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+
+clear//

+//

+

+//Variable Declaration

+E_st=200 //Youngs Modulus of Steel in GPa

+sigma_st_yp=290 //Yielding Stress in MPa

+E_al=70 //Youngs Modulus of Aluminium in GPa

+sigma_al_yp=330 //Yielding Stresss of Aluminium in MPa

+A_st=900 //Area of steel rod in mm^2

+A_al=600 //Area of Aluminium rod in mm^2

+L_st=350 //Length of the steel rod in mm

+L_al=250 //Length of the aluminium rod in mm

+

+//Calculations

+//Limit Load

+P_st=sigma_st_yp*A_st*10**-3 //Load in limiting condition in kN

+P_al=sigma_al_yp*A_al*10**-3 //Load in limiting condition in kN

+P_L=P_st+2*P_al //Total Loading in kN

+

+//Elastic Unloading

+//Solving for Pst and Pal using matri approach

+A=([[1,2;L_st*(E_st*A_st)**-1,-L_al*(E_al*A_al)**-1]])

+B=([P_L;0])

+C=linsolve(A,B) //Loading in kN

+

+//Residual Stresses

+P_res_st=-C(1)-P_st //Residual Load in kN

+P_res_al=-C(2)-P_al //Residual Load in kN

+sigma_st=P_res_st/A_st //residual Stress in Steel in MPa

+sigma_al=P_res_al/A_al //residual Stress in Aluminium in MPa

+

+

+//Result

+printf("\n The Residual stresses are as follows")

+printf("\n Sigma_st= %0.1f MPa and sigma_al= %0.1f MPa",sigma_st*10**3,sigma_al*10**3)