INPUTSGoemetry Values

Panel ID TU#3Avg. spanwise length 18.36 in.Avg. chordwise length 6.13 in.(Inbd) Distance from fastener line to panel edge 0.6125 in.(Inbd) Distance from Fastener Line to core edge 1.29 in.(Inbd) Distance from core edge to support edge 0.25 in.(Otbd) Distance from Fastener line to panel edge 0.6125 in.(Otbd) Distance from Fastener Line to core edge 1.29 in.(Otbd) Distance from core edge to support edge 0.25 in.(Fwd) Distance from fastener line to panel edge 0.6125 in.(Fwd) Distance from Fastener Line to core edge 1.29 in.(Fwd) Distance from core edge to support edge 0.25 in.(Aft) Distance from fastener line to panel edge 0.6525 in.(Aft) Distance from Fastener Line to core edge 1.41 in.(Aft) Distance from core edge to support edge 0.25 in.(Inbd) Maximum Fastener Spacing 1 in.(Otbd) Maximum Fastener Spacing 1 in.(Fwd) Maximum Fastener Spacing 1 in.(Aft) Maximum Fastener Spacing 1 in.Core cell size 0.1875 in.Core thickness 0.5 in.IFS Thickness, t1 0.0135 in.OFS Thickness, t2 0.0135 in.Overall Thickness of the laminate, t 0.527 in.Total thickness of the edgeband, t_eb 0.1 in.Max. fastener dia. 0.1875 in.

Constants ValuesEquivalent Young's modulus of laminate, E 1.41E+06 psiPoisson's ratio of face material in warp direction, Mw 1.30E-01 psiPoisson's ratio of face material in fill direction, Mf 1.30E-01 psiCompression Buckling Coefficient, Kc 10.6Core shear Modulus in X-Z plane, G13 6.62E+03 psiEquivalent Young's modulus of face material, Ef 7.41E+05 psiElastic compression modulus of core, Ecc 1.90E+04 psiEnd fixity coefficient, c for Interrivet buckling 2.3Compressive yield strength of the face material, Fcy 190000 psi

Loads & Allowables ValuesAxial Load acting over the edge of the panel_Fs_axial 37.3572593800979 lb/in.Stress acting on the edgeband, eb_axial 373.572593800979 psiMaximum bending Moment. 701.885 lb.inApplied load for Fastener shear out, P 100 lbShear force acting in X-Z Dir. For Core shear 3.52E+00 lbShear force acting in Y-Z Dir. For Core shear 1.33E+00 lbCore shear stress, fxz for fastener pull through 7.03668000223016 psiCore shear stress, fyz for fastener pull through 2.65703207159099 psiApplied Pressure, Po 3.6 psiAllowable core crushing strength of the material, Fcc 260 psiAllowable core shear stress, Fxz 143.24 psi

FWD

AFT

OB

Allowable core shear stress, Fyz 75.994Allowable shear stress for fastener shear out, Fs.all 22500 psiAllowable fastener pull through strength of the laminate, Pfpt 489.6 psiUltimate bearing strength of the material, fbr.ult 50645 psiAxial load in the edgeband for fastener bearing, eb_axial 588.037 psiAllowable interlaminar shear strength, F_intlam 4200 psi

OUTPUTSFailure Criteria Margin of safety

General Buckling 1237.67988669355Intracell Buckling 87.0849975688472Face Wrinkling 46.4303833063023Shear Crimping 69.1110261489192Local Core crushing 4.2 To be done exclusivelyFlexural Core Crushing -0.63633701387494Inter Rivet Buckling 2.58752227074236Core Shear 19.3561906971189Shear out 27.5625Fastener Pull Through 39.1215110873055Fastener Bearing 1.40117461361952Interlaminar shear strength 32.5975786786678

CORE

RAMP

MONOLITHIC REGION

Fastener Linea

b

FWD

AFT

IB

NMAT2

S.No E11 E22 E33 G12 G13 G23 V12 V131 3.50E+07 3.50E+07 1.00E+07 3.80E+06 3.80E+06 3.80E+06 1.10E-01 3.00E-012 1.00E+00 1.00E+00 1.90E+04 1.00E+00 6.62E+03 3.69E+03 0.00E+00 0.00E+00

NL 7

TL THETA MID0.0045 0 10.0045 45 10.0045 45 1

0.5 0 20.0045 45 10.0045 45 10.0045 0 1

NMAT - Number of materialsS.No - material ID - 1 for ply; 2 for coreNL - Number of layers including coreTL - Thickness of the layerTHETA - Oreintation of the layersMID - Material ID

V23 RHO3.00E-01 6.70E-020.00E+00 2.00E-03

ABD Matrix: A11 A12 A167.41E+05 3.21E+05 -4.42E-05 0.00E+00 -2.27E-12 0.00E+003.21E+05 7.41E+05 4.42E-05 -2.27E-12 0.00E+00 0.00E+00-4.42E-05 4.42E-05 3.18E+05 0.00E+00 0.00E+00 9.09E-130.00E+00 -2.27E-12 0.00E+00 3.19E+04 1.35E+04 -1.85E-06-2.27E-12 0.00E+00 0.00E+00 1.35E+04 3.19E+04 1.85E-060.00E+00 0.00E+00 9.09E-13 -1.85E-06 1.85E-06 1.34E+04

Effective Stiffness:

Exx = 1.41E+06Eyy = 1.41E+06Gxy = 7.45E+05Vxy = 4.33E-01Vyx = 4.33E-01

LOADS

Assumption:Panel is rectangular and simply supported on all sides.

The moments and forces are given by,

(Ref: Mechanics of Composite Materials, Robert M Jones)

Where

M x=16POπ 4 ∑

m=odd

∞

∑n=odd

∞ 1mnD [(ma )

2

D11+( nb )2

D12]sin(mx πa )sin(ny π

b )

M y=16POπ 4 ∑

m=odd

∞

∑n=odd

∞ 1mnD [(ma )

2

D12+( nb )2

D22 ]sin(mx πa )sin (ny π

b )

Q x=16PO

π3 ∑m=odd

∞

∑n=odd

∞ 1mnD [D11(ma )

3

+ (D12+2D66 )(ma )( nb )2 ]cos(mx π

a )sin (ny πb )

Q y=16POπ 3 ∑

m=odd

∞

∑n=odd

∞ 1mnD [D22( nb )

3

+(D12+2D66 )(ma )2

( nb )]sin(mx πa )cos (ny π

b )

a= Length of panel in x-directionb=Length of panel in y-directionPO=Applied pressureD11 , D12 , D22 , D66=Components of the laminate bending stiffness matrix

D=D11(ma )4

+2 (D12+2D66 )(mnab )

2

+D22(nb )4

color indexinputsoutput

INPUTS

Number of buckle of half wavelenghts in X-dir, m 1Number of buckle of half wavelenghts in Y-dir, n 1Avg. spanwise length, a 18.36Avg. chordwise length, b 6.13E+00Applied pressure, Po 3.60E+00D11 3.19E+04D12 1.35E+04D22 3.19E+04D66 1.34E+04

OUTPUTS

Laminate bending stiffness, D 1.62E+01Shear Force, Qx 3.52E+00Shear Force, Qy 1.33E+00Moment, Mx 1.38E+00Moment, My 2.70E+00

(Ref: Mechanics of Composite Materials, Robert M Jones)

Q x=16PO

π3 ∑m=odd

∞

∑n=odd

∞ 1mnD [D11(ma )

3

+ (D12+2D66 )(ma )( nb )2 ]cos(mx π

a )sin (ny πb )

Q y=16POπ 3 ∑

m=odd

∞

∑n=odd

∞ 1mnD [D22( nb )

3

+(D12+2D66 )(ma )2

( nb )]sin(mx πa )cos (ny π

b )

a= Length of panel in x-directionb=Length of panel in y-directionPO=Applied pressureD11 , D12 , D22 , D66=Components of the laminate bending stiffness matrix

D=D11(ma )4

+2 (D12+2D66 )(mnab )

2

+D22(nb )4

GENERAL BUCKLING

Loading: Edgewise

Caused due to

• Insufficient panel thickness• Insufficient core shear rigidity

Assumptions1) Sandwich panel is having similar orthotropic faces and is simply supported at all edges.2) The panel is subjected to edgewise compressive loads.3) The principal axes of the orthotropic material are parallel to the edges of the panel.4) The faces have identical properties and ther respective warp directions are parallel.5) The panel is rectangular with out any cutouts.

For Loading parallel to the warp direction

Where,Fc is critical buckling stress of the panelKc is Buckling coefficientE is effective modulus of the laminatet is total thickness of the panelb is width of the loaded edgeμ is poisson's ratio of the laminate

color indexinputsoutput

General buckling is one of the general instability criteriae which is treated as failure of sandwich element as a whole, with face sheet, core and bonding acting together. It is a part of overall instability check of the composite panel.

Fc=π2⋅Kc⋅E

12 (1−μ2 ) (tb )

2

INPUTS

Core thickness 0.5IFS Thickness, t1 0.0135OFS Thickness, t2 0.0135Overall Thickness of the laminate, t 5.27E-01Equivalent Young's modulus of laminate, E 1.41E+06Loaded width of the laminate, b 6.13Poisson's ratio 0.13Buckling coefficient, K 10.6Axial Load acting over the edge of the panel. 37.35726

OUTPUTS

Effective thickness taking the load 0.5135Compressive stress for loading parallel to warp direction, Fc 87805.86 psiApllied stress, fc 70.88664 psiMargin of Safety for case 1 1237.68

1) Sandwich panel is having similar orthotropic faces and is simply supported at all edges.2) The panel is subjected to edgewise compressive loads.3) The principal axes of the orthotropic material are parallel to the edges of the panel.4) The faces have identical properties and ther respective warp directions are parallel.5) The panel is rectangular with out any cutouts.

General buckling is one of the general instability criteriae which is treated as failure of sandwich element as a whole, with face sheet, core and bonding

INTRACELL BUCKLING

A local instability failure of a facing, characterized by the buckling of facings into or out of the core cells.

Assumptions

1) Panel faces are not subjected to normal pressure.

3) The principal axes of the orthotropic material are parallel to the edges of the panel.4) The faces have identical properties and ther respective warp directions are parallel.

Assuming Loading is parallel to the warp direction

Intracell Buckling stress is given by,

Where,E - Effective Young's modulus of the face material Et - Tangent modulus of the material at Fc

d - Distance between face sheets and is given by,s- core cell size

Fcy is compression yield strength of the material

η is a function of compression yield strength of the material obtained from the graph shown below.

2) The panel is subjected to edgewise compressive loads.(Compression intracell buckling)

d=c+( t1+t22 )

F ci

η=0. 75⋅E⋅( t fs )

3 /2

η=2⋅EE+Et

Ref. Bhrun c.12.5.2.b

Facing compressive stress, fc is given by

Where N - Axial loadM - Moment

color indexinputsoutput

INPUTS

Youngs Modulus of face material in fill direction, E 7.41E+05 psiCore cell size, s 0.1875 in.Load in warp direction, N 37.35725938 lb/inMoment, M 701.885 lb.in.Core height, c 0.5 in.Thickness of the lamina undergoing compression, t1 0.0135 in.Thickness of the lamina undergoing tension, t2 0.0135 in.Constant, η, from graph Compression yield strength of the face material, Fcy 1.90E+05

OUTPUTS

Distance between face sheets, d 0.5135

1.07E+04Fcy/(Fci/η) 17.6914463Fci/Fcy --- From Graph 0.65 psiIntracell Buckling Stress, Fci 1.24E+05 psiFacing compressive stress, fc (For outer face) 1402.054872 psiFacing compressive stress, fc (For inner face) 1402.054872Margin of safety, M.S (For outer face) 87.08499757Margin of safety, M.S (For inner face) 87.08499757

Fci/η

f c=( Nt1+t2 )+( M

d . t1 )

A local instability failure of a facing, characterized by the buckling of facings into or out of the core cells.

1) Panel faces are not subjected to normal pressure.

3) The principal axes of the orthotropic material are parallel to the edges of the panel.4) The faces have identical properties and ther respective warp directions are parallel.

(Compression intracell buckling)

.

CORE SHEAR CRIMPING

This is one of the general instability failures of the composite laminate caused due tolow core shear modulus or low adhesive shear strength.

Critical Crimping load, Ncr, is given by,

Where Gxz is core shear modulus in X-Z Plane.d is Distance about which load Nx actsc is Core thickness

color indexinputsoutput

INPUTS

Core thickness, c 0.5 in.Thickness of top facing, t1 0.0135 in.Thickness of bottom facing, t2 0.0135 in.Shear modulus in X-Z plane, G13 6622 psi.Load acting on the edge, Nx 37.35726 lb/in

OUTPUTS

Distance about which load Nx acts, d 0.5135 in.Critical loading, Ncr 2619.156 lb/inMargin of Safety, MS 69.11103

Ncr=0 .75 .GXZ .( d2

c )

d=c+( t1+t22 )

FACE WRINKLING

Face wrinkling of a honeycomb sandwich element is a local instability charecterized by buckling of one or both of the load carrying faces into or away from the core.

Assumptions1) Sandwich panel is flat honeycomb structure with isotropic faces.2) The panel is subjected to uniaxial compressive loads.3) The panel is rectangular with out any cutouts.

WhereE= Youngs modulus of face material

Ecc is elastic compression modulus of core in transverse direction (E33 in general)

η is a function of compression yield strength of the material obtained from the graph shown below.

Face wrinkling stress, Ffw, for sandwich panels under compression is given by the following empirical relation.

Gxz is core shear modulus in X-Z plane (Assuming loading is in X-direction which is structurally preferred orientation).

F fw

η=0 . 43⋅(E⋅Ecc⋅Gxz )

1/3

Where,N is axial load acting on the face, lb/in.t1 - thickness of the facing undergoing compression

M - moment c - core heightd - Mean distance about which load acts given by

color indexinputsoutput

INPUTS

Axial load acting on the edge, N 37.357259 lb/inMoment causing compression, M 701.885 lb.inThickness of the facing undergoing compression, t1 0.0135 inThickness of the other facing, t2 0.0135 inCore thickness, c 0.5 inCore shear modulus in X-Z plane, Gxz 6543 psiElastic compression modulus of core, Ecc 19000 psiYoungs modulus of the face material, E 7.41E+05 psiCompression yield strength of the face material, Fcy 1.90E+05 psi

OUTPUTS

Mean distance about which load acts, d 0.5135 in

19421.766 psi

9.7828386

0.35

Maximum compressive stress on the outer face, fc 1402.0549 psi

Maximum compressive stress on the inner face, fc 1402.0549

Face wrinkling stress, Ffw 6.65E+04 psi

Maximum compressive stress on the faces, fc, is given by,

t2 - thickness of other facing (incase of unequal facing thickness)

Ffw/η

Fcy/(Ffw/η)

Ffw/Fcy --- From Graph

f c=( Nt1+t2 )+( M

d . t1 )

d=c+( t1+t22 )

Margin of safety, MoS 46.430383Margin of safety, MoS 46.430383

Face wrinkling of a honeycomb sandwich element is a local instability charecterized by buckling of one or both of the load carrying faces into or away from the core.

1) Sandwich panel is flat honeycomb structure with isotropic faces.2) The panel is subjected to uniaxial compressive loads.3) The panel is rectangular with out any cutouts.

, Ffw, for sandwich panels under compression is given by the following empirical relation.

(Assuming loading is in X-direction which is structurally preferred orientation).

LOCAL CORE CRUSHING

This is local instability of core caused due to insufficient compressive strength of the core due to transverse loading.

Here the compressive stress is due to local pressure loading as shown in the figure.So it is analyzed with respect to material's allowable and pressure loading.

Allowable compression strength is FzCompressive stress through area of load applied, fc, is given by

color indexinputsoutput

INPUTS

Applied load, P 100 lbArea of appilcation, A 2 sq. inAllowable compression strength, Fz 260 psi

OUTPUTS

Pressure applied locally, p 50 psiMargin of Safety, MS 4.2

FC=PA

=pAA

=p

Where… p=pressure

This is local instability of core caused due to insufficient compressive strength of the core due to transverse loading.

FLEXURAL CORE CRUSHING

Flexural core crushing is due to bending which causes inadequate core compression strength.

Here the loading is due to maximum bending moment that happens due to flexural loading.The applied flexural core crushing stress is given by,

Where,

Flexural rigidity of panel, D, is nothing but the panel bending stiffness given by,

Where,

Margin of Safety is given by,

f cc=(Mmax )2

b2 dD

Mmax=Maximum bending moment

b=Width = 1 (Assuming unit width )d=Distance between facesD=Flexural rigidity of panel

D= d2

(1−μw μ fEx t )1

+( 1−μw μ fEx t )2

d=Distance between facesheetst= Thickness of each facesheetμw= Poisson's ratio of each facesheet in the warp directionμ f=Poisson's ratio of each facesheet in the fill directionEx=Elastic modulus of each facesheet parallel to the loading direction

MS.cc=(Fcc

f cc)−1

d=c+( t1+t22 )

Where,

Fcc is allowable core crushing strength of the material.Also fcc which is calculated above has to be taken as sum of both the X and Y directions since loading is possible in both the directions.

color indexinputsoutput

INPUTS

Maximum bending moment, M 701.885core thickness, c 0.5thickness, t1 0.0135thickness, t2 0.0135Poisson's ratio of face material in warp direction, Mw 0.13Poisson's ratio of face material in fill direction, Mf 0.13Young's modulus of the face material in loading direction, Ex 7.41E+05Allowable core crushing strength of the material, Fcc 260

OUTPUTS

distance between face sheets, d 0.5135Flexural rigidity, D 1341.891Applied flexural core crushing stress, fcc 714.9477Margin of safety, MS -0.636337

MS.cc=(Fcc

f cc)−1

Flexural core crushing is due to bending which causes inadequate core compression strength.

Also fcc which is calculated above has to be taken as sum of both the X and Y directions since loading is possible in both the directions.

INTER RIVET BUCKLING

Buckling of skin between fasteners attaching the stiffener to the skin is termed as Inter-rivet buckling.

color indexinputsoutput

INPUTS

Axial Load due to wing bending, eb_Axial 373.57259 lb/in.End fixity coefficient, c 2.3Fastener pitch (Spacing), s 1 in.Thickness of the Skin, t 0.1 in.Compressive yield stress, Fcy 13402 psiTangent Modulus of skin at Fir, Et 1666989 psi

OUTPUTS

Edge band stress (span wise), Fx_EB 3735.7259 psiRaduis of gyration of skin, Rho 0.029 in.Allowable Inter-rivet buckling Stress, Fir 31791.854 psiAllowable Inter-rivet buckling Stress(Conservative) 13402 psiMargin of Safety, MS 2.5875223

F ir=cπ2E t(s / ρ)2

Buckling of skin between fasteners attaching the stiffener to the skin is termed as Inter-rivet buckling.

CORE SHEAR

Core shear is caused due to insufficient core shear strength or panel thickness.

This is generally maximum at the mid span of the panel.

Applied shear stress has to be calculated in Spanwise and chordwise edges of the panel.

Chordwise:

X-Z Direction

Spanwise:

Y-Z Direction

Margin of safety for span and chordwise has to be evaluated by using,

color indexinputsoutput

INPUTS

f cs .S=q yt c

f cs .C=qxt c

MScs=F xz

f xz−1

Shear force acting in X-Z Dir. 3.51834 lb/in.Shear force acting in Y-Z Dir. 1.328516 lb/in.Core thickness 0.5 in.Allowable core shear stress 143.24 psiAllowable core shear stress 75.994 psi

OUTPUTS

Maximum transverse shear stress 7.03668 psiApplied shear stress chordwise 7.03668 psiApplied shear stress spanwise 2.657032 psiMargin of safety, MS, Chordwise 19.35619Margin of safety, MS, Spanwise 27.60108

SHEAR OUT

Fastener shear out occurs due to insuffucient distance from panel edge to fastener line.

Applied shear stress is given by,

whereP is appied loadA is area of c/s given by, (Refer Fig. shown above)wheret is thickness of the laminatec is distance from panel edge to fastener line

Allowable shear stress is given by,

Ccsk is countersunk factor=0.92

Margin of safety,

Ks is shear notch factor that depends on stacking sequence (Assuming Ks=1)

s

CSKsalls K

Cff

..

τ=PAs

A s=2. t .c

MSfso=f s .all

τ−1

color indexinputsoutput

INPUTS

Applied Load, P 100 lbFastener distance from edge, c 0.6125 inThickness of the laminate, t 0.1 inAllowable shear stress, Fs.all 22500 psi

OUTPUTS

Applied area of the c/s, As 0.1225 sq.inApplied shear stress, Tau 816.3265 psiMargin of safety, MS 27.5625

FASTENER PULL THROUGH

Wherefxz is Core shear stresss is maximum fastener pitchd is distance between face sheets given by,

t1 and t2 are thickness of inner and outer facesheets respectivelyc is core height

This shear force Vxz creates a moment about the fastener line along the chord wise and span edges of the panel.

Vxz is Shear force acting at the edge of the panel, Vxz, given by

V xz=f xz sd

d=c+( t1+t22 )

Xc_fcl is the distance from the core edge to the fastener centerline.

And is given by,

Xfcl_e is the arm length causing moment

WherePfpt - Allowable fastener pull through strength of the laminate

color indexinputsoutput

INPUTS

Chordwise (Inbd) Distance from fastener line to panel edge 0.6125 inChordwise (Inbd) Distance from Fastener Line to core edge 1.29 inChordwise (Inbd) Distance from core edge to support edge 0.25 inChordwise (Otbd) Distance from fastener line to panel edge 0.6125 inChordwise (Otbd) Distance from Fastener Line to core edge 1.29 inChordwise (Otbd) Distance from core edge to support edge 0.25 inSpanwise (Fwd) Distance from fastener line to panel edge 0.6125 inSpanwise (Fwd) Distance from Fastener Line to core edge 1.29 inSpanwise (Fwd) Distance from core edge to support edge 0.25 inSpanwise (Aft) Distance from fastener line to panel edge 0.6525 inSpanwise (Aft) Distance from Fastener Line to core edge 1.41 inSpanwise (Aft) Distance from core edge to support edge 0.25 inChordwise Core shear stress, fxz 7.03668000223 psiSpanwise Core shear stress, fyz 2.657032071591 psi

And the Moment is given by,

The Toe load can then be determined by summing moments about the fastener line and setting the total moment to zero.

Pfast - Fastener load given by

Margin of safety for Fastener Pull through is given by

Pfast=V xz+Ptoe

M eb=xc_fclV xz

P toe=M eb

23 xfcl_e

MSfpt .=Pfpt

|Pfast|−1

(Inbd) Maximum Fastener Spacing 1 in(Otbd) Maximum Fastener Spacing 1 in(Fwd) Maximum Fastener Spacing 1 in(Aft) Maximum Fastener Spacing 1 inDistance between facesheets, d 0.5135 inAllowable fastener pull through strength 489.6 psi

OUTPUTS

Toe load distance (Inbd) 0.285 inToe load distance (Otbd) 0.285 inToe load distance (Fwd) 0.285 inToe load distance (Aft) 0.338333333333 inShear force at spanwise edge (Fwd) 1.364385968762 lbShear force at spanwise edge (Aft) 1.364385968762 lbShear force at chordwise edge (Inbd) 3.613335181145 lbShear force at chordwise edge (Otbd) 3.613335181145 lbMoment at spanwise edge (Fwd) 0.924371493836 lb.inMoment at spanwise edge (Aft) 1.033522371337 lb.inMoment at chordwise edge (Inbd) 2.448034585226 lb.inMoment at chordwise edge (Otbd) 2.448034585226 lb.inToe Load at spanwise edge (Fwd) 3.243408750303 lbToe Load at spanwise edge (Aft) 3.054745925135 lbToe Load at Chordwise edge (Inbd) 8.58959503588 lbToe Load at Chordwise edge (Otbd) 8.58959503588 lbFastener Load (Fwd) -4.607794719065 lbFastener Load (Aft) -4.419131893897 lbFastener Load (Inbd) -12.20293021703 lbFastener Load (Otbd) -12.20293021703 lbMargin of Safety (Spanwise) 109.7909905736Margin of Safety (Chordwise) 39.12151108731

t1 and t2 are thickness of inner and outer facesheets respectively

This shear force Vxz creates a moment about the fastener line along the chord wise and span edges of the panel.

can then be determined by summing moments about the fastener line and setting the total moment to zero.

FASTENER BEARING CHECK

As fasteners are assumed to be much stronger in bearing than edge band region of laminate, only edgeband is checked for bearing strength.

Margins of safety have to be calculated for bearing stress for spanwise and chordwise edges of the panel.

Bearing stress for IB/OB edges of the panel is given by,

Where,Nx is the load acting on the edge, lb/in.teb is thickness of the edgeband region, ins is maximum fastener pitch for the corresponding IB/OB edges, indf is the diameter of the fastener, in

Margin of safety in chordwise edge of the panel, MS_c is given by

Where fbr.ult is ultimate bearing strength of the material, psi

Bearing stress at forward side of the panel is given by,

Similarly, bearing stress at aft side of the panel is given by,

Margin of safety in spanwise edges of the panel, MS_s is given by

MSC=f br .ult

Max .Value (|f br . IB, f br .OB|)

f br . fwd=( f ax .eb

t eb ) .( sOB .Max

2+d fwd . fcl .e)

d f

f br .aft=( f ax .eb

t eb ) .( sOB.Max

2+daft . fcl .e)

d f

MSS=f br .ult

Max .Value|f br . fwd , f br .aft|−1

f br( IB /OB )=( N X

t eb ) . sIB /OB

d f

color indexinputsoutput

INPUTS

Load acting on the edge, Nx 37.35726 lb/inEdgeband thickness, t_eb 0.1 inMaximum fastener spacing, (Inbd) 1 inMaximum fastener spacing, (Otbd) 1 inDiameter of the fastener, df 0.1875 in(Fwd) Distance from fastener line to panel edge 0.6125 in(Aft) Distance from fastener line to panel edge 0.6525 inAxial edgeband stress 588.037 lb/inUltimate bearing strength of the material 50645 psi

OUTPUTS

Bearing stress (Inbd) 1992.387Bearing stress (Otbd) 1992.387Bearing stress (Fwd) 34890.2Bearing stress (Aft) 36144.67Margin of Safety (Chordwise) 25.41926Margin of Safety (Spanwise) 1.401175

MSS=f br .ult

Max .Value|f br . fwd , f br .aft|−1

As fasteners are assumed to be much stronger in bearing than edge band region of laminate, only edgeband is checked for bearing strength.

Margins of safety have to be calculated for bearing stress for spanwise and chordwise edges of the panel.

MSC=f br .ult

Max .Value (|f br . IB, f br .OB|)

f br . fwd=( f ax .eb

t eb ) .( sOB .Max

2+d fwd . fcl .e)

d f

f br .aft=( f ax .eb

t eb ) .( sOB.Max

2+daft . fcl .e)

d f

MSS=f br .ult

Max .Value|f br . fwd , f br .aft|−1

MSS=f br .ult

Max .Value|f br . fwd , f br .aft|−1

INTERLAMINAR SHEAR STRENGTH

Inter laminar shear stresses are treated as 1.5 times the normal load as shown in the figure below.

Interlaminar shear stresses are calculated at all free edges to design for delamination at forward, aft, inboard and outboard edges.and is given by,

Margin of Safety is given by,

Spanwise

Chordwise

Inner doubler

Inner Face sheet

Outer Face sheet

Outer doubler Ramp stages

Honeycomb Core

Edgeband

Edgeband filler

LOAD, P

f ils=1 .5 . Ptoe

teb . s

MSils . s=F intlam

Max .Value|f ils . fwd , f ils .aft|−1

MSils . c=F intlam

Max .Value|f ils . IB, f ils .OB|−1

Where, F_intlam is allowable interlaminar shear strength, psi

color indexinputsoutput

INPUTS

Toe Load at spanwise edge (Fwd) 3.243409Toe Load at spanwise edge (Aft) 3.054746Toe Load at chordwise edge (Inbd) 8.589595Toe Load at chordwise edge (Otbd) 8.589595Maximum Fastener Spacing (Fwd) 1Maximum Fastener Spacing (Aft) 1Maximum Fastener Spacing (Inbd) 1Maximum Fastener Spacing (Otbd) 1Thickness of the edgeband, t_eb 0.1Allowable interlaminar shear strength, F_intlam 4200

OUTPUTS

Interlaminar shear stress (Fwd) 48.65113Interlaminar shear stress (Aft) 45.82119Interlaminar shear stress (Inbd) 128.8439Interlaminar shear stress (Otbd) 128.8439Margin of Safety - Spanwise 86.32893Margin of Safety - Chordwise 32.59758

MSils . c=F intlam

Max .Value|f ils . IB, f ils .OB|−1

Inter laminar shear stresses are treated as 1.5 times the normal load as shown in the figure below.

Interlaminar shear stresses are calculated at all free edges to design for delamination at forward, aft, inboard and outboard edges.

Honeycomb Core

Thickness

LOAD, P