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WING SPAR IN CARBON/EPOXY
Subject: Mechanics of Composite
Submitted to: DR. S. KAMRAN AFAQ
Submitted by: IMRAN SAJID SHAHID
ROLL NO: 12SP-MS-ME-002
Deaprtment of Mechanical Engineering
HITECH University Taxila
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Problem Statement:
Consider an airplane with the internal structure (excluding facings) shown
schematically in the following figure. It consists of a spar and several ribs. The spar is a
lmaniate of carbon/epoxy fabric with Vf=45% fiber volume fraction, the composition of
which varies with longitudinal coordinate x-axis in the flange and in the web. Apreliminary calculation of the flap in isostatic equilibrium reveals the maximum stress
resultant in the zones of the spar indicated in the figure. One proposes for each of these
zones of the composition indicated in the figure below.
1. Evaluate the elastic properties of the laminate in these two zones.
2. Verify the two corresponding laminates at rupture strength.
Thickness of layer of fabric is 0.24mm and Properties of carbon/epoxy fabric are;
EL [MPa] 54000
ET [MPa] 54000
GLT [MPa] 4000
LT 0.045
+Xt [MPa] 420
-Xt [MPa] 360
+Yt [MPa] 420
-Yt [MPa] 360
S [MPa] 55
[kg/m3] 1450
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GLOBAL STRAINS AND PLY STRESSES:
Global Strain can be calculated as:
{0} xy = [Sbar]avg
}xy
Since,
0
x= Nx / (N.L.* 0.24mm)
{0}xy Matrix becomes:
[-202 ; 0.0 ; 0.0 ]
Calculate {s}xy in each ply 00
and 450
plies:
{}xy = [Qbar] {0} xy
Transformed {s}xy in orthotropic axes of ply, by using:
{}LT = [T] {0}xy
Where,
[T] = Transformation Matrix
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MATLAB Results are:
RUPTURE STRENGTH:
Using Hill-Tasi Failure criterion for both layers
Factor of Safety for both plies can be calculated by :
Ply with lowest Safety Factor will FAIL first.
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MATLAB Results are:
2 ZONE-2:
ELASTIC MODULII CALCUALTION:
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GLOBAL STRAINS AND PLY STRESSES:
RUPTURE STRENGTH:
MATLAB PROGRAMM FOR ELASTIC MODULII & RUPTURE STRENGTH:
First part will do calculations for flanges:
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clc
clear all
% Term Project Carbon/Epoxy Flap Spar design
% --------------------INPUT DECK-------------------------------
Nx = -435; % Applied Force in x-dir
Nxy = -30 % Applied Force in xy-dir
deg0_ply=67; % Layers percentage in 0degree
deg90_ply=0; % Layers percentage in 90degree
degpplus45_ply=33; % Layers percentage in 45degree
degminus45_ply=0; % Layers percentage in -45degree
% Material Properties and Strengths
E_L = 54000; E_T=54000; G_LT=4000; v_LT=0.045; V_f=45/100;
X_t = 420;
Y_t = 420;
X_c = 360;
Y_c = 360;
S_tc = 55;
e = 0.24; % Thickness of single bidirectional Carbon/Epoxy ply
NL_F = 9; % Number of Layers in Flange
NL_W = 5; % Number of Layers in Web
%--------------------------------------------------------------------------------------------------------------------------------------
S = C_M( E_L,E_T,G_LT,v_LT ); % Compliance Matrix
Q = inv(S); % Rigidity Matrix
Q_avg=(Qbar(Q,0)*deg0_ply/100)+(Qbar(Q,90)*deg90_ply/100)+ ...
(Qbar(Q,45)*degpplus45_ply/100)+(Qbar(Q,-45)*degminus45_ply/100);
S_avg = inv(Q_avg);
Ex=1/S_avg(1,1); % Global Modulii Properties
Ey=1/S_avg(2,2);
Gxy=1/S_avg(3,3);
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vxy=-1*(S_avg(1,2)/S_avg(1,1));
vyx=-1*(S_avg(1,2)/S_avg(2,2));
disp('[Qbar]avg Matrix =')
disp(Q_avg)
disp('[Sbar]avg Matrix =')
disp(S_avg)
disp('Longitudinal Young Modulus of Laminate =')
disp(Ex)
disp('Transverse Young Modulus of Laminate =')
disp(Ey)
disp('Shear Modulus of Laminate =')
disp(Gxy)
disp('Major Poissons ratio =')
disp(vxy)
disp('Minor Poissons ratio =')
disp(vyx)
%
h_F = e * NL_F; % height of a laminate
sigma_oxy_F = [Nx/h_F; 0; 0]; % Global Stresses in xy
epsilon_oxy_F = S_avg * sigma_oxy_F; % Global Strains in xy
sigma_xy_090_F = Qbar(Q,0) * epsilon_oxy_F; % Ply stresses in 0/90 deg layers in xy dir
sigma_LT_090_F = TransformationMatrix(0) * sigma_xy_090_F; % Ply stresses in 0/90 deg layers in LT(material) dir
sigma_xy_45_F = Qbar(Q,45) * epsilon_oxy_F; % Ply stresses in 45 deg layers in xy dir
sigma_LT_45_F = TransformationMatrix(45) * sigma_xy_45_F; % Ply stresses in 45 deg layers in LT(material) dir
% Hill-Tasi Failure Criterion for 0/90 plies
HT_090_F = (sigma_LT_090_F(1,1)/X_c)^2+(sigma_LT_090_F(2,1)/Y_t)^2- ...
(sigma_LT_090_F(1,1)*sigma_LT_090_F(2,1)/X_c^2)+ ...
(sigma_LT_090_F(3,1)/S_tc)^2;
FOS_090_F = (( 1/(HT_090_F)) - 1) *100;
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Second part will do calculations for Web:
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clc
clear all
% Term Project Carbon/Epoxy Flap Spar design
% --------------------INPUT DECK-------------------------------
Nx = -435; % Applied Force in x-dir
Nxy = -30 % Applied Force in xy-dir
deg0_ply=40; % Layers percentage in 0degree
deg90_ply=0; % Layers percentage in 90degree
degpplus45_ply=60; % Layers percentage in 45degree
degminus45_ply=0; % Layers percentage in -45degree
% Material Properties and Strengths
E_L = 54000; E_T=54000; G_LT=4000; v_LT=0.045; V_f=45/100;
X_t = 420;
Y_t = 420;
X_c = 360;
Y_c = 360;
S_tc = 55;
e = 0.24; % Thickness of single bidirectional Carbon/Epoxy ply
NL_F = 9; % Number of Layers in Flange
NL_W = 5; % Number of Layers in Web
%--------------------------------------------------------------
S = C_M( E_L,E_T,G_LT,v_LT ); % Compliance Matrix
Q = inv(S); % Rigidity Matrix
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Q_avg=(Qbar(Q,0)*deg0_ply/100)+(Qbar(Q,90)*deg90_ply/100)+ ...
(Qbar(Q,45)*degpplus45_ply/100)+(Qbar(Q,-45)*degminus45_ply/100);
S_avg = inv(Q_avg);
Ex=1/S_avg(1,1); % Global Modulii Properties
Ey=1/S_avg(2,2);
Gxy=1/S_avg(3,3);
vxy=-1*(S_avg(1,2)/S_avg(1,1));
vyx=-1*(S_avg(1,2)/S_avg(2,2));
disp('[Qbar]avg Matrix =')
disp(Q_avg)
disp('[Sbar]avg Matrix =')
disp(S_avg)
disp('Longitudinal Young Modulus of Laminate =')
disp(Ex)
disp('Transverse Young Modulus of Laminate =')
disp(Ey)
disp('Shear Modulus of Laminate =')
disp(Gxy)
disp('Major Poissons ratio =')
disp(vxy)
disp('Minor Poissons ratio =')
disp(vyx)
%
h_W = e * NL_W; % height of a laminate
sigma_oxy_W = [0; 0; Nxy/h_W]; % Global Stresses in xy
epsilon_oxy_W = S_avg * sigma_oxy_W; % Global Strains in xy
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sigma_xy_090_W = Qbar(Q,0) * epsilon_oxy_W; % Ply stresses in 0/90 deg layers in xy dir
sigma_LT_090_W = TransformationMatrix(0) * sigma_xy_090_W; % Ply stresses in 0/90 deg layers in
LT(material) dir
sigma_xy_45_W = Qbar(Q,45) * epsilon_oxy_W; % Ply stresses in 45 deg layers in xy dir
sigma_LT_45_W = TransformationMatrix(45) * sigma_xy_45_W; % Ply stresses in 45 deg layers in
LT(material) dir
% Hill-Tasi Failure Criterion for 0/90 plies
HT_090_W = (sigma_LT_090_W(1,1)/X_c)^2+(sigma_LT_090_W(2,1)/Y_t)^2- ...
(sigma_LT_090_W(1,1)*sigma_LT_090_W(2,1)/X_c^2)+ ...
(sigma_LT_090_W(3,1)/S_tc)^2;
FOS_090_W = (( 1/(HT_090_W)) - 1)*100;
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