Air Conditioning Rack Structural Substantiation

INTRODUCTION

AircraftDHC-8-100Interior structural modification

ObjectiveStatic strength substantiationRack, attachments and supporting structure

Installation envelopeX545.00 – X580.50Mid/aft cabin floor region

Assessment routeFEA + hand substantiationLoads, joints, stresses, buckling and margins

Static-strength substantiation of an air-conditioning equipment rack installed in the DHC-8-100 cabin structure. The work combines load-envelope definition, FEMAP / SIMCENTER NASTRAN modeling, classical stress and stability checks, fastener/joint substantiation, and Python post-processing to demonstrate positive margins through the rack-to-airframe load path.

Air Conditioning Rack installation overview on the DHC-8-100 structure.

Core skillLoad-path engineeringRack → fittings → floor / track / intercostal → airframe

FEAFEMAP + NASTRANBeam, plate, CBUSH, RBE2 and RBE3 idealization

Hand substantiationStress + stability + jointsWelds, buckling, crippling, fasteners and margins

AutomationPython post-processingElement-force extraction, screening and governing-result reporting

DESIGN ASSESSMENT

INBOARD LOAD PATHNew seat-track segment

The inboard base reactions enter the aircraft through the newly installed seat-track support path.

OUTBOARD LOAD PATHFloor + new intercostal

The outboard base is supported by the original floor panel reinforced locally by the added intercostal.

PRIMARY RACKWelded square-tube frame

The tube framework provides the principal load-carrying skeleton; aft and outboard skins participate structurally.

NON-STRUCTURAL ACCESSRemovable forward / inboard panels

These panels provide access and maintenance functionality and are not credited as primary structural members.

Load-Path Rationale

The rack and its supporting structure were modeled separately because they answer different structural questions. Rack reactions are extracted and transferred into the local seat-track / floor / intercostal model, preserving the physical load path while keeping both FEMs efficient and auditable.

Installation interface details around the Air Conditioning Rack.

Welded square-tube structural frame of the Air Conditioning Rack.

Structural and removable panel arrangement of the Air Conditioning Rack.

Installed equipment packaging within the Air Conditioning Rack.

Installation Components

Only the primary load-carrying rack and newly added support components are retained here; removable access panels are not credited as primary structure.

The main structural components of the air conditioning rack.

Component Name	Thickness [in]	Material
AFT and Outboard Skin	0.071	AL 2024-T3 CLAD Sheet
AFT and FWD Gussets	0.125
Two Base Support Clips	0.125
Gusset Angle	0.063	AL 6061-T6 Extrusion
Attachment Angle	0.125	AL 6061-T6 Extrusion
Two Rack Mount Fittings	Variable	AL 6061-T6511 Extrusion

The supporting structural components underneath the air conditioning rack

Component Name	Thickness [in]	Material
FWD and AFT Seat Tracks	0.53	AL 7075-T6 Extrusion
FWD and AFT Seat Track Support Blocks	0.38	AL 2024-T351 Plate
AC Intercostal	0.0625	AL 2024-T3 CLAD Sheet
Intercostal Attachment Brace
Large Intercostal Clip
Small Intercostal Clip
FWD Attachment Doubler

Mass & CoG Model

Mass idealization

Retain stiffness; idealize payload.

Load-bearing geometry remains explicit in the FEM. Equipment and other omitted items are represented at their center of gravity or through distributed non-structural mass so inertia is preserved without adding artificial stiffness.

Weight basis

Hardware / wiring allowance included.

Equipment and applicable component weights include the source 1.15 scaling factor. Material-density estimates are retained for modeled structural items and non-structural components.

Weighted-Average CoG

\bar{x}=\frac{\sum_i W_i x_i}{\sum_i W_i}

\bar{y}=\frac{\sum_i W_i y_i}{\sum_i W_i}

\bar{z}=\frac{\sum_i W_i z_i}{\sum_i W_i}

A worked check for the X-coordinate is:

\bar{x}=\frac{28.87(11.61)+13.35(8.39)+9.57(16.03)+9.57(16.03)+9.57(13.71)+9.57(13.71)}{80.50}=\boxed{12.63\,in}

The same procedure produces $\bar{y} = 14.91 in$ and $\bar{z} = 18.92 in$ .

Mass reconciliation. The source weight basis gives 80.50 lb_f for the parts represented in the rack model. Simplified FEM geometry produced 81.839 lb_f; the distributed non-structural mass was therefore reduced from 19.13 to 17.791 lb_f so the model preserved the intended installation weight without adding artificial stiffness.

Payload weights and center-of-gravity locations. — Payload Weights and their CoG locations.

Supporting-structure mass model. Newly added support structure is modeled explicitly. The source structural weight is 4.07 lb and an additional 0.61 lb_f (15%) is distributed as non-structural mass to represent installation hardware.

Material Properties

Strength and stability checks use the applicable material allowables from [MMPDS-15] and the cited structural-method references.

Material properties used in the Air Conditioning Rack Installation and its supporting structure.

	AL 6061-T6 and T6511 Extrusion t≤1”	AL 6061-T6 and T6511 Extrusion t=1.001”-6.5”	AL 7075-T62 CLAD sheet t=0.04” – 0.062”	AL 7075-T6 Extrusion t=0.25” – 0.499”	AL 2024-T351 Plate t=0.25” – 0.499”	AL 2024-T3 CLAD Sheet t=0.063” – 0.128”	AL 2024-T3 Sheet t=0.010” – 0.128”	Unit
F_tu	38	38	69	81	64	62	64	ksi
F_ty	35	35	61	73	48	45	47	ksi
F_cy	34	34	62	73	39	37	39	ksi
F_su	26	19	47	43	38	38	39	ksi
F_bru	82	69	142	146	119	125	129	ksi
F_bry	60	50	109	113	86	84	88	ksi
E x10³	9.90	9.90	10.3	10.4	10.7	10.50	10.5	ksi
E_c x10³	10.10	10.10	10.5	10.7	10.9	10.70	10.7	ksi
μ	0.33	0.33	0.33	0.33	0.33	0.33	0.33	-
ρ	0.098	0.098	0.101	0.101	0.1	0.1	0.1	lb_m/in³
G x10³	3.80	3.8	-	4.0	4.0	-	4.0	ksi
e	8 or 10	10	9	7	12	15	12 or 15	%

Fastener / Joint Allowables

Joint allowable philosophy

Use the weakest applicable failure path for the actual fastener / sheet stack rather than the isolated fastener strength.

P_{allow} = \min (P_{single-shear}, P_{joint-static}, P_{bearing})

Sheet thickness and material alter joint strength.Countersunk geometry uses the applicable static-joint reduction.Bearing is checked at the critical sheet / hole interface.

Detailed joint allowables were established from the actual sheet stack, fastener type, countersink condition and bearing path using [MMPDS-15], Bruhn and the applicable vendor data. The compact cards below retain the hardware families used in the analysis; the governing result checks later use the joint-specific allowables.

CR3212 · ARM4

Type Countersunk blind rivetNominal size 1/8 inSingle shear 664 lb_fTension 285 lb_fRivet / hole Ø 0.125 / 0.1285 inApplied joints J7–J10

CR3213 · ARN4

Type Protruding blind rivetNominal size 1/8 inSingle shear 664 lb_fTension 285 lb_fRivet / hole Ø 0.125 / 0.1285 inApplied joints J3–J6

MS20426AD4 · BB4

Type Countersunk solid rivetMaterial AL 2117-T3Material F_su 30 ksiSingle shear 389 lb_fApplied joint J25

MS20470AD4 · BJ4

Type Protruding solid rivetMaterial AL 2117-T3Material F_su 30 ksiSingle shear 389 lb_fApplied joints J11–J24

MS24694-S49

Type #10-32 countersunk screwThread UNF-3A · MIL-S-7742Diameter 0.19 inMaterial Cadmium-plated carbon steelF_tu 125 ksiF_su 75 ksiApplied joints J28–J29

AN3 / AN4 Aircraft Bolt

Thread 1/4-28 UNF-3ADiameter 0.25 inMaterial Non-corrosion-resistant steelUltimate shear 3,680 lb_fUltimate tension 4,080 lb_fApplied joint J30

FE200744 Stud + Lock Fitting

Thread 3/8-24 UNRFDiameter / length 0.375 / 0.9 inMaterial Zinc-plated carbon steelTrack shear 4,200 lb_fTrack tension 5,700 lb_fApplied joints J1–J2

LOAD CASES FORMULATION

GOV

Interior installation → evaluate both flight and emergency conditions.

The governing directional case is selected by comparing the worst flight acceleration with the equivalent limit form of the emergency-landing requirement.

REGULATORY SOURCE BASISFAR Part 25 criteria used to formulate the structural load envelope

Flight-load framework

FAR 25.321 and 25.331–25.351

General flight loads and symmetric maneuver response
Flight maneuver envelope and design airspeeds
Limit maneuver factors, gust and turbulence loads
Fuel/oil, high-lift, rolling and yaw conditions

Flight loads are treated as limit loads.

Emergency landing

FAR 25.561

Forward: 9 g
Downward: 6 g
Upward: 3 g
Sideward: 3 g airframe / 4 g seats & attachments
Rearward: 1.5 g

Emergency-landing values are ultimate loads.

The rack center is taken at X563.58. Flight accelerations were interpolated at that station and compared direction-by-direction with the equivalent limit form of the FAR 25.561 emergency-landing requirements. The five governing FEM cases are retained below; the 1.5 ultimate factor is applied in the reported margins.

Governing limit-load cases applied to the FEM.

Case	Direction	Flight limit [g]	Emergency equivalent [g]	Applied [g]	Governing basis
1	Upward	5.92	2.00	5.92	Flight
2	Downward	-6.27	-4.00	-6.27	Flight
3	Outboard	1.82	2.00	2.00	Emergency landing
4	Inboard	-1.82	-2.00	-2.00	Emergency landing
5	Forward	-0.61	-6.00	-6.00	Emergency landing
-	Aft	0.16	1.00	Not separately required	Covered conservatively by Forward case

Load-Case Selection Rationale

I compared flight and emergency conditions direction by direction and retained only the larger absolute limit acceleration. This prevented duplicate cases while preserving the governing regulatory demand. The FEM therefore contained five clearly traceable load cases rather than separate, overlapping flight and emergency models.

FINITE ELEMENT MODEL (FEM)

Air Conditioning Rack Model

Finite element model of the Air Conditioning Rack. — Finite Element Model for the Air Conditioning Rack.

NSM

Non-structural detail is omitted geometrically, not inertially.

Exterior removable panels and small hardware are excluded from the mesh; their equivalent weight is distributed over the tube structure as NSM.

IDEALIZATION

Beam · tube structure

The welded square-tube frame is modeled with beam elements so section area, inertia, axial force, shear and bending are recovered efficiently along the primary load path.

IDEALIZATION

Plate · skins, gussets & brackets

Six material/thickness plate properties represent the aft/outboard skins, gussets, base clips, gusset/attachment angles and rack-mount fittings. The thin-walled parts are governed by membrane and bending response rather than through-thickness stress.

JOINT MODEL

CBUSH · mounting fasteners

Rack-mount, base-clip and attachment-angle fasteners use 1×10⁹ lb_f/in translational stiffness with free rotations. This transfers shear/tension without imposing artificial rotational fixity.

LOAD INTRODUCTION

RBE2 · fastener-hole spiders

Modeled attachment holes use RBE2 spiders to distribute connector reactions over the hole perimeter. Non-governing holes are suppressed to avoid artificial local stress peaks that do not control the primary load path.

PAYLOAD

RBE3 · equipment masses

The four evaporator modules and avionics box are introduced as point masses through RBE3 elements, transferring inertia to the structure without adding rigid-body stiffness.

CONTACT

Glued vs. non-penetrating interfaces

Opposing attachment-angle faces are glued where full transfer is intended; rack-fitting/gusset and skin interfaces use non-penetrating contact so compression is transferred without unrealistically bonding every interface.

Loads & Constraints

Air Conditioning Rack attachment points used for boundary conditions. — Air Conditioning Rack’s Attachment Points

Body accelerations are applied to the rack for the five governing cases. Restraints are changed by load direction to represent the actual attachment capability rather than imposing one artificially fixed boundary condition for every case.

The restrained degrees of freedom (DoFs) at each Attachment Points for each load case.

	FWD	Inboard	Outboard	Upward	Downward
①	T_xT_yT_z	T_xT_yT_z	T_xT_yT_z	T_xT_yT_z	T_xT_yT_z
②	T_xT_yT_z	T_xT_yT_z	T_xT_yT_z	T_xT_yT_z	T_xT_yT_z
③	Free	Free	T_z	Free	T_z
④	T_z	Free	T_z	Free	T_z
⑥	T_xT_yT_z	T_xT_yT_z	T_xT_yT_z	T_xT_yT_z	T_xT_yT_z
⑦	T_xT_yT_z	T_xT_yT_z	T_xT_yT_z	T_xT_yT_z	T_xT_yT_z
⑧	T_xT_yT_z	T_xT_yT_z	T_xT_yT_z	T_xT_yT_z	T_xT_yT_z

Supporting Structure Model

IDEALIZATION

Beam · seat tracks / blocks / T-section

These members are represented by beam properties because axial and bending response is governed primarily by section properties; solid modeling would add cost without improving the global load-path solution.

AIRFRAME INTERFACE

Grounded CBUSH · existing structure

Grounded connectors at the pre-existing T-section track represent the restraint delivered by adjacent webs, stiffeners and frames while avoiding a need to model the entire surrounding fuselage.

FASTENER MODEL

CBUSH · seat-track screws

MS24694-S49 and NAS8603-12 screws use high translational stiffness with free rotations. The connector captures global shear/tension transfer without introducing detailed bolt contact and thread geometry.

KINEMATICS

RBE2 · track end coupling

Seat-track end points rigidly transfer the selected Ty and Rx motions into the T-section support path, reproducing the constrained interface behavior without over-modeling the surrounding airframe.

IDEALIZATION

Plate · intercostal / doubler / clips / brace

Thin structural sheet components are modeled with plate elements to recover membrane, bending and shear response directly. Through-thickness solid stress is non-governing for the global substantiation.

RIVET BEHAVIOR

Directional CBUSH stiffness

MS20470AD4 rivets use 1×10⁹ lb_f/in in shear and 1×10⁵ lb_f/in in tension with free rotations, reflecting a shear-dominant riveted joint without artificially rigid tensile restraint.

CONTACT

Physical interfaces retained

Non-penetrating contact allows compression and relative interface motion where appropriate; glued contact is used only where the assembly is intended to transfer load continuously.

LOAD INTRODUCTION

RBE2 spider · outboard attachment

Concentrated rack reactions are distributed around the fastener-hole perimeter to suppress node singularities and provide a stable, physically meaningful load introduction into the sheet structure.

Finite element model of the rack supporting structure and floor. — Finite Element Model for the Air Conditioning Rack Supporting Structure along with the Floor.

Finite element model of the outboard supporting structure. — Finite Element Model for the Outboard side of the Air Conditioning Rack Supporting Structure.

Equivalent floor-panel idealization. The sandwich floor is represented by an equivalent plate that preserves the required global flexural rigidity and distributed-load transfer. This is appropriate for rack-support substantiation; local core crushing and face-sheet delamination are outside the scope of the global plate idealization.

Cargo floor panel finite element idealization. — Cargo Floor Panel Model.

Equivalent Floor-Panel Idealization - Calculation Check

The sandwich floor is represented by a homogeneous AL 2024-T3 CLAD plate for the global support-model analysis. The source model preserves the required global bending/load-transfer response while excluding local sandwich failure modes such as core crushing and face-sheet delamination.

The equivalent plate is checked against the cargo-floor downward limit demand:

q_{limit}=125\,lb_f/ft^2\times(1/144)\,ft^2/in^2\times6.27=5.443\,psi

For a simply supported rectangular plate under uniform pressure, the maximum bending stress is:

\sigma_{max}=\frac{\beta q b^2}{t^2}

β - plate coefficientb - smaller panel dimensiont - equivalent plate thicknessq - uniform pressure

Using $σ_{\max} = F_{tu} / 1.5$ , the minimum required thickness becomes:

t_{min}=\sqrt{\frac{1.5\beta q_{limit}b^2}{F_{tu}}}

For a 37.90 in × 23.00 in panel, $a / b = 1.648$ . Linear interpolation of the source plate coefficient gives:

\beta=0.5172+(1.648-1.6)\frac{0.5688-0.5172}{1.8-1.6}=0.5295

With $F_{tu} = 64 ksi$ , the source check gives:

t_{min}=\sqrt{\frac{1.5(0.5295)(5.443)(23.00)^2}{64000}}=0.189\,in

✓The equivalent-plate idealization is therefore supported by a 0.189 in minimum-thickness check for the stated cargo-floor limit demand.

Method basis: [Formulas for Stress & Strain-Raymond Roark-Table 11.4] and [MMPDS-15-Table 3.2.4.0(c1)].

Transferred Loads & Support Constraints

Rack-model reactions are applied at the corresponding support-model attachment locations. Floor edges, doubler edges, the AFT clip and intercostal brace are restrained as defined in the source model, preserving load-path continuity from the equipment rack into the local aircraft structure.

All Nodes at the Floor Edges.
All Nodes at the Doubler Edges.
Three Nodes at the AFT Side of the AFT Clip.
Fifteen Nodes at the Bottom Side of the Intercostal Brace.

Analysis

SolutionSESTATIC · SOL 101

Linear static response is appropriate for the defined ultimate/limit load cases and the global strength checks performed here.

SolverSIMCENTER NASTRAN

Member forces, plate stresses, connector reactions and constraint forces are recovered for downstream hand checks and margins.

UNIT SYSTEM

WTMASS enabled

Mass is entered in lb_m, density in lb_m/in³ and acceleration in in/s². WTMASS provides consistent mass-to-force conversion so solver forces are recovered in lb_f and stresses in psi.

FEA RESULTS

Governing reported MS+0.08AL 6061-T6 / T6511 principal-stress check

Primary frameTube + welds passCombined stress, buckling and crippling assessed

Joint substantiationPositive marginsMain attachments, skins, rack fittings and intercostal joints

Post-processingAutomated screeningPython evaluates all valid plate elements and load cases

Governing strength checks retained in this portfolio summary. All margins shown are the reported source-calculation values.

Check	Governing reported result	Minimum MS	Status
Welded tube structure	Combined tube / weld stress	+0.54	PASS
Tube column buckling	40 in critical member; source buckling check	+1.08	PASS
AL 2024-T3 CLAD sheet	Principal-stress assessment	+0.13	PASS
AL 6061-T6 / T6511	Principal-stress assessment	+0.08	PASS
Attachment-angle crippling	Needham / Gerard method	+0.40	PASS
Intercostal-flange crippling	Needham / Gerard method	+1.39	PASS
AN4 / insert attachment	Main outboard attachment shear	+0.82	PASS
AFT skin CR3212 rivets	Tension governs source check	+0.76	PASS
Rack-mount CR3213 rivets (J3)	Tension governs source check	+0.37	PASS
AFT-gusset CR3212 rivets (J8)	Fail-safe redistributed shear	+0.41	PASS

Tube Structure & Welds

Tube weld cross-section used for stress estimation. — Weld Cross-Section

Weld stress treatment. Tube member forces are recovered from the beam model, then converted to weld-section stresses using the actual weld/tube section-property ratios. This avoids modeling weld beads with solid elements while retaining the conservative change in area and bending section modulus.

The beam model recovers member axial force and bending moments. Weld stresses are then mapped from the tube section using the actual section-property ratios:

${F_{b}^{weld} = \frac{c_{weld}I_{tube}}{I_{weld}c_{tube}}f_{b}^{tube}\ = \ \frac{\frac{9}{16}\ (0.056966)}{\ \frac{1}{2}(0.069111)}f_{b}^{tube} }\boxed{F_{b}^{weld} = 0.927\ F_{b}^{tube}}$

$\boxed{F_{A}^{weld} = 1.131\ F_{A}^{tube}}$

The Maximum Axial Force and Bending Moments values for each load case. The highlighted values are the global maximum values. The results are due to applied limit loads.

	FWD	INBOARD	OUTBOARD	UPWARD	DOWNWARD
M1 [in-lb_f]	599.91	78.78	-54.30	168.86	75.59
M2 [in-lb_f]	357.98	-232.82	-52.71	-559.06	136.81
Axial [lb_f]	420.84	-87.34	69.40	146.70	-144.33

Tube-structure axial force and bending-moment contours. — Axial Force and Bending Moments contours over the tube structure for load case(s) exhibiting the global maximum values. The labeled element exhibits the maximum tensile and compressive combined stresses.The results are due to applied limit loads.

The source element-by-element combination identifies the forward case as governing. The minimum reported static-strength margin for the tube / weld assessment is retained below.

{M.S}_{t}^{tube} = \frac{38}{6.49 \times 1.5} - 1 = 2.90

{M.S}_{t}^{weld} = \frac{24}{5.97 \times 1.5} - 1 = 1.68

{M.S}_{c}^{tube} = \frac{34}{6.97 \times 1.5} - 1 = 2.25

{M.S}_{c}^{weld} = \frac{15}{6.51 \times 1.5} - 1 = 0.54

\boxed{{M.S}^{tube - struc.} = 0.54\ }

→ PASS

Stability checks. The 40 in critical member was checked for Euler-type column buckling using pinned-pinned and fixed-fixed bounds; the source averaged critical stress is 20.28 ksi and the reported buckling margin is +1.08. A Needham / Gerard crippling check gives a 75.07 ksi section crippling allowable, so the tube section also passes the source crippling assessment.

$\boxed{F_{cr} = \frac{8.11 + 32.45}{2} = 20.28\ ksi}$

{M.S}_{Buckling}^{tube} = \frac{20.28}{6.51 \times 1.5\ } - 1

\boxed{{M.S}_{Buckling}^{tube - struc.} = 1.08\ }

→ PASS

Angle #	h	t_h	b	t_b	A_n	C_e	F_ccn	A_nF_ccn
1	0.500	0.125	0.500	0.125	0.125	0.366	75.075	9.384
2	0.500	0.125	0.500	0.125	0.125	0.366	75.075	9.384
3	0.500	0.125	0.500	0.125	0.125	0.366	75.075	9.384
4	0.500	0.125	0.500	0.125	0.125	0.366	75.075	9.384
				Σ	0.500			37.537
					F_Crippling [ksi]	75.07

Tube-structure crippling calculation geometry/reference image.

Plate & Sheet-Metal Checks

Localized Peak-Stress Treatment

Purpose: prevent mesh singularities, geometric discontinuities, and other non-representative local peaks from governing the global strength assessment without engineering review.

Screen the global maximum and minimum principal stresses.
Define material-specific tensile and compressive threshold values.
Flag elements above the tensile threshold or below the compressive threshold.
Review each flagged location in the FEM and identify non-representative numerical/localized peaks.
Exclude only the confirmed non-representative elements from the failure assessment.
Recalculate the governing principal stresses from the remaining elements and compare them with F_tu and F_cy.
Retain any remaining critical elements within the thresholds as part of the conservative assessment.

This preserves conservative structural coverage while reducing the influence of numerical artifacts on the reported governing stress.

AL 2024-T3 CLAD Sheet

After engineering review of localized numerical peaks, the source assessment retains 28.08 ksi maximum tensile and 21.81 ksi maximum compressive principal stress for the failure check. Against 62 ksi tensile and 37 ksi compressive allowables, the reported governing margin is +0.13.

{M.S}_{max.T - Prn.Stresses}^{2024 - T3\ ALCAD\ } = \frac{62}{28.08 \times 1.5} - 1 = 0.47

{M.S}_{max.C - Prn.Stresses}^{2024 - T3\ ALCAD\ } = \frac{37}{21.81 \times 1.5} - 1 = 0.13

\boxed{{M.S}_{Prn.Stresses}^{2024 - T3\ ALCA} = 0.13\ }

→ PASS

AL 6061-T6 / T6511 Extrusion

Flagged AL 6061-T6 and T6511 extrusion elements outside the selected stress thresholds. — The Flagged Elements within the AL 6061-T6 and T6511 Extrusions that have a thickness value ≤ 1”.

The reviewed source result retains 23.00 ksi maximum tensile and 20.95 ksi maximum compressive principal stress. Against 38 ksi and 34 ksi allowables, the reported governing margin is +0.08. The attachment-angle crippling calculation gives a 44.06 ksi allowable and +0.40 margin.

{M.S}_{max.T - Prn.Stresses} = \frac{38}{23.00 \times 1.5} - 1 = 0.10

{M.S}_{max.C - Prn.Stresses} = \frac{34}{20.95 \times 1.5} - 1 = 0.08

\boxed{M.S = 0.08}

→ PASS

Angle #	h	t_h	b	t_b	A_n	C_e	F_ccn	A_nF_ccn
1	1.000	0.125	0.563	0.250	0.391	0.342	50.184	19.610
2	1.125	0.125	0.563	0.250	0.422	0.342	47.371	19.990
				Σ	1.040			45.833
					F_Crippling [ksi]	44.06

Attachment-angle crippling calculation geometry/reference image.

{M.S}_{Crippling}^{Att.Angle} = \frac{44.06}{20.95 \times 1.5\ } - 1

\boxed{{M.S}^{Crippling} = 0.40\ }

→PASS

Supporting Structure Sheets

Maximum and Minimum Principal Stresses for the Structural Sheet Metals. The highlighted cells represent the global maximum tensile and compressive principal stresses. The results are due to applied limit loads.

AL 2024-T3 CLAD Sheet [t=0.063” – 0.128”]		FWD		UP		DOWN		IN		OUT		MAX Tension [ksi]	MAX Compression [ksi]
AL 2024-T3 CLAD Sheet [t=0.063” – 0.128”]		F₁ [ksi]	F₂ [ksi]	F₁ [ksi]	F₂ [ksi]	F₁ [ksi]	F₂ [ksi]	F₁ [ksi]	F₂ [ksi]	F₁ [ksi]	F₂ [ksi]	MAX Tension [ksi]	MAX Compression [ksi]
Top	Tension	11.82	3.61	12.13	3.72	0.27	0.04	4.91	1.51	0.73	0.21	12.15	8.29
Top	Compression	1.11	3.45	1.86	4.66	0.06	0.33	0.74	1.82	0.08	0.70
Bot	Tension	11.85	3.94	12.15	4.06	0.29	0.11	4.93	1.65	0.73	0.23
Bot	Compression	5.42	6.93	6.36	8.29	0.16	0.42	2.55	3.30	0.52	1.04
AL 2024-T3 CLAD Sheet [t=0.129"-0.249"]		FWD		UP		DOWN		IN		OUT		MAX Tension [ksi]	MAX Compression [ksi]
AL 2024-T3 CLAD Sheet [t=0.129"-0.249"]		F₁ [ksi]	F₂ [ksi]	F₁ [ksi]	F₂ [ksi]	F₁ [ksi]	F₂ [ksi]	F₁ [ksi]	F₂ [ksi]	F₁ [ksi]	F₂ [ksi]	MAX Tension [ksi]	MAX Compression [ksi]
Top	Tension	10.79	8.02	10.75	7.96	0.19	0.12	4.34	3.21	0.77	0.55	10.79	8.63
Top	Compression	3.76	4.74	4.43	5.21	0.20	0.26	1.80	2.12	0.21	0.35
Bot	Tension	3.48	2.66	3.86	3.05	0.21	0.11	1.57	1.24	0.33	0.17
Bot	Compression	5.96	7.91	6.78	8.63	0.13	0.27	2.73	3.44	0.50	0.84

Principal stress contours for the supporting-structure AL 2024-T3 CLAD sheets. — The maximum principal stress (F1) and the minimum principal stress (F2) on both sides of the 0.0625” thick AL 2024-T3 CLAD Sheets for the Upward Load Case. The results are due to applied limit loads.

The support-model plates are reviewed across all five load cases. Localized high gradients are retained conservatively in the source assessment where appropriate; the intercostal flange is additionally checked for crippling.

Angle #	h	t_h	b	t_b	A_n	C_e	F_ccn	A_nF_ccn
1	0.913	0.063	0.813	0.063	0.108	0.342	29.759	3.210
2	0.913	0.063	0.813	0.063	0.108	0.342	29.759	3.210
				Σ	0.216			6.421
					F_Crippling [ksi]	29.76

Supporting-structure flange/crippling calculation geometry/reference image.

{M.S}_{Crippling}^{Intercostal\ Flange} = \frac{29.76}{8.29 \times 1.5\ } - 1

\boxed{{M.S}^{Crippling} = 1.39\ }

→ PASS

Fasteners & Attachments

Main Attachment Points

Main Air Conditioning Rack attachment points. — The Main Attachment Points in the Air Conditioning Rack.

Inboard: two ANCRA single-stud fittings carry maximum source limit loads of 309.37 lb_f shear and 430.37 lb_f tension in the forward case. Outboard: the AN4-11A / insert attachment reaches 626.66 lb_f shear and 336.75 lb_f tension in the upward case.

{M.S}_{s} = \frac{4,200}{309.37 \times 1.5 \times 1.15} - 1

{M.S}_{t} = \frac{5,700}{430.37 \times 1.5 \times 1.15} - 1

\boxed{{M.S}_{s} = 6.87}

→ PASS

\boxed{{M.S}_{t} = 6.68}

→ PASS

{M.S}_{s} = \frac{1,968}{626.66 \times 1.5 \times 1.15} - 1

{M.S}_{t} = \frac{4,080}{336.75 \times 1.5 \times 1.15} - 1

\boxed{{M.S}_{s} = 0.82}

→ PASS

\boxed{{M.S}_{t} = 6.02}

→ PASS

AFT Skin Rivets & Python Post-Processing

Python Workflow

The plate-force post-processing was automated to reduce repetitive manual work and improve traceability. The script reads FEMAP-exported element and nodal data, rejects triangular elements, calculates element dimensions, converts membrane resultants to elemental forces, screens all load cases, and writes governing results to a summary workbook.

Read the FEMAP Excel export and nodal coordinates.
Extract nodal-coordinate values (X-Def, Y-Def, Z-Def).
Filter valid quadrilateral plate elements.
Calculate element dimensions and local force directions.
Recover n_x, n_y, n_xy, q_x, and q_y for every element and load case.
Calculate elemental shear and tensile demand.

N_x=d_xn_x,\quad N_y=d_yn_y,\quad N_{xy,x}=d_xn_{xy},\quad N_{xy,y}=d_yn_{xy}

A conservative in-plane resultant is calculated as:

F_{s,max}=\sqrt{(N_x+N_{xy,y})^2+(N_y+N_{xy,x})^2}

Generate contour maps and a governing-result summary.
- 2D plot of elements and nodes.
- Heat maps for maximum shear load and maximum tensile load for every load case.
- Extract maximum membrane forces, shear, and tensile loads from each load case and save them to a new summary table.

Three-dimensional plate element showing membrane resultants, transverse shear resultants, bending moments, twisting moment, dimensions, and local axes used in the Python post-processing workflow.

Why I automated this stepThe governing plate element was not necessarily the element with the largest individual n_x, n_y, or n_xy component. Automation allowed every valid plate element and load case to be evaluated using one documented equation set, eliminating inconsistent spreadsheet manipulation and preserving a repeatable audit trail.

AFT skin membrane, shear-flow, and transverse-shear force results. — The (i) Membrane Forces per unit length along x and y-axes, (ii) Shear Flow per unit length, and (iii) Shear Forces per unit length over the x and y faces for AFT Skin in the forward load case. The results are due to applied limit loads.

The Maximum Elements’ Plate, Shear, and Tensile Forces and the resulted maximum Shear and Tensile loads for all load cases. The results are due to applied limit loads.

Load Case	N_x,max [lb_f]	N_y,max [lb_f]	N_xy-x,max [lb_f]	N_xy-y,max [lb_f]	Q_x,max [lb_f]	Q_y,max [lb_f]	f_s,max [lb_f]	f_t,max [lb_f]
FWD	21.45	27.02	9.34	12.52	4.61	5.08	38.18	6.06
INBD	6.06	14.06	3.28	5.74	10.81	9.61	21.89	11.56
OUTBD	11.10	9.81	5.09	7.37	4.57	9.87	20.59	8.93
UPWD	11.16	33.52	9.14	14.96	26.05	12.83	36.54	22.91
DOWNWD	3.11	11.38	6.62	11.74	26.94	36.99	40.17	37.66

Nodes and elements extracted from the FEMAP results file. — Nodes and Elements extracted from the FEMAP results file.

The automated screening identifies the source governing AFT-skin rivet demands as 38.86 lb_f shear and 37.65 lb_f tension under the downward case. The resulting reported margins are:

{M.S}_{s} = \frac{428}{38.86\ \times 1.5 \times 1.15} - 1

{M.S}_{t} = \frac{114}{37.65 \times 1.5 \times 1.15} - 1

\boxed{{M.S}_{s} = 5.38}

→ PASS

\boxed{{M.S}_{t} = 0.76}

→ PASS

Avionics Box Rivets

The avionics box is attached by 17 CR3213 rivets per side. FEM multipoint forces are low (4.03 lb_f maximum shear and 2.72 lb_f maximum tension). A conservative 3D rigid-body check assuming only two rivets per side increases the evaluated maxima to 27.96 lb_f shear and 22.04 lb_f tension; the source concludes the joint passes by observation.

Avionics Box rivet multipoint-force result illustration. — Multipoint forces at the Avionics Box rivets for the Forward and Downward load cases.

Rack-Mount Fittings & Fail-Safe Check

Extended Rack Mount Fitting fastener locations. — The Extended Rack Mount Fitting’s Fasteners.

At joint J3, the extended rack-mount fitting transfers a maximum source limit demand of 211.43 lb_f shear and 96.26 lb_f tension. The reported minimum margin is +0.37 in tension.

{M.S}_{s} = \frac{1,278}{211.43 \times 1.5 \times 1.15} - 1

{M.S}_{t} = \frac{228}{96.26 \times 1.5 \times 1.15} - 1

\boxed{{M.S}_{s} = 2.50}

→ PASS

\boxed{{M.S}_{t} = 0.37}

→ PASS

Localized fastener failure / redistribution. The high forward-case load at AFT-gusset rivet No. 10 was redistributed to adjacent rivets 11–13 as a fail-safe sensitivity check. After redistribution, the source governing rivet demand is 240.23 lb_f shear, with a reported minimum shear margin of +0.41.

{M.S}_{s} = \frac{582}{240.23 \times 1.5 \times 1.15} - 1

{M.S}_{t} = \frac{228}{53.84 \times 1.5 \times 1.15} - 1

\boxed{{M.S}_{s} = 0.41}

→ PASS

\boxed{{M.S}_{t} = 0.72}

→ PASS

Intercostal & Existing-Structure Interface

AC Intercostal fastener locations. — The AC Intercostal’s Fasteners.

The FWD/AFT intercostal clips use MS20470AD4 rivets. The source maximum is 42.27 lb_f shear and 1.61 lb_f tension, giving a minimum reported shear margin of +4.33.

{M.S}_{s} = \frac{389}{42.27 \times 1.5 \times 1.15} - 1

{M.S}_{t} = \frac{483}{1.61 \times 1.5 \times 1.15} - 1

\boxed{{M.S}_{s} = 4.33}

→ PASS

\boxed{{M.S}_{t} \gg 0}

→ PASS

Doubler / OEM frame interface. The summed constraint demand at the 23-rivet doubler joint is 54.85 lb_f maximum shear and 0.03 lb_f maximum tension across the joint. The source assessment treats this as non-governing and concludes the redistributed loads remain within the existing structure’s substantiated capacity.

REFERENCES

Structural Methods & Allowables

MMPDS-15 - Metallic Materials Properties Development and Standardization
Analysis and Design of Flight Vehicle Structures - E. F. Bruhn
Roark’s Formulas for Stress and Strain
Aluminum Design Manual 2010
Stress Analysis Manual - Air Force Flight Dynamics Laboratory, Wright-Patterson
Fastener Design Manual - NASA Reference Publication 1228

Regulatory & Aircraft Load Basis

Federal Aviation Regulations - 14 CFR Part 25
DHC-8-100 Load Cases and Applied Loads

Fasteners & Hardware Data

CherryMax Rivets technical data
NAS528 Fastener Codes
MS24694 technical data
NASM3-20 aircraft-bolt technical data

Track & Fitting Data

FE200744 stud-fitting technical data
FE748-01-PD4 aircraft-track technical data
ANCRA Aircraft Track technical data