Form KNSI-P3-004-7 Issue: 0 Rev: 0 Structural Substantiation Report DOA EASA.21J.560 STRUCTURAL SUBSTANTIATION REPORT Document number: 15K036-SSR-001-1.R Page 1 of 109 Page 1 of 109 Part 1: General Description TITLE: FUSELAGE - VHF ANTENNA INSTALLATION VALID ON AIRCRAFT: TAB No. Serial Number Registration B757-200 24868 VQ-BOX REVISION STATUS: Orig: February 26, 2015 Rev: 01 June 25, 2015 Description: This is Structural Substantiation Report provides addition substantiation data to validate the modification approved by the KNSI Classification and Certification Sheet 15K036-CCS-004-0.R. Structural Substantiation Report This document and all information and expression contained herein are the property of KNSI Limited and are provided to the recipient in confidence. This document contains proprietary information and shall at all times remain the property of KNSI Limited, no intellectual property right or licence is granted by KNSI Limited in connection with any information contained herein and the information contained herein shall be treated as confidential and not disclosed to any third party without the prior written consent of KNSI Limited Part 2: Approval Prepared By: Compliance Verification Engineer: Office of Airworthiness: Name: Aruni Senanayaka Name: Y. Dissanayake Name: K. Obeysekara Date: June 25, 2015 Date: June 25, 2015 Date: June 25, 2015
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Form KNSI-P3-004-7 Issue: 0 Rev: 0 Structural Substantiation Report
DOA EASA.21J.560
STRUCTURAL SUBSTANTIATION REPORT
Document number: 15K036-SSR-001-1.R Page 1 of 109
Page 1 of 109
Part 1: General Description
TITLE: FUSELAGE - VHF ANTENNA INSTALLATION
VALID ON AIRCRAFT:
TAB No. Serial Number Registration
B757-200 24868 VQ-BOX
REVISION STATUS:
Orig: February 26, 2015
Rev: 01 June 25, 2015
Description: This is Structural Substantiation Report provides addition substantiation data to validate the
modification approved by the KNSI Classification and Certification Sheet 15K036-CCS-004-0.R.
Structural Substantiation Report
This document and all information and expression contained herein are the property of KNSI Limited and
are provided to the recipient in confidence. This document contains proprietary information and shall at all times remain the property of KNSI Limited, no intellectual property right or licence is granted by KNSI
Limited in connection with any information contained herein and the information contained herein shall be
treated as confidential and not disclosed to any third party without the prior written consent of KNSI Limited
Part 2: Approval
Prepared By:
Compliance Verification
Engineer:
Office of Airworthiness:
Name: Aruni Senanayaka Name: Y. Dissanayake Name: K. Obeysekara
Date: June 25, 2015 Date: June 25, 2015 Date: June 25, 2015
Form KNSI-P3-004-7 Issue: 0 Rev: 0 Structural Substantiation Report
DOA EASA.21J.560
STRUCTURAL SUBSTANTIATION REPORT
Document number: 15K036-SSR-001-1.R Page 2 of 109
Page 2 of 109
Revision status
Rev 00: Initial Issue - February 26, 2015
Rev 01: Antenna location is changed to the bottom of the aircraft – June 25, 2015
General Introduction
The VHF antenna at the tail section of the aforementioned Boeing 757-200 aircraft is going to be changed
according to the KNSI change bulletin 15K036-CB-004-0.R or the latest revision.
This Structural substantiation report was raised to substantiate this change.
This report is providing the structural substantiation static, fatigue, and damage tolerance for alterations
made to a Boeing 757-200 by the installation of the VHF Antenna and transceiver.
Reference Documents
a) Structural Analysis Report No. LB-VHF.757-703SA
b) KNSI Drawing 15K036-MD-001-0.R - VHF Antenna Installation
Description
The -01 VHF Antenna installation is detailed in KNSI Drawing 15K036-MD-001-0.R. The antenna is
installed on the bottom of the aircraft at F.S. 1452 between STR 30 and STR 29R. The antenna is
attached through the aircraft skin to the -11 hat section using ten ¼-28 fasteners into nutplates attached to the -11 hat section. The -11 hat section is attached to two aft -1 5 mount channels and two -13 FWD
mount channels using three MS20470AD5 rivets per channel. The -11 hat section is also attached to the
-17 stringer support using four HL18-5 Hi-Loks. The -17 stringer support is attached to the -19 and -20 angle supports using two MS20470AD5 rivets per angle. The -19 and -20 angle supports are attached
to the existing stringers using two MS20470AD6 rivets each. The -15 channels are attached to the
existing frame web at F.S. 1 460 using two MS20470AD5 rivets each. The -13 FWD channels are attached to the existing frame web at F.S. 1440 using two MS20470AD5 rivets each. The installation drills one
1.31-in x 1.71-in feed thru hole in the 0.070-in thick skin for the antenna installation. To restore strength
to the fuselage skin the internal 0.080 inch thick 2024-T3 aluminum -11 hat section is attached to the existing aircraft skin with NAS1097AD4 rivets.
This report is providing the structural substantiation static, fatigue, and damage tolerance for alterations
made to a Boeing 757-200 by the installation of the VHF Antenna and transceiver. Refer to KNSI drawing
15K036-MD-001-0.R for details.
Inspection Intervals
The following lists the threshold and recurrent inspection intervals for the Fatigue Life Evaluation and
each crack growth model of the Damage Tolerance Evaluation (DTE). The inspections intervals listed do not change the existing inspection or maintenance program requirements for the aircraft unless the
intervals listed below would occur prior to an existing inspection.
Skin:
For Lateral Cracks:
THRESHOLD INSPECTION (based on DSG) = 25,000 Cycles (See Page No. 46) RECURRING INSPECTIONS (based on DSG) = 12,500 Cycles (See Page No. 46)
FATIGUE LIFE (based on DSG) = 50,000 Cycles (See Page No. 46)
For Longitudinal Cracks: THRESHOLD INSPECTION (based on DSG) = 25,000 Cycles (See Page No. 70)
RECURRING INSPECTIONS (based on DSG) = 12,500 Cycles (See Page No. 70)
FATIGUE LIFE (based on DSG) = 50,000 Cycles (See Page No. 70)
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Stringers:
THRESHOLD INSPECTION = 25,000 Cycles (See Page No. 88)
RECURRING INSPECTIONS = 12,500 Cycles (See Page No. 88) FATIGUE LIFE = 50,000 Cycles (See Page No. 88)
-11 Hat Section:
THRESHOLD INSPECTION = 25,000 Cycles (See Page No. 94) RECURRING INSPECTIONS = 12,500 Cycles (See Page No. 94)
FATIGUE LIFE = 50,000 Cycles (See Page No. 94)
Frames:
The 0.159-in holes drilled into the existing frames for the installation of new MS20470AD5 rivets are the
same size and have the same edge distance as other rivet holes in the frames. Therefore the inspection
schedule for the existing adjacent rivet holes shall also apply to the new rivet holes in the frames.
The above inspection intervals are based upon a High Frequency Eddy Current (HFEC) Inspection, (See
Table 5.0.4A); refer to the specific maintenance instructions for inspection details.
Damage Tolerance Assessment (DTA) Method
The Damage Tolerance Assessment (DTA) is performed in accordance with the guidance provided by the
Seattle Aircraft Certification Office (SACO) and Patrick Safarian, dated October 1999. The following
outline lists the steps required, to determine the inspection intervals for the repair or alteration, to
support continued airworthiness.
a. Select structures that require DTA to establish special inspections
The fuselage skin and doubler are considered Fatigue Critical Structure and require a DTA.
b. Obtain fatigue loads
The fatigue loads are obtained through calculation, as required by 14 CFR Part 23.571.
c. Develop flight profile
The flight profile is considered as the flight cabin pressurization cycle
d. Develop exceedance spectrum
The exceedance spectrum consists of a single pressurization cycle (one flight equal to one cycle).
e. Develop stress spectrum for each individual structure/area to be analyzed
The stress spectrum for the skin is considered for longitudinal loading and lateral loading. The spectra
are single cycle constant amplitude.
f. Establish the initial flaw sizes, to be assumed
The initial flaw sizes are established, 0.05 inches for an initial crack at a hole, and 0.010 inches for
continuing damage.
g. Determine stress intensity factors for cracking scenarios to be addressed
The stress intensity factors and crack growth properties are addressed through the use of the AFGROW program and the NASGRO Equation are determined.
h. Obtain material properties for crack growth calculations and residual strength analyses
The material properties for the crack growth and residual strength analyses are obtained from the AFGROW material database.
i. Determine required residual strength loads
The required residual strength for the longitudinal and lateral loading conditions are determined.
j. Calculate residual strength and critical crack length
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The residual strength and associated critical crack lengths are calculated.
k. Determine detectable crack length as a function of inspection method
The detectable (inspectable) crack lengths as a function of inspection method are determined as listed in Table 5.0.4A.
l. Calculate crack growth life
The crack growth life for the rivet rows and feed through holes are calculated using the AFGROW
program and described.
m. Determine inspection thresholds
The threshold inspections are described and calculated. A summary of the threshold inspections is
presented at the beginning of this document prior to the introduction.
n. Determine repeat inspections intervals
The recurring inspections are described and calculated. A summary of the recurring inspections is
presented at the beginning of this document prior to the introduction.
o. For modifications develop Instructions for Continued Airworthiness, and for repairs update
maintenance program to incorporate new special inspections.
The Instructions for Continued Airworthiness (ICA) and maintenance program updates incorporating the new special inspections are not contained within this report.
Form KNSI-P3-004-7 Issue: 0 Rev: 0 Structural Substantiation Report
Dr. Patrick Safarian F&DT course notes provide that the hoop stress can be reduced by 15%
for the lower skin due to the presence of reinforcement (frames, bulkhead, floor beam and stringers)
σHoopLEFM = 10,935 psi (85%) = 9,295 psi
For both the condition (i) and condition (ii) stresses listed above, the maximum stress is shown and the
minimum stress is zero.
Torsional Loads
The pressurization stress is added to the shear stress in the skin due to fuselage torsion. The skin loads,
due to shear of the skin panels, are determined by considering the following:
* The skin panel is designed as a shear resistant web
* The skin buckles, due to shear, at a limit load * The skin shear is due to fuselage torsion from applied
side loads
* The skin panel is of a constant thickness, for local frame skin bays
* The skin panels (2024-T3) are considered to be of a uniform thickness of 0.040 inches throughout the
interior of the skin bay. Any doublers or chem milled thicknesses around the perimeter are neglected for shear of the panel. The frame spacing is 20.0 inches and the stringer spacing is 8.64 inches.
* The torsional loads are applicable only to the fatigue loading of the installation, the static strength analysis
does not consider the torsional loads.
a = 20.0 in b = 8.64 in t = 0.070 in a/b = 20.0/8.64 in = 2.31 KS = 5.6*(case 4) η
= 1.0 ** *Ref Figure 3.1.3A
**Elastic range only, no plasticity considered
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The skin shear, critical for buckling, is considered to be a limit condition occurring at a limit 1.0g side load.
Normal Skin Shear = (275.31 lbs/in)/1.00 g = 275.31 lbs/in
Multiplying this value by a factor of 1.4 for large aircraft, accounts for the fluctuations in torsional stress that occur during a typical flight, compressing the full flight spectrum into a single cycle maximum stress.
τxy = (1.4)(3,933 psi) = 5,506 psi
This value is an ‘equivalent’ shear stress that incorporates the effects of a variable fuselage loading
spectrum into the single cycle maximum pressurization spectrum used in this analysis. This shear stress will be added to the independent lateral and longitudinal stress of the fuselage under 1-g load. NOTE:
due to the location of the repair, the tension stress due to the fuselage bending is not considered for
this analysis. However the tension stress due to the fuselage pressurization is considered. The shear and tensile stress are resolved into principal stresses to provide a tensile stress component with zero
The following conservative value is used for the condition (i) fatigue loading conditions. σ1x = 8,881 psi
The LEFM stress previously calculated is updated to include the torsional effects. The longitudinal residual stress is considered to be recalculated. Note that the torsional stress is not considered in the hoop
The maximum inertia load for the entire antenna installation is calculated below
Max inertia load = 6.5 lbs (9g) = 58.5 lbs
The maximum inertia load is not as critical as the side lift load condition. Therefore, analysis of the side lift load will also serve to substantiate the maximum inertia load condition.
Antenna Drag Load Condition
Drag Load = 14.83 lbs (x-dir)
*Ref. Fx, Section 3.0.3
The drag load is not as critical as the side lift load condition. Therefore, analysis of the side lift load will also serve to substantiate the maximum inertia load condition.
Antenna Side Lift Load Condition
The antenna is attached to the -11 hat section using ten ¼-28 screws into nutplates.
During the maximum operating condition the aerodynamic side lift load is considered applied at the c.g.
of the antenna and reacted in shear by the ten ¼-28 screws.
Side Lift Load = 440.87*lbs (y-dir)
*Ref. Fy, Section 3.0.3
Translation of the load up to the 10-32 screws produces an Mx moment. This moment is reacted as
bearing against the -11 hat section and in tension by a couple load between the inboard and outboard 10-32 screws.
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Py = Ry = 440.87 lbs (y-dir)
Mx Moment = (440.87 lbs)x(7.51-in) = 3,310.93 in-lbs
This shear load is later combined with a y-directed shear load. The -19 and -20 angle supports are fabricated as mirror opposites of each other, therefore analysis of the -19 angle support will also serve to substantiate
the -20 angle support.
The z-directed load is transferred through the -19 angle support and reacted in shear by the two MS20470AD6 rivets attaching the -19 angle to the existing 0.090-in thick 7075-T6 stringer.
Translation of the local z-directed load over to the AD6 rivets produces a local Mx moment. The local Mx
moments is reacted in shear by a couple load between the AD5 rivets attaching the -19 angle to the -17 support.
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M.S.(shear) = [(596*lbs)/(357.79 lbs x 1.15**) – 1] x 100% = +44%
*Ref. Shear Strength of AD5 rivet, Table 8.1.2(a), Ref. 1
**Ref. Fitting Figure
Translation of the z-directed loads over to the AD6 rivets in the stringers produces a local My moment which is reacted in shear by a couple load between the AD6 rivets.
Therefore, the -11 hat section, -17 supports, -19 support angle, and -20 support angles are satisfactory
to react the maximum side lift load condition to the existing stringer structure.
Skin and Doubler Analysis
Analysis of the 1.31-in x 1.71-in hole treats it as any other holes through the skin. The doubler provides
an alternative load path for the forces in the skin. To show the doubler restores the strength to the
fuselage, the joint must pass the load through the doubler, which is a function of hole size. The doubler is conservatively considered 17.0 inches long and 5.35 inches wide.
Maximum lateral load to be transferred through the doubler;
= (19.85 psi*)(81.0 in**)(1.71-in) = 2,749.42 lbs
*Ref Section 3.0.1
**Ref fuselage radius
Maximum longitudinal load to be transferred through the doubler;
There are a minimum of fourteen NAS1097AD4 rivets considered effective on all sides of the doubler.
There are a minimum of forty-two NAS1097AD4 rivets considered effective on the fore and aft sides of
the doubler. These rivets are considered effective in transferring the load from the skin to the doubler. The doubler is 0.080 inches thick 2024-T3 aluminum and the skin is 0.070 inches thick 2024-T3
aluminum. There is no immediate ultimate strength allowable for the NAS1097AD rivet, therefore the
ultimate joint strength will be calculated by using a ratio of shear strengths. Per Ref. 1, (1/8), Table 8.1.2 (b), the Fsu value for a driven rivet fabricated from 7050-T731 aluminum alloy (E material) is 43
ksi. From the same table, the Fsu value for a driven rivet fabricated from 2117-T3 aluminum alloy (AD
material) is 30 ksi. Per Ref. 1, Table 8.1.2.2(n), the ultimate strength for an NAS1097E4 in 0.071 inch thick Clad 2024-T3 sheet is 497 pounds. Per Ref. 1, Table 8.1.2.2(n), the ultimate strength for an
NAS1097E4 in 0.063 inch thick Clad 2024-T3 sheet is 485 pounds.
Using interpolation between the two shear values of the sheets, the ultimate value for the NAS1097E4 rivet in the 0.070 inch thick skin is calculated below.
Using the ratio between the two shear values of the rivets, the ultimate value for the NAS1097AD4 rivet in the 0.070 inch thick skin is calculated below.
The rivets are satisfactory to transfer the load from the skin to the doubler.
The hoop and longitudinal tension load is transferred from the skin of the aircraft through the rivets and into the doubler. The doubler is required to react the load. The tension load in the doubler is checked.
The effective width of the doubler for the feed through hole:
**Ref 12, stress concentration factor for a tension loaded plate, round hole
Alternatively consider the ultimate pressurization load scenario in which the hoop stress and longitudinal pressurization stress act simultaneously at the center feed through hole. The rivets attaching the doubler
to the skin are considered to equalize the stress in the skin and doubler.
The maximum load to be transferred to the doubler from the skin is a function of rivet joint strength, and
rivet pitch. Consider two rows of rivets effective in transferring the load. The maximum allowable load per
rivet was previously shown as 345.7 pounds, and there are two rows of rivets with a maximum 0.9 inch rivet pitch. The maximum skin stress at the feed through hole is calculated below.
The maximum stress in the skin, at the feed through hole, is considered for the biaxial tension load condition, using the larger skin stress as calculated in the two scenarios above.
Maximum Skin Longitudinal Stress = 5,360 psi = σ2
Maximum Skin Hoop Stress = 11,994 psi = σ1
The stress concentration factor for an ovaloid in an infinite width thin sheet biaxially stressed is used to determine the stress values at the longitudinal and lateral edges of the feed through hole
The fasteners and doubler are satisfactory to react the applied loads from the pressurization of the aircraft.
Fatigue Assessment and Damage Tolerance Assessment
The capabilities of the fuselage alterations are analyzed to ensure that the structure could tolerate serious fatigue, corrosion, or accidental damage during the operational life of the aircraft.
Rogue Flaw, Geometry
The models for the rogue flaw serve to establish the threshold inspection interval based upon the
chosen inspection type. The rogue flaw is conservatively grown to the first link up only provided failure
does not occur prior to the first linkup. The initial crack scenario considers one 0.05 inch corner crack with an opposing 0.010 inch corner crack at a hole.
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Rogue Flaw, Crack Growth Methodology
The 0.010 inch and 0.05 inch initial part through cracks are grown using the AFGROW advanced modeler. The initial crack sizes are determined by the location and type of flaw.
The initial part through cracks have an "a" thickness dimension equal to the thickness of the skin and
a "c" length dimension of either 0.010 inches or 0.05 inches as shown in the figures above. The plate
width is considered as four times the rivet pitch minus one rivet diameter.
Prior to linkup, the model with a 0.010 inch crack and a 0.05 inch crack at the center hole is analyzed using the calculated tensile, bending, and bearing stresses to be applied at each hole. The lead cracks
are grown in a second model using the two holes adjacent to the center hole using the same loading.
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The term "linkup" refers to the scenario where the edges of the crack emanating from the center hole
propagate to the point which they reach the edge of the adjacent holes.
Crack Growth Properties
The crack growth rate analyses were calculated using the Air Force Research Laboratory software
package AFGROW, using the NASGRO equation. The stress intensity factor expressions for a pin loaded
hole (rivet hole) and for a crack emanating from a tension and bending loaded hole are available as
analysis options within the AFGROW computer program. The AFGROW material database for 2024-T3 T-L clad sheet, shown in Figure 5.0.3A, was employed in the analysis. This resulted in the crack growth-
rate data shown in Figure 5.0.3B.
The da/dN data is coded inside the AFGROW program based upon the NASGRO crack model, Refer
Anon’ AFRL-VA-WP-TR-1999-3016 AFGROW Users Guide and Technical Manual Air Vehicle Directorate, Air Force Research Laboratory.
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NASGRO (Forman, Newman, de Koning and Henriksen) Equation
The elements of the NASGRO (Version 3.00) crack growth rate equation were developed by Forman
and Newman at NASA, de Koning at NLR, and Henriksen at ESA. It has been implemented in AFGROW as follows:
Where C, n, p, and q are empirically derived, and
The coefficients are:
Here, 'a' is the plane stress/strain constraint factor, and Smax/σo is the ratio of the maximum applied
stress to the flow stress. These values are provided by the NASGRO material database for each material.
Where:
ΔKo - threshold stress intensity range at R=0
a - crack length (a or c in AFGROW) ao - intrinsic crack length (0.0015 inches or 0.0000381 meters)
Cth - threshold coefficient
The values for ΔKo and Cth are provided by the NASGRO material database for each material. The NASGRO
equation accounts for thickness effects by the use of the critical stress intensity factor, Kcrit.
Where:
KIc - plane strain fracture toughness (Mode I)
Ak - Fit Parameter Bk - Fit Parameter
t – Thickness
to - reference thickness (plane strain condition)
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The plane strain condition is:
The values for KIc, Ak, and Bk are provided by the NASGRO material database for each material. Although the plane strain thickness, t0, is defined by the equation shown above, Kcrit will asymptotically approach
KIc as the actual thickness gets larger than t0.
Threshold Inspection Interval
The Threshold Inspection is determined from the smaller cycle count of; (Nfinal/2), (Ndetectable), or
1/2 the OEM established life limit of the component. If no OEM established life limit exists for the component a design service goal of 20,000 cycles is considered.
For the inspection purposes of this analysis, one cycle is equivalent to one flight.
The number of cycles (Nfinal) is determined by the crack growth analysis at which the detail is considered to reach a critical crack length.
The number of cycles (Ndetectable) is determined by the crack growth analysis at which a crack is
considered to reach a detectable or inspectable crack size. The detectable flaw size considered is a
function of the crack type and of the type of inspection proposed for the structure as shown in the Table 5.0.4A.
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Recurring Inspection Interval
The Recurring or Subsequent Inspection interval is determined from either; 1/2 the threshold inspection
interval, or 1/3 of (Nfinal - Ndetectable).
When considering Multiple Site Damage (MSD) with Wide Spread Fatigue Damage (WSFD) the Recurring
or Subsequent Inspection interval is determined from either; 1/2 the threshold inspection interval, or
1/3(Nfinal).
The recurring inspection interval is paired with the threshold inspection for each respective case.
Multiple Site Damage
Multiple Site Damage (MSD) considerations are evaluated for those areas of the installation that are coincident with existing or replaced fasteners of which every hole is considered to have a 0.05 inch long
crack at each edge growing until a net section failure occurs, with the assumption that there is an infinite
number of cracked holes. The MSD evaluation satisfies the requirements of 14 CFR 25.571(b) "Damage at multiple sites due to prior fatigue exposure must be included where the design is such that this type
of damage can be expected to occur".
For the Wide Spread Fatigue Damage (WSFD) considered in the analysis, the critical crack length is based solely on the Net Section Yield (NSY) failure criteria rather than the Linear Elastic Fracture
Mechanics (LEFM) criteria.
The critical crack lengths for the MSD models are determined using 90% of the skin material's 'B' basis
ultimate tensile strength (Ftu). The 90% factor is a correction knockdown factor to account for reductions
The Ktn value that is calculated is input into the S/N data curve presented in the MMPDS Ref. 1 to determine the life of the installation. The life of the installation is calculated using a logarithmic interpolation.
Crack Growth Analysis for Crack Between Rivets in Forward/Aft Row - Rogue Flaw
For the rogue flaw damage model the residual strength is based upon the combination of KMAX and NSY.
The simplified model for the lateral skin crack between two adjacent rivets in the side row of the skin is modeled
as a pin loaded hole in a flat sheet. The sheet width is taken to be twice the width of the skin bay. The applied
stress is the reference stress. The reference stress and applicable stress fractions are calculated at the beginning
of this section.
Effective skin width = 17.28 in
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Model #1 Fatigue Loading
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The residual strength curve is constructed by plotting the results of the AFGROW crack growth model
for the left 0.05 inch long initial crack. The 1000-9000 series aluminum, 7076-T6 Al, [Clad; plt & sht;
L-T & T-L; LA ] material properties from the AFGROW data base are used for the calculations.
E = 10,400 ksi
υ = 0.33 F
ty = 75 ksi,
KIC = 27 ksi√in
KC = 54 ksi√in
The applied fatigue remote stress and required residual strength are constant. The NSY curve is
defined by:
The Net Section Strength is determined by iteration (using a 0.001 convergence tolerance). The βC
factor, cycle count, and crack length for each crack growth increment are obtained from the AFGROW
output data. The critical K value (apparent fracture toughness) is defined by:
Where: index ~ Stress State Index (6 – plane strain, 2 – plane stress) The “Allowable Stress” for KCrit
is calculated as follows:
The first intersection of the 'Residual Strength Required' line with either the KMAX or NSY lines indicates
a critical crack length and resulting failure of the detail.
The chart on the following page illustrates the residual strength characteristics of the model considering
the Net Section Yield (NSY) and KMAX failure criterion.
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Evaluation of the residual strength chart indicates that the right 0.05 inch initial crack has reached a
critical crack length of 0.71 inches base on Kmax criteria. Note that the non-linear nature of the NSY curve is due to the addition of the yield zone size to the crack length at the crack tips.
The AFGROW crack growth curve for the 0.05 inch initial crack is shown on the next page. Note that the
chart shown is for a crack growth model which propagates the crack to the next free edge, in the
advanced model case when a crack reaches an adjacent hole.
The AFGROW program also has options to halt the crack growth at a user specified crack length which
is used to determine the number of cycles required to reach a detectable crack length, and option to
halt the program for NSY and KMAX failure criteria.
The first run of the program halts the crack growth at the user specified detectable crack length (with
the option selected to halt at a critical crack length). The second run of the program, using the same
model, halts the program when either the NSY or KMAX criteria have been exceeded. A third run of the program is conducted which allows the cracks to reach a free edge for illustrative purposes.
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The results of the crack growth analysis for a crack growing from one rivet hole to the adjacent rivet in
the outer row are shown on the next two pages. The analysis predicts 62,223 cycles are required to
grow the crack to an inspectable length, (0.196-in – 0.129-in)/2 + 0.10 in = 0.1335.
The inspections are done from the outside of the airplane and has direct access to the skin. Therefore,
the HFEC (High Frequency Eddy Current) method can be used.
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The analysis predicts that 179,358 cycles are required to grow the crack to a length of 0.71 inches which
is the critical crack length.
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1.382
Advanced Models Thickness : 0.070 Width : 17.280
Crack #1 (Corner Crack at Hole) Length = 0.05 Position: Hole Left
Crack #2 (Corner Crack at Hole) Length = 0.01 Position: Hole Right
Hole #1 (Hole) Diameter = 0.163 Offset = 7.74
Hole #2 (Hole) Diameter = 0.163 Offset = 8.64
Hole #3 (Hole) Diameter = 0.163 Offset = 9.54
Young's Modulus =10600 Poisson's Ratio =0.33
Coeff. of Thermal Expan. =1.29e-005
No crack growth retardation is being considered
Determine Stress State automatically (2 = Plane
stress, 6 = Plane strain) No K-Solution Filters
The Forman-Newman-de Koning- Henriksen (NASGRO) crack growth relation is being used For Reff < 0.0, Delta K = Kmax Material: 1000-9000 series aluminum, 2024-T3 Al, [ Clad; plt & sht; T-L ]
Plane strain fracture toughness: 29 Plane stress fracture toughness: 58 Effective fracture toughness for surface/elliptically shaped crack: 41 Fit parameters (KC versus Thickness Equation): Ak= 1, Bk=1 Yield stress: 48 Lower 'R' value boundary: -0.3
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Upper 'R' value boundary: 0.7 Exponents in NASGRO Equation: n=2.601, p=0.5, q=1 Paris crack growth rate constant: 2.44e-008 Threshold stress intensity factor range at R = 0: 2.9 Threshold coefficient: 1.5 Plane stress/strain constraint factor: 1.5 Ratio of the maximum applied stress to the flow stress: 0.3
Failure is based on the current load in the applied spectrum Cycle by cycle beta and spectrum calculation
**Spectrum Information
Constant amplitude loading Spectrum multiplication factor: 8.881 SPL: 0 The spectrum will be repeated up to 10000000 times Total Cycles: 1 Levels: 1 Subspectra: 1 Max Value: 1 Min Value: 0
No Spectrum Filters
Stress State in 'C' direction (PSC): 2
Transition will be based on K max or 95% thickness penetration Criteria Length Beta Tension Beta
Compression R(k) R(final) Delta-K D( )/DN
Crack #1 Left Tip C 0.05 2.1893 2.1893
0.0000 0.0000
7.7061e+000 1.2199e-006
Right Tip C
0.01 4.0090 4.0090 0.0000 0.0000
6.3106e+000 6.7272e-007 Left Tip A 0.07 2.0152 1.2055 0.0000
Crack #1 (Corner Crack at Hole) Length = 0.05 Position: Hole Left
Crack #2 (Corner Crack at Hole) Length = 0.01 Position: Hole Right
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Hole #1 (Hole) Diameter = 0.163 Offset = 7.29
Hole #2 (Hole) Diameter = 1.31 Offset = 8.64
Hole #3 (Hole) Diameter = 0.163 Offset = 9.99
Young's Modulus =10600 Poisson's Ratio =0.33
Coeff. of Thermal Expan. =1.29e-005
No crack growth retardation is being considered
Determine Stress State automatically (2 = Plane stress, 6 =
Plane strain) No K-Solution Filters
The Forman-Newman-de Koning- Henriksen (NASGRO) crack growth relation is being used For Reff < 0.0, Delta K = Kmax Material: 1000-9000 series aluminum, 2024-T3 Al, [ Clad; plt & sht; T-L ]
Plane strain fracture toughness: 29 Plane stress fracture toughness: 58 Effective fracture toughness for surface/elliptically shaped crack: 41 Fit parameters (KC versus Thickness Equation): Ak= 1, Bk=1 Yield stress: 48 Lower 'R' value boundary: -0.3 Upper 'R' value boundary: 0.7 Exponents in NASGRO Equation: n=2.601, p=0.5, q=1 Paris crack growth rate constant: 2.44e-008 Threshold stress intensity factor range at R = 0: 2.9 Threshold coefficient: 1.5 Plane stress/strain constraint factor: 1.5 Ratio of the maximum applied stress to the flow stress: 0.3
Residual stress: 4.931
Cycle by cycle beta and spectrum calculation
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Condition (i) Fuselage Loading Due to Bending and Pressure - Lateral Cracking
The critical areas for crack initiation and growth are between rivets in the outer row of rivets and cracks
emanating from the feed through hole.
The analysis considers a crack that grows from the edge of one rivet to the edge of the adjacent rivet in
the same row. These critical crack locations are illustrated below in Figure 5.2A. Only the skin is checked
as the skin has a higher stress than the doubler, the inspection of the doubler shall follow the same intervals
The spectrum will be repeated up to 10000000 times
Total Cycles: 1 Levels: 1 Subspectra: 1 Max Value: 1 Min Value: 0
No Spectrum Filters
Transition will be based on K max or 95% thickness penetration
Criteria
Length Beta Tension Beta Compression R(k)
R(final) Delta-K D( )/DN
Crack #1 Left Tip C 0.05 2.8506 2.8506
0.0000 0.0000
4.8321e+000 2.7616e-007
Right Tip C 0.01 3.2545 3.2545 0.0000 0.0000
2.4672e+000 0.0000e+000 Left Tip A 0.07 2.9560 2.9560 0.0000
0.0000 5.9287e+000 5.3944e-007
Right Tip A 0.07 0.6886 0.6886 0.0000 0.0000
1.3812e+000 0.0000e+000 Max stress 4.277, r = 0.00, 0 Cycles, Constant amp.: 1, Pass:
1
*********Transition at 95% thickness penetration
Length Beta Tension Beta Compression R(k)
R(final) Delta-K D( )/DN
Crack #1 Left Tip C 0.05 2.9384 2.9384
0.0000 0.0000
4.9809e+000 3.0607e-007
Right Tip C 0.01 3.3822 3.3822 0.0000 0.0000
2.5640e+000 0.0000e+000 Max stress 4.277, r = 0.00, 0 Cycles, Constant amp.: 1, Pass:
1
. Length Beta Tension Beta Compression R(k)
R(final) Delta-K D( )/DN
Crack #1 Left Tip C 0.14 2.3422 2.3422
0.0000 0.0000
6.6435e+000 7.7010e-007
Right Tip C 0.01 3.4948 3.4948 0.0000 0.0000
2.6493e+000 0.0000e+000 Max stress 4.277, r = 0.00, 169166 Cycles, Constant amp.
: 169167,
Pass: 169167
Length Beta Tension Beta Compression R(k)
R(final) Delta-K D( )/DN
Crack #1 Left Tip C 0.14798 2.3027 2.3027
0.0000 0.0000
6.7154e+000 7.9623e-007
Right Tip C 0.01 3.5046 3.5046 0.0000 0.0000
2.6568e+000 0.0000e+000 Max stress 4.277, r = 0.00, 179358 Cycles, Constant amp.
: 179359,
Pass: 179359
Stress State in 'C' direction (PSC): 6
Cycle count exceeded stop value - run time : 0 hour(s) 0 minute(s) 2 second(s)
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Joint Strength
The fatigue analysis of the reinforced skin is based on the Neutral Line Analysis (NLA), Reference Schijve,
et al [9,19], described in the appendix A of this report. This method is performed in two steps. The first is to calculate the fastener forces in the rivet rows used to attach the doubler to the skin. The second is to
calculate the secondary bending of the skin doubler system using the method presented by de Rijck, et al
[18]. Swift’s fastener flexibility model [20] is employed in the analysis. The geometry for this skin-doubler model is shown in Figure 5.2B.
The first two rivet rows on the LH side and the last two rivet rows on the RH side are modeled in the Neutral
Line Model. NAS1097AD4 rivets are installed in each of these rows with a rivet row spacing and rivet pitch as shown in the above Figure 5.2B.
*Ref: Section 3.1.2, Lateral LEFM stress for Fatigue
The analysis of the riveted joints uses the displacement-compatibility model shown in Figure 5.2C, with Swift’s fastener flexibility.
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The stiffnesses of the skin and doubler are calculated using the formula
where t represents the thickness, 0.070-in and 0.080 in for the skin and doubler, respectively; W representes the width of the douber, W = 17.0 in (Conservative Consideration); and the elementlength L
is the distance between rivet rows. This element length is also assigned to the “skin” elements to the left
between points 0 and SL3 and between points SR3 and N.
The compliance for Swift’s fastener model is defined for aluminum rivets as
where D represents the fastener diameter, t1 and t2 represent the skin and doubler thickesses, defined
above, and E = 10.5 (10)6 psi (Ref. Table 3.2.4.0(e1) MMPDS-06, represents Young’s modulus for the skin,
doubler and fastener. The resulting stiffness for a row of fasteners is calculated as
where Nf represents the number of fasteners in the row, thus Nf = 2 and Nf = 2 for the first and fourth forward rows of rivets repectively. The applied load P, is defined in terms of the longitudinal stress as
where the minus sign denotes the fact that the force acts in the –x direction. This load is used to calculate
displacements are calculated from the assembled stiffness matrix.
The maximun displacement occurs at point 0 and was calculated as u0 = 8.852381 x 10-4 in. The resulting
fastener loads are tabulated as
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*Ref: consider a hole size of 0.163-inch for the 1/8 rivet in a 0.129-in hole which has a head diameter of
0.196-in.
The corresponding bearing stress ratio kb is calculated as
kbrg = 12,498 psi / 9,295 psi = 1.345
The skin and doubler Stress resultants are reported in Tables 5.2B and 5.2C.
The secondary bending stresses generated by the doubler were analyzed using the Neutral Line Method suggested by Schijve [9,19]. This particular analysis incorporates the effects of fastener flexibility as
described by de Rijck [18].
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The corrective moments were computed as described in References 11 & 12 and are summarized in Table
5.2D.
The neutral line displacement solution is presented in Figure 5.2E, where the units of both axes are inches.
The bending stress is calculated from the differential moment-deflection equation
which can be written in terms of the homogeneous portion of the neutral line solution as
Substituting this moment into the bending stress equation for a flat plate
By applying the following series of managed scatter factors as shown in Scatter Reduction Factor* methods A and B that represents the alteration/installation on the aircraft, the fatigue life of the alteration
is determined. *Reference Patrick Safarian, DTA Seminar, Lesson 19, Spirit Aviation, Inc., Wichita, KS,
Feb 25-27, 2013. [Ref 15]
Scatter Reduction Factor, A
To manage scatter use the following four factors:
Testing Factor 0.7 < F < 1.0*; To account for differences in scale and fidelity of the test, including the
extent to which the loading of the test article represents the actual structure.
Confidence Factor Use 0.7 for 95% lower confidence bound*; A statistical factor to address the
uncertainty in the final value caused by the limited sample size.
Reliability Factor* 0.48/Alum, 0.26/Steel*; A conversion factor to obtain a reliable life value from mean or characteristic life data.
*(Ref 9, Scatter is less at high stress amplitudes, and larger at low stress amplitudes)
Scale Factor 0.33 < F < 0.50*; A factor to adjust the design life value based on the percentage of details in the specimen to the number of detail in the actual structure.
* see Appendix D, recommended factors and Tables for Reliability and Scales factors.
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Scatter Reduction Factor = Testing Factor x Confidence Factor x Reliability Factor x Scale Factor
Note, the life of fatigue life of the subject is reduced by multiplying the MMPDS fatigue life by this Scatter
Reduction Factor.
Scatter Reduction Factor, B
To manage scatter use the following three factors:
Scale Factor 1.0 < F < 2.0*; To account for differences in scale and fidelity of the test, including the extent to which the loading of the test article represents the actual structure.
Load Factor 1.0/Spectrum, 1.5/Const Amp Loading*; To account for the effects of loading type on the
fidelity of the data.
Reliability Factor 2.75/alum, 3.5/Steel; A conversion factor to obtain a reliable life value from mean or
characteristic life data.
* see Appendix D, recommended factors and Tables for Reliability and Scales factors.
Scatter Reduction Factor = Scale Factor x Load Factor x Reliability Factor
Note, the life of fatigue life of the subject is reduced by dividing the MMPDS fatigue life by this Scatter Reduction Factor.
Method 2 is the 'Fokker empirical prediction method' (Reference 9, Chapter 18). The stress concentration
factors for tension, bearing, and bending are calculated for the loaded rivet hole. Predictions are extrapolated from this curve by accounting of three contributions to the stress concentration at the rivet
holes of the critical end row. The contributions are associated with (i) load transmission by the rivet (pin
loading on hole), (ii) bypass loading of the rivet rows, and (iii) increased stress by secondary bending. The equation used is the following:
In this equation y is the percentage of the load transmitted to the other sheet in the critical row. Then, (1-
y) is the percentage of the bypass load. The factor k is the secondary bending factor.
Y = (Rivet Load/Rivet Pitch)/(Skin Tension)
= (142.599 lbs/0.90-in)/(650.65 lbs/in) = 0.244
As described in Peterson, Ref. 12. The case of a pinned joint in an infinite thin element has been solved
mathematically by Bickley (1928). The finite-width case has been solved by Knight (1935), where the element width is equal to twice the hole diameter d and by Theocaris (1956) for d/H = 0.2 to 0.5.
Experimental results (strain gage or photoelastic) have been obtained by Coker and Filon (1931),
Schaechterle (1934), Frocht and Hill (1940), Jessop, Snell and Holister (1958), and Cox and Brown (1964). (See Peterson for descriptions of these references).
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Nominal stress based on bearing area:
Nominal stress based on bearing area:
In Figure 5.2E, (Chart 4.67) the K t n b curve corresponds the Theocaris (1956) data for d/H = 0.2 to 0.5.
The values of Frocht and Hill (1940) and Cox and Brown (1964) are in good agreement with Chart 4.67,
although slightly lower. From d/H = 0.5 to 0.75 the foregoing 0.2-0.5 curve is extended to be consistent with the Frocht and Hill values. The resulting curve is for joints where c/H is 1.0 or greater. For c/H = 0.5,
the Ktn values are somewhat higher.
From Eq. (4.85), Ktnd = Ktnb at the d/H = 'A It would seem more logical to use the lower (full line) branches of the curves in Figure 5.2G (Chart 4.67), since, in practice; d/H is usually less than 'A This means that Eq.
(4.84), base on the bearing area, is generally used.
The rivets are considered countersunk in the doubler. This analysis will consider an initial through hole of
the average skin hole of 0.163 inches. The geometry concentration factor for the pin (Kt, pin) (i) is determined from the following graph, Peterson Chart 4.67:
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This data results in following “net” stress concentration factor.
Ktn, pin = 1.30
The geometry concentration factor for the hole in tension (Ktg, hole) (ii) is determined from Peterson Chart
4.1:
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This data results in the following “net” stress concentration factor.
Ktn= 2.56
The geometry concentration factory for the hole in bending (Ktg, bending) (iii) is determined from Peterson
Chart 4.83. The calculations are considered for simple bending.
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Ktn, hole bending = 1.68
The ratio of the bending stress to the applied tension stress (k) (iii) is obtained:
kb=0.560*
*Ref. below Figure 5.2D
The total stress concentration factor due to pin load, bypass, and secondary bending is denoted:
Fatigue life = (1.44 x 109 cycles)/[(1.5a)(1.5b)(2.75c)] = 232,727,272 cycles aRef. Scale Factor
bRef. Load Factor cRef. Reliability Factor
The recurrent inspection interval for Part 25 aircraft are not to be based on fatigue life per Patrick Safarian DTA Seminar, Feb 25-27, 2013. Fatigue life calculated with both A and B scatter factors are
acceptable. For this analysis the fatigue life with scatter factor of A is considered.
The acceptable conservative fatigue life limit for the longitudinal methods are therefore, based on Method 1.
Crack Growth Analysis for Crack between Rivets in Forward/Aft Row - Rogue Flaw
For the rogue flaw damage model the residual strength is based upon the combination of KMAX and NSY.
The simplified model for the lateral skin crack between two adjacent rivets in the side row of the skin is
modeled as a pin loaded hole in a flat sheet. The sheet width is taken to be the length of the skin bay. The
applied stress is the reference stress. The reference stress and applicable stress fractions are calculated at the beginning of this section.
Effective skin width = 20.0 in
Model #3 Fatigue Loading
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The residual strength curve is constructed by plotting the results of the AFGROW crack growth model for
the left 0.05 inch long initial crack. The 1000-9000 series aluminum, 2024-T3 Al, [Clad; plt & sht; T-L ] material properties from the AFGROW data base are used for the calculations.
E = 10,600 ksi υ = 0.33
Fty = 48 ksi,
KIC = 29 ksi√in
KC = 58 ksi√in
The applied fatigue remote stress and required residual strength are constant. The NSY curve is defined
by:
The Net Section Strength is determined by iteration (using a 0.001 convergence tolerance). The βC factor,
cycle count, and crack length for each crack growth increment are obtained from the AFGROW output data.
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The critical K value (apparent fracture toughness) is defined by:
Where:
index ~ Stress State Index (6 – plane strain, 2 – plane stress)
The “Allowable Stress” for KCrit is calculated as follows
The first intersection of the 'Residual Strength Required' line with either the KMAX or NSY lines indicates a
critical crack length and resulting failure of the detail.
The chart on the following page illustrates the residual strength characteristics of the model considering the Net Section Yield (NSY) and KMAX failure criterion.
Evaluation of the residual strength chart indicates that the right 0.05 inch initial crack has reached a critical
crack length of 0.71 inches base on Kmax criteria as it transitions to the adjacent rivet hole. Note that the
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non-linear nature of the NSY curve is due to the addition of the yield zone size to the crack length at the
crack tips.
The AFGROW crack growth curve for the 0.05 inch initial crack is shown on the next page. Note that the chart shown is for a crack growth model which propagates the crack to the next free edge, in the advanced
model case when a crack reaches an adjacent hole.
The AFGROW program also has options to halt the crack growth at a user specified crack length which is
used to determine the number of cycles required to reach a detectable crack length, and option to halt the program for NSY and KMAX failure criteria.
The first run of the program halts the crack growth at the user specified detectable crack length (with the
option selected to halt at a critical crack length). The second run of the program, using the same model, halts the program when either the NSY or KMAX criteria have been exceeded. A third run of the program is
conducted which allows the cracks to reach a free edge for illustrative purposes.
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The results of the crack growth analysis for a crack growing from one rivet hole to the adjacent rivet in the outer
row are shown on the next two pages. The analysis predicts 58,044 cycles are required to grow the crack to an inspectable length, (0.196-in – 0.129-in)/2 + 0.10 in = 0.1335-in.
The inspections are done from the outside of the airplane and has direct access to the skin. Therefore, the HFEC
(High Frequency Eddy Current) method can be used.
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The analysis predicts that 169,088 cycles are required to grow the crack to a length of 0.71 inches which is the
critical crack length.
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Crack #1 (Corner Crack at Hole) Length = 0.05 Position: Hole Left
Crack #2 (Corner Crack at Hole) Length = 0.01 Position: Hole Right
Hole #1 (Hole) Diameter = 0.163 Offset = 9.1
Hole #2 (Hole) Diameter = 0.163 Offset = 10
Hole #3 (Hole) Diameter = 0.163 Offset = 10.9
Young's Modulus =10600 Poisson's Ratio =0.33
Coeff. of Thermal Expan. =1.29e-005
No crack growth retardation is being considered
Determine Stress State automatically (2 = Plane stress,
6 = Plane strain) No K-Solution Filters
The Forman-Newman-de Koning- Henriksen (NASGRO) crack growth relation is being used For Reff < 0.0, Delta K = Kmax Material: 1000-9000 series aluminum, 2024-T3 Al, [ Clad; plt & sht; T-L ]
Plane strain fracture toughness: 29 Plane stress fracture toughness: 58 Effective fracture toughness for surface/elliptically shaped crack: 41 Fit parameters (KC versus Thickness Equation): Ak= 1, Bk=1 Yield stress: 48 Lower 'R' value boundary: -0.3
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Upper 'R' value boundary: 0.7 Exponents in NASGRO Equation: n=2.601, p=0.5, q=1 Paris crack growth rate constant: 2.44e-008 Threshold stress intensity factor range at R = 0: 2.9 Threshold coefficient: 1.5 Plane stress/strain constraint factor: 1.5 Ratio of the maximum applied stress to the flow stress: 0.3
Failure is based on the current load in the applied spectrum
Cycle by cycle beta and spectrum calculation
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Crack Growth Analysis for Crack Extending from edge of feedthru - Rogue Flaw
For the rogue flaw damage model the residual strength is based upon the combination of KMAX and NSY.
The simplified model for the longitudinal skin crack between the feed through hole and the two adjacent
rivets in the skin is modeled as an open hole in a flat sheet. The sheet width is taken to be the length
of a skin bay, 20.0-in.
Applied stress to the skin at the feedthru hole = (415.9*lbs/in)/(0.070**in) = 5,941 psi *Ref
*Ref: Lateral residual stress, calculated in Section 3.2.1 **Ref: Lateral
LEFM stress, calculated in Section 3.2.1
Effective skin width = 20.0 in
Model #4 Fatigue Loading
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The results of the crack growth analysis for a crack growing longitudinally from the feed through hole show that
during 169,088 cycles, the rogue crack grows 0.63-in to the adjacent rivet holes. The inspection intervals based on the center hole are therefore, not considered critical.
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The following data is extracted from the AFGROW output file.
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Fatigue Life - Stringers
The antenna installations drill holes in the existing stringer structures between FS 1440 and FS 1460.
The holes are drilled for the installation of MS20470AD6 rivets in the webs of the stringers.
The crack growth from the edge of a one fastener hole to the existing free edge of the stringer is
analyzed due to the tension load from the cabin pressurization and fuselage bending. These critical
crack locations are illustrated below in Figure 5.3A. The stress field is produced on the stringer due to
the cabin pressurization.
The loading of the stringers due to the cabin pressurization is calculated as suggested by Flhgge on NACA TN
2612 (section 1.1, ref 4). The fuselage radius of 81.0-in and the skin thickness of 0.070-in are considered for
the calculations. The calculations are shown in Figure 5.3D and 5.3E. The critical load factor applicable to the installation is cabin pressurization.
The stringer are calculated using 7075-T6 aluminum and the properties are calculated using AutoCAD. The stringer cross-section is scaled from the LB Aircraft drawing. The frame cross-section varies around the
diameter of the fuselage. Since the axial stresses in the stringers are a function of the frame area, the analysis
conservatively considers a frame area equal to 0.8-in2 .
Stringer Spacing ≈ 8.64 in
Frame Spacing = 20.0-in
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The effective fatigue stress in the stringers is very small and is well below the fatigue threshold for 7075-T6 aluminum, as shown in Figures 5.3E.
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Conclusion
The information contained herein supplements the basic Supplemental Structural Inspection Document only in those areas listed herein. For limitations and procedures consult the Instructions for Continued
Airworthiness, supplement to or the basic Airplane Maintenance Manuals.
Appendix A – Longitudinal Fatigue Loading (MathCAD Worksheets for Neutral Line Analysis)
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