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clear
//
//
//Initilization of Variables
//Strains
e_A=600 //microns
e_B=-450 //microns
e_C=100 //micron
E=2*10**5 //N/mm**2 //Modulus of Elasticity
mu=0.3 //Poissons ratio
theta=240
//Calculations
e_x=600
e_A=600
//e_A=(e_x+e_y)*2**-1+(e_x-e_y)*2**-1*cos(theta)+rho_x_y*2**-1*sin(theta)
//After sub values and further simplifying we get
//-450=(e_x+e_y)*2**-1-(e_x-e_y)*2**-1*(0.5)-0.866*2**-1*rho_x_y .....................(1)
//e_C=(e_x+e_y)*2**-1+(e_x-e_y)*2**-1*cos(2*theta)+rho_x_y*2**-1*sin(2*theta)
//After sub values and further simplifying we get
//100=(e_x+e_y)*2**-1-0.5*(e_x-e_y)*2**-1*(0.5)-0.866*2**-1*rho_x_y .....................(2)
//Adding Equation 1 and 2 we get equations as
//-350=e_x+e_y-(e_x-e_y)*2**-1 ...............(3)
//Further simplifying we get
e_y=(-700-e_x)*3**-1 //micron
rho_x_y=(e_C-(e_x+e_y)*2**-1-(e_x-e_y)*2**-1*cos(2*theta*%pi*180**-1))*(sin(2*theta*%pi*180**-1))**-1*2 //micron
//Principal strains
e1=(e_x+e_y)*2**-1-(((e_x-e_y)*2**-1)**2+(rho_x_y*2**-1)**2)**0.5 //microns
e2=(e_x+e_y)*2**-1+(((e_x-e_y)*2**-1)**2+(rho_x_y*2**-1)**2)**0.5 //microns
//Principal Stresses
sigma1=E*(e1+mu*e2)*(1-mu**2)**-1*10**-6 //N/mm**2
sigma2=E*(e2+mu*e1)*(1-mu**2)**-1*10**-6 //N/mm**2
//Result
printf("\n Principal Stresses are:sigma1 %0.2f N/mm**2",sigma1)
printf("\n :sigma2 %0.2f N/mm**2",sigma2)
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