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authorpriyanka2015-06-24 15:03:17 +0530
committerpriyanka2015-06-24 15:03:17 +0530
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+clc
+// initialization of variables
+clear
+//part(a)
+E=200 //GPa
+d=184 //mm
+c=99.1 //mm
+Ix=36.9e+06//mm^4
+k=14.0 //N/mm^2
+P=170 //kN
+//calculations
+E=E*10^3
+P=P*10^3
+Beta=(k/(4*E*Ix))^(1/4)
+y_max=P*Beta/(2*k)
+M_max=P/(4*Beta)
+S_max=M_max*c/Ix
+printf('part (a)')
+printf('\n y_max = %.3f mm',y_max)
+printf('\n M_max = %.2f kN.m',M_max/10^6)
+printf('\n S_max = %.1f MPa',S_max)
+// part (b)
+z1=1.7//m
+z1=z1*10^3 //mm
+z2=2*z1
+// A_bz=exp(-Beta*z)*(sin(Beta*z)+cos(Beta*z))
+// C_bz=exp(-Beta*z)*(-sin(Beta*z)+cos(Beta*z))
+A_bzo=1
+C_bzo=1
+A_bz1=exp(-Beta*z1)*(sin(Beta*z1)+cos(Beta*z1))
+A_bz2=exp(-Beta*z2)*(sin(Beta*z2)+cos(Beta*z2))
+C_bz1=exp(-Beta*z1)*(-sin(Beta*z1)+cos(Beta*z1))
+C_bz2=exp(-Beta*z2)*(-sin(Beta*z2)+cos(Beta*z2))
+y_end=P*Beta/(2*k)*(A_bzo+A_bz1+A_bz2)
+M_end=P/(4*Beta)*(C_bzo+C_bz1+C_bz2)
+y_center=P*Beta/(2*k)*(A_bzo+2*A_bz1)
+M_center=P/(4*Beta)*(C_bzo+2*C_bz1)
+y_max=max(y_end,y_center)
+M_max=max(M_end,M_center)
+S_max=M_max*c/Ix
+printf('\n part(b)')
+printf('\n y_max = %.3f mm',y_max)
+printf('\n M_max = %.2f kN.m',M_max/10^6)
+printf('\n S_max = %.1f MPa',S_max)