.005
-23.712
-50.769
0.000
16.681
10.134
-23.228
-22.362
-4.551
16.671
10.347
-22.995
8.577
-19.864
-8.479
16.557
10.913
-22.200
1
5.610
-12.808
-12.478
33
1
0.681
0.082
-12.194
12.198
12.579
34
1
-2.141
4.239
-6.818
7.527
8.576
-6.478
35
1
-2.453
0.000
0.000
1.226
0.000
-2.453
36
1
9.607
-7.095
0.000
8.351
9.607
-7.095
37
1
9.478
-6.954
-1.676
8.385
9.647
-7.123
38
1
9.081
-6.575
-3.217
8.463
9.716
-7.210
39
1
7.814
-5.378
-5.355
8.496
9.714
-7.278
40
1
4.409
-2.210
-6.665
7.442
8.541
-6.342
41
1
-0.133
-0.275
-4.728
4.729
4.525
-4.933
42
1
-2.938
0.000
0.000
1.469
0.000
-2.938
43
1
0.000
-2.368
0.000
1.184
0.000
-2.368
15.508
11.909
-19.107 -11.816
Tousif_Hw3_Feb8_2017
P a g e | 24
44
1
0.000
-2.360
0.000
1.180
0.000
-2.360
45
1
0.000
-2.401
0.000
1.200
0.000
-2.401
46
1
0.000
-2.502
0.000
1.251
0.000
-2.502
47
1
0.000
-2.420
0.000
1.210
0.000
-2.420
48
1
0.000
-2.996
0.000
1.498
0.000
-2.996
49
1
0.000
0.000
0.000
0.000
0.000
0.000
MAXIMUM STRESS (SMAX) IN LAYER 1 IS
-128.555 ( NODE 2 )
MAXIMUM NEGATIVE STRESS IN X DIRECTION =
-128.6 ( NODE 2 )
MAXIMUM POSITIVE STRESS IN X DIRECTION =
10.1 ( NODE 29 )
MAXIMUM NEGATIVE STRESS IN Y DIRECTION =
-111.4 ( NODE 2 )
MAXIMUM POSITIVE STRESS IN Y DIRECTION =
9.8 ( NODE 5 )
Result: Maximum Stress in Concrete (psi) 128.555
Node No.
2
Problem 5.7: Figure P5 .7a shows a set of dual-tandem wheels with a total we ight of 40,000 lb (10,000 per wheel), a tire pressure of 100 psi, a dual spacing of 20 in., and a tandem spacing of 40 in .The concrete slab is 8 in. thick, with a modulus of subgrade reaction of 100 pci . De termine the interior stress at point A in the y direction under the center of the dual-tandem wheels using one-quarter of the slab.
Tousif_Hw3_Feb8_2017
P a g e | 25
Solution: In this problem, a dual tandem wheel load has been applied in the interior of the infinite slab. Problem input: Here, since it is a dual wheel, there is 4 tires. Since the tire pressure q=QQ= 100 psi, Thus are a, A= (40000/4)/100=100 in2 & L= = √(100/0.5227)=13.8316 in. So for the equivalent rectangular area length= 0.8712L=0.8712*13.8316 = 12.05 in. & width= 0.6L=0.6*13.8316 =8.23 in. No. of grids in X direction= 7 No. of grids in Y direction= 7 No. of nodes in X axis of symmetry= 7 No. of nodes in Y axis of symmetry= 7 T (thickness of each slab layer= 8 in. PR (Poisson's ratio of each slab layer). = 0.15 (for concrete) YM (Young's modulus of each slab layer) = 4e6 NUDL (number of uniformly distributed load for each load group) = 1 SUBMOD (subgrade modulus of liquid foundation)= 100 pci
The analysis along with the Lgraph has been pre sented below:
Lgraph:
Tousif_Hw3_Feb8_2017
P a g e | 26
Kenslab Output:
INPUT FILE NAME -C:\KENPAVE\CE 475\classwork kenslab\Problem-5.7-book-Fahmid.TXT
NUMBER OF PROBLEMS TO BE SOLVED = 1
TITLE -problem 5.7 of book Fahmid
TYPE OF FOUNDATION (NFOUND)
=
0
TYPE OF DAMAGE ANALYSIS (NDAMA)
=
NUMBER OF PERIODS PER YEAR (NPY)
0
=
1
NUMBER OF LOAD GROUPS (NLG)
=
1
TOTAL NUMBER OF SLABS (NSLAB)
=
1
TOTAL NUMBER OF JOINTS (NJOINT)
=
0
ARRANGEMENT OF SLABS
Tousif_Hw3_Feb8_2017
P a g e | 27
SLAB NO. NODES (NX) NO. NODES (NY) JOINT NO. AT FOUR SIDES (JONO) NO. IN X DIRECTION IN Y DIRECTION 1
7
7
0
0
0
LEFT RIGHT BOTTOM TOP 0
NUMBER OF LAYERS (NLAYER)-------------------------------------= 1 NODAL NUMBER USED TO CHECK CONVERGENCE (NNCK)-----------------= 1 NUMBER OF NODES NOT IN CONTACT (NOTCON)-----------------------= 0 NUMBER OF GAPS (NGAP)-----------------------------------------= 0 NUMBER OF POINTS FOR PRINTOUT (NPRINT)------------------------= 0 CODE FOR INPUT OF GAPS OR PRECOMPRESSIONS (INPUT)- -----------= 0 BOND BETWEEN TWO LAYERS (NBOND)-------------------------------= 0 CONDITION OF WARPING (NTEMP)----------------------------------= 0 CODE INDICATING WHETHER SLAB WEIGHT IS CONSIDERED (NWT)-------= 0 MAX NO. OF CYCLES FOR CHECKING CONTACT (NCYCLE)---------------= 1 NUMBER OF ADDITIONAL THICKNESSES FOR SLAB LAYER 1 (NAT1)------= 0 NUMBER OF ADDITIONAL THICKNESSES FOR SLAB LAYER 2 (NAT2)------= 0 NUMBER OF POINTS ON X AXIS OF SYMMETRY (NSX)------------------= 7 NUMBER OF POINTS ON Y AXIS OF SYMMETRY (NSY)------------------= 7 MORE DETAILED PRINTOUT FOR EACH CONTACT CYCLE (MDPO)----------= 0 TOLERANCE FOR ITERATIONS (DEL)--------------------------------= 0.001 MAXIMUM ALLOWABLE VERTICAL DISPLACEMENT (FMAX)----------------= 1
SYSTEM OF UNITS (NUNIT)---------------------------------------= 0 (Length in in., force in lb, stress in psi, unit weigh in pcf subgrade and dowel K value in pci, and temperature in F)
FOR SLAB NO. 1 COORDINATES OF FINITE ELEMENT GRID ARE: X = 0 10 20 40 60 90 120 Y = 0 10 20 40 60 90 120
Tousif_Hw3_Feb8_2017
LAYER
THICKNESS (T)
NO. 1
POISSON'S
RATIO (PR) 8.00000
P a g e | 28
YOUNG'S
MODULUS (YM)
0.15000
4.000E+06
No. OF LOADED AREAS (NUDL) FOR EACH LOAD GROUP ARE: 1 NO. OF NODAL FORCES (NCNF) AND MOMENTS (NCMX AND NCMY) ARE: 0 0 0
FOR LOAD GROUP NO. 1 LOADS ARE APPLIED AS FOLLOWS: SLAB NO.
X COORDINATES
(LS) (XL1) 1
(XL2)
13.97500
Y COORDINATES
(YL1)
26.02500
(YL2)
5.85100
INTENSITY
(QQ) 14.14900 100.00000
NODES ON X AXIS OF SYMMETRY (NODSX) ARE: 1 8 15 22 29 36 43
NODES ON Y AXIS OF SYMMETRY (NODSY) ARE: 1 2 3 4 5 6 7
FOUNDATION ADJUSTMENT FACTOR (FSAF) FOR EACH PERIOD ARE: 1
NUMBER OF ADDITIONAL SUBGRADE MODULI (NAS) TO BE READ IN-----= 0 SUBGRADE MODULUS (SUBMOD)------------------------------------= 100
NODAL COORDINATES (XN AND YN) OF INDIVIDUAL SLAB ARE: 1
0.000
0.000
4
0.000
40.000
7
0.000 120.000
2
0.000
5 8
0.000 10.000
10.000 60.000 0.000
3
0.000
6 9
0.000
20.000 90.000
10.000 10.000
10 10.000 20.000 11
10.000 40.000 12 10.000 60.000
13 10.000 90.000 14
10.000 120.000 15
16 20.000 10.000 17
20.000 20.000 18 20.000 40.000
20.000
0.000
Tousif_Hw3_Feb8_2017
P a g e | 29
19 20.000 60.000 20 20.000 90.000 21 20.000 120.000 22 40.000
0.000 23 40.000
25 40.000 40.000 26 28 40.000 120.000 29
10.000 24 40.000
20.000
40.000 60.000 27 40.000 90.000 60.000
0.000 30 60.000 10.000
31 60.000 20.000 32
60.000 40.000 33 60.000 60.000
34 60.000 90.000 35
60.000 120.000 36 90.000
37 90.000 10.000 38
90.000 20.000 39 90.000 40.000
0.000
40 90.000 60.000 41 90.000 90.000 42 90.000 120.000 43 120.000
0.000 44 120.000
10.000 45 120.000
20.000
46 120.000
40.000 47 120.000
60.000 48 120.000
90.000
49 120.000 120.000
HALF BAND WIDTH (NB) = 27
PERIOD 1 LOAD GROUP 1 AND CYCLE NO. 1
DEFLECTIONS OF SLABS (F) ARE: (DOWNWARD POSITIVE) 1 0.03097
2 0.03015
6 0.00498 7 -0.00152
3 0.02785
4 0.02085
5 0.01360
8 0.03056 9 0.02974 10 0.02743
11 0.02049 12 0.01337 13 0.00488 14 -0.00155 15 0.02908 16 0.02833 17 0.02606 18 0.01946 19 0.01272 20 0.00459 21 -0.00165 22 0.02276 23 0.02220 24 0.02065 25 0.01575 26 0.01037 27 0.00349 28 -0.00206 29 0.01539 30 0.01506 31 0.01414 32 0.01101 33 0.00723 34 0.00189 35 -0.00277 36 0.00634 37 0.00621 38 0.00580 39 0.00434 40 0.00233 41 -0.00100 42 -0.00440 43 -0.00047 44 -0.00052 45 -0.00067 46 -0.00127 47 -0.00221 48 -0.00416 49 -0.00668
NODAL NUMBER AND REACTIVE PRESSURE (SUBR) ARE: (COMPRESSION POSITIVE)
Tousif_Hw3_Feb8_2017
P a g e | 30
1
3.097
2
3.015
3
2.785
4
2.085
5
6
0.498
7
-0.152
8
3.056
9
2.974 10
1.360 2.743
11
2.049 12
1.337 13
0.488 14
-0.155 15
2.908
16
2.833 17
2.606 18
1.946 19
1.272 20
0.459
21
-0.165 22
2.276 23
2.220 24
2.065 25
1.575
26
1.037 27
0.349 28
-0.206 29
1.539 30
1.506
31
1.414 32
1.101 33
0.723 34
0.189 35
-0.277
36
0.634 37
0.621 38
0.580 39
0.434 40
0.233
41 -0.100 42 -0.440 43 -0.047 44 -0.052 45 -0.067 46 -0.127 47 -0.221 48 -0.416 49 -0.668
SUM OF FORCES (FOSUM) = 9999.1 NODE
LAYER
STRESS X
SUM OF REACTIONS (SUBSUM) = 9999.1
STRESS Y
STRESS XY
MAX.SHEAR
MAJOR
MINOR
299.295
299.295
0
68.348
-268.17
0
56.21
-178.65
0
12.669
-162.6 155.751 153.312
-9.513
0
52.842
-9.513
-178.65 115.197
1
1
2
1
3
1
4
1
-162.6 155.751 153.312 115.197
5
1
-66.055
49.289
0
57.672
49.289
-66.055
6
1
-26.672
37.966
0
32.319
37.966
-26.672
7
1
5.495
1
0
41.797
9
1
-1.821
45.355
10
1
0 293.632 287.566 171.774
0
8
-2.848
3.696
0 210.038 196.893 170.433
11
1
-10.99 210.038 196.929 176.484 112.194
-6.74
-16.29
55.186
-4.281
-10.99 293.632 287.603 177.825 114.653
12
1
-62.568
47.298
-15.423
57.057
49.422
-64.692
13
1
-25.862
36.939
-8.083
32.424
37.963
-26.885
14
1
5.421
1
0 263.424
0
15
-10.843 275.945
0
6.261
0 263.424
-10.843 275.945
-268.17
Tousif_Hw3_Feb8_2017
P a g e | 31
16
1
17
1
284.458 201.447
18
1
-98.399
-4.253
-38.886
61.057
9.731
-217.09 112.383
19
1
-54.014
42.013
-29.284
56.239
50.238
-62.24
20
1
-23.68
34.14
-15.235
32.678
37.908
-27.449
21
1
-11.168
0
5.584
0
22
1
-47.446
0
72.775
-47.446
23
1
-40.996
-36.519
73.786
-31.325
24
1
-49.902
0 192.996 169.226 121.516
-62.76
72.256
-13.453
-11.168 192.996 178.897 157.965
25
1
-43.274
-16.124
-64.962
66.366
36.666
-96.065
26
1
-27.759
28.077
-46.406
54.156
54.316
-53.997
27
1
-16.246
24.742
-24.865
32.222
36.47
-27.974
28
1
-11.263
0
0
5.631
0
-11.263
29
1
41.006
-100.2
0
70.603
41.006
-100.2
30
1
36.75
-92.89
-24.764
69.39
41.32
-97.459
31
1
29.961
-72.79
-43.953
67.612
46.197
-89.026
32
1
10.819
-21.846
-55.17
57.537
52.024
-63.05
33
1
-0.74
11.146
-45.426
45.814
51.017
-40.611
34
1
-8.569
13.214
-26.742
28.875
31.198
-26.553
35
1
-11.764
0
0
5.882
0
-11.764
36
1
39.803
-39.087
0
39.445
39.803
-39.087
37
1
38.428
-37.367
-11.344
39.559
40.09
-39.028
38
1
34.529
-32.745
-21.001
39.655
40.546
-38.763
39
1
21.797
-18.126
-31.155
37.002
38.837
-35.166
40
1
8.45
-4.806
-30.034
30.757
32.579
-28.935
41
1
-5.174
-1.539
-20.138
20.22
16.863
-23.576
42
1
-15.332
0
0
7.666
0
-15.332
43
1
0
-16.665
0
8.333
0
-16.665
44
1
0
-16.262
0
8.131
0
-16.262
45
1
0
-15.92
0
7.96
0
-15.92
46
1
0
-13.421
0
6.711
0
-13.421
47
1
0
-10.933
0
5.466
0
-10.933
48
1
0
-13.546
0
6.773
0
-13.546
49
1
0
0
0
0
0
0
Result:
320.993 151.321
-18.47
25.978
-32.076
40.706
276.748 135.678
328.703
