parameteric study on bending stiffness - july 17
DESCRIPTION
Parameteric Study on Bending StiffnessTRANSCRIPT
-
Bending Stiffness Load Cases
Special Case: eBCF 2 point
loads case (Chapter 4 eBCF
formulation)
No overhang and mid-span force
Case 1 Case 2
Case 3
Case 5
Asymmetric Loading
Overhang
Double side Equal
Single side
Case 4
Double side Unequal
As part of the dissertation, eBCF was formulated for a special bending load case with two point loads, where the loading is mid-span along the edges and the supports are at the vertices of the structure. The effect of varying the location of loading and the supports on the bending stiffness was studied for various cases on a rectangular plate using ANSYS. Summary of each of the cases in the Venn diagram are in subsequent slides.
-
y = 3.3671x2 - 2.5853x + 401.9 R = 0.9994
400.00
420.00
440.00
460.00
480.00
500.00
520.00
0 1 2 3 4 5 6
Be
nd
ing
Stif
fne
ss (
lbf/
in)
Force location - Offset from center of plate (a) (in)
Case 1: Effect of offsetting force application points on Bending Stiffness
1
2 R I G H T
L E F T
F R
O N
T R
E A R
5
6
3
4
X
Y 5
6
a
Case Force location
offset from center (a) (in)
Force (lbf) Vertical Deflection (in) Total Deformation
(in)
Bending Stiffness (lbf/in) F5 F6 X5 X6
1 0 1 1 2.4964E-03 2.4965E-03 4.9929E-03 400.57 2 0.2 1 1 2.4957E-03 2.4958E-03 4.9915E-03 400.68 3 0.4 1 1 2.4939E-03 2.4939E-03 4.9877E-03 400.98 4 0.6 1 1 2.4907E-03 2.4907E-03 4.9814E-03 401.50 5 0.8 1 1 2.4863E-03 2.4863E-03 4.9726E-03 402.20 6 1 1 1 2.4807E-03 2.4806E-03 4.9612E-03 403.13 7 1.2 1 1 2.4737E-03 2.4737E-03 4.9474E-03 404.25 8 1.4 1 1 2.4650E-03 2.4650E-03 4.9299E-03 405.69 9 1.6 1 1 2.4557E-03 2.4557E-03 4.9115E-03 407.21
10 1.8 1 1 2.4451E-03 2.4450E-03 4.8901E-03 408.99 11 2 1 1 2.4333E-03 2.4333E-03 4.8665E-03 410.97 12 2.2 1 1 2.4203E-03 2.4202E-03 4.8405E-03 413.18 13 2.4 1 1 2.4061E-03 2.4061E-03 4.8121E-03 415.62 14 2.6 1 1 2.3906E-03 2.3906E-03 4.7812E-03 418.31 15 2.8 1 1 2.3740E-03 2.3739E-03 4.7479E-03 421.24 16 3 1 1 2.3561E-03 2.3562E-03 4.7123E-03 424.42 17 3.2 1 1 2.3372E-03 2.3372E-03 4.6744E-03 427.86 18 3.4 1 1 2.3172E-03 2.3172E-03 4.6343E-03 431.56 19 3.6 1 1 2.2959E-03 2.2959E-03 4.5919E-03 435.55 20 3.8 1 1 2.2719E-03 2.2719E-03 4.5438E-03 440.16 21 4 1 1 2.2486E-03 2.2485E-03 4.4971E-03 444.73 22 4.2 1 1 2.2242E-03 2.2241E-03 4.4483E-03 449.61 23 4.4 1 1 2.1986E-03 2.1986E-03 4.3972E-03 454.83 24 4.6 1 1 2.1721E-03 2.1721E-03 4.3441E-03 460.39 25 4.8 1 1 2.1445E-03 2.1445E-03 4.2890E-03 466.31 26 5 1 1 2.1159E-03 2.1159E-03 4.2318E-03 472.61 27 5.2 1 1 2.0863E-03 2.0863E-03 4.1726E-03 479.32 28 5.4 1 1 2.0558E-03 2.0558E-03 4.1116E-03 486.43 29 5.6 1 1 2.0244E-03 2.0244E-03 4.0488E-03 493.97 30 5.8 1 1 1.9920E-03 1.9920E-03 3.9840E-03 502.01
Quadratic effect
-
y = 1.9384x2 + 22.887x + 502.91 R = 1
500.00520.00540.00560.00580.00600.00620.00640.00660.00680.00700.00720.00
0 1 2 3 4 5 6
Be
nd
ing
Stif
fne
ss (
lbf/
in)
Front support offset (b) (in)
Case 2: Effect of moving front supports (removing material) on Bending Stiffness
1
2 R I G H T
L E F T
F R
O N
T R
E A R
3
4
X
Y 5
6
1 a
Case Front support Location
offset (a) (in)
Force (lbf) Vertical Deflection (in) Total Deformation
(in)
Bending Stiffness (lbf/in) F5 F6 X5 X6
1 0 1 1 1.9920E-03 1.9920E-03 3.9840E-03 502.00
2 0.2 1 1 1.9723E-03 1.9723E-03 3.9446E-03 507.02
3 0.4 1 1 1.9526E-03 1.9526E-03 3.9052E-03 512.14
4 0.6 1 1 1.9328E-03 1.9328E-03 3.8656E-03 517.39
5 0.8 1 1 1.9131E-03 1.9131E-03 3.8262E-03 522.71
6 1 1 1 1.8934E-03 1.8933E-03 3.7867E-03 528.16
7 1.2 1 1 1.8737E-03 1.8737E-03 3.7473E-03 533.72
8 1.4 1 1 1.8540E-03 1.8540E-03 3.7080E-03 539.37
9 1.6 1 1 1.8343E-03 1.8343E-03 3.6686E-03 545.17
10 1.8 1 1 1.8160E-03 1.8161E-03 3.6321E-03 550.64
11 2 1 1 1.7964E-03 1.7965E-03 3.5929E-03 556.66
12 2.2 1 1 1.7768E-03 1.7768E-03 3.5536E-03 562.81
13 2.4 1 1 1.7572E-03 1.7572E-03 3.5144E-03 569.09
14 2.6 1 1 1.7376E-03 1.7376E-03 3.4752E-03 575.51
15 2.8 1 1 1.7180E-03 1.7180E-03 3.4360E-03 582.08
16 3 1 1 1.6984E-03 1.6984E-03 3.3967E-03 588.80
17 3.2 1 1 1.6778E-03 1.6778E-03 3.3555E-03 596.03
18 3.4 1 1 1.6582E-03 1.6582E-03 3.3164E-03 603.06
19 3.6 1 1 1.6387E-03 1.6387E-03 3.2774E-03 610.24
20 3.8 1 1 1.6192E-03 1.6192E-03 3.2384E-03 617.59
21 4 1 1 1.5997E-03 1.5997E-03 3.1994E-03 625.11
22 4.2 1 1 1.5802E-03 1.5802E-03 3.1605E-03 632.82
23 4.4 1 1 1.5608E-03 1.5607E-03 3.1215E-03 640.72
24 4.6 1 1 1.5413E-03 1.5413E-03 3.0826E-03 648.80
25 4.8 1 1 1.5219E-03 1.5219E-03 3.0438E-03 657.07
26 5 1 1 1.5025E-03 1.5025E-03 3.0050E-03 665.56
27 5.2 1 1 1.4831E-03 1.4831E-03 2.9662E-03 674.26
28 5.4 1 1 1.4638E-03 1.4637E-03 2.9275E-03 683.18
29 5.6 1 1 1.4444E-03 1.4444E-03 2.8888E-03 692.33
30 5.8 1 1 1.4251E-03 1.4250E-03 2.8501E-03 701.74
2
Linear effect
-
Case 3: Effect of moving front supports (overhang) on Bending Stiffness
1
2 R I G H T
L E F T
F R
O N
T R
E A R
3
4
X
Y 5
6
1 b
2
Case
Front support
Location a (in)
Force (lbf) Vertical Deflection (in)
Total Deformation
(in)
Bending Stiffness (lbf/in) F5 F6 X5 X6
1 0.4 1 1 1.956E-03 1.956E-03 3.9127E-03 511.15
2 0.8 1 1 1.915E-03 1.915E-03 3.8294E-03 522.28
3 1.2 1 1 1.874E-03 1.874E-03 3.7471E-03 533.74
4 1.6 1 1 1.833E-03 1.833E-03 3.6653E-03 545.65
5 2 1 1 1.791E-03 1.791E-03 3.5829E-03 558.21
6 2.4 1 1 1.751E-03 1.751E-03 3.5022E-03 571.07
7 2.8 1 1 1.711E-03 1.711E-03 3.4218E-03 584.49
8 3.2 1 1 1.671E-03 1.671E-03 3.3422E-03 598.41
9 3.6 1 1 1.631E-03 1.631E-03 3.2624E-03 613.04
10 4 1 1 1.591E-03 1.591E-03 3.1814E-03 628.65
11 4.4 1 1 1.551E-03 1.551E-03 3.1023E-03 644.69
12 4.8 1 1 1.512E-03 1.512E-03 3.0233E-03 661.54
13 5.2 1 1 1.472E-03 1.472E-03 2.9445E-03 679.24
14 5.6 1 1 1.433E-03 1.433E-03 2.8656E-03 697.93
15 6 1 1 1.393E-03 1.393E-03 2.7854E-03 718.03
16 6.4 1 1 1.354E-03 1.354E-03 2.7072E-03 738.77
17 6.8 1 1 1.314E-03 1.314E-03 2.6289E-03 760.77
18 7.2 1 1 1.276E-03 1.276E-03 2.5512E-03 783.94
19 7.6 1 1 1.237E-03 1.237E-03 2.4733E-03 808.63
20 8 1 1 1.197E-03 1.197E-03 2.3938E-03 835.49
21 8.4 1 1 1.158E-03 1.158E-03 2.3164E-03 863.42
22 8.8 1 1 1.120E-03 1.120E-03 2.2392E-03 893.16
23 9.2 1 1 1.081E-03 1.081E-03 2.1625E-03 924.84
24 9.6 1 1 1.043E-03 1.043E-03 2.0856E-03 958.95
25 10 1 1 1.003E-03 1.003E-03 2.0069E-03 996.59
26 10.4 1 1 9.653E-04 9.653E-04 1.9306E-03 1035.95
27 10.8 1 1 9.273E-04 9.273E-04 1.8546E-03 1078.37
28 11.1 1 1 8.990E-04 8.989E-04 1.7979E-03 1112.41
y = 0.2574x3 - 0.7576x2 + 31.96x + 496.42 R = 1
500.00
600.00
700.00
800.00
900.00
1000.00
1100.00
-0.8 1.2 3.2 5.2 7.2 9.2 11.2
Ben
din
g St
iffn
ess
(lb
f/in
)
Front Support offset a (in)
Cubic effect
-
y = -0.0214x4 + 0.4951x3 - 4.3539x2 + 17.209x + 1146.2 R = 0.9974
1145.00
1150.00
1155.00
1160.00
1165.00
1170.00
1175.00
-0.8 1.2 3.2 5.2 7.2 9.2 11.2
Be
nd
ing
Stif
fne
ss (
lbf/
in)
Offset c
Case 4: Effect of sliding Supports and Loading location (double side unequal overhang) on Bending Stiffness
1
2
F R
O N
T R
E A R
5
6
3
4
X
Y 5
6
a 3
4
a a 1
2
Polynomial order 4 effect
Case Offset (a)
(in)
Force (lbf) Vertical Deflection (in) Total Deformation (in)
Bending Stiffness (lbf/in) F5 F6 X5 X6
1 0.2 1 1 8.7061E-04 8.7059E-04 1.7412E-03 1148.63
2 0.4 1 1 8.6751E-04 8.6752E-04 1.7350E-03 1152.72
3 0.8 1 1 8.6343E-04 8.6345E-04 1.7269E-03 1158.16
4 1.2 1 1 8.6070E-04 8.6071E-04 1.7214E-03 1161.84
5 1.6 1 1 8.5863E-04 8.5867E-04 1.7173E-03 1164.62
6 2 1 1 8.5699E-04 8.5700E-04 1.7140E-03 1166.87
7 2.4 1 1 8.5582E-04 8.5549E-04 1.7113E-03 1168.70
8 2.8 1 1 8.5525E-04 8.5525E-04 1.7105E-03 1169.25
9 3.2 1 1 8.5452E-04 8.5453E-04 1.7091E-03 1170.24
10 3.6 1 1 8.5401E-04 8.5402E-04 1.7080E-03 1170.94
11 4 1 1 8.5362E-04 8.5357E-04 1.7072E-03 1171.51
12 4.4 1 1 8.5346E-04 8.5348E-04 1.7069E-03 1171.69
13 4.8 1 1 8.5321E-04 8.5323E-04 1.7064E-03 1172.03
14 5.2 1 1 8.5312E-04 8.5312E-04 1.7062E-03 1172.17
15 5.6 1 1 8.5302E-04 8.5304E-04 1.7061E-03 1172.30
16 6 1 1 8.5306E-04 8.5306E-04 1.7061E-03 1172.25
17 6.4 1 1 8.5317E-04 8.5318E-04 1.7063E-03 1172.09
18 6.8 1 1 8.5332E-04 8.5331E-04 1.7066E-03 1171.90
19 7.2 1 1 8.5340E-04 8.5340E-04 1.7068E-03 1171.78
20 7.6 1 1 8.5373E-04 8.5376E-04 1.7075E-03 1171.31
21 8 1 1 8.5417E-04 8.5418E-04 1.7084E-03 1170.72
22 8.4 1 1 8.5470E-04 8.5469E-04 1.7094E-03 1170.01
23 8.8 1 1 8.5547E-04 8.5547E-04 1.7109E-03 1168.94
24 9.2 1 1 8.5593E-04 8.5591E-04 1.7118E-03 1168.33
25 9.6 1 1 8.5746E-04 8.5745E-04 1.7149E-03 1166.24
26 10 1 1 8.5913E-04 8.5912E-04 1.7183E-03 1163.97
27 10.4 1 1 8.6136E-04 8.6137E-04 1.7227E-03 1160.94
28 10.8 1 1 8.6447E-04 8.6451E-04 1.7290E-03 1156.75
29 11.1 1 1 8.6778E-04 8.6776E-04 1.7355E-03 1152.38
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Case 5: Effect of introducing double side equal overhang on Bending Stiffness
F R
O N
T R
E A R
X
Y 5
6
1 a
2
a 3
4
3
4
1
2
y = 0.9613x4 - 14.35x3 + 90.411x2 - 105.89x + 489.76 R = 0.9996
400.00
1400.00
2400.00
3400.00
4400.00
5400.00
0 2 4 6 8 10
Be
nd
ing
Stif
fne
ss (
)lb
f/in
Support location offset a (in)
Polynomial order 4 effect
Case Offset (a)
(in)
Front support Location
(in)
Rear support Location
(in)
Force (lbf) Vertical Deflection (in) Total
Deformation (in)
Bending Stiffness (lbf/in) F5 F6 X5 X6
1 0.4 0.4 33.6 1 1 2.3452E-03 2.3452E-03 4.6903E-03 426.41
2 0.8 0.8 33.2 1 1 2.1894E-03 2.1894E-03 4.3788E-03 456.75
3 1.2 1.2 32.8 1 1 2.0442E-03 2.0442E-03 4.0884E-03 489.19
4 1.6 1.6 32.4 1 1 1.9069E-03 1.9069E-03 3.8137E-03 524.42
5 2 2 32 1 1 1.7766E-03 1.7766E-03 3.5532E-03 562.87
6 2.4 2.4 31.6 1 1 1.6513E-03 1.6517E-03 3.3030E-03 605.52
7 2.8 2.8 31.2 1 1 1.5352E-03 1.5352E-03 3.0705E-03 651.36
8 3.2 3.2 30.8 1 1 1.4245E-03 1.4245E-03 2.8489E-03 702.02
9 3.6 3.6 30.4 1 1 1.3195E-03 1.3195E-03 2.6390E-03 757.87
10 4 4 30 1 1 1.2201E-03 1.2201E-03 2.4402E-03 819.60
11 4.4 4.4 29.6 1 1 1.1247E-03 1.1247E-03 2.2495E-03 889.10
12 4.8 4.8 29.2 1 1 1.0360E-03 1.0360E-03 2.0720E-03 965.26
13 5.2 5.2 28.8 1 1 9.5233E-04 9.5232E-04 1.9046E-03 1050.06
14 5.6 5.6 28.4 1 1 8.7336E-04 8.7336E-04 1.7467E-03 1145.00
15 6 6 28 1 1 7.9757E-04 7.9754E-04 1.5951E-03 1253.83
16 6.4 6.4 27.6 1 1 7.2773E-04 7.2770E-04 1.4554E-03 1374.17
17 6.8 6.8 27.2 1 1 6.6224E-04 6.6223E-04 1.3245E-03 1510.04
18 7.2 7.2 26.8 1 1 6.0087E-04 6.0087E-04 1.2017E-03 1664.26
19 7.6 7.6 26.4 1 1 5.4155E-04 5.4155E-04 1.0831E-03 1846.55
20 8 8 26 1 1 4.8818E-04 4.8818E-04 9.7636E-04 2048.43
21 8.4 8.4 25.6 1 1 4.3832E-04 4.3831E-04 8.7663E-04 2281.47
22 8.8 8.8 25.2 1 1 3.9190E-04 3.9188E-04 7.8378E-04 2551.74
23 9.2 9.2 24.8 1 1 3.4880E-04 3.4881E-04 6.9761E-04 2866.93
24 9.6 9.6 24.4 1 1 3.0719E-04 3.0717E-04 6.1435E-04 3255.46
25 10 10 24 1 1 2.7046E-04 2.7047E-04 5.4093E-04 3697.32
26 10.4 10.4 23.6 1 1 2.3670E-04 2.3669E-04 4.7339E-04 4224.83
27 10.8 10.8 23.2 1 1 2.0566E-04 2.0565E-04 4.1131E-04 4862.49
28 11.1 11.1 22.9 1 1 1.8181E-04 1.8185E-04 3.6367E-04 5499.55