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end of the appendix.
1. General notations
- Re : yield strength of the material
- Rm : tensile strength of the material subject to traction forces
- Rc : tensile strength of the material subject to shear forces
Rc = 0.6 Re
- Mfmax : maximum bend moment
2. The test table
Figure 7: Structure Resistance Calculation
35 Kg
460
180
840
180
X
20 Kg
Demonstration of the mechanical strength of Appendix 2
structures supporting airborne experiments
Edition 5.2 A2.3
2.1 Weights of the example equipment
Weight Height of centre of gravity
Test table m1 = 10 kg h1 = 370 mm
Box No. 1 m2 = 20 kg h2 = 230 mm
Box No. 2 m3 = 35 kg h3 = 720 mm
2. Technical data
Material Rm (MPa) Re (MPa) Rc (MPa)
Bay uprights A33 330
Attaching screws 35 NC 6 900 740 444
The bay is secured to the aircraft floor by 4 M10 screws.
Demonstration of the mechanical strength of Appendix 2
structures supporting airborne experiments
Edition 5.2 A2.4
3. Calculation of weight and centre of gravity
M = m1 + m2 + m3
M = 65 kg
H =
h1.m1+ h2.m2 + h3.m3
M
H = 515.4 mm
4. Crash performance
4.1. Shear stress on the attachment screws:
- the standard sets a 9 g forward acceleration in the event of a crash,
- the force experienced by the bay is thus : F = 9 M g
Hence a shear force on the attachment screws of : Fc = F
n
Where : M = Total mass capacity for cargo bay = 65 kg
g = 9.81 m/s
n = number of screws = 4
Þ Fc = 9.M.g
n
= 9 x 65 x 9.81
4
N
Û Fc = 1435 N
Safety coefficient = C = Fcmax
Fc
= 16250
1435
(see “Screw characteristics” table)
C = 11.3
Demonstration of the mechanical strength of Appendix 2
structures supporting airborne experiments
Edition 5.2 A2.5
4.2 Traction force on the attachment screws:
Assuming a crash landing, we consider that the bay rotates around the front
attachments (in the x-z plane, see section 5.1) and thus only the rear attachments take
up the force. Then, the horizontal acceleration creates the following moments:
F x H = X x d
F = 9 M x g
H = height of assembly’s centre of gravity = 515.4 mm
X = force on rear attachments
d = distance between forward and rear attachments = 800 mm
Þ X = 9.MgH
d
= 9 x 65 x 9.81 x 515.4
800
Û X = 3697N
X represents the force experienced by two M10 screws, thus a traction force on the
screws of:
X’ = X/2 = 1850 N
The pre-stressing of the screws by the 2 mkg tightening torque imposes an additional
traction force of 14000 N. The traction force on the rear screws is thus:
F = X’ + 14000 = 15850 N
Safety coefficient : : C = Ftmax
Ft
= 32940
15850
= 2,07
(see “Screw characteristics” table, page A2.7)
Demonstration of the mechanical strength of Appendix 2
structures supporting airborne experiments
Edition 5.2 A2.6
4.3 Bending strength of uprights
The bay consists of four uprights made from 60 x 40 x 5 L sections:
Mfmax = 1,402,500 Nmm (see table concerning unequal flange brackets)
Bending moment on an upright
Mf = 9MgH
n
M = Total weight of equipped bay = 65 kg
g = 9.81 m/s
H = Height of centre of gravity calculated in paragraph 3
n = number of uprights = 4
Mf = 9x65x9.81x515.4
4
Mf = 739 451 Nmm
Safety coefficient :
C = Mfmax
Mf
= 1 402 500
739 451
Þ C = 1.9
Demonstration of the mechanical strength of Appendix 2
structures supporting airborne experiments
Edition 5.2 A2.7
Characteristics of screw quality class 8.8
Nominal diameter
(mm)
Pitch (mm) Maximum
traction force (N)
Maximum shear
force (N)
5 0.8 12780 6304
6 1 18090 8924
8 1.25 32940 16250
10 1.5 52200 25572
12 1.75 75870 37429
Demonstration of the mechanical strength of Appendix 2
structures supporting airborne experiments
Edition 5.2 A2.8
Characteristics of square tubes with rounded angles
Material : A33 (Rm = 330 MPa) Material : 5086 H 111 (Rm = 250 MPa)
Width
(mm
Thickness
(mm)
Mfmax
(N.mm)
Width
(mm)
Thickness
(mm)
Mfmax
(N.mm)
35
2.5 966240
35
2.5 73200
4 1226940 4 929571
2.5 1320000 2.5 999875
40 3 1486980 40 3 1126500
4 1735800 4 1315000
45
2.5 1727880
45
2.5 1308889
3 1963830 3 1487778
50
3 2505360
50
3 1898000
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