diff options
Diffstat (limited to '3774')
79 files changed, 3062 insertions, 0 deletions
diff --git a/3774/CH1/EX1.1/Ex1_1.sce b/3774/CH1/EX1.1/Ex1_1.sce new file mode 100644 index 000000000..3c09f7fc2 --- /dev/null +++ b/3774/CH1/EX1.1/Ex1_1.sce @@ -0,0 +1,19 @@ +// exa 1.1 Pg 13 +clc;clear;close; +Nmax=1000;// rpm +Nmin=30;// rpm +z=9;// no. of steps + +//Rn=Nmax/Nmin=fi**(z-1) +fi=(Nmax/Nmin)**(1/(z-1));// common ratio + +printf('The speeds of gear box are:') +N1=Nmin;// rpm +for i=1:z + printf('\n\t\t\tN%d = %.1f rpm',i,N1) + N1=fi*N1;//rpm +end; + + + + diff --git a/3774/CH1/EX1.2/Ex1_2.sce b/3774/CH1/EX1.2/Ex1_2.sce new file mode 100644 index 000000000..0355ed31b --- /dev/null +++ b/3774/CH1/EX1.2/Ex1_2.sce @@ -0,0 +1,29 @@ +// exa 1.2 Pg 14 +clc;clear;close; +Pmax=100;// kW +Pmin=10;// kW +z=5;// no. of models + +//Rn=Pmax/Pmin=fi**(z-1) +fi=(Pmax/Pmin)**(1/(z-1));// common ratio + +printf('The power of generating sets are:') +P1=Pmin;// kW +for i=1:z + printf('\n\t\t\tP%d = %.1f kW',i,P1) + P1=fi*P1;//kW +end; + +printf('\nExpanding for 10 models.'); +z=10;// no. of models + +fi=(Pmax/Pmin)**(1/(z-1));// common ratio + +printf('\nThe power of generating sets are:') +P1=Pmin;// kW +for i=1:z + printf('\n\t\t\tP%d = %.1f kW',i,P1) + P1=fi*P1;//kW +end; + + diff --git a/3774/CH1/EX1.4/Ex1_4.sce b/3774/CH1/EX1.4/Ex1_4.sce new file mode 100644 index 000000000..1c82508d3 --- /dev/null +++ b/3774/CH1/EX1.4/Ex1_4.sce @@ -0,0 +1,29 @@ +// exa 1.4 Pg 15 +clc;clear;close; +Pmax=50;// kW +Pmin=5;// kW +z=4;// no. of models + +//Rn=Pmax/Pmin=fi**(z-1) +fi=(Pmax/Pmin)**(1/(z-1));// common ratio + +printf('The models are:') + +for i=0:z-1 + P1=fi**(i)*Pmin;// kW + printf('\n\t\t\tP%d = %.1f kW',i,P1) +end; + +printf('\n for 8 models.') + +z=8;// no. of models + +//Rn=Pmax/Pmin=fi**(z-1) +fi=(Pmax/Pmin)**(1/(z-1));// common ratio + +printf('The models are:') + +for i=0:z-1 + P1=fi**(i)*Pmin;// kW + printf('\n\t\t\tP%d = %.1f kW',i,P1) +end; diff --git a/3774/CH1/EX1.6/Ex1_6.sce b/3774/CH1/EX1.6/Ex1_6.sce new file mode 100644 index 000000000..791a14c8a --- /dev/null +++ b/3774/CH1/EX1.6/Ex1_6.sce @@ -0,0 +1,15 @@ +// exa 1.6 Pg 15 +clc;clear;close; +Pmax=75;// kW +Pmin=7.5;// kW +z=5;// no. of models + +//Rn=Pmax/Pmin=fi**(z-1) +fi=(Pmax/Pmin)**(1/(z-1));// common ratio + +printf('The models are:') + +for i=0:z-1 + P1=fi**(i)*Pmin;// kW + printf('\n\t\t\tP%d = %.1f kW',i,P1) +end; diff --git a/3774/CH3/EX3.1/Ex3_1.sce b/3774/CH3/EX3.1/Ex3_1.sce new file mode 100644 index 000000000..357bcaf6b --- /dev/null +++ b/3774/CH3/EX3.1/Ex3_1.sce @@ -0,0 +1,23 @@ +// exa 3.1 Pg 62 + +clc;clear;close; + +// Given Data +P=30;// kN +Sut=350;// MPa +n=2.5;// factor of safety + +sigma_w=Sut/n;// MPa (Working stress for the link) + +t=poly(0,'t');// thickness of link +A=2.5*t**2;// mm.sq. +I=t*(2.5*t)**3/12;// mm^4 (Moment of Inertia about N-A) +sigma_d=P/A;// N/mm.sq. +e=10+1.25*t;//mm +M=P*10**3*e;// N.mm +sigma_t=M*1.25*t/I;// N/mm.sq. +//maximum tensile stress at the top fibres = sigma_d+sigma_t=sigma_w ...eqn(1) +expr=sigma_d+sigma_t-sigma_w ;// expression of polynomial from above eqn. +t=roots(numer(expr));// solving the equation (as denominator will me be multiplied by zero on R.H.S) +t=t(1);// mm // discarding -ve roots +printf('dimension of cross section of link, t=%.f mm. Adopt t=21 mm. ',t) diff --git a/3774/CH3/EX3.10/Ex3_10.sce b/3774/CH3/EX3.10/Ex3_10.sce new file mode 100644 index 000000000..a9d5db7fa --- /dev/null +++ b/3774/CH3/EX3.10/Ex3_10.sce @@ -0,0 +1,27 @@ +// exa 3.10 Pg 71 + +clc;clear;close; + +// Given Data +d=4;// cm +M=15000;// N.cm +Syt=20000;// N/cm.sq. + +printf('\n (i) Maximum Principal Stress Theory-') +z=%pi*d**3/32;// cm.cube. +sigma_b=M/z;// N/cm.sq. +T=poly(0,'T') +tau=16*T/(%pi*d**3);// N/cm.sq. +//sigma1=(1/2)*(sigma_b+sqrt(sigma_b**2+4*tau**2)) // Maximum principal stress +//sigma1=(sigma_b/2+sqrt(sigma_b**2/4+tau**2)) // on solving +//tau=sqrt((sigma1-sigma_b/2)**2-sigma_b**2/4) +sigma1=Syt;// N/cm.sq. +T=sqrt((sigma1-sigma_b/2)**2-sigma_b**2/4)*(%pi*d**3)/16;// N.cm. +printf('\n Maximum value of torque, T = %.f N.cm.',T) + +printf('\n (ii) Maximum Shear Stress Theory') +tau_d=0.5*Syt;// N.cm. +//Te=sqrt(M**2+T**2)=(%pi/16)*d**3*tau_d +T=sqrt(((%pi/16)*d**3*tau_d)**2-M**2);// N.cm. +printf('\n Maximum value of torque, T = %.f N.cm.',T) +// Answer in the textbook is not accurate. diff --git a/3774/CH3/EX3.11/Ex3_11.sce b/3774/CH3/EX3.11/Ex3_11.sce new file mode 100644 index 000000000..529217bd8 --- /dev/null +++ b/3774/CH3/EX3.11/Ex3_11.sce @@ -0,0 +1,26 @@ +// exa 3.11 Pg 72 + +clc;clear;close; + +// Given Data +N=200;// rpm +P=25;// kW +tau_d=42;// MPa +W=900;// N +L=3;// m +Syt=56;// MPa +Syc=56;// MPa +sigma_d=56;// MPa + +T=P*60*10**3/(2*%pi*N);// N.m +M=W*L/4;// N.m +Te=sqrt(M**2+T**2);// N.m +// Te=(%pi/16)*d**3*tau_d +d=(Te*10**3/((%pi/16)*tau_d))**(1/3);// mm +printf('\n shaft diameter(using equivalent torque)-\n d=%.f mm.',d) + +Me=(1/2)*(M+sqrt(M**2+T**2));//N.m +// Me=(%pi/32)*d**3*sigma_d +d=(Me*10**3/((%pi/32)*sigma_d))**(1/3);// mm +printf('\n shaft diameter(using equivalent bending moment)-\n d=%.f mm.',d) +printf('\n adopt d=57 mm.') diff --git a/3774/CH3/EX3.12/Ex3_12.sce b/3774/CH3/EX3.12/Ex3_12.sce new file mode 100644 index 000000000..7b94e8c01 --- /dev/null +++ b/3774/CH3/EX3.12/Ex3_12.sce @@ -0,0 +1,25 @@ +// exa 3.12 Pg 72 + +clc;clear;close; + +// Given Data +sigma_w=60;// MPa +F=10;// kN +alfa=30;// degree + +FH=F*sind(alfa);// kN +FV=F*cosd(alfa);// kN +t=poly(0,'t');// mm +A=t*t;// mm.sq. +sigma_d=FV*10**3/A +M=FV*10**3*120+FH*10**3*150;// N.mm +I=t*(2*t)**3/12;// mm^4 +sigma_t=M*t/I;// N/mm.sq. +// Tensile stress at A=sigma_d+sigma_t=sigma_w ...eqn(1) +expr = sigma_d+sigma_t-sigma_w;// polynomial from above eqn. +t=roots(numer(expr));// roots of the polynomial +t=t(1);// mm // discarding -ve roots +printf('\n value of t = %.1f mm',t) +A=2*t**2;// mm.sq. +printf('\n Area of cross-section of Hanger, A = %.f mm.sq.',A) +// Note-Answer in the textbook is slighly wrong and cross section not calculated. diff --git a/3774/CH3/EX3.13/Ex3_13.sce b/3774/CH3/EX3.13/Ex3_13.sce new file mode 100644 index 000000000..bbbecc0e8 --- /dev/null +++ b/3774/CH3/EX3.13/Ex3_13.sce @@ -0,0 +1,48 @@ +// exa 3.13 Pg 74 + +clc;clear;close; + +// Given Data +P=15;// kW +n1=200;// rpm +l=600;// mm +z2=18;// no. of teeth +m2=5;// mm +alfa2=14.5;// degree +l2=120;// mm +z1=72;// no. of teeth +m1=5;// mm +alfa1=14.5;// degree +l1=150;// mm +sigma_d=80;// MPa + +d1=m1*z1;// mm +v1=%pi*d1*n1/(60*10**3);// m/s +Ft1=10**3*P/v1;// N (outwards) +Fr1=Ft1*tand(alfa1);// N (Downwards) +d2=m2*z2;// mm +v2=%pi*d2*n1/(60*10**3);// m/s +Ft2=10**3*P/v2;// N (outwards) +Fr2=Ft2*tand(alfa2);// N (Upwards) + +// RAV*600=Fr1*450+Fr2*120 (Taking moments about bearing B) +RAV=(Fr1*450+Fr2*120)/600;// N (Downwards) +RBV=(Fr1-Fr2-RAV);// N (upwards) +MCV=RAV*l1;// N.mm +MBV=Fr2*l2;// N.mm + +// RAH*600=-Ft1*450+Ft2*120 (Taking moments about bearing B) +RAH=(-Ft1*450+Ft2*120)/600;// N (Outwards) +RBH=Ft1+Ft2+RAH;// N (inwards) +MCH=RAH*l1;// N.mm +MBH=Ft2*l2;// N.mm + +// Resultant Bending Moments +MC=sqrt(MCV**2+MCH**2);// N.mm +MB=sqrt(MBV**2+MBH**2);// N.mm +Mmax=max(MC,MB);// N.mm +T=10**3*P/(2*%pi*n1);// N.m +Me=(1/2)*(Mmax+sqrt(Mmax**2+T**2));// N.mm +// Me=(%pi/32)*d**3*sigma_d +d=(Me/((%pi/32)*sigma_d))**(1/3) +printf('\n shaft diameter is : %.f mm',d) diff --git a/3774/CH3/EX3.2/Ex3_2.sce b/3774/CH3/EX3.2/Ex3_2.sce new file mode 100644 index 000000000..5414dc4be --- /dev/null +++ b/3774/CH3/EX3.2/Ex3_2.sce @@ -0,0 +1,25 @@ +// exa 3.2 Pg 63 + +clc;clear;close; + +// Given Data +P=6;// kN +alfa=30;// degree +Sut=250;// MPa +n=2.5;// factor of safety + +sigma_w=Sut/n;// MPa (Working stress for the link) +PH=P*10**3*cosd(alfa);// kN +PV=P*10**3*sind(alfa);// kN + +t=poly(0,'t');// thickness of link +A=2*t*t;// mm.sq. +sigma_d=PH/A;// N/mm.sq. +M=PH*100+PV*250;// N.mm +I=t*(2*t)**3/12;// mm^4 (Moment of Inertia) +sigma_t=M*t/I;// N/mm.sq. +//maximum tensile stress at the top fibres = sigma_d+sigma_t=sigma_w ...eqn(1) +expr=sigma_d+sigma_t-sigma_w ;// expression of polynomial from above eqn. +t=roots(numer(expr));// solving the equation (as denominator will me be multiplied by zero on R.H.S) +t=t(1);// mm // discarding -ve roots +printf('dimension of cross section of link, t=%.f mm.',t) diff --git a/3774/CH3/EX3.3/Ex3_3.sce b/3774/CH3/EX3.3/Ex3_3.sce new file mode 100644 index 000000000..6a1fcf9f1 --- /dev/null +++ b/3774/CH3/EX3.3/Ex3_3.sce @@ -0,0 +1,23 @@ +// exa 3.3 Pg 64 + +clc;clear;close; + +// Given Data +P=20;// kN +Sut=300;// MPa +n=3;// factor of safety + +sigma_w=Sut/n;// MPa (Working stress for the link) + +t=poly(0,'t');// thickness of link +A=4*t*t;// mm.sq. +sigma_d=P*10**3/A;// N/mm.sq. +e=6*t;//mm +M=P*10**3*e;// N.mm +z=t*(4*t)**2/6;// mm^3 (section modulus at x1-x2) +sigma_b=M/z;// N/mm.sq. +//maximum tensile stress at x1 = sigma_d+sigma_b=sigma_w ...eqn(1) +expr=sigma_d+sigma_b-sigma_w ;// expression of polynomial from above eqn. +t=roots(numer(expr));// solving the equation (as denominator will me be multiplied by zero on R.H.S) +t=t(2);// mm // discarding -ve roots +printf('dimension of cross section of link, t=%.2f mm. Use 23 mm.',t) diff --git a/3774/CH3/EX3.4/Ex3_4.sce b/3774/CH3/EX3.4/Ex3_4.sce new file mode 100644 index 000000000..b8f3b6496 --- /dev/null +++ b/3774/CH3/EX3.4/Ex3_4.sce @@ -0,0 +1,45 @@ +// exa 3.4 Pg 65 + +clc;clear;close; + +// Given Data +P=15;// kN +sigma_t=20;// MPa +sigma_c=60;// MPa +n=3;// factor of safety + +a=poly(0,'a');// from the diagram. +// Area of cross section +A1=2*a*a;// mm.sq. +A2=2*a*a/2;// mm.sq. +A=A1+A2;// mm.sq. + +// Location of neutral axis +//3*a**2*y_bar=2*a**2*a/2+a**2*(a+a/2) +y_bar=(2*a**2*a/2+a**2*(a+a/2))/(3*a**2);// mm + +// Moment of Inertia about neutral axis N-A +I=2*a*a**3/12+2*a**2*(y_bar-0.5*a)**2+2*((a/2)*(a**3/12)+(a**2/2)*(1.5*a-y_bar)**2);// mm^4 +yt=y_bar;//mm +yc=2*a-y_bar;// mm +e=y_bar-0.5*a;//mm +M=P*10**3*e;// N.mm +sigma_d=P*10**3/A;// N/mm.sq. +sigma_t1=M*yt/I;//N/mm.sq. +sigma_c1=M*yc/I;//N/mm.sq. +sigma_r_t=sigma_d+sigma_t1;// N/mm.sq. (sigma_r_t=resultant tensile stress at AB=sigma_d+sigma_t) +sigma_r_c=sigma_c1-sigma_d;// N/mm.sq. (sigma_r_t=resultant tensile stress at AB=sigma_d+sigma_t) + +//equating resulting tensile stress with given value sigma_t-sigma_r_t=0...eqn(1) +expr1=sigma_t-sigma_r_t;// expression of polynomial from above eqn. +a1=roots(numer(expr1));// solving the equation (as denominator will me be multiplied by zero on R.H.S) +a1=a1(2);// mm // discasrding -ve roots +printf('Equating resultant tensile stress gives, a = %.2f mm',a1) + +//equating resulting compressive stress with given value sigma_c-sigma_c_t=0...eqn(1) +expr2=sigma_c-sigma_r_c;// expression of polynomial from above eqn. +a2=roots(numer(expr2));// solving the equation (as denominator will me be multiplied by zero on R.H.S) +a2=a2(2);// mm // discarding -ve roots +printf('\n Equating resultant compressive stress gives, a = %.2f mm',a2) +a=ceil(a1);//mm +printf('\n dimension of cross section of link, a=%.2f mm. adopt a=%.f mm.',a1,a) diff --git a/3774/CH3/EX3.5/Ex3_5.sce b/3774/CH3/EX3.5/Ex3_5.sce new file mode 100644 index 000000000..a09bdbdd0 --- /dev/null +++ b/3774/CH3/EX3.5/Ex3_5.sce @@ -0,0 +1,28 @@ +// exa 3.5 Pg 67 + +clc;clear;close; + +// Given Data +Syt=760;// MPa +M=15;// kN.m +T=25;//kN.m +n=2.5;// factor of safety +E=200;// GPa +v=0.25;// Poisson's ratio + +sigma_d=Syt/n;// MPa +// let d is diameter of the shaft +sigma_b_into_d_cube=32*M*10**6/%pi;// N/mm.sq. (where sigma_b_into_d_cube = sigma_d*d**3) +tau_into_d_cube=16*T*10**6/%pi//d**3;// N/mm.sq. (where tau_into_d_cube = tau*d**3) +sigma1_into_d_cube=sigma_b_into_d_cube/2+1/2*sqrt(sigma_b_into_d_cube**2+4*tau_into_d_cube**2) ; // (where sigma1_into_d_cube=sigma1*d**3) +sigma2_into_d_cube=sigma_b_into_d_cube/2-1/2*sqrt(sigma_b_into_d_cube**2+4*tau_into_d_cube**2); // (where sigma2_into_d_cube=sigma2*d**3) +printf('\n (i) Maximum shear stress theory') +tau_max_into_d_cube=(sigma1_into_d_cube-sigma2_into_d_cube)/2; //(where tau_max_into_d_cube = tau_max*d**3) +d=(tau_max_into_d_cube/(sigma_d/2))**(1/3);//mm +printf('diameter of shaft, d=%.1f mm or %.f mm',d,ceil(d)) + +printf('\n (ii) Maximum strain energy theory') +//sigma1**2+sigma2**2-2*v*sigma1*sigma2=sigma_d**2 +d=((sigma1_into_d_cube**2+sigma2_into_d_cube**2-2*v*sigma1_into_d_cube*sigma2_into_d_cube)/sigma_d**2)**(1/6) +printf('diameter of shaft, d=%.1f mm',d) +printf('\n Adopt d=100mm') diff --git a/3774/CH3/EX3.6/Ex3_6.sce b/3774/CH3/EX3.6/Ex3_6.sce new file mode 100644 index 000000000..fc7afb40c --- /dev/null +++ b/3774/CH3/EX3.6/Ex3_6.sce @@ -0,0 +1,25 @@ +// exa 3.6 Pg 69 + +clc;clear;close; + +// Given Data +N=200;// rpm +P=200;// kW +tau_d=42;// Mpa +W=900;// N +L=3;// m +sigma_t=56;// MPa +sigma_c=56;// MPa + +T=P*60*10**3/(2*%pi*N);// N.m +M=W*L/4;// N.m +Te=sqrt(M**2+T**2);// N.m +//Te=(%pi/16)*d**3*tau_d +d=(Te/((%pi/16)*tau_d)*1000)**(1/3);// mm +printf('\n Using equivalent torque equation,\n shaft diameter d = %.f mm',d) + +Me=(1/2)*(M+sqrt(M**2+T**2));// N.m +//Me=(%pi/32)*d**3*sigma_d +d=(Me/((%pi/32)*sigma_c)*10**3)**(1/3);//mm +printf('\n Using equivalent bending moment equation,\n shaft diameter d = %.2f mm or %.f mm',d, ceil(d)) +printf('\n Adopt d=105 mm.') diff --git a/3774/CH3/EX3.8/Ex3_8.sce b/3774/CH3/EX3.8/Ex3_8.sce new file mode 100644 index 000000000..1003c0c77 --- /dev/null +++ b/3774/CH3/EX3.8/Ex3_8.sce @@ -0,0 +1,22 @@ +// exa 3.8 Pg 70 + +clc;clear;close; + +// Given Data +M=15;// N.m +P=5;// kW +N=500;// rpm +tau_d=40;// Mpa +sigma_d=58;// MPa + +T=P*60*10**3/(2*%pi*N);// N.m +Te=sqrt(M**2+T**2);// N.m +//Te=(%pi/16)*d**3*tau_d +d=(Te/((%pi/16)*tau_d)*1000)**(1/3);// mm +printf('\n Using equivalent torque equation,\n shaft diameter d = %.f mm',d) + +Me=(1/2)*(M+sqrt(M**2+T**2));// N.m +//Me=(%pi/32)*d**3*sigma_d +d=(Me/((%pi/32)*sigma_d)*10**3)**(1/3);//mm +printf('\n Using equivalent bending moment equation,\n shaft diameter d = %.2f mm or %.f mm',d, ceil(d)) +printf('\n Adopt d=23 mm.') diff --git a/3774/CH4/EX4.1/Ex4_1.sce b/3774/CH4/EX4.1/Ex4_1.sce new file mode 100644 index 000000000..e68f24ff1 --- /dev/null +++ b/3774/CH4/EX4.1/Ex4_1.sce @@ -0,0 +1,34 @@ +// exa 4.1 Pg 102 +clc;clear;close; +P=6;// kN + +//dimensions of plate +r=5;//mm +d=40;//mm +D=50;//mm +d0=10;//mm +w=40;//mm +Sut=200;//MPa +n=2.5;// factor of safety + +//Fillet - +rBYd=r/d; +DBYd=D/d; +Kt=1.75;// factor +printf('for stepped plate under tension, Kt=%.2f for r/d = %.3f & D/d = %.2f ',Kt,rBYd,DBYd) +t=poly(0,'t') +sigma_max = Kt*P/t;// N per mm sq. + +// Hole - +d0BYw=d0/w; +Kt=2.42;// factor +printf('\n for finite width plate under tension with a hole, Kt=%.2f for d0/w = %.2f',Kt,d0BYw) +sigma_max_into_t = Kt*P/(w-d0);//N/mm sq. + +//Design stress +sigma_d = Sut/n;// MPa +//putting sigma_max=sigma_d +t=sigma_max_into_t/sigma_d*1000;// mm +printf('\n Thickness of plate = %.2f mm or %.f mm',t,t) + + diff --git a/3774/CH4/EX4.10/Ex4_10.sce b/3774/CH4/EX4.10/Ex4_10.sce new file mode 100644 index 000000000..d5f0fb62d --- /dev/null +++ b/3774/CH4/EX4.10/Ex4_10.sce @@ -0,0 +1,26 @@ +// exa 4.10 Pg 116 +clc;clear;close; + +// Given Data +Sut=600;//MPa +Se=280;//MPa +sigma_x_min=50;// MPa +sigma_x_max=100;// MPa +sigma_y_min=20;// MPa +sigma_y_max=70;// MPa + +sigma_xm=(sigma_x_max+sigma_x_min)/2;// MPa +sigma_xa=(sigma_x_max-sigma_x_min)/2;// MPa +sigma_ym=(sigma_y_max+sigma_y_min)/2;// MPa +sigma_ya=(sigma_y_max-sigma_y_min)/2;// MPa + +// distortion energy theory - +sigma_m=sqrt(sigma_xm**2+sigma_ym**2-sigma_xm*sigma_ym);// MPa +sigma_a=sqrt(sigma_xa**2+sigma_ya**2-sigma_xa*sigma_ya);// MPa +theta=atand(sigma_a/sigma_m);// degree +// Sm/Sut+Sa/Se=1 where Sa=Sm*tan(theta) +Sm=1/(1/Sut+tand(theta)/Se);// MPa +Sa=tand(theta)*Sm;// MPa +n=Sa/sigma_a;// factor of safety + +printf('\n factor of safety, n = %.2f',n) diff --git a/3774/CH4/EX4.11/Ex4_11.sce b/3774/CH4/EX4.11/Ex4_11.sce new file mode 100644 index 000000000..7319081d3 --- /dev/null +++ b/3774/CH4/EX4.11/Ex4_11.sce @@ -0,0 +1,38 @@ +// exa 4.11 Pg 117 +clc;clear;close; + +// Given Data +Sut=600;//MPa +Syt=400;//MPa +Se=200;//MPa +Mmin=200;// N.m +Mmax=500;// N.m +Tmin=60;// N.m +Tmax=180;// N.m +n=2;// factor of safety + +Mm=(Mmax+Mmin)/2;// N.mm +Ma=(Mmax-Mmin)/2;// N.mm +Tm=(Tmax+Tmin)/2;// N.mm +Ta=(Tmax-Tmin)/2;// N.mm +// sigma_xm=32*Mm/%pi/d**3 +sigma_xm_into_d_cube=(32*Mm*1000)/%pi; +// sigma_xa=32*Ma/%pi/d**3 +sigma_xa_into_d_cube=(32*Ma*1000)/%pi; +//Txym=16*Tm/%pi/d**3 +Txym_into_d_cube=16*Tm*1000/%pi; +//Txya=16*Ta/%pi/d**3 +Txya_into_d_cube=16*Ta*1000/%pi; +// sigma_m=sqrt(sigma_xm**2+3*Txym**2) +sigma_m_dash=sqrt(sigma_xm_into_d_cube**2+3*Txym_into_d_cube**2);// taken sigma_m_dash = sigma_m*d**(-3) for calculation +// sigma_a=sqrt(sigma_xa**2+3*Txya**2) +sigma_a_dash=sqrt(sigma_xa_into_d_cube**2+3*Txya_into_d_cube**2);// taken sigma_a_dash = sigma_a*d**(-3) for calculation +//tan(theta) = sigma_a/sigma_m +theta = atan(sigma_a_dash/sigma_m_dash);// radian +//Sm/Sut+Sa/Se= 1 where Sa/Sm=0.4348 +Sm= 1/(1/Sut+0.4348/Se);// MPa +Sa=0.4348 * Sm;// MPa +//sigma_a=Sa/n +d=(Sa/n/sigma_a_dash)**(1/3)*1000;// mm +printf('\n diameter of shaft, d = %.2f mm',d) +// Note - Ans in the textbook is wrong. diff --git a/3774/CH4/EX4.12/Ex4_12.sce b/3774/CH4/EX4.12/Ex4_12.sce new file mode 100644 index 000000000..9075270f0 --- /dev/null +++ b/3774/CH4/EX4.12/Ex4_12.sce @@ -0,0 +1,28 @@ +// exa 4.12 Pg 119 +clc;clear;close; + +// Given Data +Sut=620;//MPa +Syt=380;//MPa +R=90/100;// Reliability +n=2.5;// factor of safety +Tmin=-200;// N.m +Tmax=400;// N.m + +Se_dash=0.5*Sut;//MPa +// for ground shaft +ka=0.92;// surface finish factor +kb=0.85;// size factor (assuming t<50 mm) +kc=0.897;// reliability factor +kd=1;// temperature factor +ke=0.577;// load factor +Ses=ka*kb*kc*kd*ke*Se_dash;// MPa( Endurance limit) +Sys=ke*Syt;// MPa +Tm=(Tmax+Tmin)/2;// N.mm +Ta=(Tmax-Tmin)/2;// N.mm +theta=atan(Ta/Tm);//radian +Sas=Ses;// MPa +Sms=Sas/3;// MPa +//Tda=Sas/n=16*Ta/%pi/d**3 +d=(16*Ta*1000/%pi/(Sas/n))**(1/3);// mm +printf('\n diameter of shaft, d = %.2f mm or %d mm',d, ceil(d)) diff --git a/3774/CH4/EX4.14/Ex4_14.sce b/3774/CH4/EX4.14/Ex4_14.sce new file mode 100644 index 000000000..0b811333b --- /dev/null +++ b/3774/CH4/EX4.14/Ex4_14.sce @@ -0,0 +1,14 @@ +// exa 4.14 Pg 121 +clc;clear;close; + +// Given Data +sigma_max=300;// MPa +sigma_min=-150;// MPa +n=1.5;// factor of safety + + +sigma_m=(sigma_max+sigma_min)/2;// MPa +sigma_a=(sigma_max-sigma_min)/2;// MPa +// Goodman failure line - sigma_m/Sut+sigma_a/Se=1/n +Sut=(sigma_m+sigma_a/(0.5))*n ;// putted Se=0.5*Sut +printf('\n Minimum required ultimate strength, Sut = %.1f MPa',Sut) diff --git a/3774/CH4/EX4.16/Ex4_16.sce b/3774/CH4/EX4.16/Ex4_16.sce new file mode 100644 index 000000000..a0b425113 --- /dev/null +++ b/3774/CH4/EX4.16/Ex4_16.sce @@ -0,0 +1,28 @@ +// exa 4.16 Pg 122 +clc;clear;close; + +// Given Data +Pmin=-15;// kN +Pmax=25;// kN +Se_dash=360;// MPa +Sy=400;// MPa +Ki=1.25;// impact factor +n=2.25;// factor of safety +ka=0.88;// surface finish factor +Kt=2.25;// stress concentration factor +Pm=(Pmax+Pmin)/2;// kN +Pa=(Pmax-Pmin)/2;// kN +q=0.8;// sensitivity factor + +// sigma_m=4*Pm/%pi/d**2 +sigma_m_into_d_sq = 4*Pm*1000/%pi; +sigma_a_into_d_sq = 4*Pa*1000/%pi; +Kf=1+q*(Kt-1);// fatigue strength factor +kf=1/Kf ;// fatigue strength reduction factor +kb=0.85;// size factor +ke=0.9;//load factor +ki=1/Ki;// reverse impact factor +Se=ka*kb*ke*kf*ki*Se_dash;// MPa +//soderburg failure equation - sigma_m/Sy+sigma_a/Se=1/n +d=sqrt((sigma_m_into_d_sq/Sy+sigma_a_into_d_sq/Se)*n) +printf('\n Size of piston rod, d = %.f mm',d) diff --git a/3774/CH4/EX4.18/Ex4_18.sce b/3774/CH4/EX4.18/Ex4_18.sce new file mode 100644 index 000000000..1c87c3fc5 --- /dev/null +++ b/3774/CH4/EX4.18/Ex4_18.sce @@ -0,0 +1,25 @@ +// exa 4.18 Pg 123 +clc;clear;close; + +// Given Data +Pmin=-300;// kN +Pmax=700;// kN +Se_dash=280;// MPa +Sy=350;// MPa +Kf=1.8;//fatigue strength factor +n=2;// factor of safety + +Pm=(Pmax+Pmin)/2;// kN +Pa=(Pmax-Pmin)/2;// kN +// sigma_m=4*Pm/%pi/d**2 +sigma_m_into_d_sq = 4*Pm*1000/%pi; +sigma_a_into_d_sq = 4*Pa*1000/%pi; +kf=1/Kf ;// fatigue strength reduction factor +kb=0.85;// size factor +ke=0.9;//load factor +ka=0.93;// surface finish factor +Se=ka*kb*ke*kf*Se_dash;// MPa +//Goodman failure equation - sigma_m/Sy+sigma_a/Se=1/n +d=sqrt((sigma_m_into_d_sq/Sy+sigma_a_into_d_sq/Se)*2.25) +printf('\n Suitable diameter of rod, d = %.f mm',d) +// Note - Ans in the textbook is wrong. diff --git a/3774/CH4/EX4.19/Ex4_19.sce b/3774/CH4/EX4.19/Ex4_19.sce new file mode 100644 index 000000000..0dcbcc259 --- /dev/null +++ b/3774/CH4/EX4.19/Ex4_19.sce @@ -0,0 +1,19 @@ +// exa 4.19 Pg 124 +clc;clear;close; + +// Given Data +w=110;// mm +Pmin=98.1;// kN +Pmax=250;// kN +Se=225;// N/mm.sq +Sy=300;// N/mm.sq +n=1.5;// factor of safety + +Pm=(Pmax+Pmin)/2;// kN +Pa=(Pmax-Pmin)/2;// kN +// sigma_m=Pm/w/t +sigma_m_into_t = Pm/w; +sigma_a_into_t = Pa/w; +//Soderburg failure equation - sigma_m/Sy+sigma_a/Se=1/n +d=(sigma_m_into_t/Sy+sigma_a_into_t/Se)*n*1000;// mm +printf('\n thickness of plate, t = %.1f mm',d) diff --git a/3774/CH4/EX4.2/Ex4_2.sce b/3774/CH4/EX4.2/Ex4_2.sce new file mode 100644 index 000000000..0660587a9 --- /dev/null +++ b/3774/CH4/EX4.2/Ex4_2.sce @@ -0,0 +1,36 @@ +// exa 4.2 Pg 104 +clc;clear;close; + +// Given Data +rBYd=0.1; +DBYd=1.2; +P=3;// kN +Syt=300;//MPa +n=3;// factor of safety +//dimensions of plate +l1=400;//mm +l2=300;//mm +l3=400;//mm + + +sigma_d=Syt/n;// MPa +Kt=1.65;// factor for circular fillet radius member +Rp=P/2;//kN (bearing reaction due to symmetry) +Mf=Rp*l1;// kN.mm (bending moment at fillet) +Mc=P*(l1+l2+l3)/4;// kN.mm (bending moment at centre) + +//Fillet +//sigma_max=Kt*32*Mf/(%pi*d**3) +sigma_max_into_d_cube_1 = Kt*32*Mf*1000/%pi + + +//Centre +//sigma_max=32*Mc/(%pi*d**3) +sigma_max_into_d_cube_2 = Kt*32*Mf*1000/%pi +sigma_max_into_d_cube=max(sigma_max_into_d_cube_1,sigma_max_into_d_cube_2);// (getting max) + +//putting sigma_max=sigma_d +t=(sigma_max_into_d_cube/sigma_d)**(1/3);// mm +printf('\n Diameter of axle = %.1f mm',t) + + diff --git a/3774/CH4/EX4.20/Ex4_20.sce b/3774/CH4/EX4.20/Ex4_20.sce new file mode 100644 index 000000000..cacd208e1 --- /dev/null +++ b/3774/CH4/EX4.20/Ex4_20.sce @@ -0,0 +1,34 @@ +// exa 4.20 Pg 124 +clc;clear;close; + +// Given Data +Mmin=200;// kN.mm +Mmax=600;// kN.mm +Tmin=60;// kN +Tmax=180;// kN +Su=550;// MPa +Sy=400;// MPa +Se=0.5*Su;// MPa +n=1.5;// factor of safety +Ktb=1.5;// stress concentration factor in blending +Kts=1.2;// stress concentration factor in torsion + +Mm=(Mmax+Mmin)/2;// kN.mm +Ma=(Mmax-Mmin)/2;// kN.mm + +//sigma_xm=32*Mm/%pi/d**3 +sigma_xm_into_d_cube=32*Mm/%pi; +//sigma_xa=32*Ma/%pi/d**3 +sigma_xa_into_d_cube=32*Ma/%pi; +Tm=(Tmax+Tmin)/2;// kN.mm +Ta=(Tmax-Tmin)/2;// kN.mm +Txym_into_d_cube=16*Tm/%pi; +Txya_into_d_cube=16*Ta/%pi; +// using distortion energy theory +// sigma_m=sqrt(sigma_xm**2+3*Txym**2) +sigma_m_into_d_cube=sqrt(sigma_xm_into_d_cube**2+3*Txym_into_d_cube**2); +// sigma_a=sqrt((Ktb*sigma_xa)**2+3*(Kts*Txym)**2) +sigma_a_into_d_cube=sqrt((Ktb*sigma_xa_into_d_cube)**2+3*(Kts*Txya_into_d_cube)**2); +// Sodeburg equation - sigma_m + (Su/Se)*sigma_a=Sy/n +d=((sigma_m_into_d_cube + (Su/Se)*sigma_a_into_d_cube)*1000/(Sy/n))**(1/3) +printf('\n shaft size, d = %.f mm',d) diff --git a/3774/CH4/EX4.21/Ex4_21.sce b/3774/CH4/EX4.21/Ex4_21.sce new file mode 100644 index 000000000..fcf97e794 --- /dev/null +++ b/3774/CH4/EX4.21/Ex4_21.sce @@ -0,0 +1,23 @@ +// exa 4.21 Pg 126 +clc;clear;close; + +// Given Data +// Hole - +d=25;//mm +w=150;//mm +Kt=2.56;// stress concentration factor +P=50;// kN +sigma_max=100;// N/mm.sq +t=Kt*P*1000/(w-d)/sigma_max;// mm +printf('Calculating for hole - \n thickness is : %.2f mm',t) + +// Notch - +d=30;//mm +w=120;//mm +w=150;//mm +Kt=2.3;// stress concentration factor +P=50;// kN +sigma_max=100;// N/mm.sq +t=Kt*P*1000/(w-d)/sigma_max;// mm +printf('\n Calculating for notch - \n thickness is : %.2f mm',t) +disp('Suggestion, Adopt t = 11 mm') diff --git a/3774/CH4/EX4.3/Ex4_3.sce b/3774/CH4/EX4.3/Ex4_3.sce new file mode 100644 index 000000000..9ebd65026 --- /dev/null +++ b/3774/CH4/EX4.3/Ex4_3.sce @@ -0,0 +1,25 @@ +// exa 4.3 Pg 105 +clc;clear;close; + +// Given Data +Sut=440;//MPa +d=25;//mm +R=95/100;// reliability +Kt=1.8;// stress concentration factor +q=0.86;// sensitivity factor + +Se_dash = 0.5*Sut;// MPa + +// for machined surface +ka=0.82;// surface finish factor +kb=0.85;// size factor +kc=0.868;// reliability factor +kd=1;// temperature factor +ke=0.577;// load factor + +Kf=1+q*(Kt-1);// fatigue strength factor +kf=1/Kf ;// fatigue strength reduction factor +Se=ka*kb*kc*kd*ke*kf*Se_dash;// (MPa) Endurance limit +printf('\n Endurance limit = %.2f MPa',Se) + + diff --git a/3774/CH4/EX4.4/Ex4_4.sce b/3774/CH4/EX4.4/Ex4_4.sce new file mode 100644 index 000000000..26b769886 --- /dev/null +++ b/3774/CH4/EX4.4/Ex4_4.sce @@ -0,0 +1,33 @@ +// exa 4.4 Pg 105 +clc;clear;close; + +// Given Data +Sut=440;//MPa +w=60;//mm +d=12;// mm +P=20;// kN +q=0.8;// sensitivity factor +R=90/100;// reliability +n=2;// factor of safety + +Kt=2.52;// stress concentration factor +Se_dash = 0.5*Sut;// MPa +// for hot rollednormalized condition +ka=0.67;// surface finish factor +kb=0.85;// size factor (assuming t<50 mm) +kc=0.897;// reliability factor +kd=1;// temperature factor +ke=0.9;// load factor +dBYw=d/w; //(for circular hole) + +Kf=1+q*(Kt-1);// fatigue strength factor +kf=1/Kf ;// fatigue strength reduction factor +Se=ka*kb*kc*kd*ke*kf*Se_dash;// (MPa) Endurance limit +sigma_d=Se/n;// MPa (design stress) +// sigma_max=P/(w-d)/t +sigma_max_into_t = P*1000/(w-d); +// putting sigma_max=sigma_d +t=sigma_max_into_t/sigma_d;// mm +printf('\n Thickness of plate = %.2f mm or 20 mm',t) + + diff --git a/3774/CH4/EX4.5/Ex4_5.sce b/3774/CH4/EX4.5/Ex4_5.sce new file mode 100644 index 000000000..91dfd1de8 --- /dev/null +++ b/3774/CH4/EX4.5/Ex4_5.sce @@ -0,0 +1,22 @@ +// exa 4.5 Pg 107 +clc;clear;close; + +// Given Data +Sut=650;//MPa +N=10**5;// cycles +Se_dash = 0.5*Sut;// MPa +of=5;// unit +ob=6;//unit +bf=ob-of;// unit +be=3;//unit + +// calculating endurance section wise +OE=log10(Se_dash); +OA=log10(0.9*Sut); +AE=OA-OE; +//log10_Sf=OD=OE+ED=OE+FC +log10_Sf=OE+(bf/be)*AE; +Sf=10**log10_Sf; // (MPa) Endurance +printf('\n Endurance of specimen = %.2f MPa',Sf) + + diff --git a/3774/CH4/EX4.6/Ex4_6.sce b/3774/CH4/EX4.6/Ex4_6.sce new file mode 100644 index 000000000..44b67139b --- /dev/null +++ b/3774/CH4/EX4.6/Ex4_6.sce @@ -0,0 +1,42 @@ +// exa 4.6 Pg 108 +clc;clear;close; + +// Given Data +Sut=540;//MPa +N=10**4;// cycles +q=0.85;// sensitivity factor +R=90/100;// reliability +P=1500;// N +l=160;// mm + +Se_dash = 0.5*Sut;// MPa +// for cold drawn steel +ka=0.79;// surface finish factor +kb=0.85;// size factor (assuming t<50 mm) +kc=0.897;// reliability factor +kd=1;// temperature factor +ke=1;// load factor + +Kt=1.33;// under bending + +Kf=1+q*(Kt-1);// fatigue strength factor +kf=1/Kf ;// fatigue strength reduction factor +Se=ka*kb*kc*kd*ke*kf*Se_dash;// MPa( Endurance limit) + +of=4;// unit +ob=6;//unit +bf=ob-of;// unit +be=3;//unit + +// calculating endurance section wise +OE=log10(Se); +OA=log10(0.9*Sut); +AE=OA-OE; +//log10_Sf=OD=OE+ED=OE+FC +log10_Sf=OE+(bf/be)*AE; +Sf=10**log10_Sf; // (MPa) Endurance + +MB=P*l;// N.mm +// 32*MB/%pi/d**3 = Sf +d=(32*MB/%pi/Sf)**(1/3) +printf('\n diameter of beam %.f mm',d) diff --git a/3774/CH4/EX4.7/Ex4_7.sce b/3774/CH4/EX4.7/Ex4_7.sce new file mode 100644 index 000000000..03ead01d3 --- /dev/null +++ b/3774/CH4/EX4.7/Ex4_7.sce @@ -0,0 +1,41 @@ +// exa 4.7 Pg 110 +clc;clear;close; + +// Given Data +Sut=600;//MPa +Syt=380;//MPa +q=0.9;// sensitivity factor +R=90/100;// reliability +n=2;// factor of safety +Pmin=-100;// N +Pmax=200;// N +l=150;// mm + +Se_dash = 0.5*Sut;// MPa +// for cold drawn steel +ka=0.76;// surface finish factor +kb=0.85;// size factor (assuming t<50 mm) +kc=0.897;// reliability factor +kd=1;// temperature factor +ke=1;// load factor + +Kt=1.4;// under bending + +Kf=1+q*(Kt-1);// fatigue strength factor +kf=1/Kf ;// fatigue strength reduction factor +Se=ka*kb*kc*kd*ke*kf*Se_dash;// MPa( Endurance limit) +Mmax=Pmax*l;// N.mm +Mmin=Pmin*l;// N.mm +Mm=(Mmax+Mmin)/2;// N.mm +Ma=(Mmax-Mmin)/2;// N.mm +theta=atand(Ma/Mm);// degree + +//equation of Goodman - sigma_m/Sut+sigma_a/Se=1 +//here sigma_a/sigma_m=3 +sigma_m=1/(1/Sut+3/Se);//MPa +sigma_a=3*sigma_m;// MPa + +sigma_da=sigma_a/n;// MPa +//sigma_da=32*Ma/%pi/d**3 +d=(32*Ma/%pi/sigma_da)**(1/3);// mm +printf('\n diameter d at fillet cross section = %.f mm',d) diff --git a/3774/CH4/EX4.8/Ex4_8.sce b/3774/CH4/EX4.8/Ex4_8.sce new file mode 100644 index 000000000..b587914e6 --- /dev/null +++ b/3774/CH4/EX4.8/Ex4_8.sce @@ -0,0 +1,30 @@ +// exa 4.8 Pg 112 +clc;clear;close; + +// Given Data +Sut=500;//MPa +Syt=300;//MPa +R=90/100;// reliability +n=2;// factor of safety +Tmin=-200;// N.m +Tmax=500;// N.m + +Se_dash = 0.5*Sut;// MPa +// for cold drawn steel +ka=0.80;// surface finish factor +kb=0.85;// size factor (assuming t<50 mm) +kc=0.897;// reliability factor +kd=1;// temperature factor +ke=0.577;// load factor + +Ses=ka*kb*kc*kd*ke*Se_dash;// MPa( Endurance limit) +Sys=ke*Syt;// MPa +Tm=(Tmax+Tmin)/2;// N.m +Ta=(Tmax-Tmin)/2;// N.m +theta=atand(Ta/Tm);// degree +Sms=Ses/tand(theta);//MPa +Sas=Ses;//MPa +tau_da=Sas/n;//MPa +//tua_da=16*Ta/%pi/d**3 +d=(16*Ta*1000/%pi/tau_da)**(1/3);//mm +printf('\n diameter of shaft = %.f mm',d) diff --git a/3774/CH4/EX4.9/Ex4_9.sce b/3774/CH4/EX4.9/Ex4_9.sce new file mode 100644 index 000000000..c2640f651 --- /dev/null +++ b/3774/CH4/EX4.9/Ex4_9.sce @@ -0,0 +1,41 @@ +// exa 4.9 Pg 113 +clc;clear;close; + +// Given Data +Sut=860;//MPa +Syt=690;//MPa +Pmin=60;// N +Pmax=120;// N +R=50/100;// reliability +l=500;//mm +d=10;//mm +Se_dash = 0.5*Sut;// MPa +// for machines surface +ka=0.70;// surface finish factor +kb=0.85;// size factor (assuming t<50 mm) +kc=1;// reliability factor +kd=1;// temperature factor +ke=1;// load factor + +Se=ka*kb*kc*kd*ke*Se_dash;// MPa( Endurance limit) +Mmax=Pmax*l;// N.mm +Mmin=Pmin*l;// N.mm +Mm=(Mmax+Mmin)/2;// N.mm +Ma=(Mmax-Mmin)/2;// N.mm +Sm=32*Mm/%pi/d**3;//MPa +sigma_m=Sm;//MPa +Sa=32*Ma/%pi/d**3;//MPa +sigma_a=Sa;//MPa +Sf=Sa*Sut/(Sut-Sm);//MPa + +//calculating section +OB=6;//unit ref. o at 3 +BE=OB-3;//unit +OC=Sf;// MPa +AE=log10(0.9*Sut)-log10(Se);//MPa +AC=log10(0.9*Sut)-log10(Sf);//MPa +CD=BE*AC/AE;// +//log10(N)=3+CD +N=10**(3+CD);// cycle +printf('\n life of the spring, N = %.f cycles',N) +//Note : answer in the textbook is wrong. diff --git a/3774/CH5/EX5.1/Ex5_1.sce b/3774/CH5/EX5.1/Ex5_1.sce new file mode 100644 index 000000000..c6132697b --- /dev/null +++ b/3774/CH5/EX5.1/Ex5_1.sce @@ -0,0 +1,92 @@ +// exa 5.1 Pg 142 +clc;clear;close; + +// Given Data +ps=2.5;// MPa +D=1.5;//m +sigma_t=80;// MPa +tau=60;// MPa +sigma_c=120;// MPa +n=5;// no. of rivets + +printf('DESIGNING LONGITUDINAL JOINT - \n') +printf('\n Plate Thickness') +eta_l=80;// % (efficiency) +t = ps*D*1000/2/sigma_t/(eta_l/100)+1;// mm +printf(', t = %.2f mm',t) +t=32;//mm (adopted for design) +printf('\n use t = %d mm',t) +printf('\n Diameter of rivet hole, do = ') +d0=6*sqrt(t);//mm (for t>8 mm) +printf('%.2f mm',d0) +d0=34.5;// suggested for design +printf('\n Use do = %.f mm',d0) +printf('\n Diameter of rivet, d = ') +d=d0-1.5;//mm +printf('%.2f mm',d) +printf('\n Pitch of rivets, p = ') +Ps=(4*1.875+1)*%pi/4*d0**2*tau;// N +// Putting Pt=Ps where Pt=(p-d0)*t*sigma_t;// N +Pt=Ps;//N +p=Pt/(t*sigma_t)+d0;// N +printf('%.1f mm',p) +C=6;// for 5 no. of rivets +pmax=C*t+40;// mm (as per IBR) +printf('\n as per IBR-\n pitch, pmax = %.f mm',pmax) +p=220;// mm (adopted for design) +printf('\n Use p = %.f mm',p) +pi=p/2;// mm +printf('\n pitch of rivets in inner row, pi = %.f mm',pi) + +//Distance between rows of rivets +dis1=0.2*p+1.115*d0;// mm +printf('\n distance between outer and adjacent row = %.1f mm',dis1) +dis1=85;//mm (adopted for design) +printf('\n take & use this distance = %.f mm', dis1) +dis2=0.165*p+0.67*d0;// mm +printf('\n distance between inner row for zig-zag riveting = %.1f mm', dis2) +dis2=60;//mm (adopted for design) +printf('\n take & use this distance = %.f mm', dis2) +printf('\n Thickness of wide butt strap, t= ') +t1=0.75*t;// mm (wide butt strap) +printf(' %.f mm',t1) +t2=0.625*t;// mm (narrow butt strap) +printf('\n Thickness of narrow butt strap, t= %.f mm',t2) +//margin +m=ceil(1.5*d0);// mm +printf('\n margin, m = %.f mm',m) +// Efficiency of joint +Pt=(p-d0)*t*sigma_t;// N +Ps=Ps;// N (shearing resistance of rivets) +Pc=n*d0*t*sigma_c;// N (crushing resistance of rivets) +sigma_com = (p-2*d0)*t*sigma_t+%pi/4*d0**2*tau;// N +printf('\n strength of the joint = %d N',sigma_com) +P=p*t*sigma_t;//N (strength of solid plate) +printf('\n strength of solid plate = %d N',P) +eta_l=sigma_com/P*100;// % (efficiency) +printf('\n Efficiency of joint, eta_l = %.1f %%',eta_l) + +printf('\n\n DESIGNING CIRCUMFERENTIAL JOINT- \n') +t=32;// mm +d0=34.5;//mm +d=33;//mm +printf('\n Plate Thickness') +printf(', t = %.2f mm',t) +printf('\n Diameter of rivet hole, do = ') +printf('%.2f mm',d0) +printf('\n Diameter of rivet, d = ') +printf('%.2f mm',d) +n=(D*1000/d0)**2*(ps/tau);// no. of rivets +printf('\n no. of rivets = %.1f',n) +n=80;// adopted for design +printf('\n take n = %d',n) +// Pitch of rivets +n1=n/2;// no. of rivets per row +pc=%pi*(D*1000+t)/n1;// mm (pitch of rivets) +printf('\n pitch of rivets, pc = %.2f mm\n use pc = %.f mm',pc,pc) +eta_c=(pc-d0)/pc*100;// % (efficiency of joint) +printf('\n Efficiency of joint, eta_c = %.2f %%',eta_c) +dis=0.33*pc+0.67*d0;// mm (distance between rows of rivets) +printf('\n for zig-zag riveting, distance between rows of rivets = %.1f mm. use 65 mm', dis) +m=1.5*d0;// mm (Margin) +printf('\n margin, m = %.f mm',m) diff --git a/3774/CH5/EX5.2/Ex5_2.sce b/3774/CH5/EX5.2/Ex5_2.sce new file mode 100644 index 000000000..98e59d846 --- /dev/null +++ b/3774/CH5/EX5.2/Ex5_2.sce @@ -0,0 +1,48 @@ +// exa 5.2 Pg 147 +clc;clear;close; + +// Given Data +w=400;//mm +t=20;//mm +sigma_t=90;// MPa +tau=60;// MPa +sigma_c=140;// MPa + +printf('\n Diameter of rivet, do = ') +d0=6*sqrt(t);//mm (for t>8 mm) +printf('%.2f mm',d0) +d0=29;//mm (standard) +printf('\n Standard diameter of rivet hole, do = %.f mm & corresponding diameter of rivet = 27 mm',d0) +Pt=(w-d0)*t*sigma_t;//N max. tearing strength of plate +Ps=1.75*%pi/4*d0**2*tau;// N (shearing strength of one rivet) +n1=Pt/Ps;// no. of rivets +n=ceil(n1); +printf('\n no. of rivets, n = %.3f. Use n = %.f ',n1,n) +t1=0.75*t;// mm +t2=t1;// mm +printf('\n thickness of inner butt strap, t1 = %.f mm', t1) +printf('\n thickness of outer butt strap, t2 = %.f mm', t2) +// section 1-1 +P1=(w-d0)*t*sigma_t;//N +// section 2-2 +P2=(w-2*d0)*t*sigma_t+1.75*%pi/4*d0**2*tau;//N +// section 3-3 +P3=(w-3*d0)*t*sigma_t+1.75*3*%pi/4*d0**2*tau;//N +// section 4-4 +P4=(w-4*d0)*t*sigma_t+1.75*6*%pi/4*d0**2*tau;//N +Ps=10*Ps;// N (shearing stress of all rivets) +Pc=10*d0*t*sigma_c;// N (shearing stress of all rivets) +Pj=P1;// N (strength f joint) +P = w*t*sigma_t;// N (strength of solid plate) +eta=P1/P*100; // % (efficiency of joint) +printf('\n efficiency of joint = %.2f %%', eta) +p1=3*d0+5;// mm (pitch of rivets) +p=100;//mm (adopt for design) +printf('\n pitch of rivets = %.f mm. Use %.f mm',p1,p) +m1=1.5*d0;// mm (margin) +m=50;//mm +w=3*p+2*m;// mm +printf('\n margin,\n m = %.1f mm. Use %.f mm', m1,m) +printf('\n w = %.f mm',w) +dis=2.5*d0;// mm +printf('\n distance between rows = %.1f mm. Use 75 mm',dis) diff --git a/3774/CH5/EX5.3/Ex5_3.sce b/3774/CH5/EX5.3/Ex5_3.sce new file mode 100644 index 000000000..f93343890 --- /dev/null +++ b/3774/CH5/EX5.3/Ex5_3.sce @@ -0,0 +1,25 @@ +// exa 5.3 Pg 150 +clc;clear;close; + +// Given Data +n=6;// no. of rivets +P=54;// kN +e=200;//mm +a=50;//mm (from fig.5.13(a)) +b=100;//mm (from fig.5.13(a)) +tau=120;// MPa + +Pd=P/n*1000;// N (direct shear load in rivet) +C=P*e;// kN.mm (Couple) +//l1=l3=l4=l6 +l1=sqrt(a**2+b**2);// mm +l3=l1;l4=l1;l6=l1//mm +l2=a;l5=a;//mm +// F1/l1*(4*l1**2+2*l2**2)=C +F1=C*1000/(4*l1**2+2*l2**2)*l1;// N +theta1=acos(a/l1);// radian +R1=sqrt(Pd**2+F1**2+2*Pd*F1*cos(theta1));// N (resultant force in rivet 1) +//R1=%pi/4*d0**2*tau +d0=sqrt(R1/(%pi/4*tau));// mm +printf('\n diameter of rivets = %.2f mm. Use d0 = 17.5 mm & d=16 mm for design.',d0) + diff --git a/3774/CH5/EX5.4/Ex5_4.sce b/3774/CH5/EX5.4/Ex5_4.sce new file mode 100644 index 000000000..194be35a3 --- /dev/null +++ b/3774/CH5/EX5.4/Ex5_4.sce @@ -0,0 +1,67 @@ +// exa 5.4 Pg 151 +clc;clear;close; + +// Given Data +D=0.75;//m +ps=1.55;// N/mm.sq +eta_l=0.75;// efficiency +sigma_t=90;// MPa +sigma_c=140;// MPa +tau=56;// MPa +n=2;// no. of rivets + +printf('DESIGNING LONGITUDINAL JOINT - \n') +printf('\n Plate Thickness') +t = ps*D*1000/2/sigma_t/eta_l+1;// mm +printf(', t = %.2f mm',t) +t=ceil(t);//mm (adopted for design) +printf('\n use t = %d mm',t) + +printf('\n Diameter of rivet hole, do = ') +d0=6*sqrt(t);//mm (for t>8 mm) +printf('%.2f mm',d0) +d0=19.5;// suggested for design +printf('\n Use do = %.1f mm',d0) +printf('\n Diameter of rivet, d = ') +d=d0-1.5;//mm +printf('%.2f mm',d) + +printf('\n Pitch of rivets, p = ') +Ps=(2*1.875)*%pi/4*d0**2*tau;// N +// Putting Pt=Ps where Pt=(p-d0)*t*sigma_t;// N +Pt=Ps;//N +p=Pt/(t*sigma_t)+d0;// N +printf('%.2f mm',p) +C=3.5;// for 2 no. of rivets +pmax=C*t+40;// mm (as per IBR) +printf('\n as per IBR-\n pitch, pmax = %.f mm',pmax) +p=75;// mm (adopted for design) +printf('\n Use p = %.f mm',p) + +//Distance between rows of rivets +dis=0.33*p+0.67*d0;// mm +printf('\n distance between rows of rivets = %.1f mm',dis) +dis=40;//mm (adopted for design) +printf('\n take & use this distance = %.f mm', dis) + +printf('\n Thickness of butt strap, t= ') +t1=0.625*t;// mm +printf(' %.2f mm',t1) +t1=7;// mm (adopted for design) +printf('\n Use thickness = %.f mm',t1) + +//margin +m=ceil(1.5*d0);// mm +printf('\n margin, m = %.f mm',m) + +// Efficiency of joint +Pt=(p-d0)*t*sigma_t;// N +Ps=Ps;// N (shearing resistance of rivets) +Pc=n*d0*t*sigma_c;// N (crushing resistance of rivets) +sigma_com = (p-2*d0)*t*sigma_t+%pi/4*d0**2*tau;// N +printf('\n strength of the joint = %d N',Pt) +P=p*t*sigma_t;//N (strength of solid plate) +printf('\n strength of solid plate = %d N',P) +eta_l=Pt/P*100;// % (efficiency) +printf('\n Efficiency of joint, eta_l = %.2f %% = 75 %% as given',eta_l) + diff --git a/3774/CH5/EX5.6/Ex5_6.sce b/3774/CH5/EX5.6/Ex5_6.sce new file mode 100644 index 000000000..b98707b70 --- /dev/null +++ b/3774/CH5/EX5.6/Ex5_6.sce @@ -0,0 +1,33 @@ +// exa 5.6 Pg 153 +clc;clear;close; + +// Given Data +n=5;// no. of rivets +P=45;// kN +alfa=30;// degree +tau=120;// MPa + + +Pd=P/n*1000;// N (direct shear load in rivet) +// C.G. of rivet group +// values below are collected direct from figure +x_bar=(3*200)/5;// mm +y_bar=(1*50+1*150+1*100+1*200)/5;// mm +ex=300+x_bar+y_bar;//mm +ey=100;//mm +l1=sqrt(x_bar**2+(y_bar/2)**2);// mm +l2=l1;//mm +l3=sqrt(100**2+80**2);// mm +l4=80;//mm +l5=l3;//mm + +//2*F1*l1+2*F3*l3+F4*l4=P*cos(alfa)*ex+P*sin(alfa)*ey +F1=(P*1000*cosd(alfa)*ex+P*1000*sind(alfa)*ey)/(2*l1**2+2*l3**2+l4**2)*l1;//N +// rivet 1 is nearest +Beta = atand(x_bar/(y_bar/2));// degree +theta1=Beta-(90-alfa);// degree +R1=sqrt(Pd**2+F1**2+2*Pd*F1*cosd(theta1));// N (resultant force in rivet 1) +//R1=%pi/4*d0**2*tau +d0=sqrt(R1/(%pi/4*tau));// mm +printf('\n diameter of rivets = %.2f mm. Use d0 = 21.5 mm & d=20 mm for design.',d0) +// Note - Ans in the textbook is wrong. diff --git a/3774/CH5/EX5.7/Ex5_7.sce b/3774/CH5/EX5.7/Ex5_7.sce new file mode 100644 index 000000000..fd53849db --- /dev/null +++ b/3774/CH5/EX5.7/Ex5_7.sce @@ -0,0 +1,35 @@ +// exa 5.7 Pg 155 +clc;clear;close; + +// Given Data +t=6;//mm +sigma_t=220;// MPa +tau=100;// MPa +sigma_c=150;// MPa +n=2;// no. of rivets / pitch length +//Ps=n*%pi/4**d0**2*tau;// shearing strength of rivets +//Pc=2*d0*t*sigma_c;// Crushing strength of rivets +d0=2*t*sigma_c/(n*%pi/4*tau);// mm (equating Ps=Pc) +printf('Diameter of rivets, d0 = %.2f mm. Take d0=13.5 mm & d=12 mm',d0) +d0=13.5;//mm +d=12;//mm +//Pt=(p-d0)*t*sigma_t;// tearing strength +// equating Pt=Ps +//p= n*%pi/4**d0**2*tau/(t*sigma_t)+d0;//mm +p= n*%pi/4*d0**2*tau/(t*sigma_t)+d0 +printf('\n Distance between rows of rivet = %.1f mm = %.f mm',p,p) +p=floor(p);//mm +pb=0.6*p;//mm (back pitch) +printf('\n back pitch = %.f mm',pb) +Pt=(p-d0)*t*sigma_t;// N (tearing strength) +printf('\n tearing strength = %.f N',Pt) +Ps=n*%pi/4*d0**2*tau;// N ( shearing strength) +printf('\n shearing strength = %.f N',Ps) +Pc=2*d0*t*sigma_c;//N (Crushing strength of rivets) +printf('\n crushing strength = %.f N',Pc) +joint_strength = Pc;// N +printf('\n joint strength = %.f N',joint_strength) +P=p*t*sigma_t;//N (strength of solid plate) +printf('\n strength of solid plate = %.f N',P) +eta = joint_strength/P*100;// % (efficiency) +printf('\n efficiency of joint = %.1f %%', eta) diff --git a/3774/CH5/EX5.8/Ex5_8.sce b/3774/CH5/EX5.8/Ex5_8.sce new file mode 100644 index 000000000..f0e5d4ded --- /dev/null +++ b/3774/CH5/EX5.8/Ex5_8.sce @@ -0,0 +1,21 @@ +// exa 5.8 Pg 156 +clc;clear;close; + +// Given Data +P=20;// kN +e=80;//mm +tau=150;// MPa + + +Pd=P/4;// kN +C=P*e;// kN.mm (Couple) +// As C.G. lies at 45mm from top rivet +l1=45;l4=45;//mm +l2=15;l3=15;//mm +//(F1/l1)*(2*l1*l4+2*l2*l3) = C +F1= C*1000/(2*l1*l4+2*l2*l3)*l1;//N +R1=sqrt(Pd**2+F1**2);// N +//R1=%pi/4*d0**2*tau +d0=sqrt(R1/(%pi/4*tau));//mm +printf('Diameter of rivets - \n d0 = %.3f mm',d0) +printf('\n Use d0 = 13.5 mm & d = 12 mm') diff --git a/3774/CH6/EX6.1/Ex6_1.sce b/3774/CH6/EX6.1/Ex6_1.sce new file mode 100644 index 000000000..da42a0ab9 --- /dev/null +++ b/3774/CH6/EX6.1/Ex6_1.sce @@ -0,0 +1,43 @@ +// exa 6.1 Pg 168 +clc;clear;close; + +// Given Data +Sut=650;// MPa +Syt=380;// MPa +F1BYF2 = 2.5;// ratio of tensions +Fmax=2.5;// kN +da=200;// mm +db=400;// mm +L=1*1000;//mm +Km=1.5;// fatigue factor +Kt=1;// shock factor + + +tau_d1=0.30*Syt;// MPa +tau_d2=0.18*Sut;// MPa +tau_d=min(tau_d1, tau_d2);// MPa (taking minimum value) +tau_d=0.75*tau_d;//MPa (Accounting keyway effect) + +// Pulley A +F1=2500;// N +F2=1000;// N +T=(F1-F2)*da/2;// N.mm +Fa=F1+F2;// N (resultant pull Downwards) + +// Pulley B +// F3 & F4 are tension in belt (assumed) +//T=(F3-F4)*db/2 +SUB_F3F4 = 2*T/db;// N (where SUB_F3F4 = F3-F4) --eqn(1) +F3BYF4=F1BYF2;// ratio of tensions --eqn(2) +F4 = SUB_F3F4/(F3BYF4-1);// N (using above 2 equations) +F3=F3BYF4*F4;// N +Fb=F3+F4;// N (resultant pull right side( -->)) + +// BENDING MOMENTS - +Mav=Fa*L/4;// N.mm (vertical force) +Mc=Fb*da;// N.mm +Mah=Mc/2;// N.mm (vertical force) +M = sqrt(Mav**2+Mah**2);// N.mm (resultant bending moment at A) +d=((16/%pi/tau_d)*sqrt((Km*M)**2+(Kt*T)**2))**(1/3);// mm + +printf('shaft diameter = %.2f mm. Use diameter = 45 mm.',d) diff --git a/3774/CH6/EX6.2/Ex6_2.sce b/3774/CH6/EX6.2/Ex6_2.sce new file mode 100644 index 000000000..11dcf709e --- /dev/null +++ b/3774/CH6/EX6.2/Ex6_2.sce @@ -0,0 +1,24 @@ +// exa 6.2 Pg 170 +clc;clear;close; + +// Given Data +Tmax=400;// N.m +Tmin=140;// N.m +Mmax=500;// N.m +Mmin=250;// N.m +Sut=540;// MPa +Syt=400;// MPa +n=2;// factor of safety +Kf=1.25;// given + +Se_dash=0.4*Sut;// Mpa +Se=Se_dash/Kf;//MPa +Sys=0.577*Syt;// MPa +Ses=0.577*Se;// MPa +Mm=(Mmax+Mmin)/2;// N.m +Ma=(Mmax-Mmin)/2;// N.m +Tm=(Tmax+Tmin)/2;// N.m +Ta=(Tmax-Tmin)/2;// N.m +// Max. Distortion energy theory - Syt/n = 32/%pi/d**3*sqrt((Mm+Ma*(Syt/Se)**2)+0.75*(Tm+Ta*(Sys/Ses))**2) +d = (32/%pi*sqrt((Mm+Ma*(Syt/Se))**2+0.75*(Tm+Ta*(Sys/Ses))**2)*1000/(Syt/n))**(1/3) ; // mm +printf('shaft diameter = %.2f mm. Use %.f mm.',d,d) diff --git a/3774/CH6/EX6.3/Ex6_3.sce b/3774/CH6/EX6.3/Ex6_3.sce new file mode 100644 index 000000000..1144db636 --- /dev/null +++ b/3774/CH6/EX6.3/Ex6_3.sce @@ -0,0 +1,16 @@ +// exa 6.3 Pg 171 +clc;clear;close; + +// Given Data +P=5;// kW +N=1000;// rpm +Syt=300;// N/mm.sq. +n=2;// factor of safety +v=0.25;// Poisson's ratio + +//P=2*%pi*N*T/(60*1000) +T=P/(2*%pi*N/(60*1000));// N.m +//tau = 16*T/%pi/d**3 // shear stress & sigma1 = tau;sigma2=0;sigma3=-tau +// max. shear strain energy theory, sigma1**2+sigma3**2+(sigma3-sigma1)**2=2*(Syt/n)**2 +d=(16*T*1000/%pi/sqrt(2/6*(Syt/n)**2))**(1/3);// mm (putting values of tau) +printf('shaft diameter = %.1f mm. Use %.f mm.',d,ceil(d)) diff --git a/3774/CH6/EX6.4/Ex6_4.sce b/3774/CH6/EX6.4/Ex6_4.sce new file mode 100644 index 000000000..13143d328 --- /dev/null +++ b/3774/CH6/EX6.4/Ex6_4.sce @@ -0,0 +1,49 @@ +// exa 6.4 Pg 171 +clc;clear;close; + +// Given Data +Sut=700;// MPa +Syt=460;// Mpa +F1BYF2=3;// ratio of tensions +dg=300;// mm +dp=400;// mm +P=25;// kW +N=600;// rpm +alfa=20;// degree +Km=1.5;// fatigue factor +Kt=1.5;// shock factor + +tau_d1=0.30*Syt;// MPa +tau_d2=0.18*Sut;// MPa +tau_d=min(tau_d1, tau_d2);// MPa (taking minimum value) +tau_d=0.75*tau_d;//MPa (Accounting keyway effect) + +// Pulley D +// P= 2*%pi*N*T/60 +T=P/(2*%pi*N/(60*1000));// N.m +// (F1-F2)*dp/2=T +SUB_F1F2 = T*2/dp;// N (where SUB_F1F2 = F1-F2) +F2 = SUB_F1F2/(F1BYF2-1) ;// N (putting value of ratio) +F1=F1BYF2*F2;// N +F=F1+F2;// N +// Gear B +Ft=T*2/dg;// N +Fr=Ft*tand(alfa);// N + +// Bearing Reactions + +//Vertical forces +//RA*2*dg+Fr*dg=F*dg; +RA=(F*dg-Fr*dg)/(2*dg);// N (downwards) +RC=RA+Fr+F;// N (upwards) +MA=0;MB_v=-RA*dg;// N.mm +MC=-F*dg;// N.mm +//Horizontal forces +MB_h=Ft*2*dg/4;// N.mm +//Resultant B.M at B +MB=sqrt(MB_v**2+MB_h**2);// N.mm +Mmax=MC;//N.mm +T=T*1000;// N.mm +// d**3=16/%pi/tau_d*sqrt((Km*M)**2+(Kt*T)**2) +d=(16/%pi/tau_d*sqrt((Km*Mmax*1000)**2+(Kt*T)**2))**(1/3) +printf('shaft diameter(using ASME Code) = %.1f mm. Use diameter = %.f mm.',d,d) diff --git a/3774/CH6/EX6.5/Ex6_5.sce b/3774/CH6/EX6.5/Ex6_5.sce new file mode 100644 index 000000000..0d22d021b --- /dev/null +++ b/3774/CH6/EX6.5/Ex6_5.sce @@ -0,0 +1,37 @@ +// exa 6.5 Pg 174 +clc;clear;close; + +// Given Data +L=1000;// mm +alfa=20;// degree +dg=500;// mm +L1=250;// mm +L2=300;// mm +dp=600;// mm +Wp=2000;// N +F1=2.5*1000;// N +F1BYF2=3;// ratio of tensions +tau_d=42;// MPa + +F2=F1/F1BYF2;// N +T=(F1-F2)*dp/2;// N.mm +Ftg=2*T/dg;// N +Frg=Ftg*tand(alfa);// N +F=F1+F2;// N + +// Vertical Loads +RAV=(Ftg*(L1+dg)+Wp*L2)/L;// N +RBV=Ftg+Wp-RAV;// N +MCV=RAV*L1;//N.mm +MDV=RBV*L2;// N.mm +// Horizontal Loads +RAH=(Frg*(L1+dg)+F*L2)/L;//N +RBH=Frg+F-RAH;// N +MCH=RAH*L1;// N.mm +MDH=RBH*L2;// N.mm +MD=sqrt(MDV**2+MDH**2);// N.mm +Mmax=MD;//N.mm +Te=MCV+MDV;// N.mm +// d**3 = 16*Te/%pi/tau_d +d = (16*Te/%pi/tau_d)**(1/3);//mm +printf('shaft diameter = %.1f mm.',d) diff --git a/3774/CH6/EX6.6/Ex6_6.sce b/3774/CH6/EX6.6/Ex6_6.sce new file mode 100644 index 000000000..f2305b281 --- /dev/null +++ b/3774/CH6/EX6.6/Ex6_6.sce @@ -0,0 +1,23 @@ +// exa 6.6 Pg 176 +clc;clear;close; + +// Given Data +Tmax=400;// N.mm +Tmin=200;// N.mm +Mmax=500;// N.mm +Mmin=250;// N.mm +Sut=540;// MPa +Syt=420;// MPa +n=2;// factor of safety + +Se=0.35*Sut;// MPa + +Mm=(Mmax+Mmin)/2;// N.m +Ma=(Mmax-Mmin)/2;// N.m +Tm=(Tmax+Tmin)/2;// N.m +Ta=(Tmax-Tmin)/2;// N.m +Sys=0.5*Syt// MPa +Ses=0.5*Se;// MPa +// Max. Distortion energy theory - Syt/n = 32/%pi/d**3*sqrt((Mm+Ma*(Syt/Se)**2)+0.75*(Tm+Ta*(Sys/Ses))**2) +d = (32/%pi*sqrt((Mm+Ma*(Syt/Se))**2+0.75*(Tm+Ta*(Sys/Ses))**2)*1000/(Syt/n))**(1/3) ; // mm +printf('shaft diameter = %.f mm.',d) diff --git a/3774/CH6/EX6.7/Ex6_7.sce b/3774/CH6/EX6.7/Ex6_7.sce new file mode 100644 index 000000000..b64b11393 --- /dev/null +++ b/3774/CH6/EX6.7/Ex6_7.sce @@ -0,0 +1,26 @@ +// exa 6.7 Pg 177 +clc;clear;close; + +// Given Data +Wmax=40;// kN +Wmin=20;// kN +L=500;// mm +Se_dash=350;// MPa +Sut=650;// MPa +Syt=500;// MPa +n=1.5;// factor of safety +ka=0.9; // surface finish factor +kb=0.85;// size factor +ke=1;// load factor +Kf=1;// fatigue strength factor + +Wm=1/2*(Wmax+Wmin);// N +Wa=1/2*(Wmax-Wmin);// N +Se=ka*kb*ke*Se_dash;//MPa +Mm=Wm*L/1000/4;// kN.m +Ma=Wa*L/1000/4;// kN.m +//sigma_m=32*Mm/%pi/d**3; & sigma_a=32*Ma/%pi/d**3 +//soderburg failure criteria - 1/n=sigma_m/Syt+Kf*sigma_a/Se +//d=((32/%pi*n/1000)*(Mm/Syt+Kf*Ma/Se))*(1/3) +d=((32/%pi/1000)*(Mm/Syt+Kf*Ma/Se)*n)**(1/3)*1000;// mm +printf('shaft diameter = %.f mm.',d) diff --git a/3774/CH6/EX6.8/Ex6_8.sce b/3774/CH6/EX6.8/Ex6_8.sce new file mode 100644 index 000000000..c56495bc3 --- /dev/null +++ b/3774/CH6/EX6.8/Ex6_8.sce @@ -0,0 +1,34 @@ +// exa 6.8 Pg 178 +clc;clear;close; + +// Given Data +Tmax=300;// N.mm +Tmin=-100;// N.mm +Mmax=400;// N.mm +Mmin=-200;// N.mm +n=1.5;// factor of safety +Sut=500;// MPa +Syt=420;// MPa +sigma_d=280;// MPa +ka=0.62; // surface finish factor +kb=0.85;// size factor +keb=1;// load factor for bending +kes=0.58;// load factor for torsion +Kfb=1;// fatigue strength factor for bending +Kfs=1;// fatigue strength factor for torsion + +Se_dash=0.5*Sut;// MPa +Se=ka*kb*keb*Se_dash;// MPa +Ses_dash=0.5*Se_dash;// MPa +Ses=ka*kb*kes*Ses_dash;// MPa +Sys=0.5*Syt;// MPa +Mm=(Mmax+Mmin)/2;// N.m +Ma=(Mmax-Mmin)/2;// N.m +Tm=(Tmax+Tmin)/2;// N.m +Ta=(Tmax-Tmin)/2;// N.m + +// tau_d/n = (16/%pi/d**3)*sqrt((Mm+Ma*(Syt/Se)**2)+(Tm+Ta*(Sys/Ses))**2) +tau_d=sigma_d/2;// MPa +d = ((16/%pi)*sqrt((Mm+Ma*(Syt/Se)**2)+(Tm+Ta*(Sys/Ses))**2)/(tau_d*10**6/n))**(1/3)*1000;// mm +printf('shaft diameter = %.2f mm.',d) +// Note - answer in the textbook is not accurate. diff --git a/3774/CH7/EX7.1/Ex7_1.sce b/3774/CH7/EX7.1/Ex7_1.sce new file mode 100644 index 000000000..bbd4ed075 --- /dev/null +++ b/3774/CH7/EX7.1/Ex7_1.sce @@ -0,0 +1,100 @@ +// exa 7.1 Pg 195 +clc;clear;close; + +// Given Data +P=20;// kW +N=240;// rpm +tau_s=45;// MPa +tau_b=30;// MPa +sigma_b=60;// MPa +sigma_cs=2*tau_s;// MPa +tau_ci=15;// MPa +//Tmax=1.25*Tm +mu=0.15;// coefficient of friction + +//SHAFT DIAMETER +// P= 2*%pi*N*Tm/60/1000 +Tm=P/(2*%pi*N/60/1000);// N.m +Tmax=1.25*Tm;// N.m +// %pi*d**3*tau_s/16= Tmax +d=(Tmax/(%pi*tau_s/16)*1000)**(1/3);// mm +printf('shaft diameter = %.2f mm. Use d = 50 mm.',d) +d=50;// mm + +// HUB DIAMETER +// Tmax=%pi/16*((d1**4-d**4)/d1)*tau_h +tau_h=tau_ci;// MPa +//d1*(Tmax/(%pi/16)/tau_h)-d1**4=d**4 -- eqn(1) +Tmax=Tmax*1000;// N.mm +p=[1 0 0 -Tmax/(%pi*tau_h/16) -d**4] ;// polynomial coefficients from eqn(1) +d1=roots(p);// roots of poly +d1=d1(1);// mm (taking +ve value) +d1=100;// mm (empirically adopted) +t1=(d1-d)/2;// mm (thickness of hub) +printf('\n thickness of hub = %.f mm',t1) +d4=d+t1;// mm (diameter of recess in flanges) +printf('\n diameter of recess in flanges = %.f mm',d4) +d3=4*d;// mm (outside diameter of protecting flange) +printf('\n outside diameter of protecting flange = %.f mm',d3) + +// Hub length +b=d/4;// mm (width of key) +l=1.5*d;// mm (length of key) +printf('\n width of key = %.1f mm. Use b = 15 mm',b) +b=15;// mm +printf('\n length of key = %.f mm.',l) +t=b;// mm (thickness for square key) +printf('\n thickness for square key = %.f mm',t) +printf('\n Hub length = %.f mm',l) + +//Number of bolts +n=floor(4*d/150+3);// no. of bolts +printf('\n Number of bolts = %.f',n) + +// Bolt diameter +r2=1.5*d;// mm +F=Tmax/r2/n;// N +//%pi/4*db**2*tau_b=F +db=sqrt(F/(%pi/4*tau_b));// mm +printf('\n Bolt diameter = %.2f mm. Use db=12 mm',db) +bolt_dia=db;//mm + +// Bolt diameter based on Tensile load +r3=d3/2;// mm +r4=d4/2;// mm +rf=2/3*((r3**3-r4**3)/(r3**2-r4**2));// mm +//Tmax=n*mu*Pi*rf;// N +Pi=Tmax/(n*mu*rf);// N +// Pi=%pi/4*db**2*sigma_t +sigma_t=sigma_b;// MPa +db=sqrt(Pi/(%pi/4*sigma_t));// mm +printf('\n Bolt diameter (based on Tensile load) = %.1f mm. Use db=15 mm',db) +db=15;// mm (adopted) + +// Flange thickness +t2=0.5*t1+6;// mm (empirically) +printf('\n Flange thickness = %.1f mm. Use t=20 mm',t2) +t2=20;// mm (adopted) +//F=n*db*t2*sigma_c +sigma_ci=F/n/db/t2;// MPa +//2*%pi*d1**2*tau*t2/4=Tmax +tau=Tmax/(2*%pi*d1**2*t2/4);// MPa +printf('\n permissible bearing stress in flange = %.2f MPa < 30 MPa',sigma_ci) +printf('\n shearing of the flange at the junction with hub = %.2f MPa < 15 MPa.',tau) +printf(' Values are acceptable.') + +// Check for crushing of bolt +//n*db*t2*sigma_cb*d2/2=Tmax +d2=d1+d;// mm +db=bolt_dia;//mm +sigma_cb=Tmax/(n*db*t2*d2/2);// MPa +printf('\n permissible crushing strength of bolts = %.1f MPa < 60 MPa.',sigma_cb) +printf(' Hence design is safe.') + +// Thickness of protecting flange +t3=0.5*t2;// mm +printf('\n Thickness of protecting flange = %.f mm', t3) +// Hub overlap +ho=3;// mm (min) +printf('\n Hub overlap = %.f mm (min)',ho) +//Note - Answer for **Bolt diameter based on Tensile load** is calculated wrong in the textbook(error in Pi calculation). diff --git a/3774/CH7/EX7.10/Ex7_10.sce b/3774/CH7/EX7.10/Ex7_10.sce new file mode 100644 index 000000000..459f61a17 --- /dev/null +++ b/3774/CH7/EX7.10/Ex7_10.sce @@ -0,0 +1,46 @@ +// exa 7.10 Pg 212 +clc;clear;close; + +// Given Data +d=35;// mm +d2=125;// mm +n=6;// factor of safety +T=800;// N.m +N=350;// rpm +tau_s=63;// MPa +tau_b=56;// MPa +tau_CI=10;// MPa +tau_k=46;// MPa + +// Diameter of bolts: +F=2*T*10**3/d2/n;// N +//%pi/4*db**2*tau_b=F +db=sqrt(F/(%pi/4*tau_b));// mm +printf('\n (i) Diameter of bolts = %.2f mm. Use 8 mm.',db) + +// Flange thickness +d1=2*d;// mm +//T=%pi/2*d1**2*t2*tau_CI +t2=T*1000/(%pi/2*d1**2*tau_CI);// mm +printf('\n (ii) Flange thickness = %.1f mm. Use t2 = 12 mm',t2) +t2=12;// mm + +//Key dimensions +b=10;// mm (width of key) +t=7;// mm (from tables) +//T=l*b*tau_k*d/2 +l=T*10**3/(b*tau_k*d/2);// mm +l=ceil(l);// mm +printf('\n (iii) Length of key = %.f mm\n\t\td=%.f mm\n\t\tb=%.f mm',l,d,b) + +// Hub length +lh=l;// mm (length of hub) +printf('\n (iv) Hub length = %.f mm',l) +tau_c=T*10**3/(%pi/16*(d1**4-d**4)/d1);// N/mm.sq. +printf('\n shear stress in hub = %.2f N/mm.sq.',tau_c) +printf('It is nearly equal to %.f N/mm.sq.',tau_CI) +printf('\n hence design parameters are fine.') + +// Power transmitted +P=2*%pi*N*T/60/10**3;// kW +printf('\n (v) Power transmitted = %.2f kW',P) diff --git a/3774/CH7/EX7.2/Ex7_2.sce b/3774/CH7/EX7.2/Ex7_2.sce new file mode 100644 index 000000000..bcc5fef40 --- /dev/null +++ b/3774/CH7/EX7.2/Ex7_2.sce @@ -0,0 +1,108 @@ +// exa 7.2 Pg 200 +clc;clear;close; + +// Given Data +P=30;// kW +N=750;// rpm +//Tmax=1.2*Tm;// MPa +tau_s=35;// MPa +tau_b=35;// MPa +tau_k=35;// MPa +sigma_cs=70;// MPa +sigma_ck=70;// MPa +sigma_cb=70;// MPa +tau_ci=15;// MPa +pb=0.8;// MPa + +//sigma_cs=2*tau_s;// MPa + +//Tmax=1.5*Tm +mu=0.15;// coefficient of friction + +//SHAFT DIAMETER +// P= 2*%pi*N*Tm/60/1000 +Tm=P/(2*%pi*N/60/1000);// N.m +Tmax=1.2*Tm;// N.m +// %pi*d**3*tau_s/16= Tmax +d=(Tmax/(%pi*tau_s/16)*1000)**(1/3);// mm +printf('shaft diameter = %.2f mm. Use d = 42 mm.',d) +d=42;// mm + +// HUB DIAMETER +// Tmax=%pi/16*((d1**4-d**4)/d1)*tau_h +tau_h=tau_ci;// MPa +//d1*(Tmax/(%pi/16)/tau_h)-d1**4=d**4 -- eqn(1) +Tmax=Tmax*1000;// N.mm +p=[1 0 0 -Tmax/(%pi*tau_h/16) -d**4] ;// polynomial coefficients from eqn(1) +d1=roots(p);// roots of poly +d1=d1(1);// mm (taking +ve value) +d1=2*d;// mm (empirically adopted) +t1=(d1-d)/2;// mm (thickness of hub) +printf('\n thickness of hub = %.f mm',t1) +//d4=d+t1;// mm (diameter of recess in flanges) +//printf('\n diameter of recess in flanges = %.f mm',d4) +d3=4*d;// mm (outside diameter of protecting flange) +printf('\n outside diameter of protecting flange = %.f mm. Use 170 mm',d3) +d3=170;// mm (adopted) + +//Key size & Hub length +b=d/4;// mm (width of key) +l=1.5*d;// mm (length of key) +printf('\n width of key = %.1f mm. Use b = 12 mm',b) +b=12;// mm +printf('\n length of key = %.f mm.',l) +t=b;// mm (thickness for square key) +printf('\n thickness for square key = %.f mm',t) +printf('\n Hub length = %.f mm',l) + +//Number of bolts +n=(0.04*d+3);// no. of bolts +printf('\n Number of bolts = %.2f. Use n=6',n) +n=6;// adopted + +// Bolt diameter +db=0.5*d/sqrt(n);// mm +printf('\n Bolt diameter = %.2f mm. Use db=20 mm for design purpose',db) +db=20;//mm (adopted) +bolt_dia=db;//mm +dsb=24;// mm(shank diameter of bolt for design) + +// Outer diameter of rubber bush +trb=2;// mm (thickness of rubber bush) +tbb=6;// mm (thickness of brass bush) +d3=dsb+2*trb+2*tbb;// mm +d2=d1+d3+2*tbb;// mm (pitch circle diameter of bolts) +printf('\n pitch circle diameter of bolts = %.f mm ',d2) + +// Check of shear in bolt +F=2*Tmax/n/d2;// N +//%pi/4*db*2*tau=F +tau=F/(%pi/4*db**2);//MPa +printf('\n Permissible shear stress in bolts = %.2f MPa < 35 MPa. Hence design is safe.', tau) + +// Length of brush +pb=0.8;// MPa(bearing pressure of brush) +//F=l2*d3*pb; +l2=F/d3/pb;// mm +printf('\n length of bush = %.f mm',l2) + +// Check for pin in bending +c=5;// mm (clearance between two flanges) +l3=(l2-c)/2+c;//mm +//M=%pi/32*db**3*sigma_b & M=F*l3 +sigma_b = F*l3/(%pi/32*db**3);// MPa +printf('\n Bending stress in pin = %.1f MPa',sigma_b) + +// Maximum shear stress in pin +tau_max=sqrt((sigma_b/2)**2+tau**2);//MPa +printf('\n Maximum shear stress in pin = %.2f MPa < 35 MPa. Hence design is safe.',tau_max) + +// Flange thickness +t2=0.5*t1+6;// mm (empirically) +printf('\n Flange thickness = %.1f mm. Use t=18 mm',t2) +t2=18;// mm (adopted) +tau=Tmax/(2*%pi*d1**2*t2/4);// MPa +printf('\n shearing of the flange at the junction with hub = %.2f MPa < 15 MPa.',tau) +printf(' Values are acceptable.') + +//Note - Answer in llast part is calculated wrong in the textbook(error in calculation). diff --git a/3774/CH7/EX7.3/Ex7_3.sce b/3774/CH7/EX7.3/Ex7_3.sce new file mode 100644 index 000000000..681ceb911 --- /dev/null +++ b/3774/CH7/EX7.3/Ex7_3.sce @@ -0,0 +1,19 @@ +// exa 7.3 Pg 204 +clc;clear;close; + +// Given Data +n=8;// no. of spline +d=52;// mm +D=60;// mm +pm=6;// MPa +mu=0.06;// coefficient of friction +N=320;// rpm +P=20;// kW + +T=60*10**3*P/2/%pi/N;// N.m +l=8*T*10**3/pm/n/(D**2-d**2);// mm +printf('length of hub = %.f mm',l) +Rm=(D+d)/4;// mm +F=T*10**3/Rm;// N +Ff=mu*F;//N (Force of friction) +printf('\n Force required to shift the connection = %.1f N',Ff) diff --git a/3774/CH7/EX7.4/Ex7_4.sce b/3774/CH7/EX7.4/Ex7_4.sce new file mode 100644 index 000000000..112ac9a80 --- /dev/null +++ b/3774/CH7/EX7.4/Ex7_4.sce @@ -0,0 +1,17 @@ +// exa 7.4 Pg 204 +clc;clear;close; + +// Given Data +d=75;// mm +tau=50;// MPa +sigma_c=75;// MPa +printf('for key to be equally strong in shear & crushing - \n') +b=d/4;// mm +printf(' b= %.2f mm. Use b=20 mm.',b) +b=20;//mm +//2*b/t=sigma_c/tau for key to be equally strong in shear & crushing +t=2*b/(sigma_c/tau);// mm +printf('\n t=%.2f mm. Use t=27 mm',t) +l= %pi*d**2/8/b;// mm (for key to be equally strong in shear as shaft) +printf('for key to be equally strong in shear as shaft - \n') +printf(' l=%.1f mm. Use l=115 mm',l) diff --git a/3774/CH7/EX7.6/Ex7_6.sce b/3774/CH7/EX7.6/Ex7_6.sce new file mode 100644 index 000000000..915d8510a --- /dev/null +++ b/3774/CH7/EX7.6/Ex7_6.sce @@ -0,0 +1,87 @@ +// exa 7.6 Pg 205 +clc;clear;close; + +// Given Data +P=135;// kW +N=120;// rpm +tau_s=55;// MPa +tau_b=45;// MPa +tau_ci=175;// MPa +sigma_ci=75;// MPa + +//sigma_cs=2*tau_s;// MPa + +//Tmax=1.5*Tm +mu=0.15;// coefficient of friction + +//SHAFT DIAMETER +// P= 2*%pi*N*Tm/60/1000 +Tm=P/(2*%pi*N/60/1000);// N.m +// %pi*d**3*tau_s/16= Tm +d=(Tm/(%pi*tau_s/16)*1000)**(1/3);// mm +d=ceil(d) +printf('shaft diameter = %.2f mm.',d) +Tmax=Tm;// N.m + +// HUB DIAMETER +// Tmax=%pi/16*((d1**4-d**4)/d1)*tau_h +tau_h=tau_ci;// MPa +//d1*(Tmax/(%pi/16)/tau_h)-d1**4=d**4 -- eqn(1) +Tmax=Tmax*1000;// N.mm +p=[1 0 0 -Tmax/(%pi*tau_h/16) -d**4] ;// polynomial coefficients from eqn(1) +d1=roots(p);// roots of poly +d1=d1(1);// mm (taking +ve value) +d1=2*d;// mm (empirically adopted) +t1=(d1-d)/2;// mm (thickness of hub) +printf('\n thickness of hub = %.f mm',t1) +d4=d+t1;// mm (diameter of recess in flanges) +printf('\n diameter of recess in flanges = %.f mm',d4) +d3=4*d;// mm (outside diameter of protecting flange) +printf('\n outside diameter of protecting flange = %.f mm.',d3) + +//Key size & Hub length +b=d/4;// mm (width of key) +l=1.5*d;// mm (length of key) +printf('\n width of key = %.1f mm.',b) +printf('\n length of key = %.f mm.',l) +t=b;// mm (thickness for square key) +printf('\n thickness for square key = %.f mm',t) +printf('\n Hub length = %.f mm',l) + +//Number of bolts +n=ceil(4*d/150+3);// no. of bolts +printf('\n Number of bolts = %.2f.',n) + +// Bolt diameter +r2=1.5*d;// mm +F=Tm*1000/r2/n;//N +//(%pi/4)*db**2*tau_b=F +db=sqrt(F/((%pi/4)*tau_b));// mm +printf('\n Bolt diameter = %.2f mm. Use db=20 mm for design purpose',db) +db=20;// mm (adopted for design) +bolt_dia=db;//mm + +// Flange thickness +t2=0.5*t1+6;// mm (empirically) +printf('\n Flange thickness = %.1f mm. Use t=20 mm',t2) +//F=n*db*t2*sigma_c +sigma_ci=F/n/db/t2;// MPa +//2*%pi*d1**2*tau*t2/4=Tmax +tau=Tmax/(2*%pi*d1**2*t2/4);// MPa +printf('\n permissible bearing stress in flange = %.2f MPa < 75 MPa',sigma_ci) +printf('\n shearing of the flange at the junction with hub = %.2f MPa < 175 MPa.',tau) +printf(' Values are acceptable.') + +// Check for crushing of bolt +//n*db*t2*sigma_cb*d2/2=Tmax +d2=d1+d;// mm +db=bolt_dia;//mm +sigma_cb=Tmax/(n*db*t2*d2/2);// MPa +printf('\n permissible crushing strength of bolts = %.2f MPa < 60 MPa.',sigma_cb) +printf(' Hence design is safe.') +// Thickness of protecting flange +t3=0.5*t2;// mm +printf('\n Thickness of protecting flange = %.f mm', t3) +// Hub overlap +ho=3;// mm (min) +printf('\n Hub overlap = %.f mm (min)',ho) diff --git a/3774/CH7/EX7.7/Ex7_7.sce b/3774/CH7/EX7.7/Ex7_7.sce new file mode 100644 index 000000000..8ec7ff5b3 --- /dev/null +++ b/3774/CH7/EX7.7/Ex7_7.sce @@ -0,0 +1,17 @@ +// exa 7.7 Pg 208 +clc;clear;close; + +// Given Data +d=50;// mm +tau=42;// MPa +sigma_c=72;// MPa +printf('for key to be equally strong in shear & crushing - \n') +b=d/4;// mm +printf(' b= %.2f mm. Use b=15 mm.',b) +b=15;//mm +//2*b/t=sigma_c/tau for key to be equally strong in shear & crushing +t=2*b/(sigma_c/tau);// mm +printf('\n t=%.2f mm. Use t=20 mm',t) +l= %pi*d**2/8/b;// mm (for key to be equally strong in shear as shaft) +printf('\n for key to be equally strong in shear as shaft - \n') +printf(' l=%.2f mm. Use l=70 mm',l) diff --git a/3774/CH7/EX7.8/Ex7_8.sce b/3774/CH7/EX7.8/Ex7_8.sce new file mode 100644 index 000000000..161af8ede --- /dev/null +++ b/3774/CH7/EX7.8/Ex7_8.sce @@ -0,0 +1,29 @@ +// exa 7.8 Pg 208 +clc;clear;close; + +// Given Data +d=25;// mm +N=550;// rpm +P=12;// kW +sigma_yt=400;// N/mm.sq. +sigma_yc=400;// N/mm.sq. +n=2.5;// factor of safety + +// P= 2*%pi*N*T/(60*10**3) +T=P/(2*%pi*N/(60*10**3));// N.m +tau=0.5*sigma_yt;// MPa +tau_d=tau/n;// N/mm.sq. +printf('design shear stress = %.f N/mm.sq.',tau_d) +sigma_d=sigma_yc/n;// N/mm.sq. +printf('\n design crushing strength = %.f N/mm.sq.',sigma_d) +b=d/4;//mm +printf('\n width of key = %.f mm. Use 7mm',b) +b=ceil(d/4);// mm +t=b;// mm +printf('\n thickness of key = %.f mm.',t) +l_s=2*T*10**3/(d*b*tau_d);// mm (length of key based on shear failure) +printf('\n length of key based on shear failure = %.2f mm or %.f mm',l_s, l_s) +l_c=4*T*10**3/(d*t*sigma_d);// mm (length of key based on crushing failure) +printf('\n length of key based on crushing failure = %.2f mm or %.f mm',l_c, l_c) + + diff --git a/3774/CH7/EX7.9/Ex7_9.sce b/3774/CH7/EX7.9/Ex7_9.sce new file mode 100644 index 000000000..c800ac040 --- /dev/null +++ b/3774/CH7/EX7.9/Ex7_9.sce @@ -0,0 +1,83 @@ +// exa 7.9 Pg 209 +clc;clear;close; + +// Given Data +d=36;// mm +P=15;// kW +N=720;// rpm +//Tmax=1.25*Tm +sigma_yt=245;// MPa (for C20 steel) +n=3;// factor of safety +sigma=82;// MPa (Design tensile stress) + +tau=0.577*sigma;// MPa (shear stress) +sigma_u=200;// MPa (for FG 200 cast Iron) +n2=5;// factor of safety (for FG 200 cast Iron) +tau2=20;// MPa shear stress (for FG 200 cast Iron) + +// Max. torque transmitted +//P=2*%pi*N*Tm/(60*10**3) +Tm=P/(2*%pi*N/(60*10**3))*1000;// N.mm +Tmax=1.25*Tm;// N.mm +printf('\n Maximum transmitted torque = %.f N.mm',Tmax) + +// Hub diameter +tau_h=20;// MPa (permissible shear stress in hub) +//Tmax=(%pi/16)*(d1**4-d**4)/d1*tau_h ...eqn(1) +d1=2*d;//mm (empirically) +tau_h=Tmax*1000/((%pi/16)*(d1**4-d**4)/d1);// MPa +t1=(d1-d)/2;// mm (thickness of hub) +printf('\n Hub diameter = %.f mm',d1) +printf('\n Thickness of hub = %.f mm',t1) +d4=d+t1;// mm +printf('\n Diameter of recess in flanges = %.f mm',d4) +d3=4*d;//mm +printf('\n Outside diameter of protecting flange = %.f mm',d3) + +//Hub length +b=d/4;// mm (width of key) +l=1.5*d;// mm (length of key) +printf('\n width of key = %.1f mm.',b) +printf('\n length of key = %.f mm.',l) +t=b;// mm (thickness for square key) +printf('\n thickness for square key = %.f mm',t) +printf('\n Hub length = %.f mm',l) + +//Number of bolts +n=ceil(4*d/150+3);// no. of bolts +printf('\n Number of bolts = %.2f.',n) + +// Bolt diameter +r2=1.5*d;// mm +F=Tmax/r2/n;//N +//(%pi/4)*db**2*tau_b=F +db=sqrt(F/((%pi/4)*tau));// mm +printf('\n Bolt diameter = %.2f mm. Use db=6 mm for design purpose',db) +db=6;// mm (adopted for design) +bolt_dia=db;//mm + +// Flange thickness +t2=0.5*t1+6;// mm (empirically) +printf('\n Flange thickness = %.1f mm. Use t=20 mm',t2) +//F=n*db*t2*sigma_c +sigma_ci=F/n/db/t2;// MPa +//2*%pi*d1**2*tau*t2/4=Tmax +tau=Tmax/(2*%pi*d1**2*t2/4);// MPa +printf('\n permissible bearing stress in flange = %.2f MPa < 40 MPa',sigma_ci) +printf('\n shearing of the flange at the junction with hub = %.2f MPa < 20 MPa.',tau) +printf(' Values are acceptable.') + +// Check for crushing of bolt +//n*db*t2*sigma_cb*d2/2=Tmax +d2=d1+d;// mm +db=bolt_dia;//mm +sigma_cb=Tmax/(n*db*t2*d2/2);// MPa +printf('\n permissible crushing strength of bolts = %.2f MPa < 82 MPa.',sigma_cb) +printf(' Hence design is safe.') +// Thickness of protecting flange +t3=0.5*t2;// mm +printf('\n Thickness of protecting flange = %.f mm', t3) +// Hub overlap +ho=3;// mm (min) +printf('\n Hub overlap = %.f mm (min)',ho) + 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) 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. |