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| author | prashantsinalkar | 2017-10-10 12:27:19 +0530 |
|---|---|---|
| committer | prashantsinalkar | 2017-10-10 12:27:19 +0530 |
| commit | 7f60ea012dd2524dae921a2a35adbf7ef21f2bb6 (patch) | |
| tree | dbb9e3ddb5fc829e7c5c7e6be99b2c4ba356132c /3705/CH14/EX14.4/Ex14_4.sce | |
| parent | b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b (diff) | |
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initial commit / add all books
Diffstat (limited to '3705/CH14/EX14.4/Ex14_4.sce')
| -rw-r--r-- | 3705/CH14/EX14.4/Ex14_4.sce | 58 |
1 files changed, 58 insertions, 0 deletions
diff --git a/3705/CH14/EX14.4/Ex14_4.sce b/3705/CH14/EX14.4/Ex14_4.sce new file mode 100644 index 000000000..e6028d7f9 --- /dev/null +++ b/3705/CH14/EX14.4/Ex14_4.sce @@ -0,0 +1,58 @@ + +clear//
+
+//Variable Declaration
+t=30 //Thickness in mm
+h=200 //Depth of the section in mm
+w=160 //Width in mm
+the=50 //Angle in degrees
+
+
+//Calculations
+A1=t*h //Area of the web portion in mm^2
+A2=(w-t)*t //Area of the flange portion in mm^2
+x_bar=(A1*t*0.5+A2*(t+(w-t)*0.5))/(A1+A2) //Location of x_bar in mm
+y_bar=(A1*h*0.5+A2*t*0.5)/(A1+A2) //Location of y_bar in mm
+
+//Simplfying the computation
+a=t*h**3*12**-1
+b=A1*(200*0.5-y_bar)**2
+c=(w-t)*t**3*12**-1
+d=A2*(t*0.5-y_bar)**2
+Ix_bar=a+b+c+d //Moment of inertia about x-axis in mm^4
+
+//Simplifying the computation
+p=h*t**3*12**-1
+q=A1*(t*0.5-x_bar)**2
+r=t*(w-t)**3*12**-1
+s=A2*((w-t)*0.5+t-x_bar)**2
+Iy_bar=p+q+r+s //Moment of inertia about y-axis in mm^4
+
+//Simplfying the computation
+a1=(t*0.5-x_bar)*(h*0.5-y_bar)
+a2=(t*0.5-y_bar)*((w-t)*0.5+t-x_bar)
+Ixy_bar=A1*a1+A2*a2 //Moment of inertia in mm^4
+
+//Part 1
+//Simplfying the computation
+a3=(Ix_bar+Iy_bar)*0.5
+a4=(0.5*(Ix_bar-Iy_bar))**2
+a5=Ixy_bar**2
+I1=a3+sqrt(a4+a5) //Moment of inertia in mm^4
+I2=a3-sqrt(a4+a5) //Moment of inertia in mm^4
+
+ThetaRHS=-(2*Ixy_bar)/(Ix_bar-Iy_bar) //RHS of the tan term
+theta1=atan(ThetaRHS)*0.5*180*%pi**-1 //Angle in degrees
+theta2=theta1+90 //Angle in degrees
+
+//Part 2
+Iu=a3+sqrt(a4)*cos(2*the*%pi*180**-1)-(Ixy_bar)*sin(2*the*%pi*180**-1) //Moment of inertia in mm^4
+Iv=a3-sqrt(a4)*cos(2*the*%pi*180**-1)+(Ixy_bar)*sin(2*the*%pi*180**-1) //Moment of inertia in mm^4
+Iuv=sqrt(a4)*sin(2*the*%pi*180**-1)+(Ixy_bar)*cos(2*the*%pi*180**-1) //Moment of inertia in mm^4
+
+
+//Result
+printf("\n The Principal Moment of inertias are as follows")
+printf("\n I1= %0.0f mm^4 and I2= %0.0f mm^4",I1,I2)
+printf("\n Princial direction are theta1= %0.1f degrees theta2= %0.1f degrees",theta1,theta2)
+printf("\n The moment of inertia along the uv-axis is %0.0f mm^4" ,Iuv)
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