CHAPTER II THEORITICAL REVIEW A. Theoritical Framework 1 ...
Theoritical Substantiation.xls
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Repair substantiation for R.OAEZ.000465-ER01 BOLT DATA Reference 1 Shear Bolt Material : Titanium Alloy d = Shear Bolt Dia = Lug Hole Dia : 9.50 mm A = Area along shear plane : 70.88 FoS = Factor of Safety 1.50 = Ultimate Tensile Strength : 896.32 Mpa = Yield Tensile Strength : 827.37 Mpa = Allowable Tensile Strength (Working Tensile strength) : 597.55 Mpa = Ultimate Shear Strength : 672.24 Mpa = Yield Shear Strength : 479.88 Mpa = Allowable Shear Strength (Working Shear strength) : 448.16 Mpa I = Moment of Inertia of Bolt Circular Area : 399.82 LUG DATA Lug Material : Aluminum Alloy 4046 = Thickness of the Lug : 4.87 mm = Hold Open Rod Support End Fitting : 10.33 mm D = Distance between the lugs : 18.65 mm g = Clearance between the Lugs : 4.16 mm w = Width of the Lug : = 37.50 mm FoS = Factor of Safety 1.50 = Ultimate Tensile Strength : 240.00 Mpa = Yield Tensile Strength : 140.00 Mpa = Allowable Tensile Strength (Working Tensile strength) : 160.00 Mpa = Ultimate Shear Strength : 180.00 Mpa = Yield Shear Strength : 81.20 Mpa = Allowable Shear Strength (Working Shear strength) : 120.00 Mpa = Projected area where bearing pressure is applied : 46.27 T/R LOAD DATA W = Weight of the Thrust Reverser : 791 Kgs P = Load on the Hold Open Rod Support Fitting : 9.81 * (W/3)= 2586.57 N = 2.59 KN MODES OF FAILURE 1) Failure by Shearing of Bolt 2) Failure by Bolt Bending 3) Failure by Tension or Compression through Bolt Hole 4) Failure by Shearing of the Lug 5) Failure by Bearing Stress 1) FAILURE BY SHEARING OF BOLT Reference 2 Since the bolt shear loading condition is Double shear, it can be assumed that Load acting on each plane of shear is 1/2 the total load = 18.246 = 18.25 Mpa 2) FAILURE BY BOLT BENDING Reference 3 Analysis and Design of Flight Vehicle Structure - EF Bruhn Chapter D1.10 = 9.1775 mm = 11.87 N-m = 56.38 56.38 Mpa It is a general assumption that the allowable bending stress is 1/2 times the allowable normal stress = 298.77 298.77 Mpa 3) FAILURE BY TENSION OR COMPRESSION OF BOLT HOLE Reference 4 Analysis and Design of Flight Vehicle Structure - EF Bruhn Chapter D1.10 = P/A Hence the maximum design load the lugcan take in tension or compression is 21817.60 N The maximum design load the lug can take in tension or compression is 21.82 KN 4) FAILURE BY SHEARING OF LUG Reference 5 Analysis and Design of Flight Vehicle Structure - EF Bruhn Chapter D1.10 = Hence the maximum design shear load, the lug can take is 32726.40 N The maximum load the bolt can take in tension or compression is 32.73 KN 5) FAILURE BY BEARING STRESS Reference 6 Analysis and Design of Flight Vehicle Structure - EF Bruhn Chapter D1.10 = 27.95 27.95 Mpa πd 2 /4 = mm 2 σu(bolt) σy(bolt) σa(bolt) σu(bolt) / FoS = τu(bolt) 0.75 * σu(bolt) ( Reference 1) = τy(bolt) 0.58 * σy(bolt) ( Reference 1) = τa(bolt) τu(bolt) / FoS = π * r 4 /4 = mm 4 t1 t2 (D - t2) / 2 = σu(lug) σy(lug) σa(lug) σu(lug) / FoS = τu(lug) 0.75 * σu(lug) ( Reference 1) = τy(lug) 0.58 * σy(lug) ( Reference 1) = τa(lug) τu(lug) / FoS = Abr d * t1 = mm 2 Maximum shear across the Shear Bolt τ P ( Reference 2) = N/mm 2 2A Maximum shear across the Shear Bolt τ Since τ < τa(bolt) (18.25 Mpa < 448.16 Mpa) The Design is considered to be safe Bending moment distance b t1/2 + t2/4 + g ( Reference 3) = Bending moment "M" Bending Stress "σb" M * r / I = N/mm 2 Allowable Bending Stress "σb(a)(bolt)" N/mm 2 Since σb < σb(a)(bolt) (56.38 Mpa < 298.77 Mpa) The Design is considered to be safe Ultimate Tensile Strength σu Pmax = σa(lug) * A Pmax = σa(lug) * (w-d) * t = nce the maximum design load the bolt hole could withstand Pmax > P, the actual load (21.82 KN > 2.59 KN) The Design is considered to be sa Ultimate Shear Strength τu P/A P τ max = τa(lug) * A P τ max = τa(lug) * (w-d) * t * 2 = = Since the maximum shear load the Lug could withstand Pτ max > P, the actual load (32.73 KN > 2.59 KN) The Design is considered to be safe Bearing Stress σbr P/Abr = N/mm 2 = Since σbr < σa(lug) (27.95 Mpa < 160 Mpa) The Design is considered to be safe
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Substantiation for double shear joint
Transcript of Theoritical Substantiation.xls
Page 1 of 4
Repair substantiation for R.OAEZ.000465-ER01
BOLT DATA Reference 1
Shear Bolt Material : Titanium Alloy
d = Shear Bolt Dia = Lug Hole Dia : 9.50 mm
A = Area along shear plane : 70.88
FoS = Factor of Safety 1.50
= Ultimate Tensile Strength : 896.32 Mpa
= Yield Tensile Strength : 827.37 Mpa
= Allowable Tensile Strength (Working Tensile strength) : 597.55 Mpa
= Ultimate Shear Strength : 672.24 Mpa
= Yield Shear Strength : 479.88 Mpa
= Allowable Shear Strength (Working Shear strength) : 448.16 Mpa
I = Moment of Inertia of Bolt Circular Area : 399.82
LUG DATA
Lug Material : Aluminum Alloy 4046
= Thickness of the Lug : 4.87 mm
= Hold Open Rod Support End Fitting : 10.33 mm
D = Distance between the lugs : 18.65 mm
g = Clearance between the Lugs : 4.16 mm
w = Width of the Lug : = 37.50 mm
FoS = Factor of Safety 1.50
= Ultimate Tensile Strength : 240.00 Mpa
= Yield Tensile Strength : 140.00 Mpa
= Allowable Tensile Strength (Working Tensile strength) : 160.00 Mpa
= Ultimate Shear Strength : 180.00 Mpa
= Yield Shear Strength : 81.20 Mpa
= Allowable Shear Strength (Working Shear strength) : 120.00 Mpa
= Projected area where bearing pressure is applied : 46.27
T/R LOAD DATA
W = Weight of the Thrust Reverser : 791 Kgs
P = Load on the Hold Open Rod Support Fitting : 9.81 * (W/3)= 2586.57 N = 2.59 KN
MODES OF FAILURE
1) Failure by Shearing of Bolt
2) Failure by Bolt Bending
3) Failure by Tension or Compression through Bolt Hole
4) Failure by Shearing of the Lug
5) Failure by Bearing Stress
1) FAILURE BY SHEARING OF BOLT Reference 2
Since the bolt shear loading condition is Double shear, it can be assumed that Load acting on each plane of shear is 1/2 the total load
= 18.246
= 18.25 Mpa
2) FAILURE BY BOLT BENDING Reference 3
Analysis and Design of Flight Vehicle Structure - EF Bruhn Chapter D1.10
= 9.1775 mm
= 11.87 N-m
= 56.38
56.38 Mpa
It is a general assumption that the allowable bending stress is 1/2 times the allowable normal stress
= 298.77
298.77 Mpa
3) FAILURE BY TENSION OR COMPRESSION OF BOLT HOLE Reference 4
Analysis and Design of Flight Vehicle Structure - EF Bruhn Chapter D1.10
= P/A
Hence the maximum design load the lugcan take in tension or compression is
21817.60 N
The maximum design load the lug can take in tension or compression is 21.82 KN
4) FAILURE BY SHEARING OF LUG Reference 5
Analysis and Design of Flight Vehicle Structure - EF Bruhn Chapter D1.10
=
Hence the maximum design shear load, the lug can take is
32726.40 N
The maximum load the bolt can take in tension or compression is 32.73 KN
5) FAILURE BY BEARING STRESS Reference 6
Analysis and Design of Flight Vehicle Structure - EF Bruhn Chapter D1.10
= 27.95
27.95 Mpa
πd2/4 = mm2
σu(bolt)
σy(bolt)
σa(bolt) σu(bolt) / FoS =
τu(bolt) 0.75 * σu(bolt) ( Reference 1) =
τy(bolt) 0.58 * σy(bolt) ( Reference 1) =
τa(bolt) τu(bolt) / FoS =
π * r4/4 = mm4
t1
t2
(D - t2) / 2 =
σu(lug)
σy(lug)
σa(lug) σu(lug) / FoS =
τu(lug) 0.75 * σu(lug) ( Reference 1) =
τy(lug) 0.58 * σy(lug) ( Reference 1) =
τa(lug) τu(lug) / FoS =
Abr d * t1 = mm2
Maximum shear across the Shear Bolt τ P ( Reference 2) = N/mm2
2A
Maximum shear across the Shear Bolt τ
Since τ < τa(bolt) (18.25 Mpa < 448.16 Mpa) The Design is considered to be safe
Bending moment distance b t1/2 + t2/4 + g ( Reference 3) =
Bending moment "M"
Bending Stress "σb" M * r / I = N/mm2
Allowable Bending Stress "σb(a)(bolt)" N/mm2
Since σb < σb(a)(bolt) (56.38 Mpa < 298.77 Mpa) The Design is considered to be safe
Ultimate Tensile Strength σu
Pmax = σa(lug) * A Pmax = σa(lug) * (w-d) * t =
Since the maximum design load the bolt hole could withstand Pmax > P, the actual load (21.82 KN > 2.59 KN) The Design is considered to be safe
Ultimate Shear Strength τu P/A
P τ max = τa(lug) * A P τ max = τa(lug) * (w-d) * t * 2 =
=
Since the maximum shear load the Lug could withstand Pτ max > P, the actual load (32.73 KN > 2.59 KN) The Design is considered to be safe
Bearing Stress σbr P/Abr = N/mm2
=
Since σbr < σa(lug) (27.95 Mpa < 160 Mpa) The Design is considered to be safe
Page 2 of 4
Repair substantiation for R.OAEZ.000465-ER01
MetalTensile strength Yield strength Tensile strength Yield strength
1000psi 1000psi psi psiCast iron 40 24 40000 24000Wrought iron 50 30 50000 30000Commercially pure iron, annealed 42 19 42000 19000
Hot-rolled 48 30 48000 30000Cold-rolled 100 95 100000 95000
Structural steel, ordinary 57.5 35 57500 35000Low-alloy, high-strength 77.5 60 77500 60000Steel, SAE 1300, annealed 70 40 70000 40000
Quenched, drawn 1,300°F 100 80 100000 80000Drawn 1,000°F 130 110 130000 110000
Drawn 700°F 200 180 200000 180000Drawn 400°F 240 210 240000 210000
Steel, SAE 4340, annealed 80 45 80000 45000Quenched, drawn 1,300°F 130 110 130000 110000
Drawn 1,000°F 190 170 190000 170000Drawn 700°F 240 215 240000 215000
Drawn 400°F 290 260 290000 260000Cold-rolled steel, SAE 1112 84 76 84000 76000Stainless steel, 18-S 90 32.5 90000 32500Steel castings, heat-treated 92.5 45 92500 45000Aluminum, pure, rolled 18 13 18000 13000Aluminum-copper alloys, cast 21 14 21000 14000Wrought , heat-treated 45 30 45000 30000Aluminum die castings 30 30000 0Aluminum alloy 17ST 56 34 56000 34000Aluminum alloy 51ST 48 40 48000 40000Copper, annealed 32 5 32000 5000Copper, hard-drawn 68 60 68000 60000Brasses, various 80 44 80000 44000Phosphor bronze 85 85000 0Tobin bronze, rolled 63 41 63000 41000Magnesium alloys, various 33 21 33000 21000Monel 400, Ni-Cu alloy 79 30 79000 30000Molybdenum, rolled 100 75 100000 75000Silver, cast , annealed 18 8 18000 8000Titanium 6–4 alloy, annealed 130 120 130000 120000Ductile iron, grade 80-55-06 80 55 80000 55000Alloy Steel AISIAiSi Mg10Titanium Alloy17-4PH SteelAluminum Alloy 4046
275.8 165.5344.7 206.8289.6 131.0330.9 206.8689.5 655.0396.4 241.3534.3 413.7482.6 275.8689.5 551.6896.3 758.4
1379.0 1241.11654.7 1447.9
551.6 310.3896.3 758.4
1310.0 1172.11654.7 1482.41999.5 1792.6
579.2 524.0620.5 224.1637.8 310.3124.1 89.6144.8 96.5310.3 206.8206.8 0.0386.1 234.4330.9 275.8220.6 34.5468.8 413.7551.6 303.4586.1 0.0434.4 282.7227.5 144.8544.7 206.8689.5 517.1124.1 55.2896.3 827.4551.6 379.2655.0 417.0
896.3 827.4
240.0 140.0
Tensile strengthin MPa
Yield strengthin MPa
