diff options
Diffstat (limited to '3774/CH9')
-rw-r--r-- | 3774/CH9/EX9.1/Ex9_1.sce | 32 | ||||
-rw-r--r-- | 3774/CH9/EX9.11/Ex9_11.sce | 22 | ||||
-rw-r--r-- | 3774/CH9/EX9.13/Ex9_13.sce | 108 | ||||
-rw-r--r-- | 3774/CH9/EX9.14/Ex9_14.sce | 40 | ||||
-rw-r--r-- | 3774/CH9/EX9.15/Ex9_15.sce | 131 | ||||
-rw-r--r-- | 3774/CH9/EX9.2/Ex9_2.sce | 29 | ||||
-rw-r--r-- | 3774/CH9/EX9.3/Ex9_3.sce | 45 | ||||
-rw-r--r-- | 3774/CH9/EX9.4/Ex9_4.sce | 38 | ||||
-rw-r--r-- | 3774/CH9/EX9.5/Ex9_5.sce | 28 | ||||
-rw-r--r-- | 3774/CH9/EX9.6/Ex9_6.sce | 120 | ||||
-rw-r--r-- | 3774/CH9/EX9.7/Ex9_7.sce | 25 | ||||
-rw-r--r-- | 3774/CH9/EX9.9/Ex9_9.sce | 55 |
12 files changed, 673 insertions, 0 deletions
diff --git a/3774/CH9/EX9.1/Ex9_1.sce b/3774/CH9/EX9.1/Ex9_1.sce new file mode 100644 index 000000000..4749d57e1 --- /dev/null +++ b/3774/CH9/EX9.1/Ex9_1.sce @@ -0,0 +1,32 @@ +// exa 9.1 Pg 256 +clc;clear;close; + +// Given Data +d=26;// mm +p=5;// mm +W=10;// kN +Do=50;// mm +Di=20;// mm +mu=0.2;// coefficient of thread friction +mu_c=0.15;// coefficient of collar friction +N=15;// rpm +pb=6;// MPa + +dm=d-p/2;// mm +dc=d-p;// mm +t=p/2;//mm +l=2*p;// mm +alfa=atand(l/(%pi*dm));// degree +fi=atand(mu);// degree +Tf=W*dm/2*tand(alfa+fi);// N.mm +Tc=mu_c*W/4*(Do+Di);// N.mm +T=Tf+Tc;// N.mm +printf('\n (a) Stress in the screw') +sigma_c=4*W*10**3/(%pi*dc**2);// N/mm.sq. +printf('\n Direct compressive stress = %.2f N/mm.sq',sigma_c) +tau=16*T*10**3/(%pi*dc**3);//N/mm.sq. +printf('\n Tortional shear stress = %.2f N/mm.sq',tau) +tau_max=sqrt(sigma_c**2/4+tau**2);//MPa +printf('\n Maximum shear stress = %.2f N/mm.sq',tau_max) +n=W*10**3/(%pi*dm*t*pb); +printf('\n\n (b) number of threads of nut in engagement = %.f',n) diff --git a/3774/CH9/EX9.11/Ex9_11.sce b/3774/CH9/EX9.11/Ex9_11.sce new file mode 100644 index 000000000..915002ead --- /dev/null +++ b/3774/CH9/EX9.11/Ex9_11.sce @@ -0,0 +1,22 @@ +// exa 9.11 Pg 273 + +clc;clear;close; + +// Given Data +d=26;// mm +L=0.25;//m +F=300;// N +mu=0.14;// coefficient of thread friction +p=5;// mm (for normal series) + +dc=d-p;// mm +dm=d-p/2;// mm +l=2*p;// mm +alfa=atand(l/%pi/dm);// degree +fi=atand(mu);// degree +To=F*L;// N.m (Torque applied by the operator) +//Tf=W*dm/2*tand(alfa+fi);// N.mm +// And Tf=To +W=To*1000/(dm/2*tand(alfa+fi));// N +printf('The force required for the job is : %.f N',W) +// Note - answer in the textbook is wrong. diff --git a/3774/CH9/EX9.13/Ex9_13.sce b/3774/CH9/EX9.13/Ex9_13.sce new file mode 100644 index 000000000..c34980b95 --- /dev/null +++ b/3774/CH9/EX9.13/Ex9_13.sce @@ -0,0 +1,108 @@ +// exa 9.13 Pg 274 + +clc;clear;close; + +// Given Data +W=50;// kN +lift=200;// mm +gc=300;// mm (ground clearance) +pb=16;// MPa +mu=0.14;// coefficient of collar friction + +//Screw C-35 +Sut=288;// MPa +n=3;// factor of safety for screw +// Nut : phosphor-bronze +sigma_t=100;// MPa +sigma_c=90;// MPa +tau=80;// MPa +n2=3;// factor of safety for nut + +sigma_ts=Sut/n;// MPa +sigma_cs=Sut/n;// MPa +tau_s=sigma_ts/2;// MPa +// sigma_cs=4*W/(%pi*dc**2) +dc= sqrt(4*W*10**3/(%pi*sigma_cs));// mm +printf('\n Screw diameter - \n Core diameter, dc = %.2f mm. Use 30 mm',dc) +dc=30;// mm (adopted for design) +p=6;// mm (for normal series square threads) +d=dc+p;//mm +printf('\n outside diameter = %.f mm',d) +dm=dc+p/2;// mm +printf('\n mean diameter = %.1f mm',dm) +t=p/2;// mm +printf('\n thread thickness = %.1f mm',t) + +printf('\n Maximum tensile & shear tress in screw -') +sigma_c=4*W*1000/%pi/dc**2;// MPa +alfa=atand(p/(%pi*dm));// degree +fi=atand(mu);// degree +Tf=dm*W*10**3/2*tand(alfa+fi);// where TfByW = Tf/W +tau=16*Tf/(%pi*dc**3);// MPa +sigma12=(1/2)*(sigma_c+sqrt(sigma_c**2+4*tau**2));// MPa +printf('\n Maximum tensile stress = %.1f MPa < %.f MPA. Hence design is safe.',sigma12,sigma_ts) +tau_max=sqrt((sigma_c/2)**2+tau**2);// MPa +printf('\n Maximum shear stress = %.2f MPa < %.f MPA. Hence design is safe.',tau_max,tau_s) + +printf('\n Height of nut-') +n=W*10**3/(%pi/4)/pb/(d**2-dc**2);// no. of threads +n= round(n);// no. of threads (rounding) +h=n*p;// mm +printf('\n h=%.f mm',h) + +printf('\n Check for stress in screw and nut') +tau_screw=W*10**3/(%pi*n*dc*t);// MPa +printf('\n shear stress in screw = %.2f MPa\',tau_screw) +tau_nut=W*10**3/(%pi*n*d*t);// MPa +printf('\n shear stress in nut = %.2f MPa',tau_nut) +printf('\n These are within permissible limits. Hence design is safe.') + +printf('\n Nut collar size-') +// %pi/4*(D1**2-d**2)*sigma_tn=W +D1=sqrt(W*10**3/(%pi/4)/(50)+d**2);// mm +printf('\n Inside diameter of collar = %.2f mm. Use D1=52 mm',D1) +D1=52;//mm (adopted for design) +// %pi/4*(D2**2-D1**2)*sigma_cn=W +D2=sqrt(W*10**3/(%pi/4)/45+D1**2);// mm +printf('\n Outside diameter of collar = %.1f mm. Use D2=65 mm',D2) +D2=65;//mm (adopted for design) + +// %pi*D1*tc*tau_cn=W +tau_cn=40;// MPa +tc=W*10**3/(%pi*D1*tau_cn);// mm +printf('\n thickness of nut = %.2f mm. Use tc=8 mm.',tc) +tc=8;// mm (adopted for design) + +printf('\n Head Dimensions-') +D3=1.75*d;// mm +printf('\n Diameter of head on top of screw = %.2f mm. use D3=64 mm.',D3) +D3=64;// mm (adopted for design) +D4=D3/4;// mm +printf('\n pin diameter in the cup = %.f mm',D4) + +printf('\n Torque required between cup and head-') +Tc=mu*W*10**3/3*((D3**3-D4**3)/(D3**2-D4**2));// N.mm +printf('\n Tc=%.f N.mm (acc. to uniform pressure theory)',Tc) +T=Tf+Tc;// N.mm +printf('\n Total Torque, T=%.f N.mm',T) + +F=300;// N (as a normal person can apply 100-300 N) +l=T/F;//mm +printf('\n length of lever = %.f mm. Use 1075 mm',l) + +M=F*l;// N.mm +dl=(32*M/%pi/sigma12)**(1/3);// mm +printf('\n Diameter of lever, dl=%.1f mm.',dl) + +H=2*dl;// mm +printf('\n Height of head, H=%.f mm',H) + +printf('\n Check for screw in buckling-') +L=lift+0.5*h;// mm +K=dc/4;// mm +C=0.25;// spring index +sigma_y=288;// MPa +Ac=%pi/4*dc**2;//mm.sq. +Wcr=Ac*sigma_y*(1-(sigma_y/4/C/%pi**2/(200*10**3))*(L/K)**2)/1000;// kN +printf('\n Buckling or critical load for screw, Wcr = %.f kN > 50kN',Wcr) +printf('\n Hence design is safe.') diff --git a/3774/CH9/EX9.14/Ex9_14.sce b/3774/CH9/EX9.14/Ex9_14.sce new file mode 100644 index 000000000..ac537e623 --- /dev/null +++ b/3774/CH9/EX9.14/Ex9_14.sce @@ -0,0 +1,40 @@ +// exa 9.14 Pg 278 + +clc;clear;close; + +// Given Data +d=32;// mm +p=5;// mm +W=12;// kN +D3=50;// mm +D4=20;// mm +mu=0.15;// coefficient of thread friction +mu_c=0.20;// coefficient of collar friction +N=24;// rpm +pb=6;// N/mm.sq. +tau_s=30;// MPa +tau_n=30;// MPa + +dm=d-p/2;// mm +dc=d-p;// mm +t=p/2;// mm +l=2*p;//mm +alfa=atand(l/%pi/dm);// degree +fi=atand(mu);// degree +Tf=W*10**3*dm/2*tand(alfa+fi);// N.mm +Tc=mu_c*W*10**3/4*(D3+D4);// N.mm +T=Tf+Tc;// N.mm +printf('\n (i) Torque required to rotate the screw = %.f N.mm',T) + +printf('\n (ii) Stresses induced in screw - ') +sigma_c=4*W*10**3/(%pi*dc**2);// N/mm.sq. +printf('\n Direct compressive stress = %.2f N/mm.sq',sigma_c) +tau=16*T/(%pi*dc**3);// N/mm.sq. +printf('\n Tortional shear stress = %.2f N/mm.sq',tau) +tau_max=sqrt((sigma_c/2)**2+tau**2);// MPa +printf('\n Maximum shear stress = %.2f MPa < %.f MPa',tau_max,tau_s) +printf('\n Hence design is safe.') +n=W*10**3/(%pi*dm*t*pb);// no. of threads +n=ceil(n);// rounding +h=n*p;//mm +printf('\n (iii) Height of nut = %.f mm',h) diff --git a/3774/CH9/EX9.15/Ex9_15.sce b/3774/CH9/EX9.15/Ex9_15.sce new file mode 100644 index 000000000..26caa5ae5 --- /dev/null +++ b/3774/CH9/EX9.15/Ex9_15.sce @@ -0,0 +1,131 @@ +// exa 9.15 Pg 279 + +clc;clear;close; + +// Given Data +W=100;// kN +lift=260;// mm +pb=15;// N/mm.sq. +mu=0.15;// coefficient of thread friction +mu_c=0.20;// coefficient of collar friction +//Screw +Suts=800;// N/mm.sq. +sigma_ss=340;// N/mm.sq. +ns=4;// factor of safety +//Nut +Sutn=552;// N/mm.sq. +sigma_sn=260;// N/mm.sq. +nn=5;// factor of safety + +sigma_ts=Suts/ns;// N/mm.sq. +sigma_cs=Suts/ns;// N/mm.sq. +tau_s=sigma_ss/ns;// N/mm.sq. +sigma_tn=Sutn/nn;// N/mm.sq. +sigma_cn=Sutn/nn;// N/mm.sq. +tau_n=sigma_sn/nn;// N/mm.sq. + +//sigma_cs=4*W/(%pi*dc**2) +dc=sqrt(4*W*10**3/(%pi*sigma_cs));// mm +printf('\n Screw Diameter-\n Core diameter of screw, dc=%.2f mm. Use dc=33 mm',dc) +dc=33;// mm +p=7;// mm (for normal series square threads) +d=dc+p;//mm +printf('\n outside diameter = %.f mm',d) +dm=dc+p/2;// mm +printf('\n mean diameter = %.1f mm',dm) +t=p/2;// mm +printf('\n thread thickness = %.1f mm',t) + +printf('\n Maximum stresses in screw -') +sigma_c=4*W*1000/%pi/dc**2;// MPa +alfa=atand(p/(%pi*dm));// degree +fi=atand(mu);// degree +Tf=dm*W*10**3/2*tand(alfa+fi);// where TfByW = Tf/W +tau=16*Tf/(%pi*dc**3);// MPa +sigma12=(1/2)*(sigma_c+sqrt(sigma_c**2+4*tau**2));// MPa +printf('\n Maximum tensile stress = %.1f N/mm.sq. < %.f N/mm.sq.. Hence design is safe.',sigma12,sigma_ts) +tau_max=sqrt((sigma_c/2)**2+tau**2);// MPa +printf('\n Maximum shear stress = %.2f N/mm.sq. < %.f N/mm.sq.. Hence design is safe.',tau_max,tau_s) + +printf('\n Height of nut-') +n=W*10**3/(%pi/4)/pb/(d**2-dc**2);// no. of threads +n= ceil(n);// no. of threads (rounding) +h=n*p;// mm +printf('\n h=%.f mm. Use 120 mm.',h) +h=120;// mm + +printf('\n Check for stress in screw and nut') +tau_screw=W*10**3/(%pi*n*dc*t);// MPa +printf('\n shear stress in screw = %.2f MPa < %.f MPa',tau_screw,tau_s) +tau_nut=W*10**3/(%pi*n*d*t);// MPa +printf('\n shear stress in nut = %.2f MPa < %.f MPa',tau_nut,tau_n) +printf('\n These are within permissible limits. Hence design is safe.') + +printf('\n Nut collar size-') +// %pi/4*(D1**2-d**2)*sigma_tn=W +D1=sqrt(W*10**3/(%pi/4)/sigma_tn+d**2);// mm +printf('\n Inside diameter of collar = %.2f mm. Use D1=55 mm',D1) +D1=55;//mm (adopted for design) +// %pi/4*(D2**2-D1**2)*sigma_cn=W +D2=sqrt(W*10**3/(%pi/4)/sigma_cn+D1**2);// mm +printf('\n Outside diameter of collar = %.2f mm. Use D2=70 mm',D2) +D2=70;//mm (adopted for design) + +// %pi*D1*tc*tau_n=W +tc=W*10**3/(%pi*D1*tau_n);// mm +printf('\n thickness of nut = %.f mm. Use tc=15 mm.',tc) +tc=15;// mm (adopted for design) + +printf('\n Head Dimensions-') +D3=1.75*d;// mm +printf('\n Diameter of head on top of screw = %.2f mm.',D3) +D4=D3/4;// mm +printf('\n pin diameter in the cup = %.1f mm. Use 20 mm.',D4) +D4=20;// mm (adopted for design) + +printf('\n Torque required between cup and head-') +Tc=mu_c*W*10**3/3*((D3**3-D4**3)/(D3**2-D4**2));// N.mm +printf('\n Tc=%.f N.mm (acc. to uniform pressure theory)',Tc) +T=Tf+Tc;// N.mm +printf('\n Total Torque, T=%.f N.mm',T) + +F=300;// N (as a normal person can apply 100-300 N) +l=T/F;//mm +printf('\n length of lever = %.f mm or %.2f m',l,l/1000) + +M=F*l;// N.mm +sigma_b=100;// N/mm.sq. (assumed) +dl=(32*M/%pi/sigma_b)**(1/3);// mm +printf('\n Diameter of lever, dl=%.1f mm. Use dl=45 mm.',dl) +dl=45;// mm (adopted for design) + +H=2*dl;// mm +printf('\n Height of head, H=%.f mm',H) + +printf('\n Check for screw in buckling-') +L=lift+0.5*h;// mm +K=dc/4;// mm +C=0.25;// spring index +sigma_y=200;// MPa +Ac=%pi/4*dc**2;//mm.sq. +Wcr=Ac*sigma_y*(1-(sigma_y/4/C/%pi**2/(200*10**3))*(L/K)**2)/1000;// kN +printf('\n Buckling or critical load for screw, Wcr = %.f kN > 100kN',Wcr) + +To=W*10**3*dm/2*tand(alfa);// N.mm +eta=To/T*100;// % +printf('\n Efficiency of screw = %.2f %%',eta) + +printf('\n Body dimensions-') +D5=1.5*D2;// mm +t2=2*tc;// mm +t3=0.25*d;//mm +D6=2.25*D2;// mm +printf('\n Diameter of body at top, D5 = %.f mm', D5) +printf('\n Thickness of base, t2 = %.f mm', t2) +printf('\n Thickness of body, t3 = %.f mm', t3) +printf('\n Inside diameter of bottom, D6 = %.1f mm. Use D6=160 mm.', D6) +D6=160;// mm (adopted for design) +D7=1.75*D6;// mm +hb=lift+h+100;// mm +printf('\n Outside diameter at the bottom, D7 = %.2f mm.', D7) +printf('\n Height of body = %.f mm.',hb) diff --git a/3774/CH9/EX9.2/Ex9_2.sce b/3774/CH9/EX9.2/Ex9_2.sce new file mode 100644 index 000000000..f4f7f1259 --- /dev/null +++ b/3774/CH9/EX9.2/Ex9_2.sce @@ -0,0 +1,29 @@ +// exa 9.2 Pg 257 +clc;clear;close; + +// Given Data +d=50;// mm +p=8;// mm +W=2;// kN +Do=100;// mm +Di=50;// mm +mu=0.15;// coefficient of thread friction +mu_c=0.10;// coefficient of collar friction +N=25;// rpm +two_beta=29;// degree + +dm=d-p/2;// mm +dc=d-p;// mm +t=p/2;//mm +l=2*p;// mm +alfa=atand(p/(%pi*dm));// degree +mu_e=mu/cosd(two_beta/2);// virtual coefficient of friction +fi=atand(mu_e);// degree +Tf=W*dm/2*tand(alfa+fi);// N.mm +Tc=mu_c*W/4*(Do+Di);// N.mm +T=Tf+Tc;// N.mm +P=2*%pi*N*T/(60*10**3);// kW +printf('\n (a) Power required = %.3f kN',P) +To=W*dm/2*tand(alfa);// N.mm +eta=To/T*100;// % (efficiency) +printf('\n (b) Efficiency of screw = %.2f %%',eta) diff --git a/3774/CH9/EX9.3/Ex9_3.sce b/3774/CH9/EX9.3/Ex9_3.sce new file mode 100644 index 000000000..a818e5233 --- /dev/null +++ b/3774/CH9/EX9.3/Ex9_3.sce @@ -0,0 +1,45 @@ +// exa 9.3 Pg 259 +clc;clear;close; + +// Given Data +d=10;// mm +p=3;// mm +mu=0.15;// coefficient of thread friction +mu_c=0.20;// coefficient of collar friction +dc=15;// mm +F=60;// N +W=4;// kN +two_beta=30;// degree +h=25;// mm +lf=150;// mm (screw free length) + +dm=d-p/2;// mm +alfa=atand(p/(%pi*dm));// degree +mu_e=mu/cosd(two_beta/2);// virtual coefficient of friction +fi=atand(mu_e);// degree +Tf=W*10**3*dm/2*tand(alfa+fi);// N.mm +Tc=mu_c*W*10**3/2*dc;// N.mm +T=Tf+Tc;// N.mm +//F*l=T +l=T/F;// mm (Length of handle) +printf('\n (a) Length of handle = %.1f mm',l) + +printf('\n\n (b) Maximum shear stress in screw') +printf('\n Section 1-1 : ') +dc=d-p;//mm +tau=16*T/(%pi*dc**3);// N/mm.sq. +M=F*lf;// N.mm +sigma_b=32*M/(%pi*dc**3);// N/mm.sq. +tau_max=sqrt((sigma_b/2)**2+tau**2);// MPa +printf('\n Maximum shear stress = %.2f MPa',tau_max) +printf('\n Section 2-2 : ') +sigma_c=4*W*10**3/(%pi*dc**2);// N/mm.sq. (Direct compressive stress) +tau2=16*Tc/(%pi*dc**3);//;// N/mm.sq. (Tortional shear stress) +tau_max=sqrt((sigma_c/2)**2+tau2**2);// MPa +printf('\n Maximum shear stress = %.2f MPa',tau_max) + +//h=n*p;// height of nut +n=ceil(h/p);// no. of threads +t=p/2;// mm (thickness of threads) +pb=W*10**3/(%pi*dm*t*n);// MPa +printf('\n\n (b) Bearing pressure on threads = %.1f MPa',pb) diff --git a/3774/CH9/EX9.4/Ex9_4.sce b/3774/CH9/EX9.4/Ex9_4.sce new file mode 100644 index 000000000..b9c2a6b60 --- /dev/null +++ b/3774/CH9/EX9.4/Ex9_4.sce @@ -0,0 +1,38 @@ +// exa 9.4 Pg 260 +clc;clear;close; + +// Given Data +W=25;// kN +two_beta=29;// degree +v=0.96;// m/min +mu=0.14;// coefficient of thread friction +Di=30;// mm +Do=66;// mm +mu_c=0.15;// coefficient of collar friction +d=36;// mm +p=6;// mm +Sut=630;// MPa +Syt=380;// MPa + +dm=d-p/2;// mm +dc=d-p;// mm +l=2*p;// mm +alfa=atand(l/(%pi*dm));// degree +mu_e=mu/cosd(two_beta/2);// virtual coefficient of friction +fi=atand(mu_e);// degree +Tf=W*10**3*dm/2*tand(alfa+fi);// N.mm +Tc=mu_c*W*10**3/4*(Do+Di);// N.mm +T=Tf+Tc;// N.mm +N=v*10**3/l;// rpm + +P=2*%pi*N*T/(60*10**3)*10**-3;// kW +printf('\n Power required to drive the slide = %.2f kN',P) +sigma_c=4*W*10**3/(%pi*dc**2);// MPa +tau=16*T/(%pi*dc**3);// MPa +sigma1=1/2*(sigma_c+sqrt(sigma_c**2+4*tau**2));// MPa +tau_max=sqrt((sigma_c/2)**2+tau**2);// MPa +n_t=Syt/sigma1;// factor of safety in tension +printf('\n factor of safety in tension = %.2f ',n_t) +n_s=Syt/2/tau_max;// factor of safety in shear +printf('\n factor of safety in shear = %.2f ',n_s) +// Note- Answer in the textbook are not accurate. diff --git a/3774/CH9/EX9.5/Ex9_5.sce b/3774/CH9/EX9.5/Ex9_5.sce new file mode 100644 index 000000000..6f5741295 --- /dev/null +++ b/3774/CH9/EX9.5/Ex9_5.sce @@ -0,0 +1,28 @@ +// exa 9.5 Pg 262 +clc;clear;close; + +// Given Data +d=12;// mm +dc=10;// mm +p=2;// mm +Do=10;//mm +mu=0.15;// coefficient of thread friction +mu_c=0.18;// coefficient of collar friction +F=100;// N +l=150;// mm + +dm=dc+p/2;// mm +alfa=atand(p/(%pi*dm));// degree +fi=atand(mu);// degree +TfByW=dm/2*tand(alfa+fi);// where TfByW = Tf/W +TcByW=mu_c/3*Do;// where TcByW = Tc/W +TByW=TfByW+TcByW;// N.mm (total torque at B-B) +Tapplied=F*l;// N.mm (torque applied by the operator) +//putting T= Tapplied +W= Tapplied/TByW;// N +printf('\n (a) Clamping force between the jaws = %.f N',W) +eta=W*dm/2*tand(alfa)/Tapplied*100;// % +printf('\n (b) Efficiency of vice = %.2f %%',eta) +Tf=TfByW*W;// N.mm +printf('\n (c) Torque at A-A, Tf = %.1f N.mm & Torque at B-B = %.f N.mm',Tf,Tapplied) +// Note- Answer in the textbook are not accurate. diff --git a/3774/CH9/EX9.6/Ex9_6.sce b/3774/CH9/EX9.6/Ex9_6.sce new file mode 100644 index 000000000..c548c7e98 --- /dev/null +++ b/3774/CH9/EX9.6/Ex9_6.sce @@ -0,0 +1,120 @@ +// exa 9.6 Pg 267 + +clc;clear;close; + +// Given Data +W=100;// kN +lift=400;// mm +sigma_ts=100;// MPa +sigma_cs=100;// MPa +tau_s=60;// MPa +tau_tn=50;// MPa +sigma_cn=45;// MPa +tau_n=40;// MPa +pb=15;// MPa +mu=0.2;// coefficient of thread friction +mu_c=0.15;// coefficient of collar friction + +//sigma_cs=4*W/(%pi*dc**2) +dc=sqrt(4*W*10**3/(%pi*sigma_cs));// mm +printf('\n Screw Diameter-\n Core diameter of screw, dc=%.2f mm. Use dc=40 mm',dc) +dc=40;// mm +p=7;// mm (for normal series square threads) +d=dc+p;//mm +printf('\n outside diameter = %.f mm',d) +dm=dc+p/2;// mm +printf('\n mean diameter = %.1f mm',dm) +t=p/2;// mm +printf('\n thread thickness = %.1f mm',t) + +printf('\n Maximum tensile & shear stress in screw -') +sigma_c=4*W*1000/%pi/dc**2;// MPa +alfa=atand(p/(%pi*dm));// degree +fi=atand(mu);// degree +Tf=dm*W*10**3/2*tand(alfa+fi);// where TfByW = Tf/W +tau=16*Tf/(%pi*dc**3);// MPa +sigma12=(1/2)*(sigma_c+sqrt(sigma_c**2+4*tau**2));// MPa +printf('\n Maximum tensile stress = %.f MPa < %.f MPA. Hence design is safe.',sigma12,sigma_ts) +tau_max=sqrt((sigma_c/2)**2+tau**2);// MPa +printf('\n Maximum shear stress = %.2f MPa < %.f MPA. Hence design is safe.',tau_max,tau_s) + +printf('\n Height of nut-') +n=W*10**3/(%pi/4)/pb/(d**2-dc**2);// no. of threads +n= ceil(n);// no. of threads (rounding) +h=n*p;// mm +printf('\n h=%.f mm',h) + +printf('\n Check for stress in screw and nut') +tau_screw=W*10**3/(%pi*n*dc*t);// MPa +printf('\n shear stress in screw = %.2f MPa < %.f MPa',tau_screw,tau_s) +tau_nut=W*10**3/(%pi*n*d*t);// MPa +printf('\n shear stress in nut = %.2f MPa < %.f MPa',tau_nut,tau_n) +printf('\n These are within permissible limits. Hence design is safe.') + +printf('\n Nut collar size-') +// %pi/4*(D1**2-d**2)*sigma_tn=W +D1=sqrt(W*10**3/(%pi/4)/tau_tn+d**2);// mm +printf('\n Inside diameter of collar = %.2f mm. Use D1=70 mm',D1) +D1=70;//mm (adopted for design) +// %pi/4*(D2**2-D1**2)*sigma_cn=W +D2=sqrt(W*10**3/(%pi/4)/sigma_cn+D1**2);// mm +printf('\n Outside diameter of collar = %.2f mm. Use D2=90 mm',D2) +D2=90;//mm (adopted for design) + +// %pi*D1*tc*tau_n=W +tc=W*10**3/(%pi*D1*tau_n);// mm +printf('\n thickness of nut = %.2f mm. Use tc=12 mm.',tc) +tc=12;// mm (adopted for design) + +printf('\n Head Dimensions-') +D3=1.75*d;// mm +printf('\n Diameter of head on top of screw = %.2f mm. use D3=84 mm.',D3) +D3=84;// mm (adopted for design) +D4=D3/4;// mm +printf('\n pin diameter in the cup = %.f mm',D4) + +printf('\n Torque required between cup and head-') +Tc=mu_c*W*10**3/3*((D3**3-D4**3)/(D3**2-D4**2));// N.mm +printf('\n Tc=%.f N.mm (acc. to uniform pressure theory)',Tc) +T=Tf+Tc;// N.mm +printf('\n Total Torque, T=%.f N.mm',T) + +F=300;// N (as a normal person can apply 100-300 N) +l=T/F;//mm +printf('\n length of lever = %.f mm. Use 3300 mm',l) + +M=F*l;// N.mm +dl=(32*M/%pi/sigma12)**(1/3);// mm +printf('\n Diameter of lever, dl=%.1f mm. Use dl=48 mm.',dl) +dl=48;// mm (adopted for design) + +H=2*dl;// mm +printf('\n Height of head, H=%.f mm',H) + +printf('\n Check for screw in buckling-') +L=lift+0.5*h;// mm +K=dc/4;// mm +C=0.25;// spring index +sigma_y=200;// MPa +Ac=%pi/4*dc**2;//mm.sq. +Wcr=Ac*sigma_y*(1-(sigma_y/4/C/%pi**2/(200*10**3))*(L/K)**2)/1000;// kN +printf('\n Buckling or critical load for screw, Wcr = %.f kN > 100kN',Wcr) + +To=W*10**3*dm/2*tand(alfa);// N.mm +eta=To/T*100;// % +printf('\n Efficiency of screw = %.1f %%',eta) + +printf('\n Body dimensions-') +D5=1.5*D2;// mm +t2=2*tc;// mm +t3=0.25*d;//mm +D6=2.25*D2;// mm +printf('\n Diameter of body at top, D5 = %.f mm', D5) +printf('\n Thickness of base, t2 = %.f mm', t2) +printf('\n Thickness of body, t3 = %.f mm', t3) +printf('\n Inside diameter of bottom, D6 = %.1f mm. Use D6=205 mm.', D6) +D6=205;// mm (adopted for design) +D7=1.75*D6;// mm +hb=lift+h+100;// mm +printf('\n Outside diameter at the bottom, D7 = %.2f mm. Use 360 mm.', D7) +printf('\n Height of body = %.f mm. Use 600mm',hb) diff --git a/3774/CH9/EX9.7/Ex9_7.sce b/3774/CH9/EX9.7/Ex9_7.sce new file mode 100644 index 000000000..0adbaae08 --- /dev/null +++ b/3774/CH9/EX9.7/Ex9_7.sce @@ -0,0 +1,25 @@ +// exa 9.7 Pg 267 + +clc;clear;close; + +// Given Data +two_beta=30;// degree +W=400*10**3;// N +d=100;// mm +p=12;// mm +mu=0.15;// coefficient of thread friction + +dm=d-p/2;// mm +dc=d-p;// mm +l=2*p;// mm +alfa=atand(l/%pi/dm);// degree +mu_e=mu/cosd(two_beta/2);// virtual coefficient of friction +fi=atand(mu);// degree +Tf=W*dm/2*tand(alfa+fi);// N.mm (Frictional torque for raising load) +T=W*dm/4*tand(fi);// N.mm +To=W*dm/2*tand(alfa);// N.mm (Torque without friction) +eta1=To/Tf*100;// % +printf('\n Efficiency during raising the load = %.2f %%',eta1) +eta2=T/To*100;// % +printf('\n Efficiency during lowering the load = %.2f %%',eta2) +// Note - answer & solution is wrong in the textbook. diff --git a/3774/CH9/EX9.9/Ex9_9.sce b/3774/CH9/EX9.9/Ex9_9.sce new file mode 100644 index 000000000..b9fd634e2 --- /dev/null +++ b/3774/CH9/EX9.9/Ex9_9.sce @@ -0,0 +1,55 @@ +// exa 9.9 Pg 272 + +clc;clear;close; + +// Given Data +d=70;// mm +mu=0.13;// coefficient of thread friction +mu_c=0.15;// coefficient of collar friction +Do=90;// mm +Di=26;// mm +L=450;// mm +// C-25 steel screw +sigma_t1=275;// MPa +sigma_c1=275;// MPa +tau1=137.5;// MPa +// Phosphor bronze nut +sigma_t2=100;// MPa +sigma_c2=90;// MPa +tau2=80;// MPa +pb=15;//MPa +n=2;// factor of safety +//screw +sigma_ts=137.5;// MPa +sigma_cs=137.5;// MPa +tau_s=68.75;// MPa +//Nut +sigma_tn=50;// MPa +sigma_cn=45;// MPa +tau_n=40;// MPa + +p=10;// mm (for normal series square threads) +dc=d-p;//mm +dm=d-p/2;//mm +t=p/2;//mm +alfa=atand(p/%pi/dm);// degree +fi=atand(mu);// degree + +K=dc/4;// mm +C=0.25;// spring index +sigma_y=275;// MPa +Ac=%pi/4*dc**2;//mm.sq. +Wcr=Ac*sigma_y*(1-(sigma_y/4/C/%pi**2/(200*10**3))*(L/K)**2);// N +printf('\n (a) Safe Capacity of press or critical load for the screw = %.f N',Wcr) + +n=Wcr/(%pi*dm*t*pb);// no. of threads +n=ceil(n);// rounding +h=n*p;// mm +printf('\n (b) Height of nut, h=%.f mm',h) + +W=Wcr;// N +Tf=W*dm/2*tand(alfa+fi)/1000;// N.mm (Frictional torque) +Tc=mu_c*W/4*(Do+Di)/1000;// N.mm (Collar torque) +T=Tf+Tc;// N.mm +printf('\n (c) Necessary torsional moment or total torque = %.2f N.mm',T) +// Note - answer in the textbook is wrong. |