initial commit / add all books

10 files changed, 362 insertions, 0 deletions

diff --git a/3774/CH8/EX8.1/Ex8_1.sce b/3774/CH8/EX8.1/Ex8_1.sce
new file mode 100644
index 000000000..e14f6c82d
--- /dev/null
+++ b/3774/CH8/EX8.1/Ex8_1.sce
@@ -0,0 +1,58 @@
+// exa 8.1 Pg 227
+clc;clear;close;
+
+// Given Data
+Fmin=250;// N
+Fmax=300;// N
+del=8;// mm
+C=8;// spring index
+tau_d=420;// MPa
+G=84;// GPa
+
+// 1. Wahl's correction factor
+Kw=(4*C-1)/(4*C-4)+0.615/C;// Wahl's correction factor
+printf("\n Wahl''s correction factor = %.3f ",Kw)
+// 2. Wire diameter
+// tau_d=Kw*8*Fmax*C/%pi/d**2
+d=sqrt(Kw*8*Fmax*C/%pi/tau_d);// mm
+printf('\n Wire diameter = %.2f mm. Use 4.25 mm.',d)
+d=4.25;// mm
+// 3. Mean coil diameter
+Dm=8*d;// mm
+printf('\n Mean coil diameter = %.f mm.',Dm)
+// 4. Stiffness of spring
+k=(Fmax-Fmin)/del;// N/mm
+// 5. no. of active turns
+n = G*10**3*d/8/C**3/k ;// no. of active turns
+printf('\n no. of active turns = %.f',n)
+// 6. total no. of turns for squared and ground ends
+nt=n+2;// total no. of turns for squared and ground ends
+printf('\n total no. of turns for squared and ground ends = %.f',nt)
+// 7. Free length of spring
+//lf=l_s+del_max+clashallowance(=0.15*del_max)
+del_max=del*Fmax/(Fmax-Fmin);//mm
+l_s=nt*d;// mm
+lf=l_s+del_max+0.15*del_max;// mm
+printf('\n Free length of spring = %.1f mm Use 124 mm',lf)
+lf=124;//mm
+// 8. Pitch of coils
+p=lf/(nt-1);//mm
+printf('\n Pitch of coils = %.2f mm',p)
+// 9. Check for buckling
+printf('\n Check for buckling - ')
+m=lf/Dm;// > 2.6 provided guide
+printf('\n ratio lf/Dm = %.3f > 2.6. So, Providing guide is necessary.',m)
+kl_1=0.22;// for hinged ends
+kl_2=0.62;// for fixed ends
+Fcr_1=k*kl_1*lf;//N (for hinged ends)
+Fcr_2=k*kl_2*lf;//N (for fixed ends)
+printf('\n Critical load for buckling - ')
+printf('\n Fcr = %.1f N for hinged ends < Fmax',Fcr_1)
+printf('\n Fcr = %.1f N for fixed ends > Fmax',Fcr_2)
+printf('\n From above two calculatio, it can be seen that spring is safe in buckling for fixed ends.')
+// 10. Lowest natural frequency for both ends fixed
+rau=7800;// N/mm.cube. (Density of spring material)
+fn=d/(%pi*n*Dm**2)*sqrt(G*10**3/8/(rau*10**-9));//
+printf('\n\n Lowest natural frequency for both ends fixed, fn = %.3f Hz',fn)
+
+
diff --git a/3774/CH8/EX8.10/Ex8_10.sce b/3774/CH8/EX8.10/Ex8_10.sce
new file mode 100644
index 000000000..917ea3632
--- /dev/null
+++ b/3774/CH8/EX8.10/Ex8_10.sce
@@ -0,0 +1,21 @@
+// exa 8.10 Pg 235
+clc;clear;close;
+
+// Given Data
+Fmin=600;// N
+Fmax=1000;// N
+C=6;// spring index
+n=1.5;// factor of safety
+Sys=700;// N/mm.sq.
+Ses_dash=350;// N/mm.sq.
+
+Kw=(4*C-1)/(4*C-4)+0.615/C;// Wahl's correction factor
+Ks=1+0.5/C;// Shear Stress factor
+Fm=(Fmax+Fmin)/2;// N
+Fa=(Fmax-Fmin)/2;// N
+tau_m_into_d_sq=Ks*(8*Fm*C)/(%pi);// where tau_m_into_d_sq = tau_m*d**2
+tau_a_into_d_sq=Kw*(8*Fa*C)/(%pi);// where tau_a_into_d_sq = tau_a*d**2
+
+//(tau_m-tau_a)/Sys+2*tua_a/Ses_dash=1/n
+d=sqrt(n)*sqrt((tau_m_into_d_sq-tau_a_into_d_sq)/Sys+2*tau_a_into_d_sq/Ses_dash);// mm
+printf('wire diameter of spring = %.2f mm',d)
diff --git a/3774/CH8/EX8.11/Ex8_11.sce b/3774/CH8/EX8.11/Ex8_11.sce
new file mode 100644
index 000000000..c4de41f3b
--- /dev/null
+++ b/3774/CH8/EX8.11/Ex8_11.sce
@@ -0,0 +1,39 @@
+// exa 8.11 Pg 236
+clc;clear;close;
+
+// Given Data
+dv=100;//mm
+C=5.5;// spring index
+pi=1;// N/mm.sq.
+p=1.075;// N/mm.sq.
+del=6;// mm
+tau_max=400;// N/mm.sq.
+G=80;// kN/mm.sq.
+
+Fi=(%pi/4)*dv**2*pi;// N (initial tension in spring)
+printf('\n initial tension in spring = %.f N', Fi)
+F=(%pi/4)*dv**2*p;// N (maximum tension in spring)
+printf('\n maximum tension in spring = %.f N', F)
+k=(F-Fi)/del;// N/mm (stiffness of spring)
+printf('\n stiffness of spring = %.2f N/mm',k)
+//Tmax=F*Dm/2 where Dm=5.5*d
+Tmax_BY_d=F*5.5/2;// calculation
+//Tmax=(%pi/16)*d**3*tau_max
+d=sqrt(Tmax_BY_d/((%pi/16)*tau_max));// mm
+printf('\n diameter of spring = %.2f mm. Use 18 mm.',d)
+d=ceil(d);// mm (rounding)
+Dm=5.5*d;//mm
+printf('\n mean coil diameter = %.f mm',Dm)
+Do=Dm+d;//mm
+printf('\n outside coil diameter = %.f mm',Do)
+Di=Dm-d;// mm
+printf('\n initial coil diameter = %.f mm',Di)
+n=G*10**3*d*del/8/(F-Fi)/C**3;// no. of turns
+printf('\n no. of turns = %.f',n)
+nt=n+1;// total no. of turns
+printf('\n total no. of turns(for extension spring) = %.f',nt)
+gi=1;// mm (initial gap)
+lf=nt*d+(nt-1)*gi;// mm
+printf('\n free length of spring = %.f mm',lf)
+p=lf/(nt-1);//mm
+printf('\n pitch of coils = %.2f mm',p)
diff --git a/3774/CH8/EX8.12/Ex8_12.sce b/3774/CH8/EX8.12/Ex8_12.sce
new file mode 100644
index 000000000..b2532a0da
--- /dev/null
+++ b/3774/CH8/EX8.12/Ex8_12.sce
@@ -0,0 +1,26 @@
+// exa 8.12 Pg 236
+clc;clear;close;
+
+// Given Data
+d=6;//mm
+Do=75;// mm
+tau=350;// N/mm.sq.
+G=84;// kN/mm.sq.
+
+printf('\n (i) neglecting the effect of curvature')
+dm=Do-d;// mm
+C=dm/d;// spring index
+Ks=1+0.5/C;// shear stress factor
+//tau=Ks*(8*Fmax*C)/(%pi*d**2)
+Fmax=tau/(Ks*(8*C)/(%pi*d**2));// N
+printf('\n Axial load = %.1f N',Fmax)
+delBYi=8*Fmax*C**3/(G*10**3*d);// mm/turn
+printf('\n deflection per active turn = %.3f mm/turn',delBYi)
+printf('\n\n (ii) considering the effect of curvature')
+Kw=(4*C-1)/(4*C-4)+0.615/C;// Wahl's correction factor
+//tau=Kw*(8*Fmax*C)/(G*d)
+Fmax=tau/(Kw*8*C/(%pi*d**2));
+printf('\n Axial load = %.1f N',Fmax)
+delBYn=8*Fmax*C**3/(G*10**3*d);// mm/turn
+printf('\n deflection per active turn = %.3f mm/turn',delBYn)
+// Note - answer in the textbook is wrong for last part.
diff --git a/3774/CH8/EX8.2/Ex8_2.sce b/3774/CH8/EX8.2/Ex8_2.sce
new file mode 100644
index 000000000..fe7f98b25
--- /dev/null
+++ b/3774/CH8/EX8.2/Ex8_2.sce
@@ -0,0 +1,22 @@
+// exa 8.2 Pg 228
+clc;clear;close;
+
+// Given Data
+Fmin=60;// N
+Fmax=140;// N
+d=3;// mm
+Dm=18;// mm
+Sut=1430;// MPa
+
+C=Dm/d;// spring index
+Kw=(4*C-1)/(4*C-4)+0.615/C;// Wahl's correction factor
+Ks=1+0.5/C;// Shear Stress factor
+Fm=(Fmax+Fmin)/2;// N
+Fa=(Fmax-Fmin)/2;// N
+tau_m=Ks*(8*Fm*C)/(%pi*d**2);// MPa
+tau_a=Kw*(8*Fa*C)/(%pi*d**2);// MPa
+Ses_dash=0.22*Sut;// MPa
+Sys=0.45*Sut;// MPa
+//tau_m/Sys+tua_a/Ses_dash*(2-Ses_dash/Sys)=1/n
+n=1/(tau_m/Sys+tau_a/Ses_dash*(2-Ses_dash/Sys));// factor of safety
+printf('\n factor of safety = %.2f',n)
diff --git a/3774/CH8/EX8.3/Ex8_3.sce b/3774/CH8/EX8.3/Ex8_3.sce
new file mode 100644
index 000000000..a2cac9a14
--- /dev/null
+++ b/3774/CH8/EX8.3/Ex8_3.sce
@@ -0,0 +1,24 @@
+// exa 8.3 Pg 229
+clc;clear;close;
+
+// Given Data
+Fi=40;// N
+d=3;// mm
+C=6;// spring index
+n=15;// factor of safety
+tau=650;// N/mm.sq.
+G=84;// kN/mm.sq.
+
+// Wahl's correction factor
+Kw=(4*C-1)/(4*C-4)+0.615/C;// Wahl's correction factor
+printf("\n Wahl''s correction factor = %.4f ",Kw)
+
+// Initial tortional shear stress
+tau_i=Kw*(8*Fi*C)/(%pi*d**2);// MPa
+printf('\n Initial tortional shear stress = %.2f MPa',tau_i)
+k=G*10**3*d/(8*C**3*n);// spring stiffness
+printf('\n spring stiffness = %.2f N/mm',k)
+// Spring load to cause yielding
+//tau=Kw*(8*Fi*C)/(%pi*d**2)
+F=tau/(Kw*(8*C)/(%pi*d**2))
+printf('\n Spring load to cause yielding = %.1f N',F)
diff --git a/3774/CH8/EX8.4/Ex8_4.sce b/3774/CH8/EX8.4/Ex8_4.sce
new file mode 100644
index 000000000..2b5d8929d
--- /dev/null
+++ b/3774/CH8/EX8.4/Ex8_4.sce
@@ -0,0 +1,33 @@
+// exa 8.4 Pg 230
+clc;clear;close;
+
+// Given Data
+Fmin=500;// N
+Fmax=1200;// N
+C=6;// spring index
+n=1.5;// factor of safety
+Sys=760;// MPa
+Ses_dash=350;// MPa
+del=25;// mm
+G=82;// kN/mm.sq.
+
+Kw=(4*C-1)/(4*C-4)+0.615/C;// Wahl's correction factor
+Ks=1+0.5/C;// Shear stress factor
+Fm=(Fmax+Fmin)/2;// N
+Fa=(Fmax-Fmin)/2;// N
+tau_m_into_d_sq=Ks*(8*Fm*C)/(%pi);// where tau_m_into_d_sq = tau_m*d**2
+tau_a_into_d_sq=Kw*(8*Fa*C)/(%pi);// where tau_a_into_d_sq = tau_a*d**2
+
+//(tau_m-tau_a)/Sys+2*tua_a/Ses_dash=1/n
+d=sqrt(n)*sqrt((tau_m_into_d_sq-tau_a_into_d_sq)/Sys+2*tau_a_into_d_sq/Ses_dash);// mm
+printf('\n diameter of spring wire = %.2f mm or %.f mm',d, ceil(d))
+d=ceil(d);// mm
+Dm=C*d;// mm
+printf('\n Mean coil diameter = %.f mm', Dm)
+//del=8*Fmax*Ci**3/(G*d)
+i=(del/(8*Fmax*C**3/(G*10**3*d)));// no. of active coils
+i=ceil(i);// no. of active coils
+printf('\n no. of active coils = %.f',i)
+nt=i+2;// no. of active coils (for square & ground ends)
+lf=nt*d+1.15*del;// mm
+printf('\n free length of spring = %.2f mm',lf)
diff --git a/3774/CH8/EX8.5/Ex8_5.sce b/3774/CH8/EX8.5/Ex8_5.sce
new file mode 100644
index 000000000..2b6bc712d
--- /dev/null
+++ b/3774/CH8/EX8.5/Ex8_5.sce
@@ -0,0 +1,34 @@
+// exa 8.5 Pg 231
+clc;clear;close;
+
+// Given Data
+p=125;// MPa
+dv=60;// mm
+del1=40;// mm
+del2=20;// mm
+tau_max=600;// MPa
+G=85;// kN/mm.sq.
+C=6;// spring index
+
+Fv=(%pi/4)*dv**2*p/100;// N (Force on the valve)
+del_max=del1+del2;// mm (Max. deflection)
+Fmax=Fv*dv/del1;// N (Max. force)
+Kw=(4*C-1)/(4*C-4)+0.615/C;// Wahl's correction factor
+// tau = 8*Fmax*C*Kw/(%pi*d**2)
+d=sqrt((8*Fmax*C*Kw/(%pi))/tau_max);// mm (Diameter of spring wire)
+Dm=6*d;// mm (Mean coil diameter)
+n=G*10**3*d*del_max/(8*Fmax*C**3);// no. of turns
+n = ceil(n);// no. of turns
+nt=n+2;// total no. of turns
+lf=nt*d+1.15*del_max;// mm (Free length)
+p=lf/(nt-1);// mm (Pitch of coil)
+printf('\n Force on the valve = %.1f N',Fv)
+printf('\n Maximum deflection = %.f mm', del_max)
+printf('\n Maximum force = %.1f N', Fmax)
+printf('\n Wahl''s correction factor = %.4f ',Kw)
+printf('\n Diameter of spring wire = %.f mm',d)
+printf('\n Mean coil diameter = %.f mm', Dm)
+printf('\n number of turns = %.f ',n)
+printf('\n Total number of turns for square & ground ends = %.f ',nt)
+printf('\n Free length = %.f mm. Use 200 mm',lf)
+printf('\n Pitch of coil = %.1f mm',p)
diff --git a/3774/CH8/EX8.7/Ex8_7.sce b/3774/CH8/EX8.7/Ex8_7.sce
new file mode 100644
index 000000000..002a1565f
--- /dev/null
+++ b/3774/CH8/EX8.7/Ex8_7.sce
@@ -0,0 +1,62 @@
+// exa 8.7 Pg 232
+clc;clear;close;
+
+// Given Data
+dv=30;// mm
+Wv=10;// N
+Wl=25;// N
+lf=100;// mm
+del1=20;// mm
+p=3.5;// N/mm.sq.
+valve_lift=2;// mm
+C=6;// spring index
+tau=500;// N/mm.sq.
+G=0.84*10**5;// N/mm.sq.
+
+W=(%pi/4)*dv**2*p;// N (load on the valve at operating condition)
+W1=W-Wv;//N (Net load on the valve at operating condition)
+//W1*100=Wl*150+S1*200+P*300 // taking momens about the fulcrum
+//S1*200+P*300=W1*100-Wl*150 ...eqn(1)
+valve_lift=20*100/200;// mm //from figure (when spring is extended by 20 mm)
+spring_extension=2*200/100;// mm // from figure (when valve is lifted 2 mm)
+valve_load=W*12/10;// N // (when valve is lifted 2 mm)
+W2=valve_load-Wv;// N // (when valve is lifted 2 mm)
+del2=del1+4;// mm (when valve is lifted)
+//S2=S1*del2/del1;// spring force when valve is lifted
+//S1*del2/del1-s2=0 ... eqn(1)
+//W2*100=Wl*150+S2*200+P*300 // taking momens about the fulcrum
+//S2*200+P*300 =W2*100-Wl*150 ... eqn(2)
+//S1*200+P*300=W1*100-Wl*150 ...eqn(3)
+// solving above 3 eqn. by matrix method
+A=[del2/del1 -1 0;200 0 300;0 200 300];
+B=[0;W1*100-Wl*150;W2*100-Wl*150];
+X=A**-1*B;// solution matrix
+S1=X(1);// N
+S2=X(2);// N
+printf('\n Spring force when valve is lifted = %.1f N',S2)
+printf('\n\n Design of spring - ')
+k=(S2-S1)/(del2-del1);// N/mm (Spring stiffness)
+printf('\n Spring stiffness = %.2f N/mm',k)
+Kw=(4*C-1)/(4*C-4)+0.615/C;// Wahl's correction factor
+printf('\n Wahl''s correction factor = %.4f',Kw)
+// tau=Kw*8*S2*C/%pi/d**2 max. shear stress
+d=sqrt(Kw*8*S2*C/%pi/tau);// mm (spring diameter)
+printf('\n spring diameter = %.2f mm or %.f mm',d,d)
+d=ceil(d);// mm
+// k=G*d/(8*C**3*n) (Spring stiffness)
+n=G*d/(8*C**3*k);// no. of active coils
+printf('\n no. of active coils = %.2f. Use n=7',n)
+n=ceil(n);// rounding
+nt=n+1;// total no. of active coils
+printf('\n total no. of active coils = %.f',nt)
+p=lf/(n-1);// mm (pitch of coils)
+printf('\n pitch of coils = %.2f mm',p)
+
+
+
+
+
+
+
+
+
diff --git a/3774/CH8/EX8.8/Ex8_8.sce b/3774/CH8/EX8.8/Ex8_8.sce
new file mode 100644
index 000000000..07dbaecf7
--- /dev/null
+++ b/3774/CH8/EX8.8/Ex8_8.sce
@@ -0,0 +1,43 @@
+// exa 8.8 Pg 234
+clc;clear;close;
+
+// Given Data
+Fmin=0;// N
+Fmax=1000;// N
+del=80;// mm
+Do=25;// mm
+n=30;// no. of turns
+G=85;// kN/mm.sq.
+
+k=(Fmax-Fmin)/del;// N/mm (Spring stiffness)
+printf('\n Spring stiffness = %.1f N/mm',k)
+// k=G*d/(8*C**3*n) (Spring stiffness)
+C_cube_BY_d=G*10**3/(k*8*n);// 
+
+function [C,d]=hitntrial(c3d,Do)
+    for C=5:-0.1:4.5
+        d=C**3/(c3d);
+        Doo=d*C+C;
+        if Doo<Do 
+            break;
+        end;
+    end
+
+endfunction;
+
+[C,d]=hitntrial(C_cube_BY_d,Do)
+printf('\n By hit and trial method and using value of C^3/d -')
+printf('\n value of Spring Index, C = %.1f ',C)
+printf('\n value of wire diameter, d = %.1f mm',d)
+printf('\n But we adopt d=4 mm.')
+d=4;// mm (adopted for design)
+C=(C_cube_BY_d*d)**(1/3);// Spring index
+printf('Hence, Spring Index = %.2f ',C)
+Dm=C*d;// mm
+printf('\n Mean coil diameter = %.2f mm', Dm)
+Do=Dm+d;// mm
+printf('\n Outside coil diameter = %.2f mm < 25 mm. Hence design is ok.', Do)
+Kw=(4*C-1)/(4*C-4)+0.615/C;// Wahl's correction factor
+printf('\n Wahl''s correction factor = %.3f ',Kw)
+tau=8*Kw*C*Fmax/(%pi*d**2);// N/mm.sq.
+printf('\n Maximum shear stress = %.2f N/mm.sq.',tau)