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+clc
+// Given that
+A = 150*6 // Cross-section of strips in mm^2
+w = 150 // Width of the strip in mm
+ti = 6 // Thickness in mm
+pA = 0.20 // Reduction in area
+d = 400 // Diameter of steel rolls in mm
+Ys = 0.35// Shear Yield stress of the material before rolling in KN/mm^2
+Ys_ = 0.4// Shear Yield stress of the material after rolling in KN/mm^2
+mu = 0.1 // Cofficient of friction
+v = 30 // Speed of rolling in m/min
+// Sample Problem 2 on page no. 113
+printf("\n # PROBLEM 3.2 # \n")
+tf =0.8*ti
+Ys_a = (Ys + Ys_)/2
+r=d/2
+thetaI = sqrt((ti-tf)/r)
+lambdaI=2*sqrt(r/tf)*atan(thetaI *sqrt(r/tf))
+lambdaN = (1/2)*((1/mu)*(log(tf/ti)) + lambdaI)
+thetaN =(sqrt(tf/r))*(tan((lambdaN/2)*(sqrt(tf/r))))
+Dtheta_a = thetaN/4
+Dtheta_b = (thetaI- thetaN)/8
+printf("The values of P_after are\n")
+i = 0
+for i = 0:4
+ theta = i*Dtheta_a
+ y = (1/2)* (tf+r*theta^2)
+ lambda = 2*sqrt(r/tf)*atand(theta*(%pi/180) *sqrt(r/tf))
+ p_a = 2*Ys_a*(2*y/tf)*(exp(mu*lambda))
+ printf("%f \n",p_a)
+end
+I1 = (Dtheta_a/3) *(0.75+.925+4*(.788+.876)+2*.830)// By Simpson's rule
+printf("The values of P_before are\n")
+for i = 0:8
+ theta1 = i*Dtheta_b + thetaN
+ y = (1/2)* (tf+r*theta1^2)
+ lambda = 2*sqrt(r/tf)*atand(theta1*(%pi/180) *sqrt(r/tf))
+ p_b = 2*Ys_a*(2*y/ti)*(exp(mu*(lambdaI-lambda)))
+ printf(" %f \n",p_b)
+end
+I2 = (Dtheta_b/3)*(0.925+.75+4*(.887+.828+.786+.759) + 2*(.855+.804+.772))//By Simpson's rule
+F = r*(I1 + I2)
+F_ = F*w
+T = (r^2)*mu*(I2-I1)
+T_ =T*w
+W = v*(1000/60)/r
+P = 2*T_*W
+printf("\n The roll separating force = %d kN,\n The power required in the rolling process = %f kW",ceil(F_),P/1000)
+// Answer in the book for the power required in the rolling process is given as 75.6 kW
+