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clear
//
//
//Initilization of Variables
F=40*10**3 //N //Shear Force
M=20*10**6 //Bending Moment
//Rectangular section
b=100 //mm //Width
d=200 //mm //Depth
x=20 //mm //Distance from Top surface upto point
y=80 //mm //Distance from point to Bottom
//Calculations
I=1*12**-1*b*d**3 //mm**4 //M.I
//At 20 mm Below top Fibre
f_x=M*I**-1*y //N/mm**2 //Stress
//Assuming sagging moment ,f_x is compressive p_x=f_x=-24 //N/mm**2
f_x=-24 //N/mm**2
p_x=-24
//Shearing stress
q=F*(b*I)**-1*(b*x*(b-x*2**-1)) //N/mm**2
//Direct stresses
p_y=0 //N/mm**2
p1=(p_x+p_y)*2**-1+(((p_x+p_y)*2**-1)**2+q**2)**0.5 //N/mm**2
p2=(p_x+p_y)*2**-1-(((p_x+p_y)*2**-1)**2+q**2)**0.5 //N/mm**2
//Result
printf("\n Directions of principal stresses at a point below 20mm is: %0.2f N/mm**2",p1)
printf("\n %0.2f N/mm**2",p2)
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