diff options
Diffstat (limited to '3392')
88 files changed, 2789 insertions, 0 deletions
diff --git a/3392/CH1/EX1.1/Ex1_1.sce b/3392/CH1/EX1.1/Ex1_1.sce new file mode 100755 index 000000000..c4e71e34f --- /dev/null +++ b/3392/CH1/EX1.1/Ex1_1.sce @@ -0,0 +1,27 @@ +clc
+// initialization of variables
+clear
+// part (a)
+a=700 // M Pa from figure 1.8
+b=100 // M Pafrom figure 1.8
+m=1/6 // from figure 1.8
+Y=450 // M Pa from figure 1.9
+//calculations
+sigma_u=a+m*b
+// results
+printf('\n part (a) \n')
+printf(' The ultimate strength is sigma = %.f M Pa',sigma_u)
+printf('\n and the yield strength is Y = %.f M Pa',Y)
+
+// part (b)
+c1=62 // from figure 1.8
+d1=0.025 // from figure 1.8
+c2=27 // from figure 1.10a
+d2=0.04 // from figure 1.10a
+// calculations
+U_f1=c1*b*d1*10^6
+U_f2=c2*b*d2*10^6
+// results
+printf('\n part (b)')
+printf('\n The modulus of toughness for alloy steel is Uf = %.3e N/m^2',U_f1)
+printf('\n and structural steel is Uf = %.3e N/m^2',U_f2)
diff --git a/3392/CH1/EX1.2/Ex1_2.sce b/3392/CH1/EX1.2/Ex1_2.sce new file mode 100755 index 000000000..9755685b4 --- /dev/null +++ b/3392/CH1/EX1.2/Ex1_2.sce @@ -0,0 +1,19 @@ +clc
+// initialization of variables
+clear
+sigma=500 // Stress M Pa
+eps=0.0073 // Strain
+sigma_A=343 // M Pa from figure 1.9
+eps_A=0.00172 // from figure 1.9
+// part (a)
+E=sigma_A/eps_A
+
+// part (B)
+eps_e=sigma/E
+eps_p=eps-eps_e
+// results
+printf(' part (a) \n')
+printf(' The modulus of elasticity of the rod is E = %.d G Pa',E/1000)
+printf('\n part (b)')
+printf('\n the permanent strain is = %.4f',eps_p)
+printf('\n and the strain recovered is = %.4f',eps_e)
diff --git a/3392/CH1/EX1.3/Ex1_3.sce b/3392/CH1/EX1.3/Ex1_3.sce new file mode 100644 index 000000000..4998a8c1e --- /dev/null +++ b/3392/CH1/EX1.3/Ex1_3.sce @@ -0,0 +1,17 @@ +clc
+// initialization of variables
+clear
+D=25 // kN
+L=60 // kN
+W=30 //kN
+Y=250 // M Pa
+safety=5/3 // AISC, 1989
+// calculations
+Q=(D+L+W)*10^3 // converted to N
+A=safety*Q/Y
+r=sqrt(A/%pi)+0.5 // additional 0.5 mm is for extra safety
+d=2*r // diameter
+// results
+printf('Part (a) \n ')
+printf('A rod of %.d mm in diameter, with a cross sectional area of %.d mm^2, is adequate',d,%pi*d^2/4)
+// The diameter is correct as given in the textbook. Area doesn't match due to rounding off error and partly because it's a design problem.
diff --git a/3392/CH10/EX10.1/Ex10_1.sce b/3392/CH10/EX10.1/Ex10_1.sce new file mode 100755 index 000000000..e81b67fea --- /dev/null +++ b/3392/CH10/EX10.1/Ex10_1.sce @@ -0,0 +1,44 @@ +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)
diff --git a/3392/CH10/EX10.2/Ex10_2.sce b/3392/CH10/EX10.2/Ex10_2.sce new file mode 100755 index 000000000..3e2ca1900 --- /dev/null +++ b/3392/CH10/EX10.2/Ex10_2.sce @@ -0,0 +1,36 @@ +clc
+// initialization of variables
+clear
+d=100 //mm
+Ix=2.45e+06 //mm^4
+E=72 //GPa
+L=6.8 //m
+K=110 //N/mm
+l=1.1 //m
+P=12 //kN
+//calculations
+E=E*10^3
+P=P*10^3
+l=l*10^3
+k=K/l
+L1=7*l
+Beta=(k/(4*E*Ix))^(1/4)
+if(l<%pi/(4*Beta))
+if(L1>3*%pi/(2*Beta))
+ y_max=P*Beta/(2*k)
+ M_max=P/(4*Beta)
+ S_max=M_max*d/(2*Ix)
+end
+end
+printf('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)
+A_bl=exp(-Beta*l)*(sin(Beta*l)+cos(Beta*l))
+A_2bl=exp(-Beta*2*l)*(sin(Beta*2*l)+cos(Beta*2*l))
+A_3bl=exp(-Beta*3*l)*(sin(Beta*3*l)+cos(Beta*3*l))
+ y_C=P*Beta/(2*k)*A_bl
+ y_B=P*Beta/(2*k)*A_2bl
+ y_A=P*Beta/(2*k)*A_3bl
+printf('\n y_C = %.2f mm',y_C)
+printf('\n y_B = %.2f mm',y_B)
+printf('\n y_A = %.2f mm',y_A)
diff --git a/3392/CH10/EX10.4/Ex10_4.sce b/3392/CH10/EX10.4/Ex10_4.sce new file mode 100755 index 000000000..a7d311e5c --- /dev/null +++ b/3392/CH10/EX10.4/Ex10_4.sce @@ -0,0 +1,36 @@ +clc
+// initialization of variables
+clear
+E=10 //GPa
+h=200 //mm
+b=100 //mm
+ko=0.04 //N/mm^3
+w=35 //N/mm
+L1=3.61 //m
+//calculations
+E=E*10^3
+L1=L1*10^3
+k=b*ko
+Ix=b*h^3/12
+Beta=(k/(4*E*Ix))^(1/4)
+ba=2.00 // ba = Beta*a based on the discussion
+//D_bz=exp(-Beta*z)*sin(Beta*z)
+D_ba=exp(-ba)*cos(ba)
+y_max=w/k*(1-D_ba)
+ba=0.777 //Beta*a
+bb=4.777 //Beta*b
+B_ba=exp(-ba)*sin(ba)
+B_bb=exp(-bb)*sin(bb)
+M_max=abs(-w*(B_ba-B_bb)/(4*Beta^2))
+c=h/2
+S_max=M_max*c/Ix
+// calculation of M_H
+ba=%pi/4 //Beta*a
+bb=4-%pi/4 //Beta*b
+B_ba=exp(-ba)*sin(ba)
+B_bb=exp(-bb)*sin(bb)
+M_H=w/(4*Beta^2)*(B_ba+B_bb)
+printf('y_max = %.3f mm',y_max)
+printf('\n M_max = %.3f kN.m',M_max/10^6)
+printf('\n S_max = %.3f MPa',S_max)
+printf('\n M_H = %.3f kN.m',M_H/10^6)
diff --git a/3392/CH10/EX10.5/Ex10_5.sce b/3392/CH10/EX10.5/Ex10_5.sce new file mode 100755 index 000000000..f0d4bcbd6 --- /dev/null +++ b/3392/CH10/EX10.5/Ex10_5.sce @@ -0,0 +1,27 @@ +clc
+// initialization of variables
+clear
+E=200 //GPa
+h=102 //mm
+b=68 //mm
+Ix=2.53e+06 //mm^4
+L1=4 //m
+ko=0.35 //N/mm^3
+P=30.0 //kN
+//calculations
+E=E*10^3
+P=P*10^3
+L1=L1*10^3
+k=b*ko
+Beta=(k/(4*E*Ix))^(1/4)
+if(L1>3*%pi/(2*Beta))
+ y_max=2*P*Beta/k
+ M_max=-0.3224*P/Beta
+ S_max=abs(M_max*h/(2*Ix))
+end
+z=%pi/(4*Beta)
+printf('y_max = %.2f mm',y_max)
+printf('\n M_max = %.2f kN.m',M_max/10^6)
+printf('\n S_max = %.1f MPa',S_max)
+printf('\n Location of Sigma_max is z = %d mm',z)
+
diff --git a/3392/CH10/EX10.6/Ex10_6.sce b/3392/CH10/EX10.6/Ex10_6.sce new file mode 100755 index 000000000..ecc25fa31 --- /dev/null +++ b/3392/CH10/EX10.6/Ex10_6.sce @@ -0,0 +1,51 @@ +clc
+// initialization of variables
+clear
+P=30.0 //kN
+a=500 //mm
+h=102 //mm
+b=68 //mm
+k=23.8 //N/mm^2
+Beta=0.001852
+Ix=2.53e+06 //mm^4
+//calculations
+P=P*10^3
+C_ba=exp(-Beta*a)*(-sin(Beta*a)+cos(Beta*a))
+D_ba=exp(-Beta*a)*cos(Beta*a)
+// y = P*Beta/(2*k)*(A_bz+2*D_ba*D_baz+C_ba*C_baz))
+// Mx = P/(4*Beta)*(C_bz-2*D_ba*B_baz-C_ba*A_baz)
+A_ba=exp(-Beta*a)*(sin(Beta*a)+cos(Beta*a))
+B_ba=exp(-Beta*a)*sin(Beta*a)
+C_ba=exp(-Beta*a)*(-sin(Beta*a)+cos(Beta*a))
+D_ba=exp(-Beta*a)*cos(Beta*a)
+z1=424 //mm
+z=z1-a
+A_bz=exp(-Beta*z)*(sin(Beta*z)+cos(Beta*z))
+B_bz=exp(-Beta*z)*sin(Beta*z)
+C_bz=exp(-Beta*z)*(-sin(Beta*z)+cos(Beta*z))
+D_bz=exp(-Beta*z)*cos(Beta*z)
+// to find out X_baz
+z=a+z
+A_baz=exp(-Beta*z)*(sin(Beta*z)+cos(Beta*z))
+B_baz=exp(-Beta*z)*sin(Beta*z)
+C_baz=exp(-Beta*z)*(-sin(Beta*z)+cos(Beta*z))
+D_baz=exp(-Beta*z)*cos(Beta*z)
+y_max = P*Beta/(2*k)*(A_bz+2*D_ba*D_baz+C_ba*C_baz)
+printf('y_max = %.4f mm',y_max)
+// For M_max
+z1=500 //mm
+z=z1-a
+A_bz=exp(-Beta*z)*(sin(Beta*z)+cos(Beta*z))
+B_bz=exp(-Beta*z)*sin(Beta*z)
+C_bz=exp(-Beta*z)*(-sin(Beta*z)+cos(Beta*z))
+D_bz=exp(-Beta*z)*cos(Beta*z)
+// to find out X_baz
+z=a+z
+A_baz=exp(-Beta*z)*(sin(Beta*z)+cos(Beta*z))
+B_baz=exp(-Beta*z)*sin(Beta*z)
+C_baz=exp(-Beta*z)*(-sin(Beta*z)+cos(Beta*z))
+D_baz=exp(-Beta*z)*cos(Beta*z)
+M_max = P/(4*Beta)*(C_bz-2*D_ba*B_baz-C_ba*A_baz)
+printf('\n M_max = %d N.mm',M_max)
+S_max=M_max*h/(2*Ix)
+printf('\n Sigma_max = %.1f MPa',S_max)
diff --git a/3392/CH10/EX10.7/Ex10_7.sce b/3392/CH10/EX10.7/Ex10_7.sce new file mode 100755 index 000000000..d17d4687d --- /dev/null +++ b/3392/CH10/EX10.7/Ex10_7.sce @@ -0,0 +1,48 @@ +clc
+// initialization of variables
+clear
+D=30 //m
+t=10 //m
+h=20 //mm
+E=200 //GPa
+v=0.29
+rho=900 //kg/m^3
+//calculations
+//part (a)
+E=E*10^3
+a=D/2*10^3
+p=t*10^3*9.807*rho*10^-9
+S_th=p*a/h
+tau_max=S_th/2
+printf('part (a)')
+printf('\n Maximum shear stress= %.2f MPa',tau_max)
+// part (b)
+k=E*h/(a^2)
+Beta=(3*(1-v^2)/(h^2*a^2))^(1/4)
+L1=3*%pi/(4*Beta) //L1=L/2
+u=S_th*a/E
+w=2*k*u/(Beta)
+M_max=w/(4*Beta)
+Szz_max=M_max*(h/2)/(h^3/12)
+Sth_max=v*Szz_max
+tau_max=Szz_max/2
+u_b=w*(1-v)*a/(2*E*h)
+printf('\n part (b)')
+printf('\n Maximum shear stress= %.2f MPa',tau_max)
+printf('\n u_bottom = %.3f mm',u_b)
+// part (c)
+w=u*k/(2*Beta)
+z=%pi/(4*Beta)
+B_bz=exp(-Beta*z)*sin(Beta*z)
+M_max=-w*B_bz/Beta
+c=6
+I=h^2
+Szz_max=(M_max*c/I)
+S_th1=v*(Szz_max)
+k=0.3224
+S_th2=(1-k)*S_th
+Sigma_th=S_th1+S_th2
+tau_max=(Sigma_th-Szz_max)/2
+printf('\n part (c)')
+printf('\n Maximum shear stress= %.2f MPa',tau_max)
+
diff --git a/3392/CH11/EX11.1/Ex11_1.sce b/3392/CH11/EX11.1/Ex11_1.sce new file mode 100755 index 000000000..44b23a32c --- /dev/null +++ b/3392/CH11/EX11.1/Ex11_1.sce @@ -0,0 +1,31 @@ +clc
+// initialization of variables
+clear
+E=200 //GPa
+v=0.29
+Di=20 //mm
+Do=100 //mm
+a=10 //mm
+b=50 //mm
+p1=300 //MPa
+//calculations
+// S_rr=p1*(a^2*(r^2-b^2))/(r^2*(b^2-a^2))
+// S_th=p1*(a^2*(r^2+b^2))/(r^2*(b^2-a^2))
+r=10
+S_rr=p1*(a^2*(r^2-b^2))/(r^2*(b^2-a^2))
+S_th=p1*(a^2*(r^2+b^2))/(r^2*(b^2-a^2))
+printf('r = %d mm',r)
+printf('\n Radial stress = %.1f MPa',S_rr)
+printf('\n circumferential stress = %.1f MPa',S_th)
+r=25
+S_rr=p1*(a^2*(r^2-b^2))/(r^2*(b^2-a^2))
+S_th=p1*(a^2*(r^2+b^2))/(r^2*(b^2-a^2))
+printf('\n r = %d mm',r)
+printf('\n Radial stress = %.1f MPa',S_rr)
+printf('\n circumferential stress = %.1f MPa',S_th)
+r=50
+S_rr=p1*(a^2*(r^2-b^2))/(r^2*(b^2-a^2))
+S_th=p1*(a^2*(r^2+b^2))/(r^2*(b^2-a^2))
+printf('\n r = %d mm',r)
+printf('\n Radial stress = %.1f MPa',S_rr)
+printf('\n circumferential stress = %.1f MPa',S_th)
diff --git a/3392/CH11/EX11.2/Ex11_2.sce b/3392/CH11/EX11.2/Ex11_2.sce new file mode 100755 index 000000000..848ab519c --- /dev/null +++ b/3392/CH11/EX11.2/Ex11_2.sce @@ -0,0 +1,22 @@ +clc
+// initialization of variables
+clear
+E=72 //GPa
+v=0.33
+Di=200 //mm
+Do=800 //mm
+a=100 //mm
+r=a
+b=Do/2 //mm
+p1=150 //MPa
+E=E*10^3
+S_rr=p1*(a^2*(r^2-b^2))/(r^2*(b^2-a^2))
+S_th=p1*(a^2*(r^2+b^2))/(r^2*(b^2-a^2))
+S_zz=p1*a^2/(b^2-a^2)
+tau_max=(S_th-S_rr)/2
+u_a=p1*a/(E*(b^2-a^2))*((1-2*v)*a^2+(1+v)*b^2)
+printf('Radial stress = %.1f MPa',S_rr)
+printf('\n circumferential stress = %.1f MPa',S_th)
+printf('\n Normal stress = %d MPa',S_zz)
+printf('\n Maximum shear stress = %d MPa',tau_max)
+printf('\n u|r=a = %.4f mm',u_a)
diff --git a/3392/CH11/EX11.3/Ex11_3.sce b/3392/CH11/EX11.3/Ex11_3.sce new file mode 100755 index 000000000..1ff9b4d82 --- /dev/null +++ b/3392/CH11/EX11.3/Ex11_3.sce @@ -0,0 +1,99 @@ +clc
+// initialization of variables
+clear
+E=200 //GPa
+a=10 //mm
+v=0.29
+ci=25.072 //mm
+co=25 //mm
+b=50 //mm
+rr=0.072 //mm
+re=0.025 //mm
+alpha=0.0000117 // per celcius
+//calculations
+E=E*10^3
+p1=300 //MPa
+term1=co/(E*(b^2-co^2))*((1-v)*co^2+(1+v)*b^2)
+term2=-ci/(E*(ci^2-a^2))*((-(1-v)*ci^2)-(1+v)*a^2)
+ps=rr/(term1+term2)
+
+// Inner cylinder p1=0 p2=ps a=10 b=25
+// outer cylinder p1=ps p2=0 a=25 b=50
+// S_rr=(p1*a^2-p2*b^2)/(b^2-a^2)-(a^2*b^2)/(r^2*(b^2-a^2))*(p1-p2)
+// S_th=(p1*a^2-p2*b^2)/(b^2-a^2)+(a^2*b^2)/(r^2*(b^2-a^2))*(p1-p2)
+// results
+// residual stresses for inner cylinder
+p1=0
+p2=ps
+r=10
+a=10
+b=25
+S_rri1=(p1*a^2-p2*b^2)/(b^2-a^2)-(a^2*b^2)/(r^2*(b^2-a^2))*(p1-p2)
+S_thi1=(p1*a^2-p2*b^2)/(b^2-a^2)+(a^2*b^2)/(r^2*(b^2-a^2))*(p1-p2)
+printf('\n Inner cylinder')
+printf('\n r = %d mm',r)
+printf('\n S_rr|R = %d MPa, S_th|R = %.1f MPa',S_rri1,S_thi1)
+r=25
+S_rri2=(p1*a^2-p2*b^2)/(b^2-a^2)-(a^2*b^2)/(r^2*(b^2-a^2))*(p1-p2)
+S_thi2=(p1*a^2-p2*b^2)/(b^2-a^2)+(a^2*b^2)/(r^2*(b^2-a^2))*(p1-p2)
+printf('\n r = %d mm',r)
+printf('\n S_rr|R = %.1f MPa, S_th|R = %.1f MPa',S_rri2,S_thi2)
+// residual stresses for outer cylinder
+p1=ps
+p2=0
+a=25
+b=50
+r=25
+S_rro1=(p1*a^2-p2*b^2)/(b^2-a^2)-(a^2*b^2)/(r^2*(b^2-a^2))*(p1-p2)
+S_tho1=(p1*a^2-p2*b^2)/(b^2-a^2)+(a^2*b^2)/(r^2*(b^2-a^2))*(p1-p2)
+printf('\n')
+printf('\n Outer cylinder')
+printf('\n r = %d mm',r)
+printf('\n S_rr|R = %d MPa, S_th|R = %.1f MPa',S_rro1,S_tho1)
+r=50
+S_rro2=(p1*a^2-p2*b^2)/(b^2-a^2)-(a^2*b^2)/(r^2*(b^2-a^2))*(p1-p2)
+S_tho2=(p1*a^2-p2*b^2)/(b^2-a^2)+(a^2*b^2)/(r^2*(b^2-a^2))*(p1-p2)
+printf('\n r = %d mm',r)
+printf('\n S_rr|R = %.1f MPa, S_th|R = %.1f MPa',S_rro2,S_tho2)
+// AN internal pressure of 300 MPa
+a=10 //mm
+b=50 //mm
+p1=300 //MPa
+r=10
+S_rr=p1*(a^2*(r^2-b^2))/(r^2*(b^2-a^2))
+S_th=p1*(a^2*(r^2+b^2))/(r^2*(b^2-a^2))
+S_rr1=S_rr+S_rri1
+S_th1=S_th+S_thi1
+printf('\n')
+printf('\n Inner cylinder')
+printf('\n r = %d mm',r)
+printf('\n S_rr = %.1f MPa, S_th = %.1f MPa',S_rr1,S_th1)
+r=25
+S_rr=p1*(a^2*(r^2-b^2))/(r^2*(b^2-a^2))
+S_th=p1*(a^2*(r^2+b^2))/(r^2*(b^2-a^2))
+S_rr2=S_rr+S_rri2
+S_th2=S_th+S_thi2
+printf('\n r = %d mm',r)
+printf('\n S_rr = %.1f MPa, S_th = %.1f MPa',S_rr2,S_th2)
+// Outer Cyllinder
+S_rr1=S_rr+S_rro1
+S_th1=S_th+S_tho1
+printf('\n')
+printf('\n Outer cylinder')
+printf('\n r = %d mm',r)
+printf('\n S_rr = %.1f MPa, S_th = %.1f MPa',S_rr1,S_th1)
+r=50
+S_rr=p1*(a^2*(r^2-b^2))/(r^2*(b^2-a^2))
+S_th=p1*(a^2*(r^2+b^2))/(r^2*(b^2-a^2))
+S_rr2=S_rr+S_rro2
+S_th2=S_th+S_tho2
+printf('\n r = %d mm',r)
+printf('\n S_rr = %.1f MPa, S_th = %.1f MPa',S_rr2,S_th2)
+//delT=u/(r*alpha)
+u=rr+re
+r=25
+delT=u/(r*alpha)
+printf('\n delT = %.1f degree Celcius',delT)
+
+
+
diff --git a/3392/CH11/EX11.4/Ex11_4.sce b/3392/CH11/EX11.4/Ex11_4.sce new file mode 100755 index 000000000..95dbbaa93 --- /dev/null +++ b/3392/CH11/EX11.4/Ex11_4.sce @@ -0,0 +1,9 @@ +clc
+// initialization of variables
+clear
+SF=1.75
+p1=300 //MPa
+S_rr=-SF*p1
+S_th=SF*325
+Y=1/sqrt(2)*sqrt((S_th-S_rr)^2+S_rr^2+S_th^2)
+printf(' Y = %.1f MPa',Y)
diff --git a/3392/CH11/EX11.5/Ex11_5.sce b/3392/CH11/EX11.5/Ex11_5.sce new file mode 100755 index 000000000..b4688ef62 --- /dev/null +++ b/3392/CH11/EX11.5/Ex11_5.sce @@ -0,0 +1,20 @@ +clc
+// initialization of variables
+clear
+p1=300 //MPa
+SF=1.75
+S_rr=SF*p1
+S_th=SF*325-550.2 //Values are obtained from running Ex11_3.sce
+Y1=1/sqrt(2)*sqrt((S_th-S_rr)^2+S_rr^2+S_th^2)
+S_rr1=37.5
+S_rre=-189.1
+S_th1=62.5
+S_the=315.1
+// ABove values are obtained from running the codes Ex11_1 and Ex11_3.sce
+S_rr=-SF*S_rr1+S_rre
+S_th=SF*S_th1+S_the
+Y2=1/sqrt(2)*sqrt((S_th-S_rr)^2+S_rr^2+S_th^2)
+if(Y2>Y1)
+ Y=Y2
+end
+printf(' Y = %.1f MPa',Y)
diff --git a/3392/CH11/EX11.6/Ex11_6.sce b/3392/CH11/EX11.6/Ex11_6.sce new file mode 100755 index 000000000..56e6072ef --- /dev/null +++ b/3392/CH11/EX11.6/Ex11_6.sce @@ -0,0 +1,51 @@ +clc
+// initialization of variables
+clear
+SF=1.8
+a=20 //mm
+b=40 //mm
+Y=450 //MPa
+//part (a)
+tau_Y=Y/sqrt(3)
+Pp=2*tau_Y*log(b/a)
+S_th=2*tau_Y*(1-log(b/a))
+S_rr=-Pp
+S_zz=(S_th+S_rr)/2
+printf('part (a)')
+printf('\n S_th = %.1f MPa',S_th)
+printf('\n S_zz = %.1f MPa',S_zz)
+// part (b)
+S_thR=S_th-Pp*(b^2+a^2)/(b^2-a^2)
+S_zzR=S_zz-Pp*(a^2)/(b^2-a^2)
+S_thR=S_thR/2
+S_zzR=S_zzR/2
+printf('\n part (b)')
+printf('\n S_th|R = %.1f MPa',S_thR)
+printf('\n S_zz|R = %.1f MPa',S_zzR)
+// par (c)
+// We need to find out p1. To do that let it be unity
+p1=1
+S_thR=-S_thR
+S_zzR=-S_zzR
+S_rr=-SF*p1
+S_th=SF*p1*(b^2+a^2)/(b^2-a^2)
+S_zz=SF*p1*a^2/(b^2-a^2)
+// 2Y^2=(s_th-S_rr)^2+(S_rr-S_zz)^2+(S_zz-S_th)^2
+// S_th=S_th*p1-S_thR
+// S_zz=S_zz*p1-S_zzR
+// a*p1^2+b*p+c=0
+a=(S_th+SF)^2+(-SF-S_zz)^2+(S_zz-S_th)^2
+c=S_thR^2+S_zzR^2+(S_thR-S_zzR)^2
+b=-2*(S_th+SF)*S_thR+2*S_zzR*(-SF-S_zz)+2*(S_zz-S_th)*(S_thR-S_zzR)
+c=c-2*Y^2
+p11=roots([a b c])
+p12=roots([a 0 -2*Y^2])
+p11=p11(1)
+p12=p12(1)
+printf('\n Internal working pressure is %.1f MPa,',p11)
+printf('\n Without residual stresses %.1f MPa',p12)
+
+
+
+
+
diff --git a/3392/CH11/EX11.8/Ex11_8.sce b/3392/CH11/EX11.8/Ex11_8.sce new file mode 100755 index 000000000..00748f968 --- /dev/null +++ b/3392/CH11/EX11.8/Ex11_8.sce @@ -0,0 +1,20 @@ +clc
+// initialization of variables
+clear
+a=100 //mm
+b=300 //mm
+Y=620 //MPa
+E=200 //GPa
+S_zz=0
+v=0.29
+rho=7.85e+03 //kg/m^3
+// part (a)
+S_thmax=Y
+Wy=sqrt(4*Y/(rho*((3+v)*b^2+(1-v)*a^2)))
+printf('part (a)')
+printf('\n Omega_y =%d rad/s',Wy*10^6)
+// part (b)
+Wp=sqrt(3*Y/(rho*(b^2+a*b+a^2)))
+ratio=Wp/Wy
+printf('\n Omega_p = %d rad/s',Wp*10^6)
+printf('\n ratio = %.2f',ratio)
diff --git a/3392/CH11/EX11.9/Ex11_9.sce b/3392/CH11/EX11.9/Ex11_9.sce new file mode 100755 index 000000000..e5fefac40 --- /dev/null +++ b/3392/CH11/EX11.9/Ex11_9.sce @@ -0,0 +1,15 @@ +clc
+// initialization of variables
+clear
+a=100 //mm
+b=300 //mm
+v=0.29
+a=a*10^-3
+b=b*10^-3
+printf('r S_rr|R/Y S_th|R/Y (S_th/R-S_rr/R)/Y')
+for i=1:21
+ r=0.09+0.01*i
+S_rrR=((r-a)/r - 3/(b^2+a*b+a^2)*((r^3-a^3)/(3*r) + (3+v)/8*(a^2+b^2-r^2-a^2*b^2/r^2)))
+S_thR=(1- 3/(8*(b^2+a*b+a^2)) * ((3+v)*(a^2+b^2+a^2*b^2/r^2) - (1+3*v)*r^2))
+printf('\n %.2f %.5f %.5f %.5f',r,S_rrR,S_thR,S_rrR-S_thR)
+end
diff --git a/3392/CH12/EX12.3/Ex12_3.sce b/3392/CH12/EX12.3/Ex12_3.sce new file mode 100755 index 000000000..d8c2ee2a7 --- /dev/null +++ b/3392/CH12/EX12.3/Ex12_3.sce @@ -0,0 +1,14 @@ +clc
+// initialization of variables
+clear
+b=25 //mm
+L=250 //mm
+E_T=31 //GPa
+Sigma_T=262 //MPa // From the curve
+r=b/sqrt(12)
+Q=%pi^2*E_T/((L/r)^2)
+// Since this is not close enough, increment E_T
+E_T=31.6 //GPa
+Q=%pi^2*E_T/((L/r)^2)
+P_T=Q*b^2
+printf('Buckling load is %d kN',P_T)
diff --git a/3392/CH12/EX12.5/Ex12_5.sce b/3392/CH12/EX12.5/Ex12_5.sce new file mode 100755 index 000000000..a7afc2595 --- /dev/null +++ b/3392/CH12/EX12.5/Ex12_5.sce @@ -0,0 +1,20 @@ +clc
+// initialization of variables
+clear
+L=1 //m
+b=40 //mm
+h=75 //mm
+SF=2.5
+K=1
+L=L*10^3
+Iy=b*h^3/12
+A=b*h
+ry=sqrt(Iy/A)
+K_y=K*L/ry
+rz=b/sqrt(12)
+K=0.5
+K_z=K*L/rz
+S_cr=229 //MPa
+P_cr=S_cr*A
+P=P_cr/SF
+printf('P = %d kN',P/10^3)
diff --git a/3392/CH13/EX13.2/Ex13_2.sce b/3392/CH13/EX13.2/Ex13_2.sce new file mode 100755 index 000000000..edab7fba2 --- /dev/null +++ b/3392/CH13/EX13.2/Ex13_2.sce @@ -0,0 +1,27 @@ +clc
+// initialization of variables
+clear
+d=3.6 //m
+w=2.7 //m
+ha=3.0 //m
+b=0.9 //m
+a=1.2 //m
+v=0.29
+E=200 //GPa
+p=ha*9.8
+//part (a)
+S_w=124 //MPa
+b_a=b/a
+M=0.04*p*b^2*10^3
+h=sqrt(6*M/S_w)
+printf('part (a)')
+printf('\n h = %.2f mm',h)
+// part (b)
+C=0.032/(1+b_a^4)
+p=p*10^3
+E=E*10^9
+b=b*10^3
+w_max=C*(1-v^2)*p*b^4/(E*h^3)
+printf('\n part (b)')
+printf('\n w_max = %.2f mm',w_max)
+
diff --git a/3392/CH13/EX13.3/Ex13_3.sce b/3392/CH13/EX13.3/Ex13_3.sce new file mode 100755 index 000000000..810b77e93 --- /dev/null +++ b/3392/CH13/EX13.3/Ex13_3.sce @@ -0,0 +1,22 @@ +clc
+// initialization of variables
+clear
+E=200 //GPa
+v=0.29
+Y=315 //MPa
+h=10 //mm
+D=200 //mm
+SF=2.0
+//part (a)
+a=D/2
+E=E*10^3
+Py=1 // Since unknown
+S_maxk=3/4*Py*a^2/h^2
+Py=Y/S_maxk
+w_max=3/16*(1-v^2)*Py*a^4/(E*h^3)
+printf('Py = %.2f MPa',Py)
+printf('\n W_max = %.3f mm',w_max)
+// part (b)
+Pw=Py/SF
+printf('\n part (b)')
+printf('\n Pw = %.2f MPa',Pw)
diff --git a/3392/CH13/EX13.4/Ex13_4.sce b/3392/CH13/EX13.4/Ex13_4.sce new file mode 100755 index 000000000..ec96920ef --- /dev/null +++ b/3392/CH13/EX13.4/Ex13_4.sce @@ -0,0 +1,24 @@ +clc
+// initialization of variables
+clear
+D=500 //mm
+h=5 //mm
+Sigma=288 //MPa
+E=72 //GPa
+SF=2
+//part (a)
+a=D/2
+E=E*10^3
+f=Sigma*a^2/(E*h^2)
+// w_max/h has to be 2.4 since f=10
+Pr=50
+p=Pr*E*h^4/a^4
+p=p/2
+printf('part (a)')
+printf('\n Allowable pressure = %d kPa',p*10^3)
+// part (b)
+q=p*a^4/(E*h^4)
+// Corresponding w_max/h = 1.8
+w_max=1.8*h
+printf('\n part (b)')
+printf('\n W_max = %.2f mm',w_max)
diff --git a/3392/CH14/EX14.1/Ex14_1.sce b/3392/CH14/EX14.1/Ex14_1.sce new file mode 100755 index 000000000..d1984cb2a --- /dev/null +++ b/3392/CH14/EX14.1/Ex14_1.sce @@ -0,0 +1,22 @@ +clc
+// initialization of variables
+clear
+// part (a)
+ab_r=100
+Sigma_1=-20 //MPa
+Sigma_2=-75 //MPa
+alphao=0.01 //rad
+//calculations
+A=(Sigma_1+Sigma_2)/(Sigma_1-Sigma_2)
+th=1/2*acos((A*sinh(2*alphao)-1/2*(sinh(2*alphao)+cosh(2*alphao)))/A)
+printf('pat (a)')
+printf('\n theta = %.4f rad',th)
+//part (b)
+S_bb=-(Sigma_1-Sigma_2)^2/(2*(Sigma_1+Sigma_2))*(1+cosh(2*alphao)/sinh(2*alphao))
+printf('\n part (b)')
+printf('\n Maximum tensile stress = %d MPa',S_bb)
+//part (c)
+Beta=exp(2*alphao)*cosh(2*alphao)-2*A^2*(sinh(2*alphao))^2
+Beta=1/2*acos(Beta/(exp(2*alphao)))
+printf('\n part (c)')
+printf('\n Beta = %.4f rad',Beta)
diff --git a/3392/CH14/EX14.2/Ex14_2.sce b/3392/CH14/EX14.2/Ex14_2.sce new file mode 100755 index 000000000..bbde7f311 --- /dev/null +++ b/3392/CH14/EX14.2/Ex14_2.sce @@ -0,0 +1,20 @@ +clc
+// initialization of variables
+clear
+S_u=420 //MPa
+SF=4.00
+D=110 //mm
+d=50.0 //mm
+w=20 //mm
+rho=10.0 //mm
+SF=4.0
+//calculations
+t=(D-d)/2
+tr=t/rho
+rd=rho/d
+S_cs=1+2*sqrt(tr)
+A=w*d
+Pf=S_u*A/1.83
+P=Pf/SF
+printf('P = %.1f kN',P/10^3)
+
diff --git a/3392/CH14/EX14.3/Ex14_3.sce b/3392/CH14/EX14.3/Ex14_3.sce new file mode 100755 index 000000000..b50d91813 --- /dev/null +++ b/3392/CH14/EX14.3/Ex14_3.sce @@ -0,0 +1,26 @@ +clc
+// initialization of variables
+clear
+//part(a)
+H=200 //mm
+h=100 //mm
+rho=10 //mm
+Sigma_u=250 //MPa
+P=1.5 //kN
+L=1.4 //m
+b=40 //mm
+P=P*10^3
+L=L*10^3
+Hr=H/h
+rh=rho/h
+S_cc=1.77
+c=h/2
+I=b*h^3/12
+S_max=S_cc*P*L*c/I
+printf('part (a)')
+printf('\n Flexural design stress = %.1f MPa',S_max)
+//part (b)
+SF=Sigma_u*I/(S_cc*P*L*c)
+printf('\n part (b)')
+printf('\n SF =%.2f ',SF)
+
diff --git a/3392/CH15/EX15.2/Ex15_2.sce b/3392/CH15/EX15.2/Ex15_2.sce new file mode 100755 index 000000000..da2f42dbd --- /dev/null +++ b/3392/CH15/EX15.2/Ex15_2.sce @@ -0,0 +1,30 @@ +clc
+// initialization of variables
+clear
+d=250 //mm
+c=30 //mm
+t=25 //mm
+// part (a)
+a=5 //mm
+lambda=a/(2*c)
+f1l=1.22 //from the tble
+f2l=1.02
+//We don't know P yet so say P=1
+P=1
+Sfl=P/(t*2*c)*f1l+3*280*P*f2l/(2*t*c^2)
+K_IC=59*sqrt(1000)
+P=K_IC/(Sfl*sqrt(a*%pi))
+printf('part (a)')
+printf('\n P = %.1f kN',P/10^3)
+// part (b)
+a=10 //mm
+lambda=a/(2*c)
+f1l=1.33 //from the tble
+f2l=1.05
+// We don't know P yet so say P=1
+P=1
+Sfl=P/(t*2*c)*f1l+3*280*P*f2l/(2*t*c^2)
+K_IC=59*sqrt(1000)
+P=K_IC/(Sfl*sqrt(a*%pi))
+printf('\n part (b)')
+printf('\n P = %.1f kN',P/10^3)
diff --git a/3392/CH15/EX15.3/Ex15_3.sce b/3392/CH15/EX15.3/Ex15_3.sce new file mode 100755 index 000000000..448498624 --- /dev/null +++ b/3392/CH15/EX15.3/Ex15_3.sce @@ -0,0 +1,18 @@ +clc
+// initialization of variables
+clear
+a=100/2 //mm
+Y=1500 //MPa
+t=6 //mm
+w=800 //mmm
+c=200 //mm
+a_c=a/c
+fl=1.045
+w=w*10^-3
+t=t*10^-3
+a=a*10^-3
+A=w*t
+Sigma=1/A
+K_I=Sigma*sqrt(%pi*a)*fl
+printf('part (a)')
+printf('\n K_I = %.2f MPa sqrt(m)',K_I)
diff --git a/3392/CH15/EX15.4/Ex15_4.sce b/3392/CH15/EX15.4/Ex15_4.sce new file mode 100755 index 000000000..e13b27422 --- /dev/null +++ b/3392/CH15/EX15.4/Ex15_4.sce @@ -0,0 +1,10 @@ +clc
+// initialization of variables
+clear
+S_u=1300 //MPa
+K_C=69 // MPa sqrt(m)
+SF=2.2
+//calculations
+S_c=S_u/2.2
+a=1/%pi*(K_C/S_c)^2
+printf('a = %.2f mm',a*10^3)
diff --git a/3392/CH15/EX15.5/Ex15_5.sce b/3392/CH15/EX15.5/Ex15_5.sce new file mode 100755 index 000000000..24b999e04 --- /dev/null +++ b/3392/CH15/EX15.5/Ex15_5.sce @@ -0,0 +1,14 @@ +clc
+// initialization of variables
+clear
+// For 30 mm crack
+a=30/2 // mm crack
+S_30 =600 //MPa
+a=a*10^-3
+C=S_30*sqrt(a)
+// For 120 mm crack
+a=120/2
+a=a*10^-3
+S_120=C/sqrt(a)
+printf('Sigma_120 = %d MPa',S_120)
+
diff --git a/3392/CH16/EX16.1/Ex16_1.sce b/3392/CH16/EX16.1/Ex16_1.sce new file mode 100755 index 000000000..f5d40f365 --- /dev/null +++ b/3392/CH16/EX16.1/Ex16_1.sce @@ -0,0 +1,29 @@ +clc
+// initialization of variables
+clear
+Y=345 //MPa
+S_u=586 //MPa
+d=20 //mm
+R=800 //mm
+//part (a)
+SF=1.8
+N=1e+07
+S_am=290 //MPa
+// P_max not yet known. take it as unity until an equation to be solved is encountered
+P_max=1
+c=d/2
+M=SF/2*P_max*R //M=T
+I=%pi*c^4/4
+Sigma=M*c/I
+J=%pi*c^4/2
+tau=M*c/J
+S_max=315 //MPa
+// P_max^2*(3*(tau/S_max)^2+(Sigmaa/S_max)^2)=1
+P_max=sqrt(1/((3*(tau/S_max)^2)+(Sigma/S_max)^2))
+P_min=-5/6*P_max
+printf('part(a)')
+printf('\n P_max = %d N',P_max)
+printf('\n P_min = %d N',P_min)
+
+
+
diff --git a/3392/CH16/EX16.2/Ex16_2.sce b/3392/CH16/EX16.2/Ex16_2.sce new file mode 100755 index 000000000..dd10cb429 --- /dev/null +++ b/3392/CH16/EX16.2/Ex16_2.sce @@ -0,0 +1,26 @@ +clc
+// initialization of variables
+clear
+b=10 //mm
+M=1
+t=50 //mm
+rho=5 //mm
+h=25 //mm
+c=60 //mm
+SF=4.0
+//part (a)
+S_cc=2.8
+q=0.94
+S_ce=1+q*(S_cc-1)
+// M is not known. take it as unity
+S_n=3*M*t/(2*h*(c^3-t^3))
+S_e=S_ce*S_n
+printf('part (a)')
+printf('\n Effective stress = %.1e M',S_e)
+//part (b)
+S_max=172 //MPa
+S_w=S_max/SF
+M=S_w/S_e
+printf('\n part (b)')
+printf('\n M =%.1f N.m',M/10^3)
+
diff --git a/3392/CH16/EX16.3/Ex16_3.sce b/3392/CH16/EX16.3/Ex16_3.sce new file mode 100755 index 000000000..baa1120a3 --- /dev/null +++ b/3392/CH16/EX16.3/Ex16_3.sce @@ -0,0 +1,19 @@ +clc
+// initialization of variables
+clear
+rho=0.75 //mm
+S_n=32.97e-06 // M
+S_cc=6.1
+q=0.69
+S_ce=1+q*(S_cc-1)
+// M is not known. take it as unity
+M=1
+S_e=S_ce*S_n
+printf('part (a)')
+printf('\n Effective stress = %.1e M',S_e)
+// part (b)
+S_w=43 //MPa
+M=S_w/S_e
+printf('\n part (b)')
+printf('\n M =%.1f N.m',M/10^3)
+
diff --git a/3392/CH16/EX16.4/Ex16_4.sce b/3392/CH16/EX16.4/Ex16_4.sce new file mode 100755 index 000000000..247258115 --- /dev/null +++ b/3392/CH16/EX16.4/Ex16_4.sce @@ -0,0 +1,43 @@ +clc
+// initialization of variables
+clear
+E=72 //Gpa
+v=0.33
+S_u=470 //MPa
+Y=330 //MPa
+S_an=190 //MPa
+N=1e+06 //cycles
+T=10 //mm
+D=59 //mm
+d=50 //mm
+t=3 //mm
+rho=t
+P_min=20 //kN
+q=0.95
+//calculations
+P_min=P_min*10^3
+S_cc=1.90
+S_ce=1+q*(S_cc-1)
+A=T*d
+S_nMin=P_min/A
+S_nam=S_an/S_ce
+//(S_na/S_nam)+(S_nm/S_u)^2=1
+// S_nm^2=S_nMin^2+S_na^2+2*S_na*S_nMin
+c=S_nMin^2-S_u^2
+a=1
+b=2*S_nMin+S_u^2/S_nam
+S_na=roots([a b c])
+S_na=S_na(2)
+// Solving gives S_na
+S_nm=S_nMin+S_na
+S_nMax=S_nMin+2*S_na
+P_max=A*S_nMax
+S_max=S_nm+S_ce*S_na
+S_min=S_nm-S_ce*S_na
+printf('P_max = %.1f kN',P_max/10^3)
+printf('\n S_max = %.1f MPa',S_max)
+printf('\n S_min = %.1f MPa',S_min)
+
+
+
+
diff --git a/3392/CH16/EX16.5/Ex16_5.sce b/3392/CH16/EX16.5/Ex16_5.sce new file mode 100755 index 000000000..3b6222560 --- /dev/null +++ b/3392/CH16/EX16.5/Ex16_5.sce @@ -0,0 +1,40 @@ +clc
+// initialization of variables
+clear
+// Equation given: E_l =E_p + E_e
+// E_p = 0.58*(2N)^-0.57
+// E_e=0.0062*(2N)^-0.09
+// Part (a)
+function [f]=func(N)
+ f = 0.58*(2*N)^(-0.57)+0.0062*(2*N)^(-0.09)-0.01;
+endfunction
+
+Nc=6390
+N=Nc
+E_p = 0.58*(2*N)^-0.57
+E_e = 0.0062*(2*N)^-0.09
+E_l=E_p+E_e
+printf('Part (a)')
+printf('\n Total strain = %.5f ',E_l)
+//part (b)
+N=1/2*10^6
+E_p = 0.58*(2*N)^-0.57
+E_e = 0.0062*(2*N)^-0.09
+E_l=E_p+E_e
+printf('\n Part (b)')
+printf('\n Total strain = %.5f ',E_l)
+// part (c)
+E_l=0.01
+// In order to solve for N We have to solve a non-linear equation
+
+N = 1;//initial guess
+f = 1;//initial guess
+while(abs(f)>0.000001),
+ f = func(N);
+ if f>0 then
+ N = N+1;
+ elseif f<0 then
+ N = N-1;
+ end
+end
+printf('\n N = %d cycles.',N);
diff --git a/3392/CH17/EX17.1/Ex17_1.sce b/3392/CH17/EX17.1/Ex17_1.sce new file mode 100644 index 000000000..8684bb90c --- /dev/null +++ b/3392/CH17/EX17.1/Ex17_1.sce @@ -0,0 +1,40 @@ +clc
+// initialization of variables
+clear
+E1=200 //GPa
+E2=200 //Gpa
+v1=0.29
+v2=0.29
+R1=60 //mm
+R11=130 //mm
+R2=80 //mm
+R22=200 //mm
+th=%pi/3
+P=4.5 //kN
+P=P*10^3
+E=E1*10^3
+B=1/4*(1/R1+1/R2+1/R11+1/R22)+1/4*((1/R1+1/R2-1/R11-1/R22)^2 - 4*(1/R1-1/R11)*(1/R2-1/R22)*(sin(th)^2))^(1/2)
+A=1/4*(1/R1+1/R2+1/R11+1/R22)-1/4*((1/R1+1/R2-1/R11-1/R22)^2 - 4*(1/R1-1/R11)*(1/R2-1/R22)*(sin(th)^2))^(1/2)
+Del=2*(1-v1^2)/(E*(A+B))
+BAr=B/A
+Cb=0.77
+Cs=0.724
+Ct=0.24
+Cg=0.22
+Cz=0.53
+Cd=2.10
+b=Cb*(P*Del)^(1/3)
+br=b/Del
+S_max=-Cs*br
+tau_max=Ct*br
+tau_oct=Cg*br
+Zs=Cz*b
+delta=Cd*P/%pi*((A+B)/br)
+printf('Sigma_max = %d MPa',S_max)
+printf('\n tau_max = %d MPa',tau_max)
+printf('\n tau_oct_max = %d MPa',tau_oct)
+printf('\n Zs = %.2f mm',Zs)
+printf('\n delta = %.3f mm',delta)
+// S_max doesn't match due to round off error
+
+
diff --git a/3392/CH17/EX17.2/Ex17_2.sce b/3392/CH17/EX17.2/Ex17_2.sce new file mode 100755 index 000000000..1a823c2d8 --- /dev/null +++ b/3392/CH17/EX17.2/Ex17_2.sce @@ -0,0 +1,57 @@ +clc
+// initialization of variables
+clear
+E=200 //GPa
+v=0.29
+Y=1600 //MPa
+Po=4.2 //kN
+Omega=3000 //rpm
+th=%pi/3
+P=1.75 //kN
+R1=4.76 //mm
+R11=R1
+R2=-4.86 //mm
+R22=18.24 //mm
+//part (a)
+E=E*10^3
+Po=Po*10^3
+P=P*10^3
+B=1/4*(1/R1+1/R2+1/R11+1/R22)+1/4*((1/R1+1/R2-1/R11-1/R22)^2 - 4*(1/R1-1/R11)*(1/R2-1/R22)*(sin(th)^2))^(1/2)
+A=1/4*(1/R1+1/R2+1/R11+1/R22)-1/4*((1/R1+1/R2-1/R11-1/R22)^2 - 4*(1/R1-1/R11)*(1/R2-1/R22)*(sin(th)^2))^(1/2)
+Del=2*(1-v^2)/(E*(A+B))
+BAr=B/A
+Cb=0.32
+k=0.075
+Cs=1.00
+Ct=0.3
+Cg=0.27
+Cz=0.78
+b=Cb*(P*Del)^(1/3)
+a=b/k
+br=b/Del
+S_max=-Cs*br
+tau_max=Ct*br
+tau_oct=Cg*br
+Zs=Cz*b
+tauo=0.486*b/(2*Del)
+Zo=0.41*b
+printf('b = %.4f mm',b)
+printf('\n a = %.3f mm',a)
+printf('\n b/Delta = %d MPa',br)
+printf('\n Sigma_max = %d MPa',S_max)
+printf('\n tau_max = %d MPa',tau_max)
+printf('\n tau_oct_max = %d MPa',tau_oct)
+printf('\n Zs = %.3f mm',Zs)
+printf('\n Tau_0 = %d MPa',tauo)
+printf('\n Zo = %.3f mm',Zo)
+
+// part (b)
+tau_oY=sqrt(2)*Y/3
+Py = 1/Del*(tau_oY/(Cg*Cb)*Del)^3
+printf('\n part (b)')
+printf('\n P_Y = %d N',Py)
+SF=Py/P
+printf('\n SF = %.2f ',SF)
+
+
+
diff --git a/3392/CH17/EX17.3/Ex17_3.sce b/3392/CH17/EX17.3/Ex17_3.sce new file mode 100755 index 000000000..2469b81e4 --- /dev/null +++ b/3392/CH17/EX17.3/Ex17_3.sce @@ -0,0 +1,25 @@ +clc
+// initialization of variables
+clear
+E=200 //GPa
+v=0.29
+R=40 //mm
+h=20 //mm
+P=24.1 //kN
+S_max=1445 //MPa
+tau_max=433 //MPa
+tau_octM=361 //MPa
+//calculations
+E=E*10^3
+P=P*10^3
+Del=2*R*(1-v^2)/E
+b=sqrt(2*P*Del/(h*%pi))
+br=b/Del
+S_maxT=2*b/(9*Del)
+S_maxC=-1.13*br
+tau_max=0.31*br
+tau_octM=0.255*br
+printf('Sigma_max (tension) = %d MPa',S_maxT)
+printf('\n Sigma_max (compression) = %d MPa',S_maxC)
+printf('\n tau_max = %d MPa',tau_max)
+printf('\n tau_oct_max = %d MPa',tau_octM)
diff --git a/3392/CH2/EX2.1/Ex2_1.sce b/3392/CH2/EX2.1/Ex2_1.sce new file mode 100755 index 000000000..48f51e500 --- /dev/null +++ b/3392/CH2/EX2.1/Ex2_1.sce @@ -0,0 +1,76 @@ +clc
+// initialization of variables
+clear
+sig_xx=-10 // MPa
+sig_yy=30 // MPa
+sig_xy=15 // MPa
+sig_xz=0 // MPa
+sig_yz=0 // MPa
+sig_zz=0 //MPa
+I1=sig_xx+sig_yy+sig_zz
+I2=sig_xx*sig_yy-sig_xy^2+sig_zz*sig_xx-sig_xz^2+sig_zz*sig_yy-sig_yz^2
+M=[sig_xx sig_xy sig_xz
+ sig_xy sig_yy sig_yz
+ sig_xz sig_yz sig_zz]
+I3=det(M)
+p=[1 -I1 I2 -I3]
+sigma=roots(p)
+printf('I1 = %d I2 = %d I3 = %d ',I1,I2,I3)
+printf('\n Sigma_1 = %d Sigma_2 = %d SIgma_3 = %d ',sigma(1),sigma(3),sigma(2))
+// We have:
+// {S_xx-S S_xy S_xz
+// S_xy S_yy-S S_yz
+// S_xz S_yz S_zz-S}*{l m n}=0
+// Substituting for Sigma_1
+a1=sig_xx-sigma(1)
+a2=sig_xy
+a3=sig_xz
+b1=sig_xy
+b2=sig_yy-sigma(1)
+b3=sig_yz
+c1=sig_xz
+c2=sig_yz
+c3=sig_zz-sigma(1)
+// You can solve it using the matrices but since the system is imcoplete we get
+n1=0
+//bl*11+b2*m1=0
+// This implies m1=-b1/b2*l1
+// We also have l1^2+m1^2+n1^2=1
+l1=1/sqrt(1+(b1/b2)^2)
+m1=-b1/b2*l1
+printf('\n N1 = %.4fi + %.4fj',l1,m1)
+printf('\n or \n N1 = %.4fi + %.4fj',-l1,-m1)
+// Similarly Substituting for Sigma_2
+a1=sig_xx-sigma(3)
+a2=sig_xy
+a3=sig_xz
+b1=sig_xy
+b2=sig_yy-sigma(3)
+b3=sig_yz
+c1=sig_xz
+c2=sig_yz
+c3=sig_zz-sigma(3)
+// here, l2 = m2 = 0
+l2=0
+m2=0
+n2=sqrt(1)
+printf('\n N2 = %.4fk',n2)
+printf('\n or \n N2 = %.4fk',-n2)
+// Similarly Substituting for Sigma_3
+a1=sig_xx-sigma(2)
+a2=sig_xy
+a3=sig_xz
+b1=sig_xy
+b2=sig_yy-sigma(2)
+b3=sig_yz
+c1=sig_xz
+c2=sig_yz
+c3=sig_zz-sigma(2)
+// On solving, we get
+l3=1/sqrt(1+(b1/b2)^2)
+m3=-b1/b2*l3
+n3=0
+printf('\n N3 = %.4fi + %.4fj',l3,m3)
+printf('\n or \n N3 = %.4fi + %.4fj',-l3,-m3)
+
+
diff --git a/3392/CH2/EX2.2/Ex2_2.sce b/3392/CH2/EX2.2/Ex2_2.sce new file mode 100755 index 000000000..866942ac9 --- /dev/null +++ b/3392/CH2/EX2.2/Ex2_2.sce @@ -0,0 +1,28 @@ +clc
+// initialization of variables
+clear
+sig_xx=20 // MPa
+sig_yy=10 // MPa
+sig_xy=30 // MPa
+sig_xz=-10 // MPa
+sig_yz=80 // MPa
+I2=-7800 // (MPa)^2
+// part (a)
+// Assume sig_zz=k and evaluate determinants to solve for k
+det1=sig_xx*sig_yy-sig_xy^2
+//det2=k*sig_xx-sig_xz^2
+//det3=k*sig_yy-sig_yz^2
+k=(I2-det1+sig_xz^2+sig_yz^2)/(sig_xx+sig_yy)
+sig_zz=k
+I1=sig_xx+sig_yy+sig_zz
+M=[sig_xx sig_xy sig_xz
+ sig_xy sig_yy sig_yz
+ sig_xz sig_yz sig_zz]
+I3=det(M)
+// p=poly([1 -I1 I2 -I3], "x")
+p=[1 -I1 I2 -I3]
+sigma=roots(p)
+// results
+printf('\n part (a) \n')
+printf(' The unknown stress component is = %.d M Pa and the stress invariants I1, I2, I3 are respectively %.d , %.d , %.d ',sig_zz,I1,I2,I3)
+printf('\n The principal stresses are sigma1= %.3f , sigma2=%.3f , sigma3=%.3f M Pa',sigma(2),sigma(3),sigma(1))
diff --git a/3392/CH2/EX2.4/Ex2_4.sce b/3392/CH2/EX2.4/Ex2_4.sce new file mode 100755 index 000000000..bc750653e --- /dev/null +++ b/3392/CH2/EX2.4/Ex2_4.sce @@ -0,0 +1,55 @@ +clc
+// initialization of variables
+clear
+sig_xx=120 // MPa
+sig_yy=55 // MPa
+sig_xy=-55 // MPa
+sig_xz=-75 // MPa
+sig_yz=33 // MPa
+sig_zz=-85 // MPa
+// Direction cosines at point A
+lA=1/sqrt(3)
+mA=1/sqrt(3)
+nA=1/sqrt(3)
+// Direction cosines at point B
+lB=1/sqrt(2)
+mB=1/sqrt(2)
+nB=0
+// calculations
+I1=sig_xx+sig_yy+sig_zz
+I2=sig_xx*sig_yy-sig_xy^2+sig_zz*sig_xx-sig_xz^2+sig_zz*sig_yy-sig_yz^2
+M=[sig_xx sig_xy sig_xz
+ sig_xy sig_yy sig_yz
+ sig_xz sig_yz sig_zz]
+I3=det(M)
+p=[1 -I1 I2 -I3]
+sig=roots(p)
+sig=gsort(sig)
+sigma(1)=sig(1)
+sigma(3)=sig(2)
+sigma(2)=sig(3)
+// results
+printf('\n The principal stresses are sigma1= %.3f , sigma2=%.3f , sigma3=%.3f M Pa',sigma(1),sigma(2),sigma(3))
+// Finding about the circles
+C11=(sigma(2)+sigma(3))/2
+C21=(sigma(1)+sigma(3))/2
+C31=(sigma(1)+sigma(2))/2
+C12=0
+C22=0
+C32=0
+R1=(sigma(2)-sigma(3))/2
+R2=(sigma(1)-sigma(3))/2
+R3=(sigma(1)-sigma(2))/2
+SnnA=lA^2*sigma(1)+mA^2*sigma(2)+nA^2*sigma(3)
+SnsA=sqrt(lA^2*sigma(1)^2+mA^2*sigma(2)^2+nA^2*sigma(3)^2-SnnA^2)
+SnnB=lB^2*sigma(1)+mB^2*sigma(2)+nB^2*sigma(3)
+SnsB=sqrt(lB^2*sigma(1)^2+mB^2*sigma(2)^2+nB^2*sigma(3)^2-SnnB^2)
+printf('\n The details of circles are given below')
+printf('\n C1 : (%.2f M Pa, %.e) R1 = %.2f M Pa \n',C11,C12,R1)
+printf('\n C2 : (%.2f M Pa, %.e) R2 = %.2f M Pa \n',C21,C22,R2)
+printf('\n C3 : (%.2f M Pa, %.e) R3 = %.2f M Pa \n',C31,C32,R3)
+printf('\n at point A')
+printf('\n Normal stress = %.d M Pa and shear stress = %.2f M Pa',SnnA,SnsA)
+printf('\n at point B')
+printf('\n Normal stress = %.d M Pa and shear stress = %.2f M Pa',SnnB,SnsB)
+
diff --git a/3392/CH2/EX2.5/Ex2_5.sce b/3392/CH2/EX2.5/Ex2_5.sce new file mode 100755 index 000000000..176537c28 --- /dev/null +++ b/3392/CH2/EX2.5/Ex2_5.sce @@ -0,0 +1,39 @@ +clc
+// initialization of variables
+clear
+sig_xx=80 // MPa
+sig_yy=60 // MPa
+sig_xy=20 // MPa
+sig_xz=40 // MPa
+sig_yz=10 // MPa
+sig_zz=20 // MPa
+// Direction cosines at point A
+l=1/sqrt(6)
+m=2/sqrt(6)
+n=1/sqrt(6)
+// calculations
+SpX=sig_xx*l+sig_xy*m+sig_xz*n
+SpY=sig_xy*l+sig_yy*m+sig_yz*n
+SpZ=sig_xz*l+sig_yz*m+sig_zz*n
+// result
+printf('part (a)')
+printf('\n The stress vector is = %.3f i + %.3f j + %.3f k',SpX,SpY,SpZ)
+// part b
+I1=sig_xx+sig_yy+sig_zz
+I2=sig_xx*sig_yy-sig_xy^2+sig_zz*sig_xx-sig_xz^2+sig_zz*sig_yy-sig_yz^2
+M=[sig_xx sig_xy sig_xz
+ sig_xy sig_yy sig_yz
+ sig_xz sig_yz sig_zz]
+I3=det(M)
+p=[1 -I1 I2 -I3]
+sigma=roots(p)
+tau_max=(sigma(1)-sigma(3))/2
+tau_oct=sqrt((sigma(1)-sigma(2))^2+(sigma(1)-sigma(3))^2+(sigma(2)-sigma(3))^2)*1/3
+n=tau_max/tau_oct
+printf('\n part (b)')
+printf('\n The principal stresses are sigma1= %.3f , sigma2=%.3f , sigma3=%.3f M Pa',sigma(1),sigma(2),sigma(3))
+printf('\n and maximum shear stress is = %d M Pa',tau_max)
+printf('\n part (c)')
+printf('\n octahedral shear stress is %.3f MPa ',tau_oct)
+printf('\n Comparing tau_oct and tau_max, we see that \n')
+printf(' tau_max = %.3f tau_oct',n)
diff --git a/3392/CH2/EX2.7/Ex2_7.sce b/3392/CH2/EX2.7/Ex2_7.sce new file mode 100755 index 000000000..c4290afff --- /dev/null +++ b/3392/CH2/EX2.7/Ex2_7.sce @@ -0,0 +1,10 @@ +clc
+// initialization of variables
+clear
+tau_max=160 //MPa
+S_max=0
+//S_min=-S_o
+S_min=S_max-2*tau_max
+S_o=-S_min
+printf('part (a)')
+printf('\n Sigma_o = %d MPa',S_o)
diff --git a/3392/CH3/EX3.1/Ex3_1.sce b/3392/CH3/EX3.1/Ex3_1.sce new file mode 100755 index 000000000..17d2e6ffc --- /dev/null +++ b/3392/CH3/EX3.1/Ex3_1.sce @@ -0,0 +1,13 @@ +clc
+// initialization of variables
+clear
+// part (a)
+E=72 // G Pa
+v=0.33 // Poisoon's ratio
+h=2 // mm
+R=600 // mm
+//calculations
+sig_cir=E*h/(2*(1-v^2)*R)
+// results
+printf('\n part (a) \n')
+printf(' The maximum circumferential stress is %.d M Pa',sig_cir*10^3)
diff --git a/3392/CH3/EX3.7/Ex3_7.sce b/3392/CH3/EX3.7/Ex3_7.sce new file mode 100755 index 000000000..7b4339708 --- /dev/null +++ b/3392/CH3/EX3.7/Ex3_7.sce @@ -0,0 +1,36 @@ +clc
+// initialization of variables
+clear
+tR=0.02 // t/R ration
+E_A=69 //G Pa
+v_A=0.33 // Poisson's ratio
+alpha_A=21.6*10^-6 // /degree Celcius (Coefficient of expansion)
+E_S=207 // G Pa
+v_S=0.280
+alpha_S=10.8*10^-6 // /degree Celcius (Coefficient of expansion)
+// calculations
+// Sig_LA=a*p+b*delT+c*sig_thS
+// Sig_LS=v_S*Sig_thS+d*delT
+E_S=E_S*10^9
+E_A=E_A*10^9
+a=1/tR*E_A/E_S
+b=-2/3*alpha_S*E_S
+c=-E_A/E_S
+d=-alpha_S*E_S
+// SigthS=e*p+f*delT
+// SigthA=g*p+h*delT
+e=37.16
+f=0.8639*10^6
+g=1/tR-e
+h=-f
+// results
+p=689.4 // kPa
+delT=100 // degree Celcius
+p=p*10^3 // Pa
+SigthA=g*p+h*delT
+SigthS=e*p+f*delT
+Sig_LA=a*p+b*delT+c*SigthS
+Sig_LS=v_S*SigthS+d*delT
+printf('Thus, for p = %.1f k Pa and delT = %.d degree celcius \n',p/10^3,delT)
+printf(' SigthA = %.1f M Pa, Sig_LA = %.d M Pa \n',SigthA/10^6,Sig_LA/10^6)
+printf(' SigthS = %.1f M Pa, Sig_LS = %.d M Pa',SigthS/10^6,Sig_LS/10^6)
diff --git a/3392/CH3/EX3.8/Ex3_8.sce b/3392/CH3/EX3.8/Ex3_8.sce new file mode 100755 index 000000000..e6dc72189 --- /dev/null +++ b/3392/CH3/EX3.8/Ex3_8.sce @@ -0,0 +1,60 @@ +clc
+// initialization of variables
+clear
+// Material constants
+Ex=14700 // M Pa
+Ey=1000 // M Pa
+Ez=735 // M Pa
+Gxy=941 // M Pa
+Gxz=1147 // M Pa
+Gyz=103 // M pa
+Vxy=0.292
+Vxz=0.449
+Vyz=0.39
+// Stresses at a point
+Sxx=7 // M pa
+Syy=2.1 // M Pa
+Szz=-2.8 //M Pa
+Sxy=1.4 // M Pa
+Sxz=0 //M Pa
+Syz=0 // M Pa
+// part (a)
+th=1/2*atan(2*Sxy/(Sxx-Syy))*180/%pi
+I1=Sxx+Syy+Szz
+I2=Sxx*Syy-Sxy^2+Szz*Sxx-Sxz^2+Szz*Syy-Syz^2
+M=[Sxx Sxy Sxz
+ Sxy Syy Syz
+ Sxz Syz Szz]
+I3=det(M)
+p=[1 -I1 I2 -I3]
+S=roots(p)
+// results
+printf('Part (a) \n')
+printf('The maximum principal stress is S1 = %.2f M Pa', S(1))
+printf('\n and occurs in direction th = %.1f degrees',th)
+printf('\n and the intermediate principal stress S2 = %.2f M Pa occurs in the direction th = %.1f degrees \n',S(3),th+90)
+printf(' The minimum principal stress is S3 = Szz = %.1f M Pa', S(2))
+Ex=Ex*10^6
+Ey=Ey*10^6
+Ez=Ez*10^6
+Gxy=Gxy*10^6
+Gxz=Gxz*10^6
+Gyz=Gyz*10^6
+// part (b) is to find strains
+Exx=Sxx/Ex-Vxy*Syy/Ey-Vxz*Szz/Ez
+Eyy=-Vxy*Sxx/Ex+Syy/Ey-Vyz*Szz/Ez
+Ezz=-Vxz*Sxx/Ex-Vyz*Syy/Ey+Szz/Ez
+Exy=Sxy/Gxy
+Exz=Sxz/Gxz
+Eyz=Syz/Gyz
+printf('\n Part (b)')
+printf('\n The srains are')
+printf('\n Exx = %.2e , Eyy = %.2e , Ezz = %.4e',Exx,Eyy,Ezz)
+printf('\n Exy = %.4e , Exz = %.2d , Eyz = %.2d',Exy,Exz,Eyz)
+// Wrong Exx value in the textbook
+th=1/2*atan(Exy/(Exx-Eyy))
+th=th*180/%pi
+th2=th+90
+printf('\n part (c)')
+printf('\n theta = %.2f or theta = %.2f degrees',th,th2)
+// Wrong theta too since Ex given in textbook is wrong
diff --git a/3392/CH4/EX4.1/Ex4_1.sce b/3392/CH4/EX4.1/Ex4_1.sce new file mode 100755 index 000000000..5413583db --- /dev/null +++ b/3392/CH4/EX4.1/Ex4_1.sce @@ -0,0 +1,64 @@ +clc
+// initialization of variables
+clear
+P=170 //kN
+A=645 // (mm)^2
+// part (a)
+E=211.4 // G Pa (from figure)
+Y=252.6 // M Pa (from figure)
+Beta=0.0799 // G Pa (from figure)
+Ey=Y/E
+// The stress strain law given is
+// Sigma= E*eps for eps< Ey
+// Sigma= (1-Beta)*Y + Beta*E*eps otherwise
+
+// part (b)
+th=atan(1.8/2.4)// radians
+F=P/(2*cos(th))
+F=F*10^3 //N
+A=A*10^-6 //m^2
+E=E*10^9 //Pa
+Y=Y*10^6 //Pa
+L=3.0 //m
+Sigma=F/A
+if(Sigma<Y)
+ eps=Sigma/E
+else
+ eps=(Sigma-(1-Beta)*Y )/(Beta*E)
+end
+u=eps*L/cos(th)
+u=u*10^3 //mm
+// results
+printf('part (b)\n')
+printf(' Deflection = %.3f mm',u)
+
+// part (c)
+P=270 //kN
+F=P/(2*cos(th))
+F=F*10^3 //N
+Sigma=F/A
+if(Sigma<Y)
+ eps=Sigma/E
+else
+ eps=(Sigma-(1-Beta)*Y )/(Beta*E)
+end
+u=eps*L/cos(th)
+u=u*10^3 //mm
+// results
+printf('\n part (c)\n')
+printf(' Deflection = %.3f mm for P = %.d kN',u,P)
+
+P=300 //kN
+F=P/(2*cos(th))
+F=F*10^3 //N
+Sigma=F/A
+if(Sigma<Y)
+ eps=Sigma/E
+else
+ eps=(Sigma-(1-Beta)*Y )/(Beta*E)
+end
+u=eps*L/cos(th)
+u=u*10^3 //mm
+// results
+printf('\n Deflection = %.3f mm for P = %.d kN',u,P)
+
diff --git a/3392/CH4/EX4.2/Ex4_2.sce b/3392/CH4/EX4.2/Ex4_2.sce new file mode 100755 index 000000000..18457bf5e --- /dev/null +++ b/3392/CH4/EX4.2/Ex4_2.sce @@ -0,0 +1,39 @@ +clc
+// initialization of variables
+clear
+// Material properties
+E=200 //GPa
+A=100 //mm^2
+Y1=500 //M Pa
+Y2=250 // MPa
+// calculations
+E=E*10^9 // Pa
+A=A*10^-6 //m^2
+Y1=Y1*10^6 // Pa
+Y2=Y2*10^6 //Pa
+L_FG=1 //m
+L_CD=2 // m
+P1=Y2*A
+e=P1*L_FG/(E*A)
+e_FG=e
+e_CD=e
+P2=E*A*e_FG/L_FG
+P3=E*A*e_CD/L_CD
+Py=2*P1+2*P2+P3
+//results
+printf('part (a) \n')
+printf(' Yield Load Py = %.1f kN and the displacement is %.2f mm',Py/10^3,e*10^3)
+
+// part(b)
+P4=Y1*A
+e=P4*L_FG/(E*A)
+P5=E*A*e/L_CD
+P=2*P1+2*P4+P5
+printf('\n part (b) \n')
+printf(' Yield Load P = %.1f kN and the displacement is %.2f mm',P/10^3,e*10^3)
+// Fully plastic load
+P6=Y2*A*2
+Pp=2*P1+2*P4+P6
+e_CD=P6*L_CD/(E*A)
+printf('\n Fully Plastic Load Pp = %.1f kN and the displacement is %.2f mm',Pp/10^3,e_CD*10^3)
+
diff --git a/3392/CH4/EX4.3/Ex4_3.sce b/3392/CH4/EX4.3/Ex4_3.sce new file mode 100755 index 000000000..9f7d46095 --- /dev/null +++ b/3392/CH4/EX4.3/Ex4_3.sce @@ -0,0 +1,34 @@ +clc
+// initialization of variables
+clear
+// Stresses
+Sxx=100 // MPa
+Syy=-14 // MPa
+Sxy=50 // MPa
+Y=300 // MPa
+// part (a)
+Szz=0 // MPa
+Syz=0 //MPa
+Sxz=0 // MPa
+// To calculate principal stresses
+I1=Sxx+Syy+Szz
+I2=Sxx*Syy-Sxy^2+Szz*Sxx-Sxz^2+Szz*Syy-Syz^2
+M=[Sxx Sxy Sxz
+ Sxy Syy Syz
+ Sxz Syz Szz]
+I3=det(M)
+p=[1 -I1 I2 -I3]
+Sigma=roots(p)
+Smax=Sigma(1)
+Smin=Sigma(2)
+// Smax=max(Sigma)
+// Smin=min(Sigma)
+tau_max=Y/2
+SF=tau_max*2/(Smax-Smin)
+printf('part (a)\n')
+printf(' SF = %.2f if the material obeys Tresca criterion',SF)
+
+// part (b)
+SF=sqrt(2)*Y/sqrt((Smax^2)+(Smin^2)+(Smin-Smax)^2)
+printf('\n part (b)')
+printf('\n SF = %.2f if the material obeys von Mises criterion',SF)
diff --git a/3392/CH5/EX5.1/Ex5_1.sce b/3392/CH5/EX5.1/Ex5_1.sce new file mode 100755 index 000000000..8c2d69236 --- /dev/null +++ b/3392/CH5/EX5.1/Ex5_1.sce @@ -0,0 +1,32 @@ +clc
+// initialization of variables
+clear
+// part (b)
+K1=2 //N/mm (K1=E1A1/L1)
+K2=3 //N/mm (K2=E2A2/L2)
+b1=400 // mm (b1=h)
+h=400 // mm
+b2=300 //mm
+u=30 //mm
+v=40 //mm
+// calculations
+// Units convertion
+K1=K1*10^3
+K2=K2*10^3
+b1=b1*10^-3
+b2=b2*10^-3
+h=h*10^-3
+u=u*10^-3
+v=v*10^-3
+L1=sqrt(b1^2+h^2)
+L2=sqrt(b2^2+h^2)
+N1=sqrt((b1+u)^2+(h+v)^2)-L1
+N2=sqrt((b1+u)^2+(h+v)^2)
+N3=sqrt((b2-u)^2+(h+v)^2)-L2
+N4=sqrt((b2-u)^2+(h+v)^2)
+P=K1*(b1+u)*N1/N2-K2*(b2-u)*N3/N4
+Q=K1*(h+v)*N1/N2+K2*(h+v)*N3/N4
+// results
+printf('part (b)')
+printf('\n P = %.1f N',P)
+printf('\n Q = %.1f N',Q)
diff --git a/3392/CH5/EX5.10/Ex5_10.sce b/3392/CH5/EX5.10/Ex5_10.sce new file mode 100755 index 000000000..6a8a45f9e --- /dev/null +++ b/3392/CH5/EX5.10/Ex5_10.sce @@ -0,0 +1,26 @@ +clc
+// initialization of variables
+clear
+// part (b)
+// Specifications
+P=150 //N
+R=200 //mm
+d=20 //mm
+E=200 //GPa
+G=77.5 //GPa
+//calculations
+R=R*10^-3
+d=d*10^-3
+E=E*10^9
+G=G*10^9
+r1=R+d/2
+r2=R-d/2
+A=314*10^-6
+I=7850*10^-12 //m^4
+Ax=3*%pi/4*P*R/(E*A)
+Sh=3*%pi/4*1.33*P*R/(G*A)
+M=(7*%pi/4+1)*P*R^3/(E*I)
+//qc=3*%pi/4*P*R/(E*A)+3*%pi/4*1.33*P*R/(G*A)+(7*%pi/4+1)*P*R^3/(E*I)
+qc=Ax+Sh+M
+printf('qc = %.2f mm among which due to Axial is %.4f mm, %.4f mm is due to shear, and %.4f mm is due to moment',qc*10^3,Ax*10^3,Sh*10^3,M*10^3)
+printf('\n which means The concentrations of axial loads and shear are negligible')
diff --git a/3392/CH5/EX5.12/Ex5_12.sce b/3392/CH5/EX5.12/Ex5_12.sce new file mode 100755 index 000000000..06ea3ede5 --- /dev/null +++ b/3392/CH5/EX5.12/Ex5_12.sce @@ -0,0 +1,45 @@ +clc
+// initialization of variables
+clear
+// Material properties and dimensions
+E=72 //G Pa
+P=10 //kN
+Q=5 //kN
+Aab=150 //mm^2
+Abc=900 //mm^2
+Acd=900 //mm^2
+Ade=900 //mm^2
+Abd=150 //mm^2
+Abe=150 //mm^2
+Lab=2 //m
+Lbc=2.5 //m
+Lbd=1.5 //m
+Lbe=2.5 //m
+Lcd=2 //m
+Lde=2 //m
+//calculations
+E=E*10^9
+P=P*10^3
+Q=Q*10^3
+Aab=150
+Aab=Aab*10^-6
+Abc=Abc*10^-6
+Acd=Acd*10^-6
+Ade=Ade*10^-6
+Abd=Abd*10^-6
+Abe=Abe*10^-6
+M=0
+Nab=4/3*(Q+2*P)-5*M/(3*Lbe)
+dNab=-5/(3*Lbe)
+Nbc=-5/3*(Q+P)
+dNbc=0
+Nbd=Q
+dNbd=0
+Nbe=5*P/3-4/3*M/Lbe
+dNbe=-4/(3*Lbe)
+Ncd=-4*P/3+5/3*M/Lbe
+dNcd=5/(3*Lbe)
+Nde=Ncd
+thBE=Nab*Lab*dNab/(E*Aab)+Nbc*Lbc*dNbc/(E*Abc)+Nbd*Lbd*dNbd/(E*Abd)+Nbe*Lbe*dNbe/(E*Abe)+2*Ncd*Lcd*dNcd/(E*Lcd)
+printf('The rotation of member BE is %.5f rad',thBE)
+// Wrong answer in the text
diff --git a/3392/CH5/EX5.2/Ex5_2.sce b/3392/CH5/EX5.2/Ex5_2.sce new file mode 100755 index 000000000..92979688f --- /dev/null +++ b/3392/CH5/EX5.2/Ex5_2.sce @@ -0,0 +1,34 @@ +clc
+// initialization of variables
+clear
+// Loads and stresses and dimensions
+P=10 //kN
+Q=30 //kN
+S0=70 //MPa
+eps0=0.001
+b1=400 //mm
+h=400 //mm
+b2=300 //mm
+A1=300 //mm^2
+A2=300 //mm^2
+// calculations
+// Units convertion
+P=P*10^3
+Q=Q*10^3
+S0=S0*10^6
+b1=b1*10^-3
+b2=b2*10^-3
+h=h*10^-3
+A1=A1*10^-6
+A2=A2*10^-6
+L1=sqrt(b1^2+h^2)
+L2=sqrt(b2^2+h^2)
+a=L1*(Q*b2+P*h)/(A1*S0*h*(b1+b2))
+b=L2*(Q*b1-P*h)/(A2*S0*h*(b1+b2))
+c=L1^2*eps0/(b1+b2)
+d=L2^2*eps0/(b1+b2)
+u=c*sinh(a)-d*sinh(b)
+v=b2/h*c*sinh(a)+b1/h*d*sinh(b)
+// results
+printf('u = %.4f mm',u*10^3)
+printf('\n v = %.4f mm',v*10^3)
diff --git a/3392/CH5/EX5.6/Ex5_6.sce b/3392/CH5/EX5.6/Ex5_6.sce new file mode 100755 index 000000000..1b61ab361 --- /dev/null +++ b/3392/CH5/EX5.6/Ex5_6.sce @@ -0,0 +1,13 @@ +clc
+// initialization of variables
+clear
+// Material constants
+E=200 //GPa
+G=77.5 // GPa
+Lh=5 // Lh = L/h
+// part (b)
+rhs1=1.8*Lh*E/G
+rhs2=7*12*Lh^3/16
+LHS=1.8*Lh*E/G+7*12*Lh^3/16
+e=rhs1/LHS*100
+printf('The error in neglecting small terms is %.2f per cent',e)
diff --git a/3392/CH5/EX5.7/Ex5_7.sce b/3392/CH5/EX5.7/Ex5_7.sce new file mode 100755 index 000000000..0e7a7cf32 --- /dev/null +++ b/3392/CH5/EX5.7/Ex5_7.sce @@ -0,0 +1,26 @@ +clc
+// initialization of variables
+clear
+// Specifications
+T=2 //kN.m
+E=72 // G Pa
+G=27 // GPa
+b=30 //mm
+h=40 //mm
+d=60 //mm
+l1=400 //mm
+l2=800 //mm
+// calculations
+E=E*10^9
+G=G*10^9
+b=b*10^-3
+h=h*10^-3
+d=d*10^-3
+l1=l1*10^-3
+l2=l2*10^-3
+T=T*10^3 //N.m
+Ix=b*h^3/12
+J=%pi*d^4/32
+thB= 2*l1^3/3*0.001^2*T/(E*Ix)+T*l2/(G*J)
+printf('The rotation of shaft B is th = %.3f rad',thB)
+// Wrong answer to an extent in the textbook
diff --git a/3392/CH5/EX5.9/Ex5_9.sce b/3392/CH5/EX5.9/Ex5_9.sce new file mode 100755 index 000000000..2475efe4e --- /dev/null +++ b/3392/CH5/EX5.9/Ex5_9.sce @@ -0,0 +1,26 @@ +clc
+// initialization of variables
+clear
+// specification
+R=65 //mm
+E=200 //GPa
+G=77.5 //GPa
+v=0.29
+P=6 //kN
+//calculations
+R=R*10^-3
+E=E*10^9
+G=G*10^9
+P=P*10^3
+A=30^2*10^-6
+I=30^4/12*10^-12
+q_p1=3*%pi*P*R/(4*E*A)+1.2*3*%pi*P*R/(4*G*A)+(9*%pi/4+2)*P*R^3/(E*I)
+printf('part (a)')
+printf('\n qp = %.4f mm',q_p1*10^3)
+//part (b)
+// if Un and Us are neglected
+q_p2=(9*%pi/4+2)*P*R^3/(E*I)
+e=(q_p1-q_p2)/q_p1*100
+printf('\n part (b)')
+printf('\n error = %.2f per cent',e)
+
diff --git a/3392/CH6/EX6.1/Ex6_1.sce b/3392/CH6/EX6.1/Ex6_1.sce new file mode 100755 index 000000000..f24a89608 --- /dev/null +++ b/3392/CH6/EX6.1/Ex6_1.sce @@ -0,0 +1,20 @@ +clc
+// initialization of variables
+clear
+// part (a)
+a=22 //mm
+b=25 //mm
+T=500 //N m
+// calculations
+a=a*10^-3
+b=b*10^-3
+J=%pi*(b^4-a^4)/2
+tau_max=T*b/J
+printf(' part (a) \n')
+printf(' Maximum shear stress in shaft = %.1f M Pa ',tau_max/10^6)
+// part (b)
+G=77 //GPa
+G=G*10^9
+th=T/(G*J)
+printf('\n part (b)')
+printf('\n The angle of twist per unit length is = %.4f rad/m',th)
diff --git a/3392/CH6/EX6.10/Ex6_10.sce b/3392/CH6/EX6.10/Ex6_10.sce new file mode 100755 index 000000000..fec1067e5 --- /dev/null +++ b/3392/CH6/EX6.10/Ex6_10.sce @@ -0,0 +1,43 @@ +clc
+// initialization of variables
+clear
+G=26 //GPa
+tau_max=40.0 //MPa
+t1=4.5 //mm
+t3=1.5 //mm
+t2=3 //mm
+l1=3*60 //mm
+l3=60 //mm
+r2=30 //mm
+
+//calculations
+// 1 indicates coefficient of q1
+// 2 indicates coefficient of q2
+
+l2=r2*%pi
+G=G*10^3
+A1=l3^2
+A2=%pi*r2^2/2
+T1=2*A1
+T2=2*A2
+tha1=l1/t1+l3/t3
+tha1=tha1/(2*G*A1)
+tha2=-l3/t3
+tha2=tha2/(2*G*A1)
+thb1=-l3/t3
+thb1=thb1/(2*G*A2)
+thb2=l2/t2+l3/t3
+thb2=thb2/(2*G*A2)
+// Since tha=thb
+Qr=(thb2-tha2)/(tha1-thb1)
+printf('q1/q2 = %.3f ',Qr)
+q2=tau_max*t2
+q1=Qr*q2
+qdif=q1-q2
+tau_1=q1/t1
+tau_2=q2/t2
+tau_3=qdif/t3
+T=2*A1*q1+2*A2*q2
+th=tha1*q1+tha2*q2
+printf('\n T = %.3f kN.m',T/10^6)
+printf('\n theta = %.4f rad/m',th*10^3)
diff --git a/3392/CH6/EX6.2/Ex6_2.sce b/3392/CH6/EX6.2/Ex6_2.sce new file mode 100755 index 000000000..42b05d520 --- /dev/null +++ b/3392/CH6/EX6.2/Ex6_2.sce @@ -0,0 +1,37 @@ +clc
+// initialization of variables
+clear
+T=113 //Nm
+L1=1 //m
+L2=1.27 //m
+Y=414 //MPa
+G=77 //GPa
+SF=2
+// part (a)
+T1=T*2
+T2=T
+Y=Y*10^6
+G=G*10^9
+tau_max=0.25*Y
+r1=(2*T1/(%pi*tau_max))^(1/3)
+d1=2*r1
+r2=(2*T2/(%pi*tau_max))^(1/3)
+d2=2*r2
+inch=25.4 //mm
+printf(' part (a) \n')
+printf(' d1 = %.2f mm d2 = %.2f mm',d1*10^3,d2*10^3)
+printf('\n Since the dimensons are not standard, we choose d1 = %.1f mm and d2 = %.2f mm',inch,0.75*inch)
+// part (b)
+d1=inch*10^-3
+r1=d1/2
+d2=0.75*inch*10^-3
+r2=d2/2
+J1=%pi*r1^4/2
+th1=T1/(G*J1)
+J2=%pi*r2^4/2
+th2=T2/(G*J2)
+beta_c=L1*th1+L2*th2
+bet_deg=beta_c*180/%pi
+printf('\n part (b)')
+printf('\n The angle of twist = %.3f rad = %.1f degrees',beta_c,bet_deg)
+// Change is answer for US people convenience
diff --git a/3392/CH6/EX6.3/Ex6_3.sce b/3392/CH6/EX6.3/Ex6_3.sce new file mode 100755 index 000000000..2ff9d33f4 --- /dev/null +++ b/3392/CH6/EX6.3/Ex6_3.sce @@ -0,0 +1,24 @@ +clc
+// initialization of variables
+clear
+tau_Y=190 //MPa
+G=27 //GPa
+L=2 //m
+Do=60 //mm
+Di=40 //mm
+SF=2 // Factor of safety
+// Angle of twist can't be greater than 0.2 rad
+thM=0.2 //rad
+Do=Do*10^-3
+Di=Di*10^-3
+G=G*10^9
+tau_Y=tau_Y*10^6
+J=%pi/2*((Do/2)^4-(Di/2)^4)
+T=tau_Y*J*2/(Do*SF)
+printf(' part (a)')
+printf('\n Design torque T = %.3f kN.m',T/10^3)
+
+// part (b)
+T=G*J*thM/SF
+printf('\n part (a)')
+printf('\n Design torque limited by angle of twist is T = %.3f kN.m',T/10^3)
diff --git a/3392/CH6/EX6.4/Ex6_4.sce b/3392/CH6/EX6.4/Ex6_4.sce new file mode 100755 index 000000000..693e23cce --- /dev/null +++ b/3392/CH6/EX6.4/Ex6_4.sce @@ -0,0 +1,44 @@ +clc
+// initialization of variables
+clear
+// Material specifications
+G=77.5 //GPa
+// Following values of torsion are obtained from figure
+Toa=-12.5 //kN
+Tab=-8.5 //kN
+Tbc=1.5 //kN
+D1=10 //cm
+D2 =5 //cm
+D3 =D1 //cm
+Loa=500 //mm
+Lab=400 //mm
+Lbc=300 //mm
+//calculations
+G=G*10^9
+Toa=Toa*10^3
+Tab=Tab*10^3
+Tbc=Tbc*10^3
+D1=D1*10^-2
+D2=D2*10^-2
+D3=D3*10^-2
+Loa=Loa*10^-3
+Lab=Lab*10^-3
+Lbc=Lbc*10^-3
+r1=D1/2
+Joa=%pi*r1^4/2
+tauOA=-Toa*D1/(2*Joa)
+r2=D2/2
+r3=D3/2
+Jbc=%pi*r2^4/2
+Jab=%pi*r3^4/2
+tauBC=Tbc*D2/(2*Jbc)
+tau=max(tauOA,tauBC)
+printf('The maximum shear stress is = %.2f M Pa in segment OA',tau/10^6)
+// part (b)
+psiA=Toa*Loa/(G*Joa)
+psiBA=Tab*Lab/(G*Jab)
+psiB=psiA+psiBA
+psiCB=Tbc*Lbc/(G*Jbc)
+psiC=psiB+psiCB
+printf('\n PsiA = %.5f rad PsiB = %.5f rad PsiC = %.5f rad ',psiA,psiB,psiC)
+
diff --git a/3392/CH6/EX6.5/Ex6_5.sce b/3392/CH6/EX6.5/Ex6_5.sce new file mode 100755 index 000000000..ac1acb252 --- /dev/null +++ b/3392/CH6/EX6.5/Ex6_5.sce @@ -0,0 +1,19 @@ +clc
+// initialization of variables
+clear
+// Shaft specifications
+Pi=100 //kW
+f1=100 //Hz
+f2=10 //Hz
+tau_Y=220 //MPa
+SF=2.5 // Safety factor
+Po=100 //kW
+//calculations
+Pi=Pi*10^3
+tau_Y=tau_Y*10^6
+Po=Po*10^3
+Tin=Pi/(2*%pi*f1)
+Tout=Po/(2*%pi*f2)
+Din=(16*SF*Tin/(tau_Y*%pi))^(1/3)
+Dout=(16*SF*Tout/(tau_Y*%pi))^(1/3)
+printf(' Din = %.2f mm and Dout = %.2f mm',Din*10^3,Dout*10^3)
diff --git a/3392/CH6/EX6.7/Ex6_7.sce b/3392/CH6/EX6.7/Ex6_7.sce new file mode 100755 index 000000000..5bc11f6c0 --- /dev/null +++ b/3392/CH6/EX6.7/Ex6_7.sce @@ -0,0 +1,31 @@ +clc
+// initialization of variables
+clear
+// Flange specifications
+T=5000 //Nm
+b_f=266 //mm
+d=779 //mm
+t_w=16.5 //mm
+t_f=30 //mm
+G=200 // GPa
+// calculations
+b_f=b_f*10^-3
+d=d*10^-3
+t_w=t_w*10^-3
+t_f=t_f*10^-3
+G=G*10^9
+//calculations
+k1=0.308 // flange (b/h)<10
+Jf=2*k1*b_f*t_f^3
+k1=0.333 // web (b/h)>10
+Jw=k1*(d-2*t_f)*t_w^3
+J=Jf+Jw
+// part (a)
+hmax=0.015
+tau_max=2*T*hmax/J
+printf('part (a)\n')
+printf(' Maximum shear stress is = %.2f MPa',tau_max/10^6)
+// part (b)
+th=T/(G*J)
+printf('\n part (b)')
+printf(' \n The angle of twist per unit length is = %.5f rad/m',th)
diff --git a/3392/CH6/EX6.8/Ex6_8.sce b/3392/CH6/EX6.8/Ex6_8.sce new file mode 100755 index 000000000..39615de32 --- /dev/null +++ b/3392/CH6/EX6.8/Ex6_8.sce @@ -0,0 +1,35 @@ +clc
+// initialization of variables
+clear
+// Rod dimensions and material properties
+b1=60 //mm
+l1=3 //m
+l2=1.5 //m
+h1=40 //mm
+b2=40 //mm
+h2=30 //mm
+G=77.5 //GPa
+T1=750 //Nm
+T2=400 //Nm
+//calculations
+b1=b1*10^-3
+h1=h1*10^-3
+b2=b2*10^-3
+h2=h2*10^-3
+G=G*10^9
+// for the left portion of the rod
+k1l=0.196
+k2l=0.231
+// for the right portion of the rod
+k1r=0.178
+k2r=0.223
+T=T1+T2
+tau_maxL=T/(k2l*b1*(h1)^2)
+tau_maxR=T2/(k2r*b2*(h2)^2)
+tau_max=max(tau_maxL,tau_maxR)
+J1=b1*h1^3/12+h1*b1^3/12
+J2=b2*h2^3/12+h2*b2^3/12
+bet=T*l1/(G*J1)+T2*l2/(G*J2)
+printf(' The maximum shear stress is = %.1f MPa',tau_max/10^6)
+printf('\n twist = %.4f rad',bet)
+//wrong answer for twist in the text
diff --git a/3392/CH6/EX6.9/Ex6_9.sce b/3392/CH6/EX6.9/Ex6_9.sce new file mode 100755 index 000000000..04d1af5bf --- /dev/null +++ b/3392/CH6/EX6.9/Ex6_9.sce @@ -0,0 +1,36 @@ +clc
+// initialization of variables
+clear
+Do=22 //mm
+Di=18 //mm
+Dm=20 //mm
+tD=0.1 // t/D
+//part (a)
+tau=70 //MPa
+G=77.5 //GPa
+//calculations
+Do=Do*10^-3
+Di=Di*10^-3
+Dm=Dm*10^-3
+tau=tau*10^6
+G=G*10^9
+A=%pi*Dm^2/4
+t=Dm*tD
+T1=2*A*tau*t
+th1=tau*%pi*Dm/(2*G*A)
+J=%pi/32*(Do^4-Di^4)
+r=Dm/2
+T2=tau*J/r
+th2=tau/(G*r)
+printf('part (a)\n')
+printf(' Using formula_1 T = %.2f Nm theta = %.7f rad/mm ',T1,th1*10^-3)
+printf('\n Using formula_2 T = %.2f Nm theta = %.7f rad/mm ',T2,th2*10^-3)
+//part (b)
+h=1 //mm
+h=h*10^-3
+b=10*%pi
+b=b*10^-3
+T=8*b*h^2*tau/3
+th=tau/(2*G*h)
+printf('\n part (b)')
+printf('\n T = %.3f N.m theta = %.7f rad/mm ',T,th*10^-3)
diff --git a/3392/CH7/EX7.1/Ex7_1.sce b/3392/CH7/EX7.1/Ex7_1.sce new file mode 100755 index 000000000..f1e9bdb5e --- /dev/null +++ b/3392/CH7/EX7.1/Ex7_1.sce @@ -0,0 +1,21 @@ +clc
+// initialization of variables
+clear
+E=200 //G Pa
+Y=250 //M Pa
+SF=1.9
+w=1 //kN/m
+L=3 //m
+S_max=Y
+// Calculations
+E=E*10^9
+Y=Y*10^6
+w=w*10^3
+Mx=-SF*w*L^2/2
+S_max=S_max*10^6
+k=2 // c_max=h/k
+//Formula to be used
+// S_max=abs(Mx)*c_max/Ix
+// Note that c_max=h/2 and Ix=h^4/24
+h=(abs(Mx)*24/(k*S_max))^(1/3)
+printf('h = %.4f m',h)
diff --git a/3392/CH7/EX7.2/Ex7_2.sce b/3392/CH7/EX7.2/Ex7_2.sce new file mode 100755 index 000000000..838cb60a3 --- /dev/null +++ b/3392/CH7/EX7.2/Ex7_2.sce @@ -0,0 +1,32 @@ +clc
+// initialization of variables
+clear
+P1=1.5 //kN
+P2=4.5 //kN
+// part (a)
+A=1000 //mm^2
+A1=500 //mm^2
+A2=500 //mm^2
+//calculation
+A=A*10^-6
+A1=A1*10^-6
+A2=A2*10^-6
+y1=25*10^-3
+y2=55*10^-3
+c1=(A1*y1+A2*y2)/A
+c2=60*10^-3-c1 // c1+c2=60 mm
+y_1=c1-25*10^-3
+y_2=c2-5*10^-3
+b1=50*10^-3
+h1=10*10^-3
+h2=50*10^-3
+b2=10*10^-3
+Ix=1/12*b1*h1^3 + A1*y_1^2 + 1/12*b2*h2^3 + A2*y_2^2
+printf('part (a)')
+R1=2550 //N
+Vy=750 //N
+Mx=975 //N.m
+S_zzT=Mx*c1/Ix
+S_zzC=Mx*(-c2)/Ix
+printf('\n Maximum Tensile stress = %.1f MPa',S_zzT/10^6)
+printf('\n Maximum Compressive stress = %.1f MPa',S_zzC/10^6)
diff --git a/3392/CH7/EX7.3/Ex7_3.sce b/3392/CH7/EX7.3/Ex7_3.sce new file mode 100755 index 000000000..2f57f1310 --- /dev/null +++ b/3392/CH7/EX7.3/Ex7_3.sce @@ -0,0 +1,27 @@ +clc
+// initialization of variables
+clear
+P=12 //kN
+Phi=%pi/3
+// calculations
+L=3 //m
+P=12 //kN
+A=10000 //mm^2
+Ix=39.69*10^6 //mm^4
+yo=82 //mm
+Iy=30.73*10^6 //mm^4
+Ixy=0
+P=P*10^3
+Ix=Ix*10^-12
+Iy=Iy*10^-12
+alpha=atan(-Ix/(Iy*tan(Phi)))
+M=-L*P
+Mx=M*sin(Phi)
+yA=-118*10^-3 //m
+xA=-70*10^-3 //m
+xB=-xA
+yB=82*10^-3 //m
+S_A=Mx*(yA-xA*tan(alpha))/(Ix-Ixy*tan(alpha))
+S_B=Mx*(yB-xB*tan(alpha))/(Ix-Ixy*tan(alpha))
+printf(' Sigma A = %.1f M Pa \n',S_A/10^6)
+printf(' Sigma B = %.1f M Pa',S_B/10^6)
diff --git a/3392/CH7/EX7.4/Ex7_4.sce b/3392/CH7/EX7.4/Ex7_4.sce new file mode 100755 index 000000000..5f583f839 --- /dev/null +++ b/3392/CH7/EX7.4/Ex7_4.sce @@ -0,0 +1,52 @@ +clc
+// initialization of variables
+clear
+P=4 //kN
+L=1.2 //m
+A=1900 //mm^2
+Ix=2.783*10^6 //mm^4
+Iy=1.003*10^6 //mm^4
+Ixy=-0.973*10^6 //mm^4
+P=P*10^3
+Ix=Ix*10^-12
+Iy=Iy*10^-12
+Ixy=Ixy*10^-12
+A=1900 //mm^2
+xo=19.74 //mm
+yo=39.74 //mm
+Phi=2*%pi/3
+Nr=Ixy-Ix/tan(Phi)
+Dr=Iy-Ixy/tan(Phi)
+alpha=atan(Nr/Dr)
+M=L*P
+Mx=M*sin(Phi)
+yA=39.74*10^-3 //m
+xA=-60.26*10^-3 //m
+xB=19.74*10^-3
+yB=-80.26*10^-3 //m
+S_A=Mx*(yA-xA*tan(alpha))/(Ix-Ixy*tan(alpha))
+S_B=Mx*(yB-xB*tan(alpha))/(Ix-Ixy*tan(alpha))
+printf('part (a)')
+printf('\n Sigma A = %.1f M Pa \n',S_A/10^6)
+printf(' Sigma B = %.1f M Pa',S_B/10^6)
+
+// part (b)
+th=1/2*atan(-2*Ixy/(Ix-Iy))
+th1=0.415 //rad
+th2=-1.156 //rad
+IX=Ix*(cos(th1))^2+Iy*(sin(th1))^2-2*Ixy*sin(th1)*cos(th1)
+IY=Ix+Iy-IX
+Phi=2*%pi/3-th1
+alphA=-IX/(IY*tan(Phi))
+alpha=alphA+th1
+XA=xA*cos(th1)+yA*sin(th1)
+YA=yA*cos(th1)-xA*sin(th1)
+XB=xB*cos(th1)+yB*sin(th1)
+YB=yB*cos(th1)-xB*sin(th1)
+MX=M*sin(Phi)
+MY=-M*cos(Phi)
+S_A=MX*YA/IX-MY*XA/IY
+S_B=MX*YB/IX-MY*XB/IY
+printf('\n part (b)')
+printf('\n Sigma A = %.1f M Pa \n',S_A/10^6)
+printf(' Sigma B = %.1f M Pa',S_B/10^6)
diff --git a/3392/CH7/EX7.5/Ex7_5.sce b/3392/CH7/EX7.5/Ex7_5.sce new file mode 100755 index 000000000..1512877ab --- /dev/null +++ b/3392/CH7/EX7.5/Ex7_5.sce @@ -0,0 +1,31 @@ +clc
+// initialization of variables
+clear
+A=3085.9 //mm^2
+Ix=29.94e-6 //m^4
+Iy=4.167e-6 //m^4
+Ixy=0
+ybar=207.64 //mm
+tau_max=165e6 //Pa
+//calculations
+A=A*1e-6
+ybar=ybar*1e-3
+Mxk=-6.1*cos(%pi/6) // Mx=Mxk*P
+Myk=-6.1*sin(%pi/6) //My=Myk*P
+// Equation to be followed
+// S_zz=Mx*y/Ix-My*x/Iy
+// At A x=100 mm y=-92.36 mm
+x=100e-3
+y=-92.36e-3
+S_zzA=Mxk*y/Ix-Myk*x/Iy //Sigma_zz=S_zz*P
+// At B x=-100 mm y=-92.36 mm
+x=-100e-3
+y=-92.36e-3
+S_zzB=Mxk*y/Ix-Myk*x/Iy //Sigma_zz=S_zz*P
+// At C x=-3.125 mm y=207.64 mm
+x=-3.125e-3
+y=207.64e-3
+S_zzC=Mxk*y/Ix-Myk*x/Iy //Sigma_zz=S_zz*P
+// To find P
+P=2*tau_max/max(S_zzA,S_zzB,S_zzC)
+printf('P = %.2f kN',P/10^3)
diff --git a/3392/CH7/EX7.6/Ex7_6.sce b/3392/CH7/EX7.6/Ex7_6.sce new file mode 100755 index 000000000..df799b495 --- /dev/null +++ b/3392/CH7/EX7.6/Ex7_6.sce @@ -0,0 +1,29 @@ +clc
+// initialization of variables
+clear
+P=35 //kN
+Phi=5*%pi/9
+E=72e9 //Pa
+L=3 //m
+Ix=39.69*10^6 //mm^4
+Iy=30.73*10^6 //mm^4
+Ixy=0
+//calculations
+P=P*1e3
+Ix=Ix*10^-12
+Iy=Iy*10^-12
+alpha=atan(-Ix/(Iy*tan(Phi)))
+M=P*L/4
+Mx=M*sin(Phi)
+yA=-118*10^-3 //m
+xA=70*10^-3 //m
+xB=-xA
+yB=82*10^-3 //m
+S_comp=Mx*(yA-xA*tan(alpha))/(Ix-Ixy*tan(alpha))
+S_tens=Mx*(yB-xB*tan(alpha))/(Ix-Ixy*tan(alpha))
+printf(' Tensile strength = %.1f M Pa \n',S_tens/10^6)
+printf(' Compressive Strength = %.1f M Pa',S_comp/10^6)
+v=P*L^3*sin(Phi)/(48*E*Ix)
+u=-v*tan(alpha)
+delta=sqrt(u^2+v^2)
+printf('\n The total deflection is %.2f mm',delta*10^3)
diff --git a/3392/CH7/EX7.7/Ex7_7.sce b/3392/CH7/EX7.7/Ex7_7.sce new file mode 100755 index 000000000..40dc9e304 --- /dev/null +++ b/3392/CH7/EX7.7/Ex7_7.sce @@ -0,0 +1,29 @@ +clc
+// initialization of variables
+clear
+L=3 //m
+Ix=56.43e6 //mm^4
+Iy=18.11e6 //mm^4
+Ixy=22.72e6 //mm^4
+Phi=%pi/3
+E=200e9 //Pa
+Y=300e6 //Pa
+//calculations
+Ix=Ix*10^-12
+Iy=Iy*10^-12
+Ixy=Ixy*10^-12
+yA=-120*10^-3 //m
+xA=-91*10^-3 //m
+Nr=Ixy-Ix/tan(Phi)
+Dr=Iy-Ixy/tan(Phi)
+alpha=atan(Nr/Dr)
+// M=-L*P To know P we do the following
+Mxk=-L*sin(Phi)//Mx=Mxk*P
+P=Y*(Ix-Ixy*tan(alpha))/(Mxk*(yA-xA*tan(alpha)))
+printf('P = %.2f kN \n',P/10^3)
+v=P*L^3*sin(Phi)/(3*E*(Ix-Ixy*tan(alpha)))
+u=-v*tan(alpha)
+delta=sqrt(u^2+v^2)
+printf(' deflection = %.2f mm',delta*10^3)
+// Wrong calculation starting from v in Textbook
+
diff --git a/3392/CH7/EX7.8/Ex7_8.sce b/3392/CH7/EX7.8/Ex7_8.sce new file mode 100755 index 000000000..3edb5283b --- /dev/null +++ b/3392/CH7/EX7.8/Ex7_8.sce @@ -0,0 +1,26 @@ +clc
+// initialization of variables
+clear
+Ix=937e+06 //mm^4
+Iy=18.7e+6 //mm^4
+Ixy=0
+yA=305 //mm
+xA=90.5 //mm
+Phi=1.5533 //rad
+//calculations
+Ix=Ix*10^-12
+Iy=Iy*10^-12
+Ixy=Ixy*10^-12
+yA=yA*10^-3 //m
+xA=xA*10^-3 //m
+alpha=atan(-Ix/(Iy*tan(Phi)))
+Mxk=sin(Phi) // Mx=Mxk*M
+Sigma_Ak1=Mxk*(yA-xA*tan(alpha))/(Ix-Ixy*tan(alpha))
+//Sigma_A=Aigma_Ak*M
+// When the plane of the loads coincide with the y axes
+Sigma_Ak2=yA/Ix
+ratio=Sigma_Ak1/Sigma_Ak2
+percent=(ratio-1)*100
+printf('alpha = %.3f rad',alpha)
+printf('\n The maximum stress in the beam is increased %.1f percent when the plane of the loads is merely 1 degre from the symmetrical vertical plane',percent)
+// Wrong alpha given in the textbook
diff --git a/3392/CH7/EX7.9/Ex7_9.sce b/3392/CH7/EX7.9/Ex7_9.sce new file mode 100755 index 000000000..b9d20c2fd --- /dev/null +++ b/3392/CH7/EX7.9/Ex7_9.sce @@ -0,0 +1,20 @@ +clc
+// initialization of variables
+clear
+Y=280 //MPa
+AB=40 //mm
+BC=60 //mm
+//calculations
+Y=Y*10^6
+alpha=atan(BC/AB)
+C11=20/3 //mm
+C12=-10 //mm
+C21=-20/3 //mm
+C22=10 //mm
+Beta=atan((C11-C21)/(C22-C12))
+Phi=%pi/2+Beta
+d=sqrt((AB/2-C11)^2+(BC/2-C22)^2)
+d=d*10^-3 //m
+At=1/2*AB*BC/2*10^-6
+Mp=At*Y*d
+printf('Mp = %.3f kN.m',Mp/10^3)
diff --git a/3392/CH8/EX8.1/Ex8_1.sce b/3392/CH8/EX8.1/Ex8_1.sce new file mode 100755 index 000000000..f9b33bc9d --- /dev/null +++ b/3392/CH8/EX8.1/Ex8_1.sce @@ -0,0 +1,22 @@ +clc
+// initialization of variables
+clear
+t=4 //mm
+// calculations
+l1=100 //mm See figure
+l2=50 //mm See figure
+ybar=125 //mm
+t=t*10^-3
+ybar=ybar*10^-3
+l1=l1*10^-3
+l2=l2*10^-3
+Ix=2*t*(2*(l1+l2))^3/12-t*(2*l1)^3/12
+qAk=l1*t*ybar // qA=qAk*V
+qBk=qAk+l1*t*l1/2
+qave=qAk+2/3*(qBk-qAk)
+F2k=200*qave*10^-3 //F2=F2k*V
+DO=100/tan(30*%pi/180) // from figure
+// Now we need to solve the following equation
+// (DO-e)*V=DO*F2
+e=DO*(1-F2k/Ix)
+printf('e = %.1f mm',e)
diff --git a/3392/CH8/EX8.2/Ex8_2.sce b/3392/CH8/EX8.2/Ex8_2.sce new file mode 100644 index 000000000..5ed7e2ded --- /dev/null +++ b/3392/CH8/EX8.2/Ex8_2.sce @@ -0,0 +1,53 @@ +clc
+// initialization of variables
+clear
+// Defining the legs
+a=50 //mm Top horizontal leg
+b=100 //mm Verical leg
+c=100 //mm bottom leg
+t=4 //mm
+Ix=1.734e6 //mm^4
+Iy=0.876e6 //mm^4
+Ixy=-0.5e6 //mm^4
+I=[Ix Ixy
+ Ixy Iy]
+theta=1/2*atan(-2*Ixy/(Ix-Iy))
+Q=[cos(theta) -sin(theta)
+ sin(theta) cos(theta)]
+I_1=Q*I*Q' // I_1=[IX IXY| IXY IY]
+// Finding out the centroidal coordinates
+// We have x_bar = Summation(Ai*Xi)/Summation(Ai)
+// We take D as reference
+Aa=a*t
+Ab=b*t
+Ac=c*t
+A=Aa+Ab+Ac
+x_D=((Ac*c/2)+(Aa*a/2))/A
+y_D=((Ab*b/2)+(Aa*b))/A
+//Finding out B coordinates
+xb=a-x_D
+yb=b-y_D
+x=[xb;yb]
+X=Q'*x //New coordinates of B in transformed system
+function y=f(l),
+ y=t*l/I_1(1)*(X(2)+1/2*l*sin(theta)),
+endfunction
+F3=intg(0,a,f) // This is the coefficient of VY
+e_X=b*F3
+printf('eX = %.2f mm',e_X)
+// To find eY
+function y1=g(l),
+ y1=t*l/I_1(4)*(X(1)-1/2*l*cos(theta)),
+endfunction
+F3=intg(0,a,g) // This is the coefficient of VX
+e_Y=b*F3
+printf('\n eY = %.2f mm',e_Y)
+XC=Q'*[x_D
+ y_D]
+XC=XC+[e_X
+ -e_Y]
+printf('\n In terms of intial coordinates, the shear center C is located at \n XC = %.2f mm',XC(1))
+printf('\n YC = %.2f mm',XC(2))
+xC=Q*XC
+printf('\n The x and y coordinates of shear center C are \n xC = %.2f mm',xC(1))
+printf('\n yC = %.2f mm',xC(2))
diff --git a/3392/CH8/EX8.3/Ex8_3.sce b/3392/CH8/EX8.3/Ex8_3.sce new file mode 100755 index 000000000..dd051e3a0 --- /dev/null +++ b/3392/CH8/EX8.3/Ex8_3.sce @@ -0,0 +1,21 @@ +clc
+// initialization of variables
+clear
+t1=1 //mm
+t2=2 //mm
+oT=9.67 //mm distance between base and the centroid of each T-ection
+y2_bar=100+10+1+oT //mm (follwos from the figure)
+A1=400 //mm^2
+y1_bar=100 //mm
+A2=324 //mm^2
+Ix=2*A1*y1_bar^2+2*A2*y2_bar^2
+q1k=A2*y2_bar //q1=q1k*Vy/Ix
+F1k=(oT+t1/2)*q1k // Fi=Fik*Vy/Ix
+F2k=60*q1k
+F3k=(10+t1/2)*q1k
+q2k=q1k+(A1*y1_bar)
+F4k=(10+t2/2)*q2k
+F5k=200*q2k
+V_pk=2*(F1k+2*F3k+F5k)/Ix // V_p=V_pk*Vy
+e=(-2*F1k*71-2*F3k*11+F2k*221+F4k*200)/Ix
+printf('e = %.2f mm',e)
diff --git a/3392/CH8/EX8.4/Ex8_4.sce b/3392/CH8/EX8.4/Ex8_4.sce new file mode 100755 index 000000000..321aef577 --- /dev/null +++ b/3392/CH8/EX8.4/Ex8_4.sce @@ -0,0 +1,19 @@ +clc
+// initialization of variables
+clear
+b=300 //mm
+h=500 //mm
+t1=20 //mm
+t2=10 //mm
+t3=t2
+Ix=687.5e+06 //mm^4
+q_P=b*t2*h/2
+q_Q=q_P+h/2*t1*h/4
+q_S=h/2*t3*h/4
+q_A=-1/(h/t1+b/t2+h/t3+b/t2)*((-q_P-2/3*(q_Q-q_P))*h/t1-q_P/2*b/t2+2/3*q_S*h/t3-q_P/2*b/t2)
+e=1/Ix*((444.4+2/3*625)*b*h+444.4/2*177.76*h-q_A/(1000*2)*122.24*h)
+V1=(q_P-q_A+2/3*(q_Q-q_P))*h
+V2=(q_A+2/3*q_S)*h
+V=V1+V2
+printf('e = %d mm',e*10^3)
+printf('\n V = %d kN',V/1000)
diff --git a/3392/CH8/EX8.5/Ex8_5.sce b/3392/CH8/EX8.5/Ex8_5.sce new file mode 100755 index 000000000..5b7747264 --- /dev/null +++ b/3392/CH8/EX8.5/Ex8_5.sce @@ -0,0 +1,42 @@ +clc
+// initialization of variables
+clear
+a=500 //mm
+b=a
+t1=5 //mm
+t2=10 //mm
+t3=20 //mm
+// calculations
+Ix=2343.75e+06//mm^4
+q_B=b*t2*a/2
+q_C=q_B+a/2*t1*a/4
+q_S=a/2*t3*a/4
+q_G=2*b*t2*a/2
+q_H=q_G+a/2*t3*a/4
+// th_L = th_R = 0
+// Writing the above in following form
+//Ab=c ; b={q_A q_F}
+A11=a/t1+b/t2+a/t3+b/t2
+A12=a/t3
+c1=(q_B+2/3*(q_C-q_B))*a/t1 + 1/2*q_B*b/t2 - 2/3*q_S*a/t3 + 1/2*q_B*b/t2
+A21=A12
+A22=a/t3+2*b/t2+a/t3+2*b/t2
+c2=(q_G+2/3*(q_H-q_G))*a/t3+1/2*q_G*2*b/t2-2/3*q_S*a/t3+1/2*q_G*2*b/t2
+A=[A11 A12
+ A21 A22]
+c=[c1
+ c2]
+b=inv(A)*c
+q_A=b(1)/1000 //kN/mm
+q_F=b(2)/1000 //kN/mm
+q_B=q_B/1000
+q_C=q_C/1000
+q_S=q_S/1000
+q_G=q_G/1000
+q_H=q_H/1000
+b=a // rewriting to it's initival value
+ // To find out e, balance the moments
+ e=-((q_B-q_A+2/3*(q_C-q_A-(q_B-q_A)))*a*b + 1/2*(q_B-q_A)*219.1*a - 1/2*q_A*280.9*a + 1/2*q_F*471.9*a -1/2*(q_G-q_F)*528.1*a-(q_G-q_F+2/3*(q_H-q_F-(q_G-q_F)))*a*2*b)
+e=e/Ix
+ printf('e = %.1f mm',e*10^3)
+ // Wrong answer in the text
diff --git a/3392/CH9/EX9.1/Ex9_1.sce b/3392/CH9/EX9.1/Ex9_1.sce new file mode 100755 index 000000000..06bfe15ee --- /dev/null +++ b/3392/CH9/EX9.1/Ex9_1.sce @@ -0,0 +1,22 @@ +clc
+// initialization of variables
+clear
+a=30 //mm
+c=80 //mm
+b=50 //mm
+P=9.5 //kN
+d=100 //mm position of P
+//calculations
+P=P*10^3
+A=b^2
+A=b*(c-a)
+Am=b*log(c/a)
+R=(a+c)/2
+p=d+R
+Mx=p*P
+r=a
+S_thB=P/A+(Mx*(A-r*Am))/(A*r*(R*Am-A))
+r=c
+S_thC=P/A+(Mx*(A-r*Am))/(A*r*(R*Am-A))
+printf('The maximum tensile stress is (at point B) = %.1f MPa',S_thB)
+printf('\n The maximum cpmpressive stress is (at point C) = %.1f MPa',S_thC)
diff --git a/3392/CH9/EX9.10/Ex9_10.sce b/3392/CH9/EX9.10/Ex9_10.sce new file mode 100755 index 000000000..d61b5d7bc --- /dev/null +++ b/3392/CH9/EX9.10/Ex9_10.sce @@ -0,0 +1,24 @@ +clc
+// initialization of variables
+clear
+P=11.2 //kN
+E=200 //GPa
+v=0.3
+Ix=181.7e+03 //mm^4
+k1=0.643
+b1=34.7 //mm
+h1=10 //mm
+b2=40 //mm
+h2=10 //mm
+t=10 //mm
+h=50 //mm
+E=E*10^3
+A=b1*h1+b2*h2
+R=(b1*h1*35+b2*h2*60)/A
+Am=b1*log(40/30)+h1*log(80/40)
+G=E/(2*(1+v))
+Aw=t*h
+P=P*10^3
+delta_P=2*P*100/(Aw*G) + 2*P/(E*3*Ix)*100^3 + P*48.4*%pi/(2*Aw*G) + P*48.4*%pi/(2*A*E) + P*16.9/(A*(48.4*16.9-A)*E)*(100^2*%pi+%pi/2*(48.4)^2+2*100*2*48.4)
+printf('seperation = %.3f mm',delta_P)
+
diff --git a/3392/CH9/EX9.2/Ex9_2.sce b/3392/CH9/EX9.2/Ex9_2.sce new file mode 100755 index 000000000..5ff32f81d --- /dev/null +++ b/3392/CH9/EX9.2/Ex9_2.sce @@ -0,0 +1,33 @@ +clc
+// initialization of variables
+clear
+// part (c)
+r_A=1.47 //m
+theta=%pi
+// S_th=-125*cos(theta)+(14.2857-9.5250*r)/r*(1-cos(theta))*10^5 //kPa
+r=r_A
+S_th=-125*cos(theta)+(14.2857-9.5250*r)/r*(1-cos(theta))*10^5 //kPa
+S_A=S_th
+
+r_B=1.53 //m
+r=r_B
+S_th=-125*cos(theta)+(14.2857-9.5250*r)/r*(1-cos(theta))*10^5 //kPa
+S_B=S_th
+printf('part (c)')
+printf('\n The tensile stress at A is %.2f MPa',S_A/1000)
+printf('\n The compressive stress at B is %.2f MPa',S_B/1000)
+
+// part (d)
+theta=%pi/2
+r=r_A
+S_th=-125*cos(theta)+(14.2857-9.5250*r)/r*(1-cos(theta))*10^5 //kPa
+S_A=S_th
+r=r_B
+S_th=-125*cos(theta)+(14.2857-9.5250*r)/r*(1-cos(theta))*10^5 //kPa
+S_B=S_th
+printf('\n part (d)')
+printf('\n The tensile stress at A is %.2f MPa',S_A/1000)
+printf('\n The compressive stress at B is %.2f MPa',S_B/1000)
+
+//part (e)
+
diff --git a/3392/CH9/EX9.3/Ex9_3.sce b/3392/CH9/EX9.3/Ex9_3.sce new file mode 100755 index 000000000..567563d2b --- /dev/null +++ b/3392/CH9/EX9.3/Ex9_3.sce @@ -0,0 +1,30 @@ +clc
+// initialization of variables
+clear
+Y=500 //MPa
+SF=2.00
+A1=1658.76 //mm^2
+R1=73.81 //mm
+Am1=22.64 //mm
+A2=6100 //mm^2
+R2=126.62 //mm
+Am2=50.57 //mm
+A3=115.27 //mm^2
+R3=186.01 //mm
+Am3=0.62 //mm
+A=A1+A2+A3
+Am=Am1+Am2+Am3
+R=(A1*R1+A2*R2+A3*R3)/A
+rB=60 //mm
+rC=rB+24+100+5 //follows from figure
+//P unknown, so put unity to solve for it later
+P=1
+Mx=116.37*P
+r=rB
+S_thB=P/A+(Mx*(A-r*Am))/(A*r*(R*Am-A))
+r=rC
+S_thC=P/A+(Mx*(A-r*Am))/(A*r*(R*Am-A))
+S_th=max(abs(S_thB),abs(S_thC))
+Pf=Y/S_th
+P=Pf/SF
+printf('P = %.d N',P)
diff --git a/3392/CH9/EX9.4/Ex9_4.sce b/3392/CH9/EX9.4/Ex9_4.sce new file mode 100755 index 000000000..05d1e7773 --- /dev/null +++ b/3392/CH9/EX9.4/Ex9_4.sce @@ -0,0 +1,57 @@ +clc
+// initialization of variables
+clear
+// part (b)
+// Following is the formula used in evaluating the circumferential stress
+// Nr=(ro+ri)*(ro-ri-r*log(ro/ri))
+// Dr=r*((ro+ri)*log(ro/ri)-2*(ro-ri))
+// S_th=P*((sin(th)-th*cos(th))/(%pi*(r0-ri)*t))*(1+Nr/Dr)
+ri=60 //mm
+ro=180 //mm
+t=50 //mm
+th=%pi/2
+// For, maximum tensile stress r=ri
+r=ri
+Nr=(ro+ri)*(ro-ri-r*log(ro/ri))
+Dr=r*((ro+ri)*log(ro/ri)-2*(ro-ri))
+// Question was asked in terms of P, so let it be unity
+P=1
+S_th=P*((sin(th)-th*cos(th))/(%pi*(ro-ri)*t))*(1+Nr/Dr)
+S_max1=S_th
+// For maximum compressive stress r=ro
+r=ro
+Nr=(ro+ri)*(ro-ri-r*log(ro/ri))
+Dr=r*((ro+ri)*log(ro/ri)-2*(ro-ri))
+S_th=P*((sin(th)-th*cos(th))/(%pi*(ro-ri)*t))*(1+Nr/Dr)
+S_max2=S_th
+printf('part (b)')
+printf('\n for theta=90 degrees')
+printf('\n Maximum tensile stress = %.6f P',S_max1)
+printf('\n Maximum compressive stress = %.6f P',S_max2)
+
+
+th=%pi
+// For, maximum tensile stress r=ri
+r=ri
+Nr=(ro+ri)*(ro-ri-r*log(ro/ri))
+Dr=r*((ro+ri)*log(ro/ri)-2*(ro-ri))
+// Question was asked in terms of P, so let it be unity
+P=1
+S_th=P*((sin(th)-th*cos(th))/(%pi*(ro-ri)*t))*(1+Nr/Dr)
+S_max1=S_th
+// For maximum compressive stress r=ro
+r=ro
+Nr=(ro+ri)*(ro-ri-r*log(ro/ri))
+Dr=r*((ro+ri)*log(ro/ri)-2*(ro-ri))
+S_th=P*((sin(th)-th*cos(th))/(%pi*(ro-ri)*t))*(1+Nr/Dr)
+S_max2=S_th
+printf('\n for theta=180 degrees')
+printf('\n Maximum tensile stress = %.6f P',S_max1)
+printf('\n Maximum compressive stress = %.6f P',S_max2)
+
+//part(c)
+S_thMax=340 //MPa
+SF=2.2
+P=S_thMax/(SF*S_max1)
+printf('\n part(c)')
+printf('\n The maximum allowable load is %.2f kN',P/1000)
diff --git a/3392/CH9/EX9.5/Ex9_5.sce b/3392/CH9/EX9.5/Ex9_5.sce new file mode 100755 index 000000000..92706c109 --- /dev/null +++ b/3392/CH9/EX9.5/Ex9_5.sce @@ -0,0 +1,23 @@ +clc
+// initialization of variables
+clear
+P=120 //kN
+b1=120 //mm
+b2=120 //mm
+h1=48 //mm
+h2=24 //mm
+P=P*10^3
+A=h1*b1+b2*h2
+R=(b1*h1*96+b2*h2*180)/A
+Am=b1*log(b1/72)+h2*log(240/b2)
+r=72
+Mx=364*P
+S_thB=P/A+(Mx*(A-r*Am))/(A*r*(R*Am-A))
+
+r1=120 //mm
+t=24 //mm
+A1=h1*r1
+Am1=r1*log(r1/r)
+S_rr=(A*Am1-A1*Am)*Mx/(t*r1*A*(R*Am-A))
+printf('Circumferential stress is %.1f MPa',S_thB)
+printf('\n Radial stress is %.1f MPa',S_rr)
diff --git a/3392/CH9/EX9.6/Ex9_6.sce b/3392/CH9/EX9.6/Ex9_6.sce new file mode 100755 index 000000000..e8a8fb871 --- /dev/null +++ b/3392/CH9/EX9.6/Ex9_6.sce @@ -0,0 +1,40 @@ +clc
+// initialization of variables
+clear
+Mo=96 //kN
+P=120 //kN
+b1=150 //mm
+h1=60 //mm
+b2=120 //mm
+h2=50 //mm
+b3=b1
+h3=40 //mm
+ro=80 //mm
+r1=140 //mm
+r2=260 //mm
+r3=300 //mm
+// calculations
+Mo=Mo*10^6 // N.mm
+P=P*10^3 // N
+A=b1*h1+b2*h2+b3*h3
+Am=b1*log(r1/ro)+h2*log(r2/r1)+b3*log(r3/r2)
+R=(b1*h1*110+b2*h2*200+b3*h3*280)/A
+Mx=Mo+P*R
+r=80 //mm
+S_th=P/A+(Mx*(A-r*Am))/(A*r*(R*Am-A))
+
+A1=9000 //mm^2
+r1=140 //mm
+t=50 //mm
+Am1=b1*log(r1/ro)
+N=120000
+S_rr=A1*N/(A*t*r1) + (A*Am1-A1*Am)*Mx/(t*r1*A*(R*Am-A))
+printf('Circumferential stress is %.2f MPa',S_th)
+printf('\n Radial stress at B1 is %.2f MPa',S_rr)
+// to find radial stress at C;
+A1=b1*h1+b2*h2
+Am1=b1*log(r1/ro)+h2*log(r2/r1)
+r1=260 //mm
+t=50 //mm
+S_rr=A1*N/(A*t*r1) + (A*Am1-A1*Am)*Mx/(t*r1*A*(R*Am-A))
+printf('\n Radial stress at C1 is %.2f MPa',S_rr)
diff --git a/3392/CH9/EX9.7/Ex9_7.sce b/3392/CH9/EX9.7/Ex9_7.sce new file mode 100755 index 000000000..5ebfe9db4 --- /dev/null +++ b/3392/CH9/EX9.7/Ex9_7.sce @@ -0,0 +1,32 @@ +clc
+// initialization of variables
+clear
+l=15 //m
+R=10 //m
+d=0.8 //m
+b=0.13 //m
+Po=2400 //N/m
+P=4800 //N/m
+//calculations
+a=R-d/2
+c=R+d/2
+A=b*d
+Am=b*log(c/a)
+Mx=(Po+P)*l^2/8
+S_thMax=Mx*(A-a*Am)/(A*a*(R*Am-A))
+// To find out max radial stress
+// Nr=d*log(r/a)-(r-a)*log(c/a)
+// Dr=r*d*(R*log(c/a)-d)
+// S_rr=Mx/b*Nr/Dr
+r=a*exp(1-(a/d*log(c/a)))
+Nr=d*log(r/a)-(r-a)*log(c/a)
+Dr=r*d*(R*log(c/a)-d)
+S_rrMax=Mx/b*Nr/Dr
+printf('\n part (a)')
+printf('\n Maximum circumferential stress is %.1f MPa',S_thMax/10^6)
+printf('\n Maximum radial stress is %.3f MPa',S_rrMax/10^6)
+// part (b)
+Ix=b*d^3/12
+S_th=Mx*d/(2*Ix)
+printf('\n part (b)')
+printf('\n Maximum circumferential stress using straight beam formula is %.1f MPa',S_th/10^6)
diff --git a/3392/CH9/EX9.8/Ex9_8.sce b/3392/CH9/EX9.8/Ex9_8.sce new file mode 100755 index 000000000..4719c632f --- /dev/null +++ b/3392/CH9/EX9.8/Ex9_8.sce @@ -0,0 +1,39 @@ +clc
+// initialization of variables
+clear
+// part(a)
+Y=280 //MPa
+A=4000 //mm^2
+Am=44.99 //mm
+R=100.0 //mm
+r=180 //mm
+r=60 //mm
+// Mx is not yet known take it as unity
+Mx=1 //unity
+r=180
+S_thMax=Mx*(A-r*Am)/(A*r*(R*Am-A))
+Mx=Y/(abs(S_thMax))
+printf('part(a)')
+printf('\n Mx = %.2f kN.m',Mx/10^6)
+// part(b)
+k1=1.143
+t_w=20
+b_p=40
+alpha=0.651
+Beta=1.711
+r=60 //mm
+b1=2*alpha*b_p+t_w
+A=b1*t_w+t_w*R
+R=(b1*t_w*70+t_w*R*130)/A
+Am=b1*log(80/r)+t_w*log(180/80)
+// Mx not yet known teke it as unity
+Mx=1
+S_thMax=Mx*(A-r*Am)/(A*r*(R*Am-A))
+r=70 //mm
+S_thbar=Mx*(A-r*Am)/(A*r*(R*Am-A))
+S_xx=-Beta*S_thbar
+//tau_max=Y/2=(S_thMax-S_xx)/2
+Mx=Y/(S_thMax-S_xx)
+printf('\n part (b)')
+printf('\n Mx = %.2f kN.m',Mx/10^6)
+
diff --git a/3392/CH9/EX9.9/Ex9_9.sce b/3392/CH9/EX9.9/Ex9_9.sce new file mode 100755 index 000000000..ca734ccc2 --- /dev/null +++ b/3392/CH9/EX9.9/Ex9_9.sce @@ -0,0 +1,22 @@ +clc
+// initialization of variables
+clear
+E=72 //GPa
+t=60 //mm
+M=24 //kN.m
+//part(a)
+ro=100 //mm
+r1=150 //mm
+A=t*r1
+Am=t*log((ro+r1)/ro)
+R=ro+r1/2
+E=E*10^3
+Mx=M*10^6
+Phi=Am*Mx*%pi/(A*(R*Am-A)*E)
+printf('part(a)')
+printf('\n Phi = %.5f rad',Phi)
+//part(b)
+//Mx=Mx+P*R*sin(th)
+delta_P=Am*Mx*R*2/(A*(R*Am-A)*E)
+printf('\n part(b)')
+printf('\n deflection = %.3f mm',delta_P)
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