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Initial Data Material
Form
Aluminium Epoxy Balsa wood Paper Honeycomb Carbon Fibre Prepreg Glass Fibre Prepreg
Sheet Adhesive Sheet Sheet Sheet Sheet
For a Solid Beam Skin on Core
Thickness
m 0
0 0.01
0.01 0.02 0 0
Best Bending stiffness to weight ratio E/ρ3 E/r
.320 m .050 m
Bending Stiffness
Solid Beam Equation
I = wt3/12 [EI]Total=EI
Aluminium Sheets 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Thickness (50 Sheet Max) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Hollow Beam For a hollow beam only Paper Honeycomb ti = Variable to = ta +ti w0= 0.050 m wi= w0-(ta)
Where t a = Thickness of Shell Material
Paper Honneycomb Interior ti Sheets 1
Thickness 0.01 0.01 0.01 0.01
Aluminum Shell Sheets 2 4 6 8
Thickness ta 0 0 0 0
10
40
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.4 0.4 0.4 0.4 0.4 0.4
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 2 4 6 8 10 12
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01 0 0 0 0 0 0
0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01
Bending Strength σ=EγmaxM/[EI] γmax=τ/G
Solid Beam Aluminium Sheets 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
E 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000
γmax 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
M (Nm) 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
[EI] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
E 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000
γmax 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Hollow Beam Honeycomb 1
Aluminium Sheets 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
Shell M (Nm) 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
[EI] 2.52 5.17 7.94 10.84 13.87 17.04 20.35 23.8 27.39 31.13 35.03 39.07 43.28 47.64 52.17 56.87 61.74 66.77
10
40
38 40 42 44 46 48 50 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
71.99 77.38 82.96 88.72 94.67 100.82 107.15 385.18 771.57 1159.16 1547.97 1937.98 2329.21 2721.66 3115.33 3510.22 3906.35 4303.7 4702.29 5102.12 5503.18 5905.49 6309.05 6713.86 7119.92 7527.23 7935.81 8345.64 8756.75 9169.12 9582.76 9997.68 13539.73 27084.27 40633.61 54187.76 67746.73 81310.51 94879.1 108452.52 122030.76 135613.83 149201.73 162794.47 176392.04 189994.45 203601.71 217213.81 230830.76 244452.57 258079.23 271710.75
42 44 46 48 50
7100000000 7100000000 7100000000 7100000000 7100000000
0 0 0 0 0
20 20 20 20 20
285347.13 298988.37 312634.49 326285.47 339941.33
Initial Data
ess
m 0 0.01 0.02 0 0
Density ρ kg/m3 2800 1200 100-200 57 1620 1980
E
σt
G
N/m2
N/m N/m 7100000000 ### 130000000 4000000000 ### 60000000 3750000000 120000000 27500000 0 0 2000000 150000000000 ### 2000000000 42000000000 ### 1300000000 2
2
τt MN/m2 65000000 50000000 3500000 600000 100000000 67000000
Width (w) 0.05 0.05 0.05 0.05 0.05 0.05
Torsional stiffness to weight ratio G/ρ2 G/ρ
g Stiffness
Epoxy I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[EI]Total 0 0 0 0 0 0.01 0.01 0.02 0.03 0.05 0.06 0.09 0.11 0.14 0.18 0.22 0.27 0.32
Thickness (50 Sheet Max) Sheets 0 0 0.01 0.01 0.02 0.02 0.03 0.03 0.04 0.04 0.05 0.05 0.06 0.06 0.07 0.07 0.08 0.08
I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[EI]Total 0 2.08 16.67 56.25 133.33 260.42 450 714.58 1066.67 1518.75 2083.33 2772.92 3600 4577.08 5716.67 7031.25 8533.33
m
Height m 0.32 0.32 0.32 0.32 0.32 0.32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.38 0.45 0.52 0.6 0.69 0.79 0.9 1.02 1.14 1.28 1.43 1.59 1.75 1.94 2.13 2.34 2.55 2.79 3.03 3.29 3.57 3.86 4.16 4.48 4.82 5.17 5.54 5.92 6.33 6.75 7.19 7.65 8.12
to 0.01 0.01 0.01 0.01
w0= 0.050 m
wi= w0-ta
0.05 0.05 0.05 0.05
0.05 0.05 0.05 0.05
I (For Shell) 0 0 0 0
I (For Core) 0 0 0 0
[EI]Total 2.52 5.17 7.94 10.84
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.02 0.02 0.02 0.02 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.11 0.11 0.11 0.11 0.11 0.11 0.4 0.4 0.4 0.4 0.4 0.4
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.04 0.04 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.04 0.04 0.05 0.05 0.05 0.05 0.05 0.05
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13.87 17.04 20.35 23.8 27.39 31.13 35.03 39.07 43.28 47.64 52.17 56.87 61.74 66.77 71.99 77.38 82.96 88.72 94.67 100.82 107.15 385.18 771.57 1159.16 1547.97 1937.98 2329.21 2721.66 3115.33 3510.22 3906.35 4303.7 4702.29 5102.12 5503.18 5905.49 6309.05 6713.86 7119.92 7527.23 7935.81 8345.64 8756.75 9169.12 9582.76 9997.68 13539.73 27084.27 40633.61 54187.76 67746.73 81310.51
0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.41 0.41 0.41 0.41 0.41 0.41
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.04 0.04
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
94879.1 108452.52 122030.76 135613.83 149201.73 162794.47 176392.04 189994.45 203601.71 217213.81 230830.76 244452.57 258079.23 271710.75 285347.13 298988.37 312634.49 326285.47 339941.33
E 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000
γmax 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03
g Strength
Balsa Wood σ>σt
σ ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ###
TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
Sheets 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
M (Nm) 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
[EI] 3.38 27 91.13 216 421.88 729 1157.63 1728 2460.38 3375 4492.13 5832 7414.88 9261 11390.63 13824 16581.38 19683 23149.13 27000 31255.88
### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ###
TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
σ>σt σ ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE
Core σ>σt TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000
Honeycomb
Balsa
1
10
40
Sheets 2 4 6 8 2 4 6 8 2 4 6 8
0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03
20 35937 20 41063.63 20 46656 20 52734.38 20 59319 20 66430.13 20 74088 20 82312.88 20 91125 20 100544.63 20 110592 20 121287.38 20 132651 20 144703.13 20 157464 20 170953.88 20 185193 20 200201.63 20 216000 20 232608.38 20 250047 20 268336.13 20 287496 20 307546.88 20 328509 20 350402.63 20 373248 20 397065.38 20 421875
Shell E 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000
γmax 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03
M (Nm) 20 20 20 20 20 20 20 20 20 20 20 20
### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### 29250.4 27582.2 ### ### 23531.2 ### ### ### ### 14504.2 7250.81 4833.02 3624.12 2898.78 2415.22 2069.82 1810.77 1609.29 1448.1 1316.22 1206.32 1113.33 1033.62 964.54 904.1 850.77 803.36 760.94 722.76
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
TRUE TRUE TRUE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
688.22 656.82 628.16 601.87 577.7
FALSE FALSE FALSE FALSE FALSE
FALSE FALSE FALSE FALSE FALSE
Balsa Wood (.003m) Thickness (50 Sheet Max) I Sheets 0 0 0 1 0 0 2 0.01 0 3 0.01 0 4 0.01 0 5 0.02 0 6 0.02 0 7 0.02 0 8 0.02 0 9 0.03 0 10 0.03 0 11 0.03 0 12 0.04 0 13 0.04 0 14 0.04 0 15 0.05 0 16 0.05 0 17 0.05 0
Balsa Wood (.006m) [EI]Total 0 0.42 3.38 11.39 27 52.73 91.13 144.7 216 307.55 421.88 561.52 729 926.86 1157.63 1423.83 1728 2072.67
Thickness (50 Sheet Max) I Sheets 0 0 0 1 0.01 0 2 0.01 0 3 0.02 0 4 0.02 0 5 0.03 0 6 0.04 0 7 0.04 0 8 0.05 0 9 0.05 0 10 0.06 0 11 0.07 0 12 0.07 0 13 0.08 0 14 0.08 0 15 0.09 0 16 0.1 0 17 0.1 0
[EI]Total 0 3.38 27 91.13 216 421.88 729 1157.63 1728 2460.38 3375 4492.13 5832 7414.88 9261 11390.63 13824 16581.38
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
0.05 0.06 0.06 0.06 0.07 0.07 0.07 0.08 0.08 0.08 0.08 0.09 0.09 0.09 0.1 0.1 0.1 0.11 0.11 0.11 0.11 0.12 0.12 0.12 0.13 0.13 0.13 0.14 0.14 0.14 0.14 0.15 0.15
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2460.38 2893.64 3375 3906.98 4492.13 5132.95 5832 6591.8 7414.88 8303.77 9261 10289.11 11390.63 12568.08 13824 15160.92 16581.38 18087.89 19683 21369.23 23149.13 25025.2 27000 29076.05 31255.88 33542.02 35937 38443.36 41063.63 43800.33 46656 49633.17 52734.38
Paper Honneycomb Interior ti Sheets 1
Thickness 0.01 0.01 0.01 0.01
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
0.11 0.11 0.12 0.13 0.13 0.14 0.14 0.15 0.16 0.16 0.17 0.17 0.18 0.19 0.19 0.2 0.2 0.21 0.22 0.22 0.23 0.23 0.24 0.25 0.25 0.26 0.26 0.27 0.28 0.28 0.29 0.29 0.3
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19683 23149.13 27000 31255.88 35937 41063.63 46656 52734.38 59319 66430.13 74088 82312.88 91125 100544.63 110592 121287.38 132651 144703.13 157464 170953.88 185193 200201.63 216000 232608.38 250047 268336.13 287496 307546.88 328509 350402.63 373248 397065.38 421875
Balsa Wood w0= 0.050 m wi= w0-ta Sheets 2 4 6 8
Thickness ta 0.01 0.02 0.04 0.05
to 0.02 0.03 0.05 0.06
0.05 0.05 0.05 0.05
0.04 0.03 0.01 0
I (For Shell) 0 0 0 0
10
40
0.1 0.1 0.1 0.1 0.4 0.4 0.4 0.4
2 4 6 8 2 4 6 8
0.01 0.02 0.04 0.05 0.01 0.02 0.04 0.05
0.11 0.12 0.14 0.15 0.41 0.42 0.44 0.45
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
0.04 0.03 0.01 0 0.04 0.03 0.01 0
0 0 0 0 0 0 0 0
σ>σt σ ### ### ### ### ### ### ### ### 889092.11 648148.15 486963.3 375085.73 295015.09 236205.59 192043.9 158239.29 131925.13 111136.51 94496.01 81018.52 69986.84
TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
60870.41 53270.99 46885.72 41481.48 36876.89 32929.34 29525.7 26575.43 24005.49 21756.51 19779.91 18035.68 16490.64 15117.16 13892.06 12795.85 11812 10926.48 10127.31 9404.22 8748.36 8152.09 7608.8 7112.74 6658.87 6242.82 5860.71 5509.17 5185.19
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
Shell [EI] 154.5 606 1516.5 3048 10077 21666 34929 50028 332727 671016 1015029 1364928
σ>σt σ ### FALSE ### FALSE ### FALSE 717683.73 FALSE 217078.5 FALSE 100964.65 FALSE 62627.04 FALSE 43725.51 FALSE 6574.46 FALSE 3259.98 FALSE 2155.11 FALSE 1602.65 FALSE
Core σ>σt TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
Balsa Wood (.01m) Thickness (50 Sheet Max)I Sheets 0 0 0 1 0.01 0 2 0.02 0 3 0.03 0 4 0.04 0 5 0.05 0 6 0.06 0 7 0.07 0 8 0.08 0 9 0.09 0 10 0.1 0 11 0.11 0 12 0.12 0 13 0.13 0 14 0.14 0 15 0.15 0 16 0.16 0 17 0.17 0
Paper Honeycomb (0.01m) [EI]Total 0 15.63 125 421.88 1000 1953.13 3375 5359.38 8000 11390.63 15625 20796.88 27000 34328.13 42875 52734.38 64000 76765.63
Thickness (50 Sheet Max) Sheets 0 0 1 0.01 2 0.02 3 0.03 4 0.04 5 0.05 6 0.06 7 0.07 8 0.08 9 0.09 10 0.1 11 0.11 12 0.12 13 0.13 14 0.14 15 0.15 16 0.16 17 0.17
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
91125 107171.88 125000 144703.13 166375 190109.38 216000 244140.63 274625 307546.88 343000 381078.13 421875 465484.38 512000 561515.63 614125 669921.88 729000 791453.13 857375 926859.38 1000000 1076890.63 1157625 1242296.88 1331000 1423828.13 1520875 1622234.38 1728000 1838265.63 1953125
Paper Honneycomb Interior ti I (For Core) [EI]Total 0 154.5 0 606 0 1516.5 0 3048
Sheets 1
Thickness 0.01 0.01 0.01 0.01
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5
Carbon Fiber Sheets Thickness ta 2 0 4 0 6 0 8 0
to 0.01 0.01 0.01 0.01
0 0 0 0 0 0 0 0
10077 21666 34929 50028 332727 671016 1015029 1364928
10
40
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.4 0.4 0.4 0.4 0.4 0.4
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 2 4 6 8 10 12
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01 0 0 0 0 0 0
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.02 0.02 0.02 0.02 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.11 0.11 0.11 0.11 0.11 0.11 0.4 0.4 0.4 0.4 0.4 0.4
0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01
0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.41 0.41 0.41 0.41 0.41 0.41
aper Honeycomb (0.01m) I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[EI]Total 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Paper Honeycomb (0.019m) Thickness (50 Sheet Max) Sheets 0 0 1 0.02 2 0.04 3 0.06 4 0.08 5 0.1 6 0.11 7 0.13 8 0.15 9 0.17 10 0.19 11 0.21 12 0.23 13 0.25 14 0.27 15 0.29 16 0.3 17 0.32
I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[EI]Total 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
w0= 0.050 m
wi= w0-ta
0.05 0.05 0.05 0.05
0.05 0.05 0.05 0.05
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
I (For Shell)I (For Core) 0 0 0 0 0 0 0 0
0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.49 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.65 0.67 0.68 0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.84 0.86 0.87 0.89 0.91 0.93 0.95
[EI]Total 51.18 104.77 160.81 219.38
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.04 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.04 0.05 0.05 0.05 0.05 0.05 0.05
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
280.52 344.3 410.77 480 552.04 626.95 704.79 785.63 869.5 956.48 1046.63 1140 1236.65 1336.64 1440.03 1546.88 1657.24 1771.17 1888.74 2010 2135.01 7824.23 15671.95 23543.23 31438.13 39356.69 47298.98 55265.07 63255 71268.84 79306.64 87368.47 95454.38 103564.42 111698.67 119857.18 128040 136247.2 144478.83 152734.95 161015.63 169320.91 177650.86 186005.54 194385 202789.31 275046.88 550187.58 825422.14 1100750.63 1376173.1 1651689.61
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.04
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1927300.22 2203005 2478803.99 2754697.27 3030684.87 3306766.88 3582943.33 3859214.3 4135579.83 4412040 4688594.85 4965244.45 5241988.86 5518828.13 5795762.31 6072791.48 6349915.69 6627135 6904449.46
Carbon Fiber Prepreg Thickness (50 Sheet Max)I Sheets 0 0 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 10 0 0 11 0 0 12 0 0 13 0 0 14 0 0 15 0 0 16 0 0 17 0 0
Glass Fiber Prepreg [EI]Total 0 0 0.01 0.03 0.08 0.15 0.26 0.42 0.63 0.89 1.22 1.62 2.11 2.68 3.35 4.12 5 6
Thickness (50 Sheet Max)I Sheets 0 0 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 10 0 0 11 0 0 12 0 0 13 0 0 14 0 0 15 0 0 16 0 0 17 0 0
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7.12 8.37 9.77 11.3 13 14.85 16.88 19.07 21.46 24.03 26.8 29.77 32.96 36.37 40 43.87 47.98 52.34 56.95 61.83 66.98 72.41 78.13 84.13 90.44 97.05 103.98 111.24 118.82 126.74 135 143.61 152.59
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ber Prepreg [EI]Total 0 0 0 0.01 0.02 0.04 0.07 0.12 0.18 0.25 0.34 0.45 0.59 0.75 0.94 1.15 1.4 1.68
1.99 2.34 2.73 3.17 3.64 4.16 4.73 5.34 6.01 6.73 7.5 8.34 9.23 10.18 11.2 12.28 13.43 14.65 15.95 17.31 18.76 20.28 21.88 23.56 25.32 27.18 29.12 31.15 33.27 35.49 37.8 40.21 42.72
Form
Aluminium Epoxy Balsa wood Paper Honeycomb Carbon Fibre Prepreg Glass Fibre Prepreg
Sheet Adhesive Sheet Sheet Sheet Sheet
For a Solid Beam Skin on Core
Thickness
m 0
0 0.01
0.01 0.02 0 0
Best Bending stiffness to weight ratio E/ρ3 E/r
.320 m .050 m
Bending Stiffness
Solid Beam Equation
I = wt3/12 [EI]Total=EI
Aluminium Sheets 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Thickness (50 Sheet Max) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Hollow Beam For a hollow beam only Paper Honeycomb ti = Variable to = ta +ti w0= 0.050 m wi= w0-(ta)
Where t a = Thickness of Shell Material
Paper Honneycomb Interior ti Sheets 1
Thickness 0.01 0.01 0.01 0.01
Aluminum Shell Sheets 2 4 6 8
Thickness ta 0 0 0 0
10
40
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.4 0.4 0.4 0.4 0.4 0.4
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 2 4 6 8 10 12
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01 0 0 0 0 0 0
0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01
Bending Strength σ=EγmaxM/[EI] γmax=τ/G
Solid Beam Aluminium Sheets 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
E 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000
γmax 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
M (Nm) 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
[EI] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
E 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000
γmax 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Hollow Beam Honeycomb 1
Aluminium Sheets 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
Shell M (Nm) 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
[EI] 2.52 5.17 7.94 10.84 13.87 17.04 20.35 23.8 27.39 31.13 35.03 39.07 43.28 47.64 52.17 56.87 61.74 66.77
10
40
38 40 42 44 46 48 50 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000 7100000000
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
71.99 77.38 82.96 88.72 94.67 100.82 107.15 385.18 771.57 1159.16 1547.97 1937.98 2329.21 2721.66 3115.33 3510.22 3906.35 4303.7 4702.29 5102.12 5503.18 5905.49 6309.05 6713.86 7119.92 7527.23 7935.81 8345.64 8756.75 9169.12 9582.76 9997.68 13539.73 27084.27 40633.61 54187.76 67746.73 81310.51 94879.1 108452.52 122030.76 135613.83 149201.73 162794.47 176392.04 189994.45 203601.71 217213.81 230830.76 244452.57 258079.23 271710.75
42 44 46 48 50
7100000000 7100000000 7100000000 7100000000 7100000000
0 0 0 0 0
20 20 20 20 20
285347.13 298988.37 312634.49 326285.47 339941.33
Initial Data
ess
m 0 0.01 0.02 0 0
Density ρ kg/m3 2800 1200 100-200 57 1620 1980
E
σt
G
N/m2
N/m N/m 7100000000 ### 130000000 4000000000 ### 60000000 3750000000 120000000 27500000 0 0 2000000 150000000000 ### 2000000000 42000000000 ### 1300000000 2
2
τt MN/m2 65000000 50000000 3500000 600000 100000000 67000000
Width (w) 0.05 0.05 0.05 0.05 0.05 0.05
Torsional stiffness to weight ratio G/ρ2 G/ρ
g Stiffness
Epoxy I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[EI]Total 0 0 0 0 0 0.01 0.01 0.02 0.03 0.05 0.06 0.09 0.11 0.14 0.18 0.22 0.27 0.32
Thickness (50 Sheet Max) Sheets 0 0 0.01 0.01 0.02 0.02 0.03 0.03 0.04 0.04 0.05 0.05 0.06 0.06 0.07 0.07 0.08 0.08
I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[EI]Total 0 2.08 16.67 56.25 133.33 260.42 450 714.58 1066.67 1518.75 2083.33 2772.92 3600 4577.08 5716.67 7031.25 8533.33
m
Height m 0.32 0.32 0.32 0.32 0.32 0.32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.38 0.45 0.52 0.6 0.69 0.79 0.9 1.02 1.14 1.28 1.43 1.59 1.75 1.94 2.13 2.34 2.55 2.79 3.03 3.29 3.57 3.86 4.16 4.48 4.82 5.17 5.54 5.92 6.33 6.75 7.19 7.65 8.12
to 0.01 0.01 0.01 0.01
w0= 0.050 m
wi= w0-ta
0.05 0.05 0.05 0.05
0.05 0.05 0.05 0.05
I (For Shell) 0 0 0 0
I (For Core) 0 0 0 0
[EI]Total 2.52 5.17 7.94 10.84
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.02 0.02 0.02 0.02 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.11 0.11 0.11 0.11 0.11 0.11 0.4 0.4 0.4 0.4 0.4 0.4
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.04 0.04 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.04 0.04 0.05 0.05 0.05 0.05 0.05 0.05
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13.87 17.04 20.35 23.8 27.39 31.13 35.03 39.07 43.28 47.64 52.17 56.87 61.74 66.77 71.99 77.38 82.96 88.72 94.67 100.82 107.15 385.18 771.57 1159.16 1547.97 1937.98 2329.21 2721.66 3115.33 3510.22 3906.35 4303.7 4702.29 5102.12 5503.18 5905.49 6309.05 6713.86 7119.92 7527.23 7935.81 8345.64 8756.75 9169.12 9582.76 9997.68 13539.73 27084.27 40633.61 54187.76 67746.73 81310.51
0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.41 0.41 0.41 0.41 0.41 0.41
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.04 0.04
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
94879.1 108452.52 122030.76 135613.83 149201.73 162794.47 176392.04 189994.45 203601.71 217213.81 230830.76 244452.57 258079.23 271710.75 285347.13 298988.37 312634.49 326285.47 339941.33
E 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000
γmax 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03
g Strength
Balsa Wood σ>σt
σ ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ###
TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
Sheets 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
M (Nm) 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
[EI] 3.38 27 91.13 216 421.88 729 1157.63 1728 2460.38 3375 4492.13 5832 7414.88 9261 11390.63 13824 16581.38 19683 23149.13 27000 31255.88
### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ###
TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
σ>σt σ ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE ### FALSE
Core σ>σt TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000
Honeycomb
Balsa
1
10
40
Sheets 2 4 6 8 2 4 6 8 2 4 6 8
0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03
20 35937 20 41063.63 20 46656 20 52734.38 20 59319 20 66430.13 20 74088 20 82312.88 20 91125 20 100544.63 20 110592 20 121287.38 20 132651 20 144703.13 20 157464 20 170953.88 20 185193 20 200201.63 20 216000 20 232608.38 20 250047 20 268336.13 20 287496 20 307546.88 20 328509 20 350402.63 20 373248 20 397065.38 20 421875
Shell E 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000 3750000000
γmax 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03
M (Nm) 20 20 20 20 20 20 20 20 20 20 20 20
### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### 29250.4 27582.2 ### ### 23531.2 ### ### ### ### 14504.2 7250.81 4833.02 3624.12 2898.78 2415.22 2069.82 1810.77 1609.29 1448.1 1316.22 1206.32 1113.33 1033.62 964.54 904.1 850.77 803.36 760.94 722.76
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
TRUE TRUE TRUE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
688.22 656.82 628.16 601.87 577.7
FALSE FALSE FALSE FALSE FALSE
FALSE FALSE FALSE FALSE FALSE
Balsa Wood (.003m) Thickness (50 Sheet Max) I Sheets 0 0 0 1 0 0 2 0.01 0 3 0.01 0 4 0.01 0 5 0.02 0 6 0.02 0 7 0.02 0 8 0.02 0 9 0.03 0 10 0.03 0 11 0.03 0 12 0.04 0 13 0.04 0 14 0.04 0 15 0.05 0 16 0.05 0 17 0.05 0
Balsa Wood (.006m) [EI]Total 0 0.42 3.38 11.39 27 52.73 91.13 144.7 216 307.55 421.88 561.52 729 926.86 1157.63 1423.83 1728 2072.67
Thickness (50 Sheet Max) I Sheets 0 0 0 1 0.01 0 2 0.01 0 3 0.02 0 4 0.02 0 5 0.03 0 6 0.04 0 7 0.04 0 8 0.05 0 9 0.05 0 10 0.06 0 11 0.07 0 12 0.07 0 13 0.08 0 14 0.08 0 15 0.09 0 16 0.1 0 17 0.1 0
[EI]Total 0 3.38 27 91.13 216 421.88 729 1157.63 1728 2460.38 3375 4492.13 5832 7414.88 9261 11390.63 13824 16581.38
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
0.05 0.06 0.06 0.06 0.07 0.07 0.07 0.08 0.08 0.08 0.08 0.09 0.09 0.09 0.1 0.1 0.1 0.11 0.11 0.11 0.11 0.12 0.12 0.12 0.13 0.13 0.13 0.14 0.14 0.14 0.14 0.15 0.15
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2460.38 2893.64 3375 3906.98 4492.13 5132.95 5832 6591.8 7414.88 8303.77 9261 10289.11 11390.63 12568.08 13824 15160.92 16581.38 18087.89 19683 21369.23 23149.13 25025.2 27000 29076.05 31255.88 33542.02 35937 38443.36 41063.63 43800.33 46656 49633.17 52734.38
Paper Honneycomb Interior ti Sheets 1
Thickness 0.01 0.01 0.01 0.01
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
0.11 0.11 0.12 0.13 0.13 0.14 0.14 0.15 0.16 0.16 0.17 0.17 0.18 0.19 0.19 0.2 0.2 0.21 0.22 0.22 0.23 0.23 0.24 0.25 0.25 0.26 0.26 0.27 0.28 0.28 0.29 0.29 0.3
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19683 23149.13 27000 31255.88 35937 41063.63 46656 52734.38 59319 66430.13 74088 82312.88 91125 100544.63 110592 121287.38 132651 144703.13 157464 170953.88 185193 200201.63 216000 232608.38 250047 268336.13 287496 307546.88 328509 350402.63 373248 397065.38 421875
Balsa Wood w0= 0.050 m wi= w0-ta Sheets 2 4 6 8
Thickness ta 0.01 0.02 0.04 0.05
to 0.02 0.03 0.05 0.06
0.05 0.05 0.05 0.05
0.04 0.03 0.01 0
I (For Shell) 0 0 0 0
10
40
0.1 0.1 0.1 0.1 0.4 0.4 0.4 0.4
2 4 6 8 2 4 6 8
0.01 0.02 0.04 0.05 0.01 0.02 0.04 0.05
0.11 0.12 0.14 0.15 0.41 0.42 0.44 0.45
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
0.04 0.03 0.01 0 0.04 0.03 0.01 0
0 0 0 0 0 0 0 0
σ>σt σ ### ### ### ### ### ### ### ### 889092.11 648148.15 486963.3 375085.73 295015.09 236205.59 192043.9 158239.29 131925.13 111136.51 94496.01 81018.52 69986.84
TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
60870.41 53270.99 46885.72 41481.48 36876.89 32929.34 29525.7 26575.43 24005.49 21756.51 19779.91 18035.68 16490.64 15117.16 13892.06 12795.85 11812 10926.48 10127.31 9404.22 8748.36 8152.09 7608.8 7112.74 6658.87 6242.82 5860.71 5509.17 5185.19
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
Shell [EI] 154.5 606 1516.5 3048 10077 21666 34929 50028 332727 671016 1015029 1364928
σ>σt σ ### FALSE ### FALSE ### FALSE 717683.73 FALSE 217078.5 FALSE 100964.65 FALSE 62627.04 FALSE 43725.51 FALSE 6574.46 FALSE 3259.98 FALSE 2155.11 FALSE 1602.65 FALSE
Core σ>σt TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
Balsa Wood (.01m) Thickness (50 Sheet Max)I Sheets 0 0 0 1 0.01 0 2 0.02 0 3 0.03 0 4 0.04 0 5 0.05 0 6 0.06 0 7 0.07 0 8 0.08 0 9 0.09 0 10 0.1 0 11 0.11 0 12 0.12 0 13 0.13 0 14 0.14 0 15 0.15 0 16 0.16 0 17 0.17 0
Paper Honeycomb (0.01m) [EI]Total 0 15.63 125 421.88 1000 1953.13 3375 5359.38 8000 11390.63 15625 20796.88 27000 34328.13 42875 52734.38 64000 76765.63
Thickness (50 Sheet Max) Sheets 0 0 1 0.01 2 0.02 3 0.03 4 0.04 5 0.05 6 0.06 7 0.07 8 0.08 9 0.09 10 0.1 11 0.11 12 0.12 13 0.13 14 0.14 15 0.15 16 0.16 17 0.17
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
91125 107171.88 125000 144703.13 166375 190109.38 216000 244140.63 274625 307546.88 343000 381078.13 421875 465484.38 512000 561515.63 614125 669921.88 729000 791453.13 857375 926859.38 1000000 1076890.63 1157625 1242296.88 1331000 1423828.13 1520875 1622234.38 1728000 1838265.63 1953125
Paper Honneycomb Interior ti I (For Core) [EI]Total 0 154.5 0 606 0 1516.5 0 3048
Sheets 1
Thickness 0.01 0.01 0.01 0.01
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5
Carbon Fiber Sheets Thickness ta 2 0 4 0 6 0 8 0
to 0.01 0.01 0.01 0.01
0 0 0 0 0 0 0 0
10077 21666 34929 50028 332727 671016 1015029 1364928
10
40
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.4 0.4 0.4 0.4 0.4 0.4
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 2 4 6 8 10 12
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01 0 0 0 0 0 0
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.02 0.02 0.02 0.02 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.11 0.11 0.11 0.11 0.11 0.11 0.4 0.4 0.4 0.4 0.4 0.4
0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01
0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.41 0.41 0.41 0.41 0.41 0.41
aper Honeycomb (0.01m) I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[EI]Total 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Paper Honeycomb (0.019m) Thickness (50 Sheet Max) Sheets 0 0 1 0.02 2 0.04 3 0.06 4 0.08 5 0.1 6 0.11 7 0.13 8 0.15 9 0.17 10 0.19 11 0.21 12 0.23 13 0.25 14 0.27 15 0.29 16 0.3 17 0.32
I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[EI]Total 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
w0= 0.050 m
wi= w0-ta
0.05 0.05 0.05 0.05
0.05 0.05 0.05 0.05
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
I (For Shell)I (For Core) 0 0 0 0 0 0 0 0
0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.49 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.65 0.67 0.68 0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.84 0.86 0.87 0.89 0.91 0.93 0.95
[EI]Total 51.18 104.77 160.81 219.38
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.04 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.04 0.05 0.05 0.05 0.05 0.05 0.05
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
280.52 344.3 410.77 480 552.04 626.95 704.79 785.63 869.5 956.48 1046.63 1140 1236.65 1336.64 1440.03 1546.88 1657.24 1771.17 1888.74 2010 2135.01 7824.23 15671.95 23543.23 31438.13 39356.69 47298.98 55265.07 63255 71268.84 79306.64 87368.47 95454.38 103564.42 111698.67 119857.18 128040 136247.2 144478.83 152734.95 161015.63 169320.91 177650.86 186005.54 194385 202789.31 275046.88 550187.58 825422.14 1100750.63 1376173.1 1651689.61
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.04
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1927300.22 2203005 2478803.99 2754697.27 3030684.87 3306766.88 3582943.33 3859214.3 4135579.83 4412040 4688594.85 4965244.45 5241988.86 5518828.13 5795762.31 6072791.48 6349915.69 6627135 6904449.46
Carbon Fiber Prepreg Thickness (50 Sheet Max)I Sheets 0 0 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 10 0 0 11 0 0 12 0 0 13 0 0 14 0 0 15 0 0 16 0 0 17 0 0
Glass Fiber Prepreg [EI]Total 0 0 0.01 0.03 0.08 0.15 0.26 0.42 0.63 0.89 1.22 1.62 2.11 2.68 3.35 4.12 5 6
Thickness (50 Sheet Max)I Sheets 0 0 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 10 0 0 11 0 0 12 0 0 13 0 0 14 0 0 15 0 0 16 0 0 17 0 0
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7.12 8.37 9.77 11.3 13 14.85 16.88 19.07 21.46 24.03 26.8 29.77 32.96 36.37 40 43.87 47.98 52.34 56.95 61.83 66.98 72.41 78.13 84.13 90.44 97.05 103.98 111.24 118.82 126.74 135 143.61 152.59
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ber Prepreg [EI]Total 0 0 0 0.01 0.02 0.04 0.07 0.12 0.18 0.25 0.34 0.45 0.59 0.75 0.94 1.15 1.4 1.68
1.99 2.34 2.73 3.17 3.64 4.16 4.73 5.34 6.01 6.73 7.5 8.34 9.23 10.18 11.2 12.28 13.43 14.65 15.95 17.31 18.76 20.28 21.88 23.56 25.32 27.18 29.12 31.15 33.27 35.49 37.8 40.21 42.72
