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+clear
+//
+//
+
+//Initilization of Variables
+
+d_o=500 //mm //Outer Diameter
+r_o=250 //mm //Outer Radius
+d1=300 //mm //Inner Diameter
+r1=150 //mm //Inner Radius
+d2=400 //mm //Junction Diameter
+E=2*10**5 //N/mm**2 //Modulus ofElasticity
+alpha=12*10**-6 //Per degree celsius
+dell_d=0.2 //mm
+dell_r=0.1 //mm
+
+//Calculations
+
+//Let p be the radial pressure developed at junction
+//Let Lame's Equation for internal cyclinder be
+//p_x=b*(x**2)**-1-a   ................................(1)
+//F_x=b*(x**2)**-1+a     ...............................(2)
+
+//At 
+x=150 //mm 
+p_x=0
+//Sub in equation 1 we get
+//0=b*(150**2)**-1-a    .........................(3)
+
+//At 
+x2=200 //mm
+//p_x2=p
+//p=b*(200**2)**-1-a    ......................(4)
+  
+//From Equation 3 and 4
+//p=b*(200**2)**-1-b(150**2)**-1
+//after further simplifying we get
+//b=-51428.571*p
+
+//sub in equation 3 we get
+//a1=-2.2857*p
+
+//therefore hoop stress at junction is
+//F_2_1=-21428.571*p*(200**2)**-1-2.2857*p
+//after Further simplifying we geet
+//F_2_1=3.5714*p
+
+//Let Lame's Equation for cyclinder be 
+//p_x=b*(x**2)**-1-a    .........................5
+//F_x=b*(x**2)**-1+a   .............................6
+
+//At 
+x=200 //mm
+//p_x=p2
+//p2=b2*(20**2)**-1-a2    ...................7
+
+//At
+x2=200 //mm
+p_x2=0
+//0=b2*(250**2)**-1-a2    ....................8
+
+//from equation 7 and 8 we get
+//p2=b2*(200**2)**-1-b2*(250**2)**-1
+//After further simplifying we get
+//p2=b2*(250**2-200**2)*(200**2*250**2)**-1
+//b2=111111.11*p
+
+//from equation 7
+//a2=b2*(250**2)**-1
+//further simplifying we get
+//a2=1.778*p
+
+//At the junctionhoop stress in outer cyclinder 
+//F_2_0=b2*(200**2)**-1+a2
+//After further simplifying we get
+//F_2_0=4.5556*p
+
+//Considering circumferential strain,the compatibility condition
+//rho_r*r2**-1=1*E**-1*(F_2_1+F_2_0)
+//where F_2_1 is compressive and F_2_0 is tensile
+//furter simplifying we get
+p=0.1*200**-1*2*10**5*(3.5714+4.5556)**-1
+
+//Let T be the rise in temperature required
+//dell_d=d*alpha*T
+//After sub values and further simplifying we get
+d=250 //mm
+T=dell_d*(d*alpha)**-1 //Per degree celsius
+
+//Result
+printf("\n Radial Pressure Developed at junction %0.2f  N/mm**2",p)
+printf("\n Min Temperatureto outer cyclinder %0.2f  Per degree Celsius",T)