diff options
Diffstat (limited to '3456/CH2')
| -rw-r--r-- | 3456/CH2/EX2.1/Ex2_1.sce | 19 | ||||
| -rw-r--r-- | 3456/CH2/EX2.2/Ex2_2.sce | 13 | ||||
| -rw-r--r-- | 3456/CH2/EX2.3/Ex2_3.sce | 15 | ||||
| -rw-r--r-- | 3456/CH2/EX2.4/Ex2_4.sce | 29 |
4 files changed, 76 insertions, 0 deletions
diff --git a/3456/CH2/EX2.1/Ex2_1.sce b/3456/CH2/EX2.1/Ex2_1.sce new file mode 100644 index 000000000..024ebaa28 --- /dev/null +++ b/3456/CH2/EX2.1/Ex2_1.sce @@ -0,0 +1,19 @@ +//Example 2.1
+//State of Stress in two dimensions
+//Page No. 25
+clc;clear;close;
+
+sigma_x=25; //no unit
+sigma_y=5; //no unit
+theta=45; //in degrees
+sigma_x_=50; //in Mpa
+T_x_y_=5; //in Mpa
+A=[(sigma_x+sigma_y)/2+(sigma_x-sigma_y)/2*cosd(2*theta),sind(2*theta);(sigma_y-sigma_x)/2*sind(2*theta),cosd(2*theta)];
+B=[sigma_x_;T_x_y_];
+X=inv(A)*B;
+p=X(1);
+T_xy=X(2);
+sigma_x1=sigma_x*p;
+sigma_y1=sigma_y*p;
+sigma_y_=sigma_x1+sigma_y1-sigma_x_;
+printf('\nsigma_x= %g MPa\nsigma_y= %g MPa\nT_xy= %g MPa\nsigma_y`= %g MPa',sigma_x1,sigma_y1,T_xy,sigma_y_);
diff --git a/3456/CH2/EX2.2/Ex2_2.sce b/3456/CH2/EX2.2/Ex2_2.sce new file mode 100644 index 000000000..adbd12766 --- /dev/null +++ b/3456/CH2/EX2.2/Ex2_2.sce @@ -0,0 +1,13 @@ +//Example 2.2
+//State of Stress in three dimensions
+//Page No. 29
+clc;clear;close;
+
+s=poly(0,'s')
+A=[s-0,-240,0;-240,s-200,0;0,0,s+280]; //in Mpa
+p=determ(A);
+X=roots(p);
+for i=1:3
+ printf('\nsigma%i = %g MPa',i,X(i));
+end
+printf('\n\nLogic: The matrix provided in the book is a state of stress of a body which includes a combination of normal and shear stresses acting in a triaxial direction. So the determinant of the matrix results in the cubic equation in ""sigma"" which when solved gives the principal stresses');
diff --git a/3456/CH2/EX2.3/Ex2_3.sce b/3456/CH2/EX2.3/Ex2_3.sce new file mode 100644 index 000000000..4c0b75afb --- /dev/null +++ b/3456/CH2/EX2.3/Ex2_3.sce @@ -0,0 +1,15 @@ +//Example 2.3
+//Calculation of Stresses from elastic strains
+//Page No. 52
+clc;clear;close;
+
+E=200; //in GPa
+nu=0.33; //no unit
+e1=0.004; //no unit
+e2=0.001; //no unit
+sigma1=E*(e1+nu*e2)/(1-nu^2);
+sigma2=E*(e2+nu*e1)/(1-nu^2);
+sigma1=sigma1*1000; //conversion to MPa
+sigma2=sigma2*1000; //conversion to MPa
+printf('\nsigma1 = %g MPa\nsigma2 = %g MPa\n',sigma1,sigma2);
+printf('\nNote: Slight calculation errors in Book')
diff --git a/3456/CH2/EX2.4/Ex2_4.sce b/3456/CH2/EX2.4/Ex2_4.sce new file mode 100644 index 000000000..1a877cf24 --- /dev/null +++ b/3456/CH2/EX2.4/Ex2_4.sce @@ -0,0 +1,29 @@ +//Example 2.4
+//Elastic Anisotropy
+//Page No. 60
+clc;clear;close;
+
+S11_Fe=0.8; //in 1/Pa
+S12_Fe=-0.28; //in 1/Pa
+S44_Fe=0.86; //in 1/Pa
+S11_W=0.26; //in 1/Pa
+S12_W=-0.07; //in 1/Pa
+S44_W=0.66; //in 1/Pa
+D_100_l=1;
+D_100_m=0;
+D_100_n=0;
+D_110_l=1/sqrt(2);
+D_110_m=1/sqrt(2);
+D_110_n=0;
+D_111_l=1/sqrt(3);
+D_111_m=1/sqrt(3);
+D_111_n=1/sqrt(3);
+
+printf('\nFor Iron:\n\n');
+Fe_E_111=1/(S11_Fe-2*((S11_Fe-S12_Fe)-S44_Fe/2)*(D_111_l^2*D_111_m^2+D_111_n^2*D_111_m^2+D_111_l^2*D_111_n^2));
+Fe_E_100=1/(S11_Fe-2*((S11_Fe-S12_Fe)-S44_Fe/2)*(D_100_l^2*D_100_m^2+D_100_n^2*D_100_m^2+D_100_l^2*D_100_n^2));
+printf('E_111 = %g x 10^11 Pa\nE_100 = %g x 10^11 Pa\n',Fe_E_111,Fe_E_100);
+printf('\n\n\nFor Tungten:\n\n');
+W_E_111=1/(S11_W-2*((S11_W-S12_W)-S44_W/2)*(D_111_l^2*D_111_m^2+D_111_n^2*D_111_m^2+D_111_l^2*D_111_n^2));
+W_E_100=1/(S11_W-2*((S11_W-S12_W)-S44_W/2)*(D_100_l^2*D_100_m^2+D_100_n^2*D_100_m^2+D_100_l^2*D_100_n^2));
+printf('E_111 = %g x 10^11 Pa\nE_100 = %g x 10^11 Pa\n\nTherefore tungsten is elastically isotropic while iron is elasitcally anisotropic',W_E_111,W_E_100);
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