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+// 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)
+
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