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-rw-r--r--3204/CH12/EX12.10/Ex12_10.sce49
-rw-r--r--3204/CH12/EX12.14/Ex12_14.sce14
-rw-r--r--3204/CH12/EX12.15/Ex12_15.sce29
-rw-r--r--3204/CH12/EX12.7/Ex12_7.sce14
-rw-r--r--3204/CH12/EX12.8/Ex12_8.sce32
-rw-r--r--3204/CH12/EX12.9/Ex12_9.sce32
6 files changed, 170 insertions, 0 deletions
diff --git a/3204/CH12/EX12.10/Ex12_10.sce b/3204/CH12/EX12.10/Ex12_10.sce
new file mode 100644
index 000000000..8ee58271f
--- /dev/null
+++ b/3204/CH12/EX12.10/Ex12_10.sce
@@ -0,0 +1,49 @@
+// Initilization of variables
+b1=120 // mm // width of the flange pate of L-section
+d1=20 // mm // depth of the flange plate
+b2=20 // mm // width/thickness of the web
+d2=130 // mm // depth of the web
+// Calculations
+// (a) Location of the centroid of the composite area
+A_1=b1*d1 // mm^2 // area of the flange plate
+A_2=b2*d2 // mm^2 // area of the web
+y_1=d2+(d1/2) // mm // y-coordinate of the centroid
+y_2=d2/2 // mm // y-coordinate of the centroid
+x_1=60 // mm // x-coordinate of the centroid
+x_2=110 // mm // x-coordinate of the centroid
+y_c=((A_1*y_1)+(A_2*y_2))/(A_1+A_2) // mm // from the bottom edge
+x_c=((A_1*x_1)+(A_2*x_2))/(A_1+A_2) // mm // from the bottom edge
+// (b) Moment of Inertia of the composite area about the centroidal x-axis
+// Area (A_1) M.I of area A_1 about x-axis
+I_x1=(b1*(d1^3))/12 // mm^4
+// M.I of the area A_1 about the centroidal x-axis of the composite area (By parallel-axis theorem)
+OC_1=d2+(d1/2) // mm // from the bottom edge
+OC_2=d2/2 // mm // from the bottom edge
+OC=y_c // mm // from the bottom edge
+d_1=(d2-y_c)+(d1/2) // mm
+d_2=y_c-OC_2 // mm
+I_X1=(I_x1)+(A_1*d_1^2) // mm^4
+// Area(A_2) M.I of area A_2 about x-axis
+I_x2=(b2*d2^3)/12 // mm^4
+// M.I of the area A_2 about the centroidal x-axis of the composite area (By parallel-axis theorem)
+I_X2=(I_x2)+(A_2*d_2^2) // mm^4
+// COMPOSITE AREA:M.O.I of the composite area about the centroidal x-axis
+I_x=(I_X1)+(I_X2) // mm^4
+// (c) Moment of Inertia of the composite area about the centroidal y-axis
+// Area (A_1) M.I of area A_1 about y-axis
+I_y1=(d1*(b1^3))/12 // mm^4
+// M.I of the area A_1 about the centroidal y-axis of the composite area (By parallel-axis theorem)
+d_3=x_c-(b1/2) // mm // distance between c &c1 along x axis
+I_Y1=(I_y1)+(A_1*d_3^2) // mm^4
+// Area(A_2) M.I of area A_2 about y-axis
+I_y2=(d2*b2^3)/12 // mm^4
+// M.I of the area A_2 about the centroidal y-axis of the composite area (By parallel-axis theorem)
+d_4=b1-x_c-(b2/2) // mm // distance between c &c2 along x axis
+I_Y2=(I_y2)+(A_2*d_4^2) // mm^4
+// COMPOSITE AREA:M.O.I of the composite area about the centroidal y-axis
+I_y=(I_Y1)+(I_Y2) // mm^4
+// Results
+clc
+printf('The M.O.I of the composite area about the centroidal x-axis is %f mm^4 \n',I_x)
+printf('The M.O.I of the composite area about the centroidal Y-axis is %f mm^4 \n',I_y)
+// NOTE: The answer for I_x given in text book is 0.76*10^6 insted of 10.76*10^6
diff --git a/3204/CH12/EX12.14/Ex12_14.sce b/3204/CH12/EX12.14/Ex12_14.sce
new file mode 100644
index 000000000..c615359db
--- /dev/null
+++ b/3204/CH12/EX12.14/Ex12_14.sce
@@ -0,0 +1,14 @@
+// Initilization of variables
+b=1 // cm // smaller side of the L-section
+h=4 // cm // larger side of the L-section
+// Calculations
+// (A) RECTANGLE A_1: Using the paralel axis theorem
+Ixy=0
+I_xy1=(Ixy)+((h*b)*(b/2)*(h/2)) // cm^4
+// (B) RECTANGLE A_2: Using the paralel axis theorem
+I_xy2=(Ixy)+((b*(h-1))*(1+(3/2))*(b/2)) // cm^4
+// Product of inertia of the total area
+I_xy=I_xy1+I_xy2 // cm^4
+// Calculations
+clc
+printf('The Product of inertia of the L-section is %f cm^4 \n',I_xy)
diff --git a/3204/CH12/EX12.15/Ex12_15.sce b/3204/CH12/EX12.15/Ex12_15.sce
new file mode 100644
index 000000000..3f391ca12
--- /dev/null
+++ b/3204/CH12/EX12.15/Ex12_15.sce
@@ -0,0 +1,29 @@
+// Initilization of variables
+I_x=1548 // cm^4 // M.O.I of the Z-section about X-axis
+I_y=2668 // cm^4 // M.O.I of the Z-section about Y-axis
+b=12 // cm // width of flange of the Z-section
+d=3 // cm // depth of flange of the Z-section
+t=2 // cm // thickness of the web of the Z-section
+h=6 // cm // depth of the web of the Z-section
+//Calculations
+A_1=b*d // cm^2 // area of top flange
+x_1=-5 // cm // distance of the centroid from X-axis for top flange
+y_1=4.5 // cm // distance of the centroid from Y-axis for top flange
+A_2=t*h // cm^2 // area of web
+x_2=0 // cm // distance of the centroid from X-axis for the web
+y_2=0 // cm // distance of the centroid from Y-axis for the web
+A_3=b*d // cm^2 // area of bottom flange
+x_3=5 // cm // distance of the centroid from X-axis for top flange
+y_3=-4.5 // cm // distance of the centroid from Y-axis for top flange
+// Product of Inertia of the total area is,
+I_xy=((A_1*x_1*y_1)+(A_3*x_3*y_3)) // cm^4
+// The direction of the principal axes is,
+theta_m=(atand((2*I_xy)/(I_y-I_x)))/2 // degree
+// Principa M.O.I
+I_max=((I_x+I_y)/2)+(sqrt(((I_x-I_y)/2)^2+(I_xy)^2)) // cm^4
+I_mini=((I_x+I_y)/2)-(sqrt(((I_x-I_y)/2)^2+(I_xy)^2)) // cm^4
+// Results
+clc
+printf('The principal axes of the section about O is %f degree \n',theta_m)
+printf('The Maximum value of principal M.O.I is %f cm^4 \n',I_max)
+printf('The Minimum value of principal M.O.I is %f cm^4 \n',I_mini)
diff --git a/3204/CH12/EX12.7/Ex12_7.sce b/3204/CH12/EX12.7/Ex12_7.sce
new file mode 100644
index 000000000..13059d1b9
--- /dev/null
+++ b/3204/CH12/EX12.7/Ex12_7.sce
@@ -0,0 +1,14 @@
+// Initilization of variables
+A= 50 // cm^2 // area of the shaded portion
+J_A=22.5*10^2 // cm^4 // polar moment of inertia of the shaded portion
+d=6 // cm
+// Calculations
+J_c=J_A-(A*d^2)
+// substuting the value of I_x from eq'n 2 in eq'n 1 we get,
+I_y=J_c/3 // cm^4 // M.O.I about Y-axis
+// Now from eq'n 2,
+I_x=2*I_y // cm^4 // M.O.I about X-axis
+// Results
+clc
+printf('The centroidal moment of inertia about X-axis (I_x) is %f cm^4 \n',I_x)
+printf('The centroidal moment of inertia about Y-axis (I_y) is %f cm^4 \n',I_y)
diff --git a/3204/CH12/EX12.8/Ex12_8.sce b/3204/CH12/EX12.8/Ex12_8.sce
new file mode 100644
index 000000000..1d174e15a
--- /dev/null
+++ b/3204/CH12/EX12.8/Ex12_8.sce
@@ -0,0 +1,32 @@
+// Initilization of variables
+b=20 // cm // width of the pate
+d=30 // cm // depth of the plate
+r=15 // cm // radius of the circular hole
+h=20 // cm // distance between the centre of the circle & the x-axis
+// Calculations
+// (a) Location of the centroid of the composite area
+A_1=b*d // cm^2 // area of the plate
+y_1=d/2 // cm // y-coordinate of the centroid
+A_2=(%pi*r^2)/4 // cm^2 // area of the circle removed (negative)
+y_2=h // cm // y-coordinate of the centroid
+y_c=((A_1*y_1)-(A_2*y_2))/(A_1-A_2) // cm // from the bottom edge
+// (b) Moment of Inertia of the composite area about the centroidal x-axis
+// Area (A_1) M.I of area A_1 about x-axis
+I_x1=(b*(d^3))/12 // cm^4
+// M.I of the area A_1 about the centroidal x-axis of the composite area (By parallel-axis theorem)
+OC_1=15 // cm // from the bottom edge
+OC_2=20 // cm
+OC=12.9 // cm // from the bottom edge
+d_1=OC_1-OC // cm
+d_2=OC_2-OC // cm
+I_X1=(I_x1)+(A_1*d_1^2) // cm^4
+// Area(A_2) M.I of area A_2 about x-axis
+I_x2=(%pi*r^4)/64 // cm^2
+// M.I of the area A_2 about the centroidal x-axis of the composite area (By parallel-axis theorem)
+I_X2=(I_x2)+(A_2*d_2^2) // cm^4
+// COMPOSITE AREA:M.O.I of the composite area about the centroidal x-axis
+I_x=(I_X1)-(I_X2) // cm^4
+// Results
+clc
+printf('The M.O.I of the composite area about the centroidal x-axis is %f cm^4 \n',I_x)
+// There may be a small error in the answer due to decimal point discrepancy
diff --git a/3204/CH12/EX12.9/Ex12_9.sce b/3204/CH12/EX12.9/Ex12_9.sce
new file mode 100644
index 000000000..b20336816
--- /dev/null
+++ b/3204/CH12/EX12.9/Ex12_9.sce
@@ -0,0 +1,32 @@
+// Initilization of variables
+b1=80 // mm // width of the flange pate
+d1=20 // mm // depth of the flange plate
+b2=40 // mm // width/thickness of the web
+d2=60 // mm // depth of the web
+// Calculations
+// (a) Location of the centroid of the composite area
+A_1=b1*d1 // mm^2 // area of the flange plate
+y_1=d2+(d1/2) // mm // y-coordinate of the centroid
+A_2=b2*d2 // mm^2 // area of the web
+y_2=d2/2 // mm // y-coordinate of the centroid
+y_c=((A_1*y_1)+(A_2*y_2))/(A_1+A_2) // mm // from the bottom edge
+// (b) Moment of Inertia of the composite area about the centroidal x-axis
+// Area (A_1) M.I of area A_1 about x-axis
+I_x1=(b1*(d1^3))/12 // mm^4
+// M.I of the area A_1 about the centroidal x-axis of the composite area (By parallel-axis theorem)
+OC_1=70 // mm // from the bottom edge
+OC_2=30 // mm // from the bottom edge
+OC=y_c // mm // from the bottom edge
+d_1=(d2-y_c)+(d1/2) // mm
+d_2=y_c-OC_2 // mm
+I_X1=(I_x1)+(A_1*d_1^2) // mm^4
+// Area(A_2) M.I of area A_2 about x-axis
+I_x2=(b2*d2^3)/12 // mm^4
+// M.I of the area A_2 about the centroidal x-axis of the composite area (By parallel-axis theorem)
+I_X2=(I_x2)+(A_2*d_2^2) // mm^4
+// COMPOSITE AREA:M.O.I of the composite area about the centroidal x-axis
+I_x=(I_X1)+(I_X2) // mm^4
+// Results
+clc
+printf('The M.O.I of the composite area about the centroidal x-axis is %f mm^4 \n',I_x)
+// NOTE: The answer given in the text book is 2.31*10^3 insted of 2.31*10^6.
generated by cgit (git 2.34.1) at 2024-12-20 19:20:37 +0000