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authorpriyanka2015-06-24 15:03:17 +0530
committerpriyanka2015-06-24 15:03:17 +0530
commitb1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b (patch)
treeab291cffc65280e58ac82470ba63fbcca7805165 /1898/CH9
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Diffstat (limited to '1898/CH9')
-rwxr-xr-x1898/CH9/EX9.1/Ex9_1.sce26
-rwxr-xr-x1898/CH9/EX9.10/Ex9_10.sce27
-rwxr-xr-x1898/CH9/EX9.11/Ex9_11.sce37
-rwxr-xr-x1898/CH9/EX9.12/Ex9_12.sce36
-rwxr-xr-x1898/CH9/EX9.13/Ex9_13.sce37
-rwxr-xr-x1898/CH9/EX9.14/Ex9_14.sce31
-rwxr-xr-x1898/CH9/EX9.15/Ex9_15.sce22
-rwxr-xr-x1898/CH9/EX9.2/Ex9_2.sce28
-rwxr-xr-x1898/CH9/EX9.5/Ex9_5.sce29
-rwxr-xr-x1898/CH9/EX9.6/Ex9_6.sce32
-rwxr-xr-x1898/CH9/EX9.9/Ex9_9.sce32
11 files changed, 337 insertions, 0 deletions
diff --git a/1898/CH9/EX9.1/Ex9_1.sce b/1898/CH9/EX9.1/Ex9_1.sce
new file mode 100755
index 000000000..f76c3b2ec
--- /dev/null
+++ b/1898/CH9/EX9.1/Ex9_1.sce
@@ -0,0 +1,26 @@
+
+clear all; clc;
+
+disp("Scilab Code Ex 9.1 : ")
+
+//Given:
+tou = 25; //MPa
+sigma1 = 50; //MPa
+sigma2 = 80; //MPa
+phi = 30*(%pi/180);
+
+// Calculations:
+sigma_x1 = (sigma1*cos(phi)*cos(phi))- (tou*cos(phi)*sin(phi)) - (sigma2*sin(phi)*sin(phi))- (tou*sin(phi)*cos(phi));
+tou1 = (sigma1*cos(phi)*sin(phi))+ (tou*cos(phi)*cos(phi)) + (sigma2*sin(phi)*cos(phi))- (tou*sin(phi)*sin(phi));
+sigma_x2 = (tou*cos(phi)*sin(phi))- (sigma2*cos(phi)*cos(phi)) + (tou*sin(phi)*cos(phi))+ (sigma1*sin(phi)*sin(phi));
+tou2 = (tou*cos(phi)*cos(phi))+ (sigma2*cos(phi)*sin(phi)) - (tou*sin(phi)*sin(phi))+ (sigma1*sin(phi)*cos(phi));
+
+//Display:
+
+printf("\n\nThe normal stress component in the x diection is = %1.2f MPa',sigma_x1);
+printf("\n The shear stress component in the x diection is = %1.1f MPa',tou1);
+printf("\n The normal stress component in the y diection is = %1.1f MPa',sigma_x2);
+printf("\n The shear stress component in the y diection is = %1.1f MPa',tou2);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
diff --git a/1898/CH9/EX9.10/Ex9_10.sce b/1898/CH9/EX9.10/Ex9_10.sce
new file mode 100755
index 000000000..4b44e4f39
--- /dev/null
+++ b/1898/CH9/EX9.10/Ex9_10.sce
@@ -0,0 +1,27 @@
+clear all; clc;
+
+disp("Scilab Code Ex 9.10 : ")
+
+//Given:
+sigma_x = -20; //MPa
+sigma_y = 90; //MPa
+tou_xy = 60; //MPa
+
+//Construction of the circle:
+sigma_avg = (sigma_x+sigma_y)/2;
+R = sqrt(((sigma_x-sigma_avg))^2 + (tou_xy)^2);
+
+//Maximum In plane Shear Stress:
+tou_max = R;
+
+theta_s1 = atan(-(sigma_x - sigma_avg)/(tou_xy));
+theta_s1 = theta_s1/2*(180/%pi);
+
+//Display:
+
+printf('\n\nThe maximum in-plane shear stresses are = %1.1f MPa',tou_max);
+printf('\n = %1.1f MPa',sigma_avg);
+printf('\nThe orientation of the element is = %1.1f degrees',theta_s1);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
diff --git a/1898/CH9/EX9.11/Ex9_11.sce b/1898/CH9/EX9.11/Ex9_11.sce
new file mode 100755
index 000000000..1312422b7
--- /dev/null
+++ b/1898/CH9/EX9.11/Ex9_11.sce
@@ -0,0 +1,37 @@
+
+clear all; clc;
+
+disp("Scilab Code Ex 9.11 : ")
+
+//Given:
+sigma_x = -8; //MPa
+sigma_y = 12; //MPa
+tou_xy = -6; //Mpa
+
+//Construction of the circle:
+sigma_avg = (sigma_x+sigma_y)/2;
+
+R = sqrt( 10^2 + tou_xy^2);
+
+//Stresses on 30 degree element:
+phi = atan(6/10);
+psi = (%pi/3) - phi;
+
+//On face BD:
+sigma_x1 = 2 - (R*cos(psi));
+tou_xy1 = (R*sin(psi));
+
+//On face DE:
+sigma_x2 = 2 + (R*cos(psi));
+tou_xy2 = -(R*sin(psi));
+
+//Display:
+
+printf('\n\nThe normal stress on plane BD inclined at 30 degrees is = %1.2f MPa',sigma_x1);
+printf('\nThe normal stress on plane DE inclined at 60 degrees is = %1.1f MPa',sigma_x2);
+printf('\nThe shear stress is = %1.2f MPa',tou_xy1);
+
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
+
diff --git a/1898/CH9/EX9.12/Ex9_12.sce b/1898/CH9/EX9.12/Ex9_12.sce
new file mode 100755
index 000000000..8ad3ea4bc
--- /dev/null
+++ b/1898/CH9/EX9.12/Ex9_12.sce
@@ -0,0 +1,36 @@
+clear all; clc;
+
+disp("Scilab Code Ex 9.12 : ")
+
+//Given:
+P = 900; //N
+T = 2.5; //Nm
+d = 40/1000; //m
+r = d/2;
+c = r;
+
+//Stress Components:
+J = (%pi/2)*(r^4);
+tou = (T*c)/(J*1000);
+
+A = (%pi*r^2);
+sigma = P/(A*1000);
+
+//Principal Stresses:
+sigma_avg = (0 + sigma)/2;
+
+R = sqrt( sigma_avg^2 + tou^2);
+sigma1 = sigma_avg + R;
+sigma2 = sigma_avg - R;
+
+//Display:
+
+printf('\n\nThe prinicpal stresses at point P are:');
+printf('\n %1.1f kPa',sigma1);
+printf('\n %1.1f kPa',sigma2);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
+
+
+
diff --git a/1898/CH9/EX9.13/Ex9_13.sce b/1898/CH9/EX9.13/Ex9_13.sce
new file mode 100755
index 000000000..06c41fee9
--- /dev/null
+++ b/1898/CH9/EX9.13/Ex9_13.sce
@@ -0,0 +1,37 @@
+clear all; clc;
+
+disp("Scilab Code Ex 9.13 : ")
+
+//Given:
+w = 120; //kN/m
+I = 67.4*(10^-6);
+V= 84; //kN
+M = 30.6; //kNm
+t = 10/1000; //m
+
+//Stress Components:
+y = 0.200/2;
+sigma = -(M*10^3*y)/(I*10^6);
+
+Q = (0.100 + 0.015/2)*(0.175)*(0.015);
+tou = (V*Q*10^3)/(I*t*10^6);
+
+//Principal Stresses:
+
+k = sigma/2;
+R = sqrt( (-sigma+k)^2 + tou^2);
+sigma1 = R + k;
+sigma2 = k -R ;
+
+theta_p2 = atan(-tou/(sigma-k));
+theta_p2 =theta_p2/2*(180/%pi);
+
+//Display:
+
+
+printf('\n\nThe prinicpal stresses at point P are:');
+printf('\n %1.1f MPa',sigma1);
+printf('\n %1.1f MPa',sigma2);
+printf('\nThe angle of rotation of the plane %1.1f degrees',theta_p2);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
diff --git a/1898/CH9/EX9.14/Ex9_14.sce b/1898/CH9/EX9.14/Ex9_14.sce
new file mode 100755
index 000000000..d27a4216b
--- /dev/null
+++ b/1898/CH9/EX9.14/Ex9_14.sce
@@ -0,0 +1,31 @@
+clear all; clc;
+
+disp("Scilab Code Ex 9.14 : ")
+
+//Given:
+tou = 40; //kPa
+sigma = -20; //kPa
+
+//Principal Stresses:
+sigma_avg = sigma/2;
+R = sqrt( (-sigma + sigma_avg)^2 + tou^2);
+sigma_max = sigma_avg + R ;
+sigma_min = sigma_avg - R ;
+
+theta = atan(tou/(-sigma+sigma_avg));
+theta = theta/2;
+
+//Absolute Maximum Shear Stress:
+tou_max = (sigma_max - sigma_min)/2;
+sigma_avg = (sigma_max + sigma_min)/2;
+
+//Display:
+
+printf('\n\nThe prinicpal stresses at the point are:');
+printf('\n %1.1f kPa',sigma_max);
+printf('\n %1.1f kPa',sigma_min);
+printf('\nThe absolute maximum shear stress at the point %1.1f kPa',tou_max);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
+
diff --git a/1898/CH9/EX9.15/Ex9_15.sce b/1898/CH9/EX9.15/Ex9_15.sce
new file mode 100755
index 000000000..1e140816e
--- /dev/null
+++ b/1898/CH9/EX9.15/Ex9_15.sce
@@ -0,0 +1,22 @@
+clear all; clc;
+
+disp("Scilab Code Ex 9.15 : ")
+
+//Given:
+sigma_max = 32; //MPa
+sigma_min = 0; //MPa
+sigma_int = 16; //MPa
+
+tou_max = (sigma_max - sigma_min)/2 ; //MPa
+sigma_avg = (sigma_max + sigma_min)/2 ; //MPa
+
+tou_in_plane = (sigma_max - sigma_int)/2;
+sigma_avg2 = sigma_avg + (tou_in_plane);
+
+//Display:
+
+printf('\n\nThe maximum absolute shear stress = %1.2f MPa',tou_max);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
+
diff --git a/1898/CH9/EX9.2/Ex9_2.sce b/1898/CH9/EX9.2/Ex9_2.sce
new file mode 100755
index 000000000..c34707ace
--- /dev/null
+++ b/1898/CH9/EX9.2/Ex9_2.sce
@@ -0,0 +1,28 @@
+clear all; clc;
+
+
+disp("Scilab Code Ex 9.2 : ")
+
+//Given:
+phi = -30*(%pi/180);
+theta = 60*(%pi/180);
+sigma_x = -80; //MPa
+sigma_y = 50; //MPa
+tou_xy = -25; //MPa
+
+//Plane CD:
+sigma_x1 = (sigma_x+sigma_y)/2 + ((sigma_x-sigma_y)*cos(2*phi))/2 + (tou_xy*sin(2*phi)); //Eqn 9.1
+tou_xy1 = ((-(sigma_x - sigma_y)*sin(2*phi))/2) + (tou_xy*cos(2*phi)); //Eqn 9.2
+
+//Plane BC:
+sigma_x2 = (sigma_x+sigma_y)/2 + ((sigma_x-sigma_y)*cos(2*theta))/2 + (tou_xy*sin(2*theta)); //Eqn 9.1
+tou_xy2 = (-(sigma_x - sigma_y)*sin(2*theta))/2 + tou_xy*cos(2*theta); //Eqn 9.2
+
+//Display:
+
+printf('\n\nThe normal stress of plane CD inclined at 30 degrees = %1.1f MPa',sigma_x1);
+printf('\nThe shear stress of plane CD inclined at 30 degrees = %1.1f MPa',tou_xy1);
+printf('\nThe normal stress of plane BC inclined at 60 degrees = %1.2f MPa',sigma_x2);
+printf('\nThe shear stress of plane BC inclined at 60 degrees = %1.1f MPa',tou_xy2);
+
+//-------------------------------------------------------------------------END---------------------------------------------------------------------------------------
diff --git a/1898/CH9/EX9.5/Ex9_5.sce b/1898/CH9/EX9.5/Ex9_5.sce
new file mode 100755
index 000000000..644aba730
--- /dev/null
+++ b/1898/CH9/EX9.5/Ex9_5.sce
@@ -0,0 +1,29 @@
+clear all; clc;
+
+disp("Scilab Code Ex 9.5 : ")
+
+//Given:
+sigma_x = -20; //MPa
+sigma_y = 90; //MPa
+tou_xy = 60; //MPa
+
+//Orientation of Element:
+theta_p2 = atan((2*tou_xy)/(sigma_x - sigma_y));
+theta_p2 = theta_p2/2;
+theta_p1 = (180+2*theta_p2)/2;
+
+//Principal Stresses:
+
+sigma1 = ((sigma_x+sigma_y)/2)+(sqrt(((sigma_x - sigma_y)/2)^2 + tou_xy^2));
+sigma2 = ((sigma_x+sigma_y)/2)- sqrt(((sigma_x-sigma_y)/2)^2 + tou_xy^2);
+sigma_x2 = ((sigma_x+sigma_y)/2)+ (((sigma_x-sigma_y)/2)*cos(2*theta_p2)) + (tou_xy*sin(2*theta_p2));
+
+//Display:
+
+printf("\n\nThe first principal stress is = %1.0f MPa',sigma1);
+printf("\nThe second principal stress is = %1.1f MPa',sigma2);
+printf('\nThe normal stress acting on the 23.7 degrees plane = %1.1f MPa',sigma_x2);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
+
diff --git a/1898/CH9/EX9.6/Ex9_6.sce b/1898/CH9/EX9.6/Ex9_6.sce
new file mode 100755
index 000000000..fba8aa647
--- /dev/null
+++ b/1898/CH9/EX9.6/Ex9_6.sce
@@ -0,0 +1,32 @@
+
+clear all; clc;
+
+disp("Scilab Code Ex 9.6 : ")
+
+//Given:
+sigma_x = -20; //MPa
+sigma_y = 90; //MPa
+tou_xy =60; //Mpa
+
+//Orientation of Element:
+theta_s2 = atan(-(sigma_x - sigma_y)/(2*tou_xy));
+theta_s2 = theta_s2/2;
+theta_s1 = %pi + 2*theta_s2;
+theta_s1 = theta_s1/2;
+
+//Maximum in plane Shear Stress:
+tou_max = (sqrt(((sigma_x - sigma_y)/2)^2 + tou_xy^2));
+tou_xy1 = -(sigma_x - sigma_y)*(sin(2*theta_s2))/2 + (tou_xy*cos(2*theta_s2));
+
+//Average Normal Stress:
+sigma_avg = (sigma_x+sigma_y)/2;
+
+//Display:
+
+printf("\n\nThe maximum in-plane shear stress is = %1.1f MPa',tou_xy1);
+printf("\nThe average normal stress is = %1.0f MPa',sigma_avg);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
+
+
diff --git a/1898/CH9/EX9.9/Ex9_9.sce b/1898/CH9/EX9.9/Ex9_9.sce
new file mode 100755
index 000000000..317baf009
--- /dev/null
+++ b/1898/CH9/EX9.9/Ex9_9.sce
@@ -0,0 +1,32 @@
+clear all; clc;
+
+disp("Scilab Code Ex 9.9 : ")
+
+//Given:
+sigma_x = -12; //MPa
+sigma_y = 0;
+tou_xy = -6; //MPa
+
+//Construction of the circle:
+sigma_avg = (sigma_x+sigma_y)/2;
+R = sqrt((-sigma_x+sigma_avg)^2 + (tou_xy)^2);
+
+//Principal Stresses:
+sigma2 = -R+sigma_avg;//From the Mohr's circle
+sigma1 = R+sigma_avg;
+
+theta_p2 = atan((-tou_xy)/(-sigma_x+sigma_avg));
+theta_p2 = theta_p2/2*(180/%pi);
+
+//Display:
+
+printf('\n\nThe first principal stress is = %1.2f MPa',sigma1);
+printf('\nThe second principal stress is = %1.1f MPa',sigma2);
+printf('\nThe direction of the principal plane is = %1.1f degrees',theta_p2);
+
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
+
+
+
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