In [1]:

```
import math
#initialisation
A1 = 6*0.5 # Partial Area in in2
A2 = 20.8 # from table E1 and E3
A3 = 8.82 # from table E1 and E3
y1 = (18.47/2.0) + (0.5/2.0) # Distance between centroid C1 and C2
y2 = 0 # Distance between centroid C2 and C2
y3 = (18.47/2.0) + 0.649 # Distance between centroid C3 and C2
#calculation
A = A1 + A2 + A3 # Area of entire cross section
Qx = (y1*A1) + (y2*A2) - (y3*A3) # First moment of entire cross section
y_bar = Qx/A # Distance between x-axis and centroid of the cross section
print "The distance between x-axis and centroid of the cross section is ", round(-y_bar,2), "inch"
```

In [2]:

```
import math
#initialisation
A1 = 6*0.5 # Partial Area in in2
A2 = 20.8 # from table E1 and E3
A3 = 8.82 # from table E1 and E3
y1 = (18.47/2.0) + (0.5/2.0) # Distance between centroid C1 and C2
y2 = 0 # Distance between centroid C2 and C2
y3 = (18.47/2.0) + 0.649 # Distance between centroid C3 and C2
#calculation
A = A1 + A2 + A3 # Area of entire cross section
Qx = (y1*A1) + (y2*A2) - (y3*A3) # First moment of entire cross section
y_bar = Qx/A # Distance between x-axis and centroid of the cross section
c_bar = -(y_bar)
I1 = (6*0.5**3)/12.0 # Moment of inertia of A1
I2 = 1170 # Moment of inertia of A2 from table E1
I3 = 3.94 # Moment of inertia of A3 from table E3
Ic1 = I1 + (A1*(y1+c_bar)**2) # Moment of inertia about C-C axis of area C1
Ic2 = I2 + (A2*(y2+c_bar)**2) # Moment of inertia about C-C axis of area C2
Ic3 = I3 + (A3*(y3-c_bar)**2) # Moment of inertia about C-C axis of area C3
Ic = Ic1 + Ic2 + Ic3 # Moment of inertia about C-C axis of whole area
print "The moment of inertia of entire cross section area about its centroidal axis C-C", round(Ic), "in^4"
```

In [3]:

```
import math
import numpy
#initialisation
Ix = 29.29e06 # Moment of inertia of crosssection about x-axis
Iy = 5.667e06 # Moment of inertia of crosssection about y-axis
Ixy = -9.336e06 # Moment of inertia of crosssection
#calculation
tp1 = (numpy.degrees(numpy.arctan((-(2*Ixy)/(Ix-Iy)))))/2.0 # Angle definig a Principle axix
tp2 = 90 + tp1
print "The Principle axis is inclined at an angle", round(tp1,2), "degree"
print "Second angle of inclination of Principle axis is", round(tp2,2), "degree"
Ix1 = (Ix+Iy)/2.0 + ((Ix-Iy)/2.0)*math.cos(math.radians(tp1)) - Ixy*math.sin(math.radians(tp1))
Ix2 = (Ix+Iy)/2.0 + ((Ix-Iy)/2.0)*math.cos(math.radians(tp2)) - Ixy*math.sin(math.radians(tp2))
print "Principle Moment of inertia corresponding to tp1", round(Ix1), "mm^4"
print "Principle Moment of inertia corresponding to tp2", round(Ix2), "mm^4"
```