Aircraft Structural
Considerations
J. Byron Rogers, P.E.
J.B.Rogers/Structures
Structural Considerations
In Simple Terms
•
The structure will not fail!
-
Not statically under any static design ultimate load case
• Ultimate Load is typically 1.5 * Limit Load
• Covers part tolerances, statistical allowables, load exceedance
•
The structure will not deflect such that something does not work
anymore!
•
Not after repeated loads within the lifetime of the vehicle
Doors will open when they are supposed to
Nothing will yield
Control surfaces will move through expected range
No unexpected shock waves will form
Structure will meet specified durability/ damage tolerance/ fail safety
requirements.
-
No failures with specified damage within allowed inspection intervals
What Do You Need to Consider?
Imagine yourself as the Certifying or Procuring Agency designated
representative. You are responsible for assuring that the vehicle complies with
all structural criteria and requirements. What would it take to convince you that
the design was safe and should be certified?
•
•
•
Are the external loads accurate and complete?
•
Do the material allowables meet the criteria/requirements? (Static strength,
DDT, thermal, manufacturing/processing considerations)
•
Does the certification basis demonstrate compliance with criteria/requirements
– Detail analysis
– Tests
– Reports
Are good internal load paths provided?
Are the internal loads balanced for each component and part? (Are free body
diagrams provided?)
J. B. Rogers/Structures
Aircraft Structural Considerations
Different Objectives - Different Configurations - Similar Process
•
•
•
•
•
•
400 passengers
Criteria
Requirements
Objectives
• FAR’s
• MIL Specs
• SOW/PDS
40 year service life
All weather
Maintainable
Reliable
Configuration
Damage Tolerant
•
•
•
•
•
•
•
Military Fighter/Attack
External Loads
Environments
•Pressures
•Inertia
•Thermal
•Acoustic
Carrier Suitable
Mach 2
nz = 7.5g
RPV
Long Range
Loiter XX Hours w/o refueling
Internal Loads
Load Paths
Analysis
Sizing
Certification
•Tests
•Reports
Methods
Allowables
Aircraft Loads, Conditions & Requirements
Requirements Have Evolved With Experience/Lessons Learned
Flight Loads:
• Maneuver
• Gust
• Control Deflection
• Buffet
• Inertia
• Vibration
Ground Loads:
• Vertical Load Factor
• Braking
• Bumps
• Turns
• Catapult
• Arrested Landing
• Aborted Takeoff
• Spin-Up
• Spring Back
• One Wheel/Two Wheel
• Towing
• Ground Winds
• Break Away
Specific Conditions are defined per:
• FAR Vol III (23 and 25)…………………….Commercial
• Mil-A-8860-8870 and SD-24L……………. Military
Other Loads & Conditions:
• Jacking
• Pressurization
• Crash
• Actuation
• Bird Strike
• Lightning Strike
• Hail
• Power Plant
• Thermal
• Fatigue
• Damage Tolerance
• Fail Safety
• Acoustics
• Ground Handling
Aircraft Loads, Conditions & Requirements
Requirement: Bird Strike
Commercial Transport
• Wings/Body
The airplane must be capable of successfully completing a flight during which likely structural
damage occurs as a result of - Impact with a 4-pound bird when the velocity of the airplane
relative to the bird along the airplane's flight path is equal to Vc at sea level or 0.85Vc at 8,000
feet, whichever is more critical;
• Empennage
The empennage structure must be designed to assure capability of continued safe flight and
landing of the airplane after impact with an 8-pound bird when the velocity of the airplane
(relative to the bird along the airplane's flight path) is equal to VC at sea level
Military
Specifications typically require that catastrophic structural failure or loss of control of aircraft be
prevented after a defined limit of structural damage has occurred as a result of in-flight bird
strike.
No penetration of cockpit
• Danger to crew
No penetration of fuel tanks:
• In-flight fire hazard
• Fuel loss
No damage to control surface actuation/controls
This sounds like a nice
safeguard, but is it really
necessary?
Aircraft Loads, Conditions & Requirements
Every Requirement and Condition is There for a Reason!
747/767/777 Daily Highlight Report
03 April 2001
Multiple Bird Strike - One Bird Entered Flight Deck 767 (L/N 447)
American Airlines reported that on April 2nd during climb from Paris,
at 12,000 feet, the reference airplane struck multiple birds impacting
various locations on the aircraft. One bird entered the flight deck
via the P1-1 panel on the captain's left side. All flight controls and
systems functioned normally. The crew elected to return to Paris where
an uneventful landing was made. The airplane is currently AOG in
Paris.
Aircraft Loads, Conditions & Requirements
Requirement: Bird Strike
• USAF - 34,856 bird strikes reported between Jan 1985 and Feb
1998
– 33,262 non-damaging (less than $10,000)
– 7,358 struck wings
– 764 were Horned Larks
– 348 were Turkey Vultures (+98 Black Vultures)
• Over 25,000 reported strikes to Civil aircraft between 1988 and
1992
• CAA estimates that UK registered A/C of over 12,000 lbs strike a
bird about once every 1,000 flights
Aircraft Loads, Conditions & Requirements
Lightning Strike:
Same Story
Lightening Striking All Nippon Airlines, Osaka, Japan
Aircraft Loads, Conditions & Requirements
In-Flight Hail: Same Story
S/N 1019 took off from Lyon, France and climbed to
approximately 3000 ft when large hail/ice was
encountered. The slats were stowed as the aircraft
took damage for approximately 3-5 second. Aircraft
landed back at Lyon successfully. No other aircraft
in the area incurred similar damage.
The fan blades were inspected and were said to be
in pristine condition.
The aircraft will be ferried from Lyon to Marshalls of
Cambridge to be repaired.
Aircraft Loads, Conditions & Requirements
Typical Commercial Transport Critical Static Load Conditions
Positive Dynamic
Gust
Positive Maneuver
and Static Gust
Aileron Roll
Yaw Maneuver and
Lateral Gust
Negative Maneuver
Negative Maneuver
and Braking
Buffet
Positive Checked
Maneuver
Negative Checked
Maneuver
Gust
Taxi
Cabin Pressure
Different Load Conditions
are Critical for Different Areas
Lateral Maneuver
Negative Gust
Engine Blade Out
Aircraft Loads, Conditions & Requirements
Typical Commercial Transport
Critical Load Conditions
Jack Screw Ftg
Center Box Rib 2
Rib 5
Logo
Lights
Rib 8
Rib 10
Auxiliary
Front Spar
Rib 12
Surge Tank
Rib 14
Leading
Edge
Rear
Fixed
Spar
Trailing Edge
9G Crash
Rib 1
Stall Buffet
Bird Strike
Structural Considerations
•
•
•
•
•
•
•
External loads (pressures/inertia)
Durability/Damage Tolerance
Crash
Failed Refueling Valve
Hail and bird strike
Lightning strike
Material utilization
Surge Tank
Vent Scoop
Fuel Vent
Tube/Return
Line
Wet Area
Lower Surface Skin/Stringers
Negative Maneuver
Upper Surface Skin/Stringers
Durability/Damage Tolerance
Positive Maneuver
Balanced Maneuver
Abrupt Elevator
Lightning Strike
minimum skin thickness
Negative Maneuver
Stall Buffet
Negative Gust
Abrupt Up Elevator
Failed Refuel
Valve
3G Side Load
Crash
Internal Loads/Load Paths
• Aircraft structure is designed to be light weight
=> Typically very thin gage
• Members are arranged to carry loads efficiently
(in-plane)
• shear webs
• axial members
• Out-of-plane loads are carried to redistribution
members where the loads are converted to inplane components
Stiffened Skin Panel
Built-Up Spar
Body Panel
Internal Loads/Load Paths
So how do we get internal members to carry loads efficiently?
Lift
CG
Balance
Load
Moment
Drag
Thrust
Weight
•
•
Consider all load conditions and requirements
Develop a static load balance for each critical condition
–
–
•
•
Apply loads realistically
Determine where they are going to be balanced
Cut sections to determine local internal loads
Provide a path for the loads to follow
(Load will follow stiffest path!)
Note: Most members serve more than one function
Do this for local
loads as well as for
general vehicle
loads
Internal Loads/Load Paths
•
Primary Structural Components are fuselage, wing, and tail
(horizontal and vertical stabilizers)
•
•
Fuselage consists of skins, longerons, and frames
Wing and Stabilizers consist of covers, spars, and ribs
Ribs
What do these
members do?
Frames
Spars
Longerons
Internal Loads/Load Paths - Fuselage
Consider fuselage to act as a beam
For a downward tail load, body will
carry a shear and a bending moment
Bending moment is carried
based on Mc/I distribution
11.5"
11.5"
1
1'
2000
Crown longerons and skin
carry tension loads due to
bending moment
2000
2'
2
3
3'
4
4'
5
5'
z
y
6
6'
7
7'
Skins carry shear load inplane with VQ/I distribution
8'
8
9
9'
10
10'
11
11'
Bruhn Section 21.12 (Fig A21.62)
-16.57
-31.82
-57.22
0.
16.57
31.82
57.22
-66.62
Lower longerons (with effective skin)
carry compression axial loads due to
bending moment
66.62
z
-71.32
71.32
y
-66.62
66.62
-57.22
57.22
-31.82
-16.57
0.
16.57
31.82
Bruhn Figure A21.62
Keel Beam added to restore load path on lower
surface (wing carry through and wheel well areas)
Internal Loads/Load Paths - Fuselage
Crown Panel
d
d
h
Longeron System
d<h
h
Stringer System
d>h
Longerons (stringers)
carry axial loads
Skins carry shear, torsion
and tension
Frames provided to reduce
longeron column length
Frames also support cargo floor and passenger
floor beams (react end loads into skins as shear)
Seat rails run fore-aft and are supported by floor beams
Floor beams tied to frames
(react vertical load) and to a
longitudinal beam to react
forward loads (landing and
crash)
Internal Loads/Load Paths - Fuselage
Body skins also carry
external and compartment
pressures as a membrane.
For duel-lobe configurations, longitudinal beam
(crease beam) and floor beams react out-of-plane
load component at lobe intersection
Internal Loads/Load Paths - Wing/Stabilizer
Internal structure consists primarily of Covers, Spars, and Ribs
Internal Loads/Load Paths - Wing/Stabilizer
Wing acts like cantilevered beam
under distributed pressure loading.
Shear, Moment, and Torsion (about
elastic axis) are beamed to fuselage
and balance tail load, inertia, and
other side wing load.
V
T
Elastic Axis
M
T
V
Shear (10^3 lbs), Moment (10^5 inlbs), Torsion (10^5 in-lbs)
Typical VMT for Horizontal Stabilizer
250
200
150
Shear (V)
100
Moment (M)
Torsion (T)
50
0
0
0.2
0.4
0.6
0.8
-50
Percent Semispan
1
1.2
Internal Loads/Load Paths - Wing/Stabilizer
Main Types of Wing Primary Structure
Thin Skin ( many stringers and ribs)
Transports & Bombers
• Deep Sections
• Skin Supported by
Stringers Carries
Bending Moments
Thick Skin ( many spars, few ribs)
Fighters
• Thin Sections
• Unstiffened Skins
• Skin and Spar
Chords Carry
Bending Moment
Section Bending Moments
Stringers would
not be efficient
Section Shear Flow
28.3
7.7
6.44
10.0
17.4
51.9
28.3
23.3
7.7
Vz = 1000 lbs
10.0
11.23
18.81
17.4
6.44
Spar Webs Carry Shear (V)
Shell Carries Torque (T)
4.71
18.92
5.53
1.84
18.51
4.71
Vz = 1000 lbs
5.53
7.74
1.84
Internal Loads/Load Paths - Wing/Stabilizer
External + Internal Pressures + Inertia
Effective Area
Stringer
S
Covers
Ribs
bs
Rib
Pressure + Inertia Loads
Effective Area for Pressure Loads
Pseg i
2
Prib = Pseg i * (sin 2 - sin 1) i
P
P
1
Segment
Q
L1
L2
Rib
Pseg i
P
Q
P
Prib i
Q = PM (L1 + L2)
EI
2
Crushing Loads on a Rib
Rib
Mid-span
between ribs
Mid-span
between ribs
1, 2 are the “as built” angles
Pseg i is load at ribi
Built-In Curvature Loads
Internal Loads/Load Paths - Wing/Stabilizer
Ribs redistribute pressure and inertia
loads into cellular box structure.
Internal + External Pressure, Inertia,
Curvature, and Crushing Loads
1.7 1.6 1.5 1.4 1.2 1.0 .8
1.0 1.3 1.6
.7
.6
.4
qt
qv
5"
V=19,200 #
10"
15"
18" 21"
T=47,000 in-#
6.67"
.1
.3
.6
.9
.9
60"
.3
.6
.6
.1
Loads at Shear Center Balanced by Shear Flows
a. Applied Rib Loads (Load in 103 lbs)
1.2
2.6
3.3
3.0
2.4
1.6
.7
T=47,000 in-#
S.C.
V=19,200 #
.2
.6
1.1
.9
.8
.6
.2
b. Loads Resolved to Stiffeners and Reacted at Shear Center
Calculated Shear Flow Balance - Stiffened Skin
Internal Loads/Load Paths - Wing/Stabilizer
Ribs
•
•
•
•
FLOOR FITTING
FLOOR FITTING
FLOOR FITTING
FLOOR FITTING
React panel crushing loads
React curvature loads
Maintain wing/stabilizer chordwise
contour
Up
MACHINED RIB
•
Limit skin or skin/stringer column
length
•
React Local Concentrated Loads
• Landing gear
• Power plant
• Fuselage attachments
• Ailerons
• Flaps
• Lift devices
•
Shear Tied Rib
React and distribute air/fuel pressure
loads
May Act as Fuel Boundaries
FORWARD FITTING
Aft
AFT FITTING
Intermediate Rib
Rear Spar
Stringer Tie
Spar Tie
Front Spar
Internal Loads/Load Paths - Wing/Stabilizer
Emergency Landing (Crashworthy) Fuel Loads
If the time ‘T’ for fuel to flow from the upstream
side of the barrier to fill a volume of air defined
in the 1g flight condition is greater that 0.5
second, the internal baffle can be considered to
be a solid pressure barrier.
Conversely, an internal baffle may not be
considered as a pressure boundary if the
volume of air in the fuel cell downstream of the
barrier is not adequate to meet the above
criteria. In such cases, the pressures due to the
hydrostatic fuel head must be calculated
without consideration of this internal baffle.
Fuel Loading - Roll Rate
F = Mr2

r

F = Mr
 = angular acceleration
 = angular velocity
Rib 2
Rib 8
136.3"
83.0"
219.3"
P = 0.34 * K * L
(6.5 pound/gallon fuel density)
Where: P = design pressure at location ‘a’; L = reference
distance, feet, between the point of pressure and the
farthest tank boundary in the direction of loading; K is
defined in the table.
Loading Condition
Forward
Aft
Inboard
Outboard
Downward
Upward
K
9
1.5
1.5
1.5
6
3
Internal Loads/Load Paths - Wing/Stabilizer
Ribs redistribute concentrated loads into cellular box structure.
Concentrated Loads
•
•
•
•
•
•
Landing Gear
Engine Pylon
Front Spar
Power Plant
Wing Elastic Axis
Fuselage Attachments
Ailerons
Flaps
Lift devices
PP C.G.
Internal Loads/Load Paths - Wing/Stabilizer
Spars are Primarily Shear Beams
•
•
•
•
Carry Wing Shear Loads
3 Basic Types of Spars
Fuel Loads
Bird Strike
Cost
Upright or Rib Post
With Covers, Carry Torsion
React Local Concentrated Loads
Web
Chord
Stiffened Web
May Also Act as Fuel Boundaries
Exception to
in-plane
shear loading
Fuel Pressures
Thin Section
Fighter Wing
Sinewave
Rib Post
wmax = (bs1/2 + bs2/2) * p
L
bs1/2 + bs2/2
Strut
Chord
Access
bs1
Truss Beam
Internal Loads/Load Paths - Wing/Stabilizer
Web Type Spar
5.0" (5 PL)
Most Common Type
(Usually Diagonal Tension)
Light Weight/Low Cost
Simple Internal Loads
Poor Access
Moderate to High Assembly Cost
q2
q1
q3
20.0"
Chords:
Area =0.6 in2
Iy =.20 in4
Struts/Posts:
Area =0.45 in2
Iy =.06 in4
Web:
t =0.1 in
q1 = 200 lbs/in
q2 = 200 lbs/in
q3 = 500 lbs/in
Example Geometry and Applied Loads
Upper Chord
9500
13000
17500
2500
6000
0
Upper Sill
L1
q = 900
L2
q=
q=
900
q=
700
q=
700
700
q=
500
Lower Sill
Lower Chord
q(applied) = 200
Framed Out Access Hole
17500
13000
q(applied) = 200
9500
Web Type Spar
For a shear beam,
q = V/h
(web shear flow)
P = M/h
(chord load)
h = Distance between chord centroids
6000
2500
q(applied) = 500
0
Internal Loads/Load Paths - Wing/Stabilizer
Simple Truss
17,500
13,000
9500
9500
2,500
9500
2,500
2,500
14,000
Eccentricity Issues
Less Simple Joint Loads
Simple Assembly
Good Access
14,431
10,307
0
14,431
14,431
10,000
q(applied) =500 lbs/in
q(applied) =200 lbs/in
q =900 lbs/in
q(applied) = 200 lbs/in
q =900 lbs/in
14,431
17,500
14,431
14,431
0
10,307
4,000
13,000
6,000
13,000 6,000
0
0
6,000
Simple Truss
Chord Centroidal Axis
Strut Centroidal Axis
640
17,500
1,727
14,970 9,514
640
9514
14,000
Line Up Loads!
4,926
640
11,014
155
2,210
q(applied) =200 lbs/in
q =900 lbs/in
1,473
1,727
9514
1,294
2,676
3,871
2,600
12,974
640
212
1,294
13,657
q =900 lbs/in
0
12,336
3,877
12,336
9,685
q(applied) =500 lbs/in
1,844
1,775
179
187 9,151
12,974
212
163
5,996
2,712
1339
9,151
1,361
13,657
11,014
2,712
8,936
155
119
1,827
1,908
2489
1,081
q(applied) = 200 lbs/in
155
1872
13,000
1,207
187
179
2,210
17,500
87
1,985 2,420
2,489
87
2,676
2165
Fixed End Truss
Complicated Internal Loads
Complex Joint Loads
Low Assembly Cost
Good Access
9514
609
5,996
205
163
609
5,996
163
Truss with Full Fixity at Ends of Struts
1,422
163
1064
119
2,793
1763
1064
5,996
1763
155
155
155
1064
3558
Internal Loads/Load Paths - Wing/Stabilizer
Stiffened Skin
(many ribs)
Shear Tied Ribs @
Concentrated Load
Locations
Internal Loads/Load Paths - Arrangement
This Slide Intentionally Left Blank
See Class Handout
Internal Loads/Load Paths - Arrangement
Longeron System
(d < h)
Wing Fold
Frames @ Direction
Changes in Load
Carrying Members
Multi-Spar
(unstiffened
skins, few ribs)
Frames @ Concentrated
Load Points
Internal Loads/Load Paths - Arrangement
Longeron System
(d < h)
Wing Fold
Stub Ribs
Dielectric material
Multi-Spar
(unstiffened
skins, few ribs)
Frames @ Concentrated
Load Points
Internal Loads/Load Paths - Arrangement
No Fuselage, No Vertical Stabilizer
Ribs @ Concentrated Load Points
Deep Section
Stiffened Skins
(many ribs)
Internal Loads/Load Paths - Arrangement
Two Structural Boxes
Forward
Structural
Box
Aft Structural Box
Big Hole in the Middle
Aircraft Structural Considerations
Now you have
• Developed a Configuration to Address the Requirements,
Criteria, & Objectives
• Provided Internal Load Paths
• Developed the Internal Loads
What’s Next?
Conduct Analysis & Sizing
• Identify Internal Loads for Each Part
• Balance Loads & Reactions (free body diagrams)
• Develop Shear, Moment, and Axial Loads (and diagrams)
• Conduct Analyses/Sizing using Appropriate Loads, Methods, and
Allowables
Certification
• Tests
• Reports
Note: “Aircraft Materials”
and “Design Validation
Testing” will be the
subjects of future lectures
Internal Load Balance
In-Plane Load Balance
Web shear flows and stiffener loads
were developed for each load
condition
Condition 1
10.4g Down + 2.6g Fwd + 4.0 rad/sec + Pitch Up
Floor Load Balance
91
-420
-259
7.45"
156
439
47
1890
-103
759
440
582
2482
65
18
-11
165
86
Shear
flow
(lbs/in)
2566
54
67
302
Lateral stiffener
loads (lbs)
54
2279
760
223
Fore-aft stiffener
loads (lbs)
1942
597
-245
143
420
138
67
48
107
452
596
-955
557
67
48
18
115
451
909
22
389
48
18
-2085
97
36
689
895
-1767
216
18
-11
41
432
676
893
-861
54
-597
-11
41
60
294
-441
675
583
367
372
38
41
60
79
47
-451
60
134
1875
115
Ultimate
103
832
Internal Load Balance
Load Balance:
• Normal Pressures
• In-Plane Components
23.1p lbs
p = Pressure (psi)
wmax = 7.475p lbs/in
23.1p lbs
104.9p lbs
88.4p lbs
58.61 in
88.4p lbs
Develop shear,
moment, axial,
and torsion
diagrams
V
104.9p lbs
M = 1665p in- lbs
M
Analysis Methods
Most Methods are Unique to Aerospace Industry and are Semi-empirical
• Diagonal Tension
– Forced Crippling
– Permanent Buckling
– Gross Allowable Web Stress (Shear Rupture)
– Secondary Bending Moments
• Lightening Holes/Flanged Holes
• Beaded Shear Panels
• Local Buckling
• Crippling
• Effective Width of Buckled Sheet
• Sheet Wrinkling
• Buckling in Bending
– Formed members with or w/o attached skin
– Extruded members with or w/o attached skin
• Tension Fittings/Clips
• Lugs
• Joggles
• Bearing/Bypass Interaction @ Fastened Joints
• Effects of Defects
Most Static Load
Critical Structure
is Stability Driven
Analysis Methods
Methods Generally Developed from:
• NACA Tests and Reports
• IRAD and CRAD Tests/Studies
• Experience/Lessons Learned
Each Company Has its own Methods
Manuals
Preliminary Sizing - CT Horizontal Stabilizer
Main Box Cover Panel
CONSTRAINTS
•
•
•
•
•
bS
C/S Depth
Skin min gage (.08”fuel areas or .05” other)
Stringer attach flange width (e/d & clearance)
Minimum stringer machining gage (.05”)
Producibility
tOpad
tF
bA
tO
tA
H
tF
bF
STATIC CHECKS ( Each Stringer; Each Rib Bay)
•
•
•
•
•
•
•
•
•
Crippling
Johnson-Euler Column (Axial Compression) Fixity Coefficient C = 1
Johnson-Euler Column (Axial Compression) + Shear C = 1
Flexure (pressure acting singularly, C = 4)
Beam Column (C = 4)
Skin Stability between stringers (compression + shear) @ Cruise
Preliminary D/DT Cutoff
Flexure-Torsion Mode Stability
Pure Torsion Mode Stability
Preliminary Sizing - CT Horizontal Stabilizer
CONSTRAINTS
•
•
•
•
•
Front Spar
wb
w1
Standard sheet thicknesses
Minimum chord machining gage (.08”)
t2 = tav g
t1
Upright attach flange thickness
Upright and chord attach flange widths
wa
t3
Shear stability limits (80% DLL in wet areas)
STATIC CHECKS (Each Bay)
•
w2
Webs/Uprights
- Net shear
- Shear rupture
- Bearing
- Fastener shear
- Uprt/Chd net shear + tension
- Irequired
- Forced crippling
- Upright column
- Upright flexure
•
Chords
- Crippling
- Maximum compression
- Column stability
- Net tension
- D/DT cutoff
w3
Aircraft Structural Considerations
Now you have
• Developed a Configuration to Address the Requirements,
Criteria, & Objectives
• Provided Internal Load Paths
• Developed the Internal Loads
Conducted Analysis & Sizing
• Identified Internal Loads for Each Part
• Balanced Loads & Reactions (free body diagrams)
• Developed Shear, Moment, and Axial Loads (and diagrams)
• Conducted Analyses/Sizing using Appropriate Loads, Methods,
and Allowables
Cycle would be iterated 1 - 3 times.
Certification
• Tests
• Reports
Preliminary Sizing
Considering How Little Time You Have, What Can You Do?
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Develop External Loads
Provide Good Internal Load Paths
Develop the Internal Loads at a Few Locations
• 2 Body Cuts
• Mc/(Ad2)
• Vq/(Ad2) or V/(h)
• T/(2Aencl)
• 2 Wing Cuts
Aencl is enclosed area
• M/h
Cover Axial Loads
• Split V between spars
(balance about SC or centroid)
• T/2Aencl
Assume covers and outer
spars carry all torsion
V - Va/L
Size to Cut-Off Ultimate Stress or Strain
• Aluminum 40 ksi (compression)
40 ksi (tension)
• CEP
.004 in/in (compression)
.0045 in/in (tension)
Assume Shear Resistant for Shear and Torsion
Fighter Covers no Buckling at Ultimate
z
y
h
z
V/(2h)
V/(2h)
y
q = T/(2Aencl)
T
S.C.
V
Va/L
a
L
Aencl
h