diff options
Diffstat (limited to '3863')
71 files changed, 1497 insertions, 0 deletions
diff --git a/3863/CH1/EX1.1/Ex1_1.sce b/3863/CH1/EX1.1/Ex1_1.sce new file mode 100644 index 000000000..89f476e26 --- /dev/null +++ b/3863/CH1/EX1.1/Ex1_1.sce @@ -0,0 +1,22 @@ +clear +// +//Given +//Variable declaration +L=150 //Length of the rod in cm +D=20 //Diameter of the rod in mm +P=20*10**3 //Axial pull in N +E=2.0e5 //Modulus of elasticity in N/sq.mm + +//Calculation +A=(%pi/4)*(D**2) //Area in sq.mm + //case (i):stress +sigma=P/A //Stress in N/sq.mm + //case (ii):strain +e=sigma/E //Strain + //case (iii):elongation of the rod +dL=e*L //Elongation of the rod in cm + +//Result +printf("\n Stress = %0.3f N/mm^2",sigma) +printf("\n Strain = %0.6f ",e) +printf("\n Elongation = %0.4f cm",dL) diff --git a/3863/CH1/EX1.15/Ex1_15.sce b/3863/CH1/EX1.15/Ex1_15.sce new file mode 100644 index 000000000..a5059bfc4 --- /dev/null +++ b/3863/CH1/EX1.15/Ex1_15.sce @@ -0,0 +1,16 @@ +clear +// + +//Given +//Variable declaration +D1=40 //Larger diameter in mm +D2=20 //Smaller diameter in mm +L=400 //Length of rod in mm +P=5000 //Axial load in N +E=2.1e5 //Youngs modulus in N/sq.mm + +//Calculation +dL=((4*P*L)/(%pi*E*D1*D2)) //extension of rod in mm + +//Result +printf("\n Extension of the rod = %0.3f mm",dL) diff --git a/3863/CH1/EX1.16/Ex1_16.sce b/3863/CH1/EX1.16/Ex1_16.sce new file mode 100644 index 000000000..deb4a4610 --- /dev/null +++ b/3863/CH1/EX1.16/Ex1_16.sce @@ -0,0 +1,16 @@ +clear +// + +//Given +//Variable declaration +D1=30 //Larger diameter in mm +D2=15 //Smaller diameter in mm +L=350 //Length of rod in mm +P=5.5*10**3 //Axial load in N +dL=0.025 //Extension in mm + +//Calculation +E=int((4*P*L)/(%pi*D1*D2*dL)) //Modulus of elasticity in N/sq.mm + +//Result +printf("\n Modulus of elasticity,E = %.5eN/mm^2",E) diff --git a/3863/CH1/EX1.17/Ex1_17.sce b/3863/CH1/EX1.17/Ex1_17.sce new file mode 100644 index 000000000..d3636286c --- /dev/null +++ b/3863/CH1/EX1.17/Ex1_17.sce @@ -0,0 +1,18 @@ +clear +// + +//Given +//Variable declaration +L=2.8*10**3 //Length in mm +t=15 //Thickness in mm +P=40*10**3 //Axial load in N +a=75 //Width at bigger end in mm +b=30 //Width at smaller end in mm +E=2e5 //Youngs Modulus in N/sq.mm + +//Calculation +dL=((((P*L)/(E*t*(a-b)))*((log(a)-log(b))))) //extension of rod in mm + + +//Result +printf("\n Extension of the rod,dL = %0.3f mm",dL) diff --git a/3863/CH1/EX1.18/Ex1_18.sce b/3863/CH1/EX1.18/Ex1_18.sce new file mode 100644 index 000000000..1f0fb9f97 --- /dev/null +++ b/3863/CH1/EX1.18/Ex1_18.sce @@ -0,0 +1,18 @@ +clear +// + +//Given +//Variable declaration +dL=0.21 //Extension in mm +L=400 //Length in mm +t=10 //Thickness in mm +a=100 //Width at bigger end in mm +b=50 //Width at smaller end in mm +E=2e5 //Youngs Modulus in N/sq.mm + +//Calculation +P=int(dL/(((L)/(E*t*(a-b)))*((log(a)-log(b)))))*1e-3 //Axial load in kN + + +//Result +printf("\n Axial load = %0.3f kN",P) diff --git a/3863/CH1/EX1.2/Ex1_2.sce b/3863/CH1/EX1.2/Ex1_2.sce new file mode 100644 index 000000000..c95c74ef3 --- /dev/null +++ b/3863/CH1/EX1.2/Ex1_2.sce @@ -0,0 +1,14 @@ +clear +// + +//Given +//variable declaration +P=4000 //Load in N +sigma=95 //Stress in N/sq.mm + +//Calculation +D=(sqrt(P/((%pi/4)*(sigma)))) //Diameter of steel wire in mm + + +//Result +printf("\n Diameter of a steel wire = %0.3f mm",D) diff --git a/3863/CH1/EX1.20/Ex1_20.sce b/3863/CH1/EX1.20/Ex1_20.sce new file mode 100644 index 000000000..30b18e069 --- /dev/null +++ b/3863/CH1/EX1.20/Ex1_20.sce @@ -0,0 +1,33 @@ +clear +// + +//Given +//Variable declaration +Di_s=140 //Internal diameter of steel tube in mm +De_s=160 //External diameter of steel tube in mm +Di_b=160 //Internal diameter of brass tube in mm +De_b=180 //External diameter of brass tube in mm +P=900e3 //Axial load in N +L=140 //Length of each tube in mm +Es=2e5 //Youngs modulus for steel in N/sq.mm +Eb=1e5 //Youngs modulus for brass in N/sq.mm + +//Calculation +As=(%pi/4*(De_s**2-Di_s**2)) //Area of steel tube in sq.mm + +Ab=(%pi/4*(De_b**2-Di_b**2)) //Area of brass tube in sq.mm + +sigmab=(P/(2*As+Ab)) //Stress in steel in N/sq.mm + +sigmas=2*sigmab //Stress in brass in N/sq.mm +Pb=int(sigmab*Ab)*1e-3 //Load carried by brass tube in kN +Ps=(P*1e-3)-(Pb) //Load carried by steel tube in kN +dL=(sigmab/Eb*(L)) //Decrease in length in mm + + +//Result +printf("\n Stress in brass = %0.3f N/mm^2",sigmab) +printf("\n Stress in steel = %0.3f N/mm^2",sigmas) +printf("\n Load carried by brass tube = %0.3f kN",Pb) +printf("\n Load carried by stress tube = %0.3f kN",Ps) +printf("\n Decrease in the length of the compound tube= %0.3f mm",dL) diff --git a/3863/CH1/EX1.28/Ex1_28.sce b/3863/CH1/EX1.28/Ex1_28.sce new file mode 100644 index 000000000..28bce8d1c --- /dev/null +++ b/3863/CH1/EX1.28/Ex1_28.sce @@ -0,0 +1,17 @@ +clear +//Given +//Variable declaration +L=2*10**2 //Length of rod in cm +T1=10 //Initial temperature in degree celsius +T2=80 //Final temperature in degree celsius +E=1e5*10**6 //Youngs Modulus in N/sq.m +alpha=0.000012 //Co-efficient of linear expansion + +//Calculation +T=T2-T1 //Rise in temperature in degree celsius +dL=alpha*T*L //Expansion of the rod in cm +sigma=int((alpha*T*E)*1e-6) //Thermal stress in N/sq.mm + +//Result +printf("\n Expansion of the rod = %0.3f cm",dL) +printf("\n Thermal stress = %0.3f N/mm^2",sigma) diff --git a/3863/CH1/EX1.29/Ex1_29.sce b/3863/CH1/EX1.29/Ex1_29.sce new file mode 100644 index 000000000..abb347fc8 --- /dev/null +++ b/3863/CH1/EX1.29/Ex1_29.sce @@ -0,0 +1,32 @@ +clear +// + +//Given +//Variable declaration +d=3*10 //Diameter of the rod in mm +L=5*10**3 //Area of the rod in sq.mm +T1=95 //Initial temperature in degree celsius +T2=30 //Final temperature in degree celsius +E=2e5*10**6 //Youngs Modulus in N/sq.m +alpha=12e-6 //Co-efficient of linear expansion in per degree celsius + +//Calculation +A=%pi/4*(d**2) //Area of the rod +T=T1-T2 //Fall in temperature in degree celsius + +//case(i) When the ends do not yield +stress1=int(alpha*T*E*1e-6) //Stress in N/sq.mm +Pull1=(stress1*A) //Pull in the rod in N + + +//case(ii) When the ends yield by 0.12cm +delL=0.12*10 +stress2=int((alpha*T*L-delL)*E/L*1e-6) //Stress in N/sq.mm +Pull2=(stress2*A) //Pull in the rod in N + + +//Result +printf("\n Stress when the ends do not yield = %0.3f N/mm^2",stress1) +printf("\n Pull in the rod when the ends do not yield = %0.3f N",Pull1) +printf("\n Stress when the ends yield = %0.3f N/mm^2",stress2) +printf("\n Pull in the rod when the ends yield = %0.3f N",Pull2) diff --git a/3863/CH1/EX1.3/Ex1_3.sce b/3863/CH1/EX1.3/Ex1_3.sce new file mode 100644 index 000000000..5d869ed89 --- /dev/null +++ b/3863/CH1/EX1.3/Ex1_3.sce @@ -0,0 +1,19 @@ +clear +// + +//Given +//Variable declaration +D=25 //Diameter of brass rod in mm +P=50*10**3 //Tensile load in N +L=250 //Length of rod in mm +dL=0.3 //Extension of rod in mm + +//Calculation +A=(%pi/4)*(D**2) //Area of rod in sq.mm +sigma=(P/A) //Stress in N/sq.mm + +e=dL/L //Strain +E=(sigma/e) //Youngs Modulus in N/sq.m + +//Result +printf("\n Youngs Modulus of a rod,E = %0.3f GN/m^2",E*(10**-3)) diff --git a/3863/CH1/EX1.30/Ex1_30.sce b/3863/CH1/EX1.30/Ex1_30.sce new file mode 100644 index 000000000..9afac61f6 --- /dev/null +++ b/3863/CH1/EX1.30/Ex1_30.sce @@ -0,0 +1,24 @@ +clear +// +// +//Given +//Variable declaration +Ds=20 //Diameter of steel rod in mm +Di_c=40 //Internal diameter of copper tube in mm +De_c=50 //External diameter of copper tube in mm +Es=200*10**3 //Youngs modulus of steel in N/sq.mm +Ec=100*10**3 //Youngs modulus of copper in N/sq.mm +alpha_s=12e-6 //Co-efficient of linear expansion of steel in per degree celsius +alpha_c=18e-6 //Co-efficient of linear expansion of copper in per degree celsius +T=50 //Rise of temperature in degree celsius + +//Calculation +As=(%pi/4)*(Ds**2) //Area of steel rod in sq.mm +Ac=(%pi/4)*(De_c**2-Di_c**2) //Area of copper tube in sq.mm +sigmac=(((alpha_c-alpha_s)*T)/(((Ac/As)/Es)+(1/Ec))) //Compressive stress in copper +sigmas=(sigmac*(Ac/As)) //Tensile stress in steel + + +//Result +printf("\n Stress in copper = %0.3f N/mm^2",sigmac) +printf("\n Stress in steel = %0.3f N/mm^2",sigmas) diff --git a/3863/CH1/EX1.31/Ex1_31.sce b/3863/CH1/EX1.31/Ex1_31.sce new file mode 100644 index 000000000..395352333 --- /dev/null +++ b/3863/CH1/EX1.31/Ex1_31.sce @@ -0,0 +1,28 @@ +clear +// + +//Given +//Variable declaration +Dc=15 //Diameter of copper rod in mm +Di_s=20 //Internal diameter of steel in mm +De_s=30 //External diameter of steel in mm +T1=10 //Initial temperature in degree celsius +T2=200 //Raised temperature in degree celsius +Es=2.1e5 //Youngs modulus of steel in N/sq.mm +Ec=1e5 //Youngs modulus of copper in N/sq.mm +alpha_s=11e-6 //Co-efficient of linear expansion of steel in per degree celsius +alpha_c=18e-6 //Co-efficient of linear expansion of copper in per degree celsius + +//Calculation +Ac=(%pi/4)*Dc**2 //Area of copper tube in sq.mm +As=(%pi/4)*(De_s**2-Di_s**2) //Area of steel rod in sq.mm +T=T2-T1 //Rise of temperature in degree celsius +sigmas=(((alpha_c-alpha_s)*T)/(((As/Ac)/Ec)+(1/Es))) + +sigmac=(sigmas*(As/Ac)) + + +//Result +printf("\n NOTE: The answers in the book for stresses are wrong.The correct answers are,") +printf("\n Stress in steel = %0.3f N/mm^2",sigmas) +printf("\n Stress in copper = %0.3f N/mm^2",sigmac) diff --git a/3863/CH1/EX1.32/Ex1_32.sce b/3863/CH1/EX1.32/Ex1_32.sce new file mode 100644 index 000000000..a41ec9c9e --- /dev/null +++ b/3863/CH1/EX1.32/Ex1_32.sce @@ -0,0 +1,26 @@ +clear +// +//Given +//Variable declaration +Dg=20 //Diameter of gun metal rod in mm +Di_s=25 //Internal diameter of steel in mm +De_s=30 //External diameter of steel in mm +T1=30 //Temperature in degree celsius +T2=140 //Temperature in degree celsius +Es=2.1e5 //Youngs modulus of steel in N/sq.mm +Eg=1e5 //Youngs modulus of gun metal in N/sq.mm +alpha_s=12e-6 //Co-efficient of linear expansion of steel in per degree celsius +alpha_g=20e-6 //Co-efficient of linear expansion of gun metal in per degree celsius + +//Calculation +Ag=(%pi/4)*Dg**2 //Area of gun metal in sq.mm +As=(%pi/4)*(De_s**2-Di_s**2) //Area of steel in sq.mm +T=T2-T1 //Fall in temperature in degree celsius +sigmag=(((alpha_g-alpha_s)*T)/(((Ag/As)/Es)+(1/Eg))) + +sigmas=(sigmag*(Ag/As)) + + +//Result +printf("\n Stress in gun metal rod = %0.3f N/mm^2",sigmag) +printf("\n Stress in steel = %0.3f N/mm^2",sigmas) diff --git a/3863/CH1/EX1.33/Ex1_33.sce b/3863/CH1/EX1.33/Ex1_33.sce new file mode 100644 index 000000000..b30c10bf3 --- /dev/null +++ b/3863/CH1/EX1.33/Ex1_33.sce @@ -0,0 +1,16 @@ +clear +// + +//Given +//Variable declaration +P=600e3 //Axial load in N +L=20e3 //Length in mm +w=0.00008 //Weight per unit volume in N/sq.mm +A2=400 //Area of bar at lower end in sq.mm + +//Calculation +sigma=int(P/A2) //Uniform stress on the bar in N/sq.mm +A1=(A2*(%e^((w*L/sigma)))) + +//Result +printf("\n Area of the bar at the upper end = %0.3f mm^2",A1) diff --git a/3863/CH1/EX1.4/Ex1_4.sce b/3863/CH1/EX1.4/Ex1_4.sce new file mode 100644 index 000000000..e6106d966 --- /dev/null +++ b/3863/CH1/EX1.4/Ex1_4.sce @@ -0,0 +1,41 @@ +clear +// + +//Given +//Variable Declaration +D=3 //Diameter of the steel bar in cm +L=20 //Gauge length of the bar in cm +P=250 //Load at elastic limit in kN +dL=0.21 //Extension at a load of 150kN in mm +Tot_ext=60 //Total extension in mm +Df=2.25 //Diameter of the rod at the failure in cm + +//Calculation +A=((%pi/4)*(D**2)) //Area of the rod in sq.m + + +//case (i):Youngs modulus +e=((150*1000)/(7.0685)) //stress in N/sq.m + +sigma=dL/(L*10) //strain +E=((e/sigma)*(10**-5)) //Youngs modulus in GN/sq.m + + +//case (ii):stress at elastic limit +stress=int(((P*1000)/A))*1e-2 //stress at elastic limit in MN/sq.m + + +//case (iii):percentage elongation +Pe=(Tot_ext*1e2)/(L*10) + +//case (iv):percentage decrease in area +Pd=(D**2-Df**2)/D**2*1e2 + + +//Result +printf("\n NOTE:The Youngs Modulus found in the book is incorrect.The correct answer is,") +printf("\n Youngs modulus,E = %0.3f GN/m^2",E) +printf("\n Stress at the elastic limit,Stress = %0.3f MN/m^2",stress) +printf("\n Percentage elongation = %d%%",Pe) + +printf("\n Percentage decrease in area = %.2f%%",Pd) diff --git a/3863/CH1/EX1.5/Ex1_5.sce b/3863/CH1/EX1.5/Ex1_5.sce new file mode 100644 index 000000000..024d60832 --- /dev/null +++ b/3863/CH1/EX1.5/Ex1_5.sce @@ -0,0 +1,16 @@ +clear +// + +//Given +//Variable declaration +sigma=125*10**6 //Safe stress in N/sq.m +P=2.1*10**6 //Axial load in N +D=0.30 //External diameter in m + +//Calculation + +d=(sqrt((D**2)-P*4/(%pi*sigma)))*1e2 //internal diameter in cm + + +//Result +printf("\n internal diameter = %0.3f cm",d) diff --git a/3863/CH1/EX1.6/Ex1_6.sce b/3863/CH1/EX1.6/Ex1_6.sce new file mode 100644 index 000000000..b76750860 --- /dev/null +++ b/3863/CH1/EX1.6/Ex1_6.sce @@ -0,0 +1,16 @@ +clear +// + +//Given +//Variable declaration +stress=480 //ultimate stress in N/sq.mm +P=1.9*10**6 //Axial load in N +D=200 //External diameter in mm +f=4 //Factor of safety + +//Calculation +sigma=stress/f //Working stress or Permissable stress in N/sq.mm +d=sqrt((D**2)-((P*4)/(%pi*sigma))) //internal diameter in mm + +//Result +printf("\n internal diameter = %0.3f mm",d) diff --git a/3863/CH10/EX10.19/Ex10_19.sce b/3863/CH10/EX10.19/Ex10_19.sce new file mode 100644 index 000000000..2c4b532e3 --- /dev/null +++ b/3863/CH10/EX10.19/Ex10_19.sce @@ -0,0 +1,31 @@ +clear +// +// +//Given +//Variable declaration +h=20 //height in m +D=4 //External diameter in m +d=2 //Internal diameter in m +p=1 //Horizontal wind pressure in kN/sq.m +w=22 //specific weight in kN/m^3 +K=2/3 //Co-efficient of wind resistance + +//Calculation +A1=(%pi/4)*(D**2-d**2) //Area of cross-section +W=w*A1*h //Weigth of the chimney in kN +sigma0=W/A1 //Direct stress in kN/sq.mm +A2=D*h //Projected area of the surface exposed to wind in sq.m +F=K*p*A2 //Wind Force in kN +M=F*h/2 //Bending moment in kNm +I=(%pi/64)*(D**4-d**4) //Moment of inertia +y=D/2 //Distance between C.G. of the base section and extreme edge of the base +Z=I/y //Section modulus +sigmab=M/Z //Bending stress +sigma_max=(sigma0+sigmab) //Maximum stress in kN/sq.m + +sigma_min=(sigma0-sigmab) //Minimum stress in kN/sq.m + + +//Result +printf("\n Maximum stress = %0.3f kN/m^2",sigma_max) +printf("\n Minimum stress = %0.3f kN/m^2",sigma_min) diff --git a/3863/CH12/EX12.1/Ex12_1.sce b/3863/CH12/EX12.1/Ex12_1.sce new file mode 100644 index 000000000..52e25e1a3 --- /dev/null +++ b/3863/CH12/EX12.1/Ex12_1.sce @@ -0,0 +1,20 @@ +clear +// + +//Given +//Variable declaration +L=6*1000 //Length in mm +W=50*1000 //Point load in N +I=78e6 //Moment of Inertia in mm^4 +E=2.1e5 //Young's modulus in N/sq.mm + +//Calculation +yc=((W*L**3)/(48*E*I)) //The deflection at the centre in mm + +thetaB=((180/%pi)*((W*L**2)/(16*E*I))) //The slope at the supports + + +//Result +printf("\n Deflection at the centre = %0.3f mm",yc) +printf("\n NOTE:The answer given for slope at the support is wrong.The correct answer is,") +printf("\n Slope at the support = %0.3f degree",thetaB) diff --git a/3863/CH12/EX12.2/Ex12_2.sce b/3863/CH12/EX12.2/Ex12_2.sce new file mode 100644 index 000000000..cdd152ddc --- /dev/null +++ b/3863/CH12/EX12.2/Ex12_2.sce @@ -0,0 +1,14 @@ +clear +// + +//Given +//Variable declaration +L=4*1000 //Length in mm + +//Calculation +thetaA=((%pi/180)*(1)) //Slope at the ends in radians + +yc=(thetaA*(L/3)) //Deflection at the centre in mm + +//Result +printf("\n Deflection at the centre = %0.3f mm",yc) diff --git a/3863/CH12/EX12.3/Ex12_3.sce b/3863/CH12/EX12.3/Ex12_3.sce new file mode 100644 index 000000000..5accbe7e5 --- /dev/null +++ b/3863/CH12/EX12.3/Ex12_3.sce @@ -0,0 +1,14 @@ +clear +// + +//Given +//Variable declaration +L=3*1000 //Length in mm + +//Calculation +thetaA=((%pi/180)*(1)) //Slope at the ends in radians + +yc=(thetaA*(L/3)) //Deflection at the centre in mm + +//Result +printf("\n Deflection at the centre = %0.3f mm",yc) diff --git a/3863/CH12/EX12.4/Ex12_4.sce b/3863/CH12/EX12.4/Ex12_4.sce new file mode 100644 index 000000000..365ae9017 --- /dev/null +++ b/3863/CH12/EX12.4/Ex12_4.sce @@ -0,0 +1,25 @@ +clear +// + +//Given +//Variable declaration +L=5*1000 //Length in mm +W=5*1000 //Point load in N +a=3*1000 //Distance between point load and left end in mm +E=2e5 //Young's modulus in N/sq.mm +I=1e8 //Moment of Inertia in mm^4 + +//Calculation +b=L-a //Width in mm +//case(i):The slope at the left support +thetaA=-(W*a*b)/(6*E*I*L)*(a+2*b) +//case(iii): The deflection under the load +yc=(W*a**2*b**2)/(3*E*I*L) +//case(iii):The maximum deflection +y_max=((W*b)/(9*sqrt(3)*E*I*L)*(((a**2)+(2*a*b))**(3/2))) + + +//Result +printf("\n slope at the left support = %0.3f radians",thetaA) +printf("\n Deflection under the load = %0.3f mm",yc) +printf("\n Maximum deflection = %0.3f mm",y_max) diff --git a/3863/CH12/EX12.5/Ex12_5.sce b/3863/CH12/EX12.5/Ex12_5.sce new file mode 100644 index 000000000..49f9db2c1 --- /dev/null +++ b/3863/CH12/EX12.5/Ex12_5.sce @@ -0,0 +1,27 @@ +clear +// +// + +//Given +//Variable declaration +b=200 //Width in mm +d=300 //Depth in mm +L=5*1000 //Span in mm +L_star=5 //Span in m +w=9*1000 //Uniformly distributed load in N/m +E=1e4 //Youngs modulus in N/sq.mm + +//Calculation +W=w*L_star //Total load in N +I=b*d**3/12 //Moment of Inertia in mm^4 + +//case(i):the slope at the support +thetaA=(-(W*(L**2))/(24*E*I)) + + +//case(ii):maximum deflection +yc=(W*L**3)/(E*I)*(5/384) + +//Result +printf("\n Slope at the support = %0.3f radians",-thetaA) +printf("\n Maximum deflection = %0.3f mm",yc) diff --git a/3863/CH12/EX12.6/Ex12_6.sce b/3863/CH12/EX12.6/Ex12_6.sce new file mode 100644 index 000000000..37772c289 --- /dev/null +++ b/3863/CH12/EX12.6/Ex12_6.sce @@ -0,0 +1,23 @@ +clear +//Given +//Variable declaration +L=5*1000 //Length in mm +L_star=5 //Length in m +w=9 //Uniformly distributed load in kN/m +f=7 //Bending stress in N/sq.mm +E=1e4 //Young's modulus in N/sq.mm +yc=10 //Central deflection in mm + +//Calculation +W=w*L_star*1e3 //Total load in N +bd3=((W*(L**3)*12*5)/(E*yc*384)) //width X depth^3 in mm^4 +M=(W*L/8) //Maximum bending moment in Nmm +bd2=(M*12/(f*2)) //width X depth^2 in mm^3 + +d=(bd3/bd2) //Depth of beam in mm + +b=(M*12/(f*2)/d**2) //Width of beam in mm + +//Result +printf("\n Depth of beam = %0.3f mm",d) +printf("\n Width of beam = %0.3f mm",b) diff --git a/3863/CH12/EX12.7/Ex12_7.sce b/3863/CH12/EX12.7/Ex12_7.sce new file mode 100644 index 000000000..7eb5a2292 --- /dev/null +++ b/3863/CH12/EX12.7/Ex12_7.sce @@ -0,0 +1,14 @@ +clear +//Given +//Variable declaration +L=5*1000 //Length in mm +f=8 //Bending stress in N/sq.mm +yc=10 //Central deflection in mm +E=1.2e4 //Youngs modulus in N/sq.mm + +//Calculation +d=((5*L**2*(f*2*8))/(E*384*yc)*1e-1) //Depth of beam in cm + + +//Result +printf("\n Depth of beam = %0.3f cm",d) diff --git a/3863/CH12/EX12.8/Ex12_8.sce b/3863/CH12/EX12.8/Ex12_8.sce new file mode 100644 index 000000000..a5784a1e9 --- /dev/null +++ b/3863/CH12/EX12.8/Ex12_8.sce @@ -0,0 +1,16 @@ +clear +//Given +//Variable declaration +L=6*1000 //Length in mm +W=40*1000 //Point load in N +a=4*1000 //Distance of point load from left support in mm +I=7.33e7 //Moment of Inertia in mm^4 +E=2e5 //Youngs modulus in sq.mm + +//Calculation +b=L-a //Width of beam in mm +yc=(-(W*a**2*b**2)/(3*E*I*L)) //Deflection under the load in mm + + +//Result +printf("\n Deflection under the load = %0.3f mm",yc) diff --git a/3863/CH13/EX13.1/Ex13_1.sce b/3863/CH13/EX13.1/Ex13_1.sce new file mode 100644 index 000000000..97e4f1c41 --- /dev/null +++ b/3863/CH13/EX13.1/Ex13_1.sce @@ -0,0 +1,21 @@ +clear +// + +//Given +//Variable declaration +L=3*1000 //Length in mm +W=25*1000 //Point load in N +I=1e8 //Moment of Inertia in mm^4 +E=2.1e5 //Youngs modulus in N/sq.mm + +//Calculation +//case(i):Slope of the cantilever at the free end +thetaB=((W*(L**2))/(2*E*I)) + +//case(ii):Deflection at the free end +yB=((W*L**3)/(E*I*3)) + + +//Result +printf("\n Slope at the free end = %0.3f rad",thetaB) +printf("\n Deflection at the free end = %0.3f mm",yB) diff --git a/3863/CH13/EX13.10/Ex13_10.sce b/3863/CH13/EX13.10/Ex13_10.sce new file mode 100644 index 000000000..441d324ea --- /dev/null +++ b/3863/CH13/EX13.10/Ex13_10.sce @@ -0,0 +1,21 @@ +clear +// + +//Given +//Variable declaration +L=4*1000 //Length in mm +w=50 //load at fixed end in N/mm +I=1e8 //Moment of Inertia in mm^4 +E=2e5 //Youngs modulus in N/sq.mm + +//Calculation +//case(i):Slope at the free end +thetaB=(-(w*(L**3))/(24*E*I)) + +//case(ii):Deflection at the free end +yB=((w*L**4)/(E*I*30)) + + +//Result +printf("\n Slope at the free end = %0.3f rad",-thetaB) +printf("\n Deflection at the free end = %0.3f mm",yB) diff --git a/3863/CH13/EX13.2/Ex13_2.sce b/3863/CH13/EX13.2/Ex13_2.sce new file mode 100644 index 000000000..0102fca2a --- /dev/null +++ b/3863/CH13/EX13.2/Ex13_2.sce @@ -0,0 +1,21 @@ +clear +// + +//Given +//Variable declaration +L=3*1000 //Length in mm +W=50*1000 //Point load in N +a=2*1000 //Distance between the load and fixed end in mm +I=1e8 //Moment of Inertia in mm^4 +E=2e5 //Youngs modulus in N/sq.mm + +//Calculation +//case(i):Slope at the free end +thetaB=(W*(a**2))/(2*E*I) +//case(ii):Deflection at the free end +yB=(((W*a**3)/(E*I*3))+((W*(a**2))/(2*E*I)*(L-a))) + + +//Result +printf("\n Slope at the free end = %0.3f rad",thetaB) +printf("\n Deflection at the free end = %0.3f mm",yB) diff --git a/3863/CH13/EX13.3/Ex13_3.sce b/3863/CH13/EX13.3/Ex13_3.sce new file mode 100644 index 000000000..509a35042 --- /dev/null +++ b/3863/CH13/EX13.3/Ex13_3.sce @@ -0,0 +1,17 @@ +clear +// + +//Given +//Variable declaration +L=2.5*1000 //Length in mm +w=16.4 //Uniformly distributed load in kN/m +I=7.95e7 //Moment of Inertia in mm^4 +E=2e5 //Youngs modulus in N/sq.mm + +//Calculation +W=w*L //Total load in N +yB=((W*L**3)/(E*I*8)) //Deflection at the free end in mm + + +//Result +printf("\n Deflection at the free end = %0.3f mm",yB) diff --git a/3863/CH13/EX13.4/Ex13_4.sce b/3863/CH13/EX13.4/Ex13_4.sce new file mode 100644 index 000000000..cdc581f9d --- /dev/null +++ b/3863/CH13/EX13.4/Ex13_4.sce @@ -0,0 +1,16 @@ +clear +//Given +//Variable declaration +b=120 //Width in mm +d=200 //Depth in mm +L_star=2.5 //Length in m +L=2.5*1000 //Length in mm +yB=5 //Deflection at free end in mm +E=2e5 //Youngs modulus in N/sq.mm + +//Calculation +I=(b*d**3)/12 //Moment of Inertia in mm^4 +w=(yB*8*E*I)/(L**3*L_star)/1e3 //Uniformly distributed load in N/m + +//Result +printf("\n Uniformly distributed load = %0.3f kN/m",w) diff --git a/3863/CH13/EX13.5/Ex13_5.sce b/3863/CH13/EX13.5/Ex13_5.sce new file mode 100644 index 000000000..713bb0da1 --- /dev/null +++ b/3863/CH13/EX13.5/Ex13_5.sce @@ -0,0 +1,21 @@ +clear +// + +//Given +//Variable declaration +L=3*1000 //Length in mm +w=10 //Uniformly distributed load in N/mm +a=2*1000 //Length of Uniformly distributed load from fixed end in mm +I=1e8 //Moment of Inertia in mm^4 +E=2e5 //Youngs modulus in N/sq.mm + +//Calculation +//case(i):Slope at the free end +thetaB=(w*(a**3))/(6*E*I) +//case(ii):Deflection at the free end +yB=(((w*a**4)/(E*I*8))+((w*(a**3))/(6*E*I)*(L-a))) + + +//Result +printf("\n Slope at the free end = %0.3f rad",thetaB) +printf("\n Deflection at the free end = %0.3f mm",yB) diff --git a/3863/CH13/EX13.6/Ex13_6.sce b/3863/CH13/EX13.6/Ex13_6.sce new file mode 100644 index 000000000..e916e3048 --- /dev/null +++ b/3863/CH13/EX13.6/Ex13_6.sce @@ -0,0 +1,22 @@ +clear +// + +//Given +//Variable declaration +L=3*1000 //Length in mm +w=10 //Uniformly distributed load in N/mm +a=2*1000 //Length of Uniformly distributed load from fixed end in mm +I=1e8 //Moment of Inertia in mm^4 +E=2e5 //Youngs modulus in N/sq.mm + +//Calculation +//case(i):Slope at the free end +thetaB=(((w*(L**3))/(6*E*I))-((w*((L-a)**3))/(6*E*I))) + +//case(ii):Deflection at the free end +yB=(((w*L**4)/(E*I*8))-(((w*(L-a)**4)/(8*E*I))+((w*(L-a)**3)/(6*E*I)*a))) + + +//Result +printf("\n Slope at the free end = %0.3f rad",thetaB) +printf("\n Deflection at the free end = %0.3f mm",yB) diff --git a/3863/CH16/EX16.1/Ex16_1.sce b/3863/CH16/EX16.1/Ex16_1.sce new file mode 100644 index 000000000..28049627a --- /dev/null +++ b/3863/CH16/EX16.1/Ex16_1.sce @@ -0,0 +1,12 @@ +clear +// +//Given +//Variable declaration +D=150 //Diameter of the shaft in mm +tau=45 //Maximum shear stress in N/sq.mm + +//Calculation +T=int(%pi/16*tau*D**3)*1e-3 //Maximum torque transmitted by the shaft in N-m + +//Result +printf("\n Maximum torque = %0.3f N-m",T) diff --git a/3863/CH16/EX16.10/Ex16_10.sce b/3863/CH16/EX16.10/Ex16_10.sce new file mode 100644 index 000000000..01881dc79 --- /dev/null +++ b/3863/CH16/EX16.10/Ex16_10.sce @@ -0,0 +1,17 @@ +clear +// +//Given +//Variable declaration +P=75e3 //Power transmitted in W +N=200 //R.P.M of the shaft +tau=70 //Shear stress in N/sq.mm + +//Calculation +T=P*60/(%pi*2*N)*1e3 //Mean Torque transmitted in Nmm +Tmax=1.3*T //Maximum Torque transmitted in Nmm +D=((16*Tmax/(%pi*tau))**(1/3)) //Suitable diameter of the shaft in mm + + +//Result +printf("\n Diameter of the shaft = %d mm",D) + diff --git a/3863/CH16/EX16.11/Ex16_11.sce b/3863/CH16/EX16.11/Ex16_11.sce new file mode 100644 index 000000000..cf8ac4757 --- /dev/null +++ b/3863/CH16/EX16.11/Ex16_11.sce @@ -0,0 +1,22 @@ +clear +// +//Given +//Variable declaration +P=300e3 //Power transmitted in W +N=80 //speed of the shaft in r.p.m +tau=60 //Maximum shear stress in N/sq.mm + +//Calculation +T=P*60/(%pi*2*N)*1e3 //Mean Torque transmitted in Nmm +Tmax=1.4*T //Maximum Torque transmitted in Nmm +D=((16*Tmax/(%pi*tau))**(1/3)) //Suitable diameter of the shaft in mm + +Do=(((Tmax*16)/(%pi*tau*(1-0.6**4)))**(1/3)) //External diameter of hollow shaft in mm + +Di=0.6*Do //Internal diameter of hollow shaft in mm + +//Result +printf("\n External diameter of hollow shaft = %d mm",Do) + +printf("\n Internal diameter of hollow shaft = %d mm",Di) + diff --git a/3863/CH16/EX16.3/Ex16_3.sce b/3863/CH16/EX16.3/Ex16_3.sce new file mode 100644 index 000000000..fd2ad92f4 --- /dev/null +++ b/3863/CH16/EX16.3/Ex16_3.sce @@ -0,0 +1,15 @@ +clear +// + +//Given +//Variable declaration +Do=200 //Outer diameter in mm +Di=100 //Inner diameter in mm +tau=40 //Maximum shear stress in N/sq.mm + +//Calculation +T=int(((%pi)/16*tau*((Do**4-Di**4)/Do)))*1e-3 //Maximum torque transmitted by the shaft in Nm + + +//Result +printf("\n Maximum torque transmitted by the shaft = %0.3f Nm",T) diff --git a/3863/CH16/EX16.7/Ex16_7.sce b/3863/CH16/EX16.7/Ex16_7.sce new file mode 100644 index 000000000..40aa960c0 --- /dev/null +++ b/3863/CH16/EX16.7/Ex16_7.sce @@ -0,0 +1,19 @@ +clear +// +// + +//Given +//Variable declaration +Do=120 //External diameter in mm +P=300*1000 //Power in W +N=200 //Speed in r.p.m +tau=60 //Maximum shear stress in N/sq.mm + +//Calculation +T=((P*60)/(2*%pi*N))*1e3 //Torque transmitted in Nmm + +Di=(((Do**4)-((T*16*Do)/(%pi*tau)))**(1/4)) //Maximum internal diameter in mm + + +//Result +printf("\n Maximum Internal diameter = %0.3f mm",Di) diff --git a/3863/CH16/EX16.8/Ex16_8.sce b/3863/CH16/EX16.8/Ex16_8.sce new file mode 100644 index 000000000..76322bace --- /dev/null +++ b/3863/CH16/EX16.8/Ex16_8.sce @@ -0,0 +1,14 @@ +clear +// +//Given +//Variable declaration +D=15*10 //Diameter of shaft in mm +P=150*1e3 //Power transmitted in W +N=180 //Speed of shaft in r.p.m + +//Calculation +T=(P*60)/(2*%pi*N)*1e3 //Torque transmitted in Nmm +tau=int((16*T)/(%pi*D**3)) //Maximum shear stress in N/sq.mm + +//Result +printf("\n Maximum shear stress = %0.3f N/mm^2",tau) diff --git a/3863/CH16/EX16.9/Ex16_9.sce b/3863/CH16/EX16.9/Ex16_9.sce new file mode 100644 index 000000000..ac09cb3a0 --- /dev/null +++ b/3863/CH16/EX16.9/Ex16_9.sce @@ -0,0 +1,24 @@ +clear +// +// +//Given +//Variable declaration +P=300*1000 //Power in W +N=100 //Speed in r.p.m +tau=80 //Maximum shear stress in N/sq.mm + +//Calculation +//case(a): +T=(P*60)/(2*%pi*N)*1e3 //Torque transmitted in Nmm +D=(((16*T)/(%pi*tau))**(1/3)) //Diameter of solid shaft in mm + +//case(b): +Do=(((T*16)/(%pi*tau*(1-0.6**4)))**(1/3)) //External diameter of hollow shaft in mm + +Di=0.6*Do //Internal diameter of hollow shaft in mm +Per=(D**2-(Do**2-Di**2))/(D**2)*100 //Percentage saving in weight + +//Result +printf("\n Diameter of solid shaft = %0.3f mm",D) +printf("\n Percentage saving in weight = %.2f%%",Per) + diff --git a/3863/CH2/EX2.1/Ex2_1.sce b/3863/CH2/EX2.1/Ex2_1.sce new file mode 100644 index 000000000..5042378b5 --- /dev/null +++ b/3863/CH2/EX2.1/Ex2_1.sce @@ -0,0 +1,25 @@ +clear +// +// + +//Given +//Variable declaration +L=4*(10**3) //Length of the bar in mm +b=30 //Breadth of the bar in mm +t=20 //Thickness of the bar in mm +P=30*(10**3) //Axial pull in N +E=2e5 //Youngs modulus in N/sq.mm +mu=0.3 //Poisson's ratio + +//Calculation +A=b*t //Area of cross-section in sq.mm +long_strain=P/(A*E) //Longitudinal strain +delL=long_strain*L //Change in length in mm +lat_strain=mu*long_strain //Lateral strain +delb=b*lat_strain //Change in breadth in mm +delt=t*lat_strain //Change in thickness in mm + +//Result +printf("\n change in length = %0.3f mm",delL) +printf("\n change in breadth = %0.3f mm",delb) +printf("\n change in thickness = %0.3f mm",delt) diff --git a/3863/CH2/EX2.10/Ex2_10.sce b/3863/CH2/EX2.10/Ex2_10.sce new file mode 100644 index 000000000..d6e708904 --- /dev/null +++ b/3863/CH2/EX2.10/Ex2_10.sce @@ -0,0 +1,13 @@ +clear +//Given +//Variable declaration +E=1.2e5 //Youngs modulus in N/sq.mm +C=4.8e4 //Modulus of rigidity in N/sq.mm + +//Calculation +mu=(E/(2*C))-1 //Poisson's ratio +K=int(E/(3*(1-2*mu))) //Bulk modulus in N/sq.mm + +//Result +printf("\n Bulk modulus = %.0e N/mm^2",K) + diff --git a/3863/CH2/EX2.11/Ex2_11.sce b/3863/CH2/EX2.11/Ex2_11.sce new file mode 100644 index 000000000..1b1190ccc --- /dev/null +++ b/3863/CH2/EX2.11/Ex2_11.sce @@ -0,0 +1,20 @@ +clear +//Given +//Variable declaration +A=8*8 //Area of section in sq.mm +P=7000 //Axial pull in N +Ldo=8 //Original Lateral dimension in mm +Ldc=7.9985 //Changed Lateral dimension in mm +C=0.8e5 //modulus of rigidity in N/sq.mm + +//Calculation +lat_strain=(Ldo-Ldc)/Ldo //Lateral strain +sigma=P/A //Axial stress in N/sq.mm +mu=(1/((sigma/lat_strain)/(2*C)-1)) //Poisson's ratio + +E=((sigma/lat_strain)/((sigma/lat_strain)/(2*C)-1)) //Modulus of elasticity in N/sq.mm + + +//Result +printf("\n Modulus of elasticity = %.4e N/mm^2",E) + diff --git a/3863/CH2/EX2.2/Ex2_2.sce b/3863/CH2/EX2.2/Ex2_2.sce new file mode 100644 index 000000000..41d9815d7 --- /dev/null +++ b/3863/CH2/EX2.2/Ex2_2.sce @@ -0,0 +1,20 @@ +clear +//Given +//Variable declaration +L=30 //Length in cm +b=4 //Breadth in cm +d=4 //Depth in cm +P=400*(10**3) //Axial compressive load in N +delL=0.075 //Decrease in length in cm +delb=0.003 //Increase in breadth in cm + +//Calculation +A=(b*d)*1e2 //Area of cross-section in sq.mm +long_strain=delL/L //Longitudinal strain +lat_strain=delb/b //Lateral strain +mu=lat_strain/long_strain //Poisson's ratio +E=int((P)/(A*long_strain)) //Youngs modulus + +//Result +printf("\n Youngs modulus = %.e N/mm^2",E) + diff --git a/3863/CH2/EX2.3/Ex2_3.sce b/3863/CH2/EX2.3/Ex2_3.sce new file mode 100644 index 000000000..0a842e901 --- /dev/null +++ b/3863/CH2/EX2.3/Ex2_3.sce @@ -0,0 +1,17 @@ +clear +//Given +//Variable declaration +L=4000 //Length of the bar in mm +b=30 //Breadth of the bar in mm +t=20 //Thickness of the bar in mm +mu=0.3 //Poisson's ratio +delL=1.0 //delL from problem 2.1 + +//Calculation +ev=(delL/L)*(1-2*mu) //Volumetric strain +V=L*b*t //Original volume in mm^3 +delV=ev*V //Change in volume in mm^3 +F=int(V+delV) //Final volume in mm^3 + +//Result +printf("\n Final volume = %0.3f mm^3",F) diff --git a/3863/CH2/EX2.4/Ex2_4.sce b/3863/CH2/EX2.4/Ex2_4.sce new file mode 100644 index 000000000..e63751f21 --- /dev/null +++ b/3863/CH2/EX2.4/Ex2_4.sce @@ -0,0 +1,20 @@ +clear +// +//Given +//Variable declaration +L=300 //Length in mm +b=50 //Width in mm +t=40 //Thickness in mm +P=300*10**3 //Pull in N +E=2*10**5 //Youngs modulus in N/sq.mm +mu=0.25 //Poisson's ratio + +//Calculation +V=L*b*t //Original volume in mm^3 +Area=b*t //Area in sq.mm +stress=P/Area //Stress in N/sq.mm +ev=(stress/E)*(1-2*mu) //Volumetric strain +delV=int(ev*V) //Change in volume in mm^3 + +//Result +printf("\n Change in volume = %0.3f mm^3",delV) diff --git a/3863/CH2/EX2.7/Ex2_7.sce b/3863/CH2/EX2.7/Ex2_7.sce new file mode 100644 index 000000000..c3ad4cb5c --- /dev/null +++ b/3863/CH2/EX2.7/Ex2_7.sce @@ -0,0 +1,27 @@ +clear +// + +//Given +//Variable declaration +L=5*10**3 //Length in mm +d=30 //Diameter in mm +P=50*10**3 //Tensile load in N +E=2e5 //Youngs modulus in N/sq.mm +mu=0.25 //Poisson's ratio + +//Calculation +V=int(((%pi*d**2*L)/4)) //Volume in mm^3 + +e=P*4/(%pi*(d**2)*E) //Strain of length +delL=(e*L) //Change in length in mm + +lat_strain=(mu*(e)) //Lateral strain + +deld=lat_strain*d //Change in diameter in mm +delV=(V*(0.0003536-(2*lat_strain))) //Change in volume in mm^3 + + +//Result +printf("\n Change in length = %0.3f mm",delL) +printf("\n Change in diameter = %0.3f mm",deld) +printf("\n Change in volume = %0.3f mm^3",delV) diff --git a/3863/CH24/EX24.10/Ex24_10.sce b/3863/CH24/EX24.10/Ex24_10.sce new file mode 100644 index 000000000..494d7c28e --- /dev/null +++ b/3863/CH24/EX24.10/Ex24_10.sce @@ -0,0 +1,26 @@ +clear +// +// + +//Given +//Variable declaration +P=9*1000 //Axial pull in N +F=4.5*1000 //Shear force in N +sigmat_star=225 //Elastic limit in tension in N/sq.mm +Sf=3 //Factor of safety +mu=0.3 //Poisson's ratio +sigma3=0 //third principle stress + +//Calculation +sigmat=sigmat_star/Sf +sigma=(P/(%pi/4)) +tau=(F/(%pi/4)) +sigma1=((tau)+int((sqrt((sigma/2)**2+tau**2)))) + +sigma2=((tau)-int((sqrt((sigma/2)**2+tau**2)))) + +d=(((((sigma1-sigma2)**2+(sigma2-sigma3)**2+(sigma3-sigma1)**2)/(2*(sigmat**2)))**(1/4))) + + +//Result +printf("\n Diameter of the bolt = %0.3f mm",d) diff --git a/3863/CH24/EX24.12/Ex24_12.sce b/3863/CH24/EX24.12/Ex24_12.sce new file mode 100644 index 000000000..933c2f32f --- /dev/null +++ b/3863/CH24/EX24.12/Ex24_12.sce @@ -0,0 +1,27 @@ +clear +// +// +//Given +//Variable declaration +d=1.2 //Diameter in m +p=1.5 //Internal pressure in MN/sq.m +sigmat_star=200 //Yield stress in MN/sq.m +Sf=3 //Factor of safety + +//Calculation +sigmat=sigmat_star/Sf //Permissible stress in simple tension in MN/sq.m + +//case(i):Thickness on the basis of Maximum principal stress theory +t1=((p*d)/2)/sigmat*1e3 + +//case(ii):Thickness on the basis of Maximum shear stress theory +t2=((p*d)/2)/sigmat*1e3 + +//case(iii):Thickness on the basis of Maximum shear strain energy theory +t3=(sqrt((((p*d/2)**2)+((p*d/4)**2)-((p*d/2)*(p*d/4)))/(sigmat**2))) + + +//Result +printf("\n Thickness of plate on the basis of maximum principal stress theory = %0.3f mm ",t1) +printf("\n Thickness of plate on the basis of maximum shear stress theory = %0.3f mm ",t2) +printf("\n Thickness of plate on the basis of maximum shear strain energy theory = %0.3f mm ",t3) diff --git a/3863/CH3/EX3.13/Ex3_13.sce b/3863/CH3/EX3.13/Ex3_13.sce new file mode 100644 index 000000000..658228413 --- /dev/null +++ b/3863/CH3/EX3.13/Ex3_13.sce @@ -0,0 +1,19 @@ +clear +// + +//Given +//Variable declaration +sigma1=120 //Major tensile stress in N/sq.mm +sigma2=-90 //Minor compressive stress in N/sq.mm +sigma_gp=150 //Greatest principal stress in N/sq.mm + +//Calculation + //case(a):Magnitude of the shearing stresses on the two planes +tau=(sqrt(((sigma_gp-((sigma1+sigma2)/2))**2)-(((sigma1-sigma2)/2)**2))) + + //case(b):Maximum shear stress at the point +sigmat_max=int((sqrt((sigma1-sigma2)**2+(4*tau**2)))/2) + +//Result +printf("\n Shear stress on the two planes = %0.3f N/mm^2",tau) +printf("\n Maximum shear stress at the point = %0.3f N/mm^2",sigmat_max) diff --git a/3863/CH3/EX3.16/Ex3_16.sce b/3863/CH3/EX3.16/Ex3_16.sce new file mode 100644 index 000000000..38a814b8a --- /dev/null +++ b/3863/CH3/EX3.16/Ex3_16.sce @@ -0,0 +1,24 @@ +clear +// + +//Given +//Variable declaration +sigma1=600 //Major tensile stress in N/sq.mm +sigma2=300 //Minor tensile stress in N/sq.mm +tau=450 //Shear stress in N/sq.mm +theta1=45 //Angle of inclination in degrees +theta2=135 //Angle of inclination in degrees + +//Calculation +sigman1=int(((sigma1+sigma2)/2)+(((sigma1-sigma2)/2)*cos((%pi/180)*(2*theta1)))+(tau*sin((%pi/180)*(2*theta1)))) +sigman2=int(((sigma1+sigma2)/2)+(((sigma1-sigma2)/2)*cos((%pi/180)*(2*theta2)))+(tau*sin((%pi/180)*(2*theta2)))) +sigmat1=int(((sigma1-sigma2)/2*(sin((%pi/180)*(2*theta1)))-(tau*cos((%pi/180)*(2*theta1))))) + +sigmat2=int(((sigma1-sigma2)/2*(sin((%pi/180)*(2*theta2)))-(tau*cos((%pi/180)*(2*theta2))))) + + +//Result +printf("\n Normal stress(when theta is 45 degrees)= %0.3f N/mm^2",sigman1) +printf("\n Normal stress(when theta is 135 degrees)= %0.3f N/mm^2",sigman2) +printf("\n Tangential stress(when theta is 45 degrees)= %0.3f N/mm^2",sigmat1) +printf("\n Tangential stress(when theta is 135 degrees)= %0.3f N/mm^2",sigmat2) diff --git a/3863/CH3/EX3.8/Ex3_8.sce b/3863/CH3/EX3.8/Ex3_8.sce new file mode 100644 index 000000000..0c4c4b647 --- /dev/null +++ b/3863/CH3/EX3.8/Ex3_8.sce @@ -0,0 +1,23 @@ +clear +// + +//Given +//Variable declaration +sigma1=100 //Major principal stress in N/sq.mm +sigma2=-60 //Minor principal stress in N/sq.mm +theta=90-50 //Angle of inclination in degrees + +//Calculation +sigman=(((sigma1+sigma2)/2)+(((sigma1-sigma2)/2)*cos((%pi/180)*(2*theta)))) + +sigmat=((sigma1-sigma2)/2*(sin((%pi/180)*(2*theta)))) + +sigmaR=(sqrt(sigman**2+sigmat**2)) + +sigmat_max=int((sigma1-sigma2)/2) + +//Result +printf("\n Normal stress = %0.3f N/mm^2",sigman) +printf("\n Shear stress = %0.3f N/mm^2",sigmat) +printf("\n Resultant stress = %0.3f N/mm^2",sigmaR) +printf("\n Maximum shear stress = %0.3f N/mm^2",sigmat_max) diff --git a/3863/CH3/EX3.9/Ex3_9.sce b/3863/CH3/EX3.9/Ex3_9.sce new file mode 100644 index 000000000..8aacb78f1 --- /dev/null +++ b/3863/CH3/EX3.9/Ex3_9.sce @@ -0,0 +1,22 @@ +clear +// + +//Given +//Variable declaration +sigma1=100 //Major principal stress in N/sq.mm +sigma2=-40 //Minor principal stress in N/sq.mm +theta=90-60 //Angle of inclination in degrees + +//Calculation +sigman=((sigma1+sigma2)/2)+(((sigma1-sigma2)/2)*cos((%pi/180)*(2*theta))) +sigmat=((sigma1-sigma2)/2*(sin((%pi/180)*(2*theta)))) + +sigmaR=(sqrt(sigman**2+sigmat**2)) + +sigmat_max=int((sigma1-sigma2)/2) +phi=int((180/%pi)*(atan(sigmat/sigman))) + +//Result +printf("\n Resultant stress in magnitude = %0.3f N/mm^2",sigmaR) +printf("\n Direction of resultant stress = %0.3f degrees",phi) +printf("\n Maximum shear stress = %0.3f N/mm^2",sigmat_max) diff --git a/3863/CH4/EX4.1/Ex4_1.sce b/3863/CH4/EX4.1/Ex4_1.sce new file mode 100644 index 000000000..cc43c5926 --- /dev/null +++ b/3863/CH4/EX4.1/Ex4_1.sce @@ -0,0 +1,31 @@ +clear +// + +//Given +//Variable declaration +P=60*10**3 //Load in N +d=4*10 //diameter in mm +L=5*10**3 //Length of rod in mm +E=2e5 //Youngs Modulus in N/sq.mm + + +//Calculation +A=(%pi/4)*d**2 //Area in sq.mm +V=int(A*L) //Volume of rod in cubic.mm +//case (ii):stress in the rod +sigma=(P/A) //stress in N/sq.mm + + +//case (i):stretch in the rod +x=((sigma/E)*L) //stretch or extension in mm + + +//case (iii):strain energy absorbed by the rod +U=((sigma**2/(2*E)*V))*1e-3 //strain energy absorbed by the rod in Nm + + + +//Result +printf("\n stress in the rod = %0.3f N/mm^2",sigma) +printf("\n stretch in the rod = %0.3f mm",x) +printf("\n strain energy absorbed by the rod = %0.3f N-m",U) diff --git a/3863/CH4/EX4.10/Ex4_10.sce b/3863/CH4/EX4.10/Ex4_10.sce new file mode 100644 index 000000000..997208cbe --- /dev/null +++ b/3863/CH4/EX4.10/Ex4_10.sce @@ -0,0 +1,27 @@ +clear +// +//Given +//Variable declaration +P=100 //Impact load in N +h=2*10 //Height in mm +L=1.5*1000 //Length of bar in mm +A=1.5*100 //Area of bar in sq.mm +E=2e5 //Modulus of elasticity in N/sq.mm + +//Calculation +V=A*L //Volume in mm^3 +//case(i):Maximum instantaneous stress induced in the vertical bar +sigma=((P/A)*(1+(sqrt(1+((2*E*A*h)/(P*L)))))) + +//case(ii):Maximum instantaneous elongation +delL=(sigma*L/E) + +//case(iii):Strain energy stored in the vertical rod +U=(sigma**2/(2*E)*V*1e-3) + + +//Result +printf("\n NOTE:The answer in the book for instantaneous stress is incorrect.The correct answer is,") +printf("\n Maximum instantaneous stress = %0.3f N/mm^2",sigma) +printf("\n Maximum instantaneous elongation = %0.3f mm",delL) +printf("\n Strain energy = %0.3f N-m",U) diff --git a/3863/CH4/EX4.11/Ex4_11.sce b/3863/CH4/EX4.11/Ex4_11.sce new file mode 100644 index 000000000..24af8f5fe --- /dev/null +++ b/3863/CH4/EX4.11/Ex4_11.sce @@ -0,0 +1,23 @@ +clear +// +//Given +//Variable declaration +delL=2.1 //Instantaneous extension in mm +L=3*10**3 //Length of bar in mm +A=5*100 //Area of bar in mm +h=4*10 //Height in mm +E=2e5 //Modulus of elasticity in N/sq.mm + +//Calculation +V=A*L //Volume of bar in mm^3 + +//case(i):Instantaneous stress induced in the vertical bar +sigma=int(E*delL/L) + +//case(ii):Unknown weight +P=(((sigma**2)/(2*E)*V)/(h+delL)) + + +//Result +printf("\n Instantaneous stress = %0.3f N/mm^2",sigma) +printf("\n Unknown weight = %0.3f N",P) diff --git a/3863/CH4/EX4.13/Ex4_13.sce b/3863/CH4/EX4.13/Ex4_13.sce new file mode 100644 index 000000000..c4540ae77 --- /dev/null +++ b/3863/CH4/EX4.13/Ex4_13.sce @@ -0,0 +1,22 @@ +clear +// +//Given +//Variable declaration +d=12 //Diameter of bar in mm +delL=3 //Increase in length in mm +W=8000 //Steady load in N +P=800 //Falling weight in N +h=8*10 //Vertical distance in mm +E=2e5 //Youngs modulus in N/sq.mm + +//Calculation +A=((%pi/4)*d**2) //Area of bar in sq.mm + +L=(E*A*delL/W) //Length of the bar in mm + +sigma=((P/A)*(1+(sqrt(1+((2*E*A*h)/(P*L)))))) + +sigma=(sigma) //Stress produced by the falling weight in N/sq.mm + +//Result +printf("\n Stress produced by the falling weight = %0.3f N/mm^2",sigma) diff --git a/3863/CH4/EX4.14/Ex4_14.sce b/3863/CH4/EX4.14/Ex4_14.sce new file mode 100644 index 000000000..731aa56c8 --- /dev/null +++ b/3863/CH4/EX4.14/Ex4_14.sce @@ -0,0 +1,23 @@ +clear +// +//Given +//Variable declaration +d=12.5 //Diameter of the rod in mm +delL=3.2 //Increase in length in mm +W=10*1000 //Steady load in N +P=700 //Falling load in N +h=75 //Falling height in mm +E=2.1e5 //Youngs modulus in N/sq.mm + +//Calculation +A=((%pi/4)*d**2) //Area of rod in sq.mm + +L=(E*A*delL/W) //Length of the rod in mm + +sigma=((P/A)*(1+(sqrt(1+((2*E*A*h)/(P*L)))))) //Stress produced by the falling weight in N/mm^2 + + +//Result +printf("\n NOTE:The given answer for stress is wrong.The correct answer is,") +printf("\n Stress = %.2f N/mm^2",sigma) + diff --git a/3863/CH4/EX4.15/Ex4_15.sce b/3863/CH4/EX4.15/Ex4_15.sce new file mode 100644 index 000000000..28208b0b9 --- /dev/null +++ b/3863/CH4/EX4.15/Ex4_15.sce @@ -0,0 +1,30 @@ +clear +// + +//Given +//Variable declaration +L=1.82*1000 //Length of rod in mm +h1=30 //Height through which load falls in mm +h2=47.5 //Fallen height in mm +sigma=157 //Maximum stress induced in N/sq.mm +E=2.1e5 //Youngs modulus in N/sq.mm + +//Calculation +U=sigma**2/(2*E) //Strain energy stored in the rod in N-m +delL=sigma*L/E //Extension of the rod in mm +Tot_dist=h1+delL //Total distance in mm + +//case(i):Stress induced in the rod if the load is applied gradually +sigma1=((U/Tot_dist)*L) + + +//case(ii):Maximum stress if the load had fallen from a height of 47.5 mm +sigma2=((sigma1)*(1+(sqrt(1+((2*E*h2)/(sigma1*L)))))) + + +//Result +printf("\n Stress induced in the rod = %.1f N/mm^2",sigma1) + +printf("\n NOTE:The given answer for stress(2nd case) in the book is wrong.The correct answer is,") +printf("\n Maximum stress if the load has fallen = %.2f N/mm^2",sigma2) + diff --git a/3863/CH4/EX4.17/Ex4_17.sce b/3863/CH4/EX4.17/Ex4_17.sce new file mode 100644 index 000000000..53ec41545 --- /dev/null +++ b/3863/CH4/EX4.17/Ex4_17.sce @@ -0,0 +1,27 @@ +clear +// + +//Given +//Variable declaration +L=4*10**3 //Length of bar in mm +A=2000 //Area of bar in sq.mm +P1=3000 //Falling weight in N(for 1st case) +h1=20*10 //Height in mm(for 1st case) +P2=30*1000 //Falling weight in N(for 2nd case) +h2=2*10 //Height in mm(for 2nd case) +E=2e5 //Youngs modulus in N/sq.mm + +//Calculation +V=A*L //Volume of bar in mm^3 + +//case(i):Maximum stress when a 3000N weight falls through a height of 20cm +sigma1=(((sqrt((2*E*P1*h1)/(A*L))))) + + +//case(ii):Maximum stress when a 30kN weight falls through a height of 2cm +sigma2=((P2/A)*(1+(sqrt(1+((2*E*A*h2)/(P2*L)))))) + + +//Result +printf("\n Maximum stress induced(when a weight of 3000N falls through a height of 20cm)= %0.3f N/mm^2",sigma1) +printf("\n Maximum stress induced(when a weight of 30kN falls through a height of 2cm)= %0.3f N/mm^2",sigma2) diff --git a/3863/CH4/EX4.18/Ex4_18.sce b/3863/CH4/EX4.18/Ex4_18.sce new file mode 100644 index 000000000..30207c5e8 --- /dev/null +++ b/3863/CH4/EX4.18/Ex4_18.sce @@ -0,0 +1,21 @@ +clear +// +// + +//Given +//Variable declaration +A=6.25*100 //Area in sq.mm +W=10*10**3 //Load in N +V=(40/60) //Velocity in m/s +L=10000 //Length of chain unwound in mm +E=2.1e5 //Youngs modulus in N/sq.mm +g=9.81 //acceleration due to gravity + +//Calculation +K_E=(((W/g)*(V**2))/2)*1e3 //K.E of the crane in N mm + +sigma=(sqrt(K_E*E*2/(A*L))) //Stress induced in the chain in N/sq.mm + + +//Result +printf("\n Stress induced in the chain due to sudden stoppage = %0.3f N/mm^2",sigma) diff --git a/3863/CH4/EX4.19/Ex4_19.sce b/3863/CH4/EX4.19/Ex4_19.sce new file mode 100644 index 000000000..3ce7a930f --- /dev/null +++ b/3863/CH4/EX4.19/Ex4_19.sce @@ -0,0 +1,19 @@ +clear +// + +//Given +//Variable declaration +W=60*10**3 //Weight in N +V=1 //Velocity in m/s +L=15*10**3 //Free length in mm +A=25*100 //Area in sq.mm +E=2e5 //Youngs modulus in N/sq.mm +g=9.81 //acceleration due to gravity + +//Calculation +K_E=((W/g)*(V**2))/2*1e3 //Kinetic Energy of the cage in N mm +sigma=(sqrt(K_E*E*2/(A*L))) //Maximum stress in N/sq.mm + + +//Result +printf("\n Maximum stress produced in the rope = %0.3f N/mm^2",sigma) diff --git a/3863/CH4/EX4.20/Ex4_20.sce b/3863/CH4/EX4.20/Ex4_20.sce new file mode 100644 index 000000000..3c55aaa15 --- /dev/null +++ b/3863/CH4/EX4.20/Ex4_20.sce @@ -0,0 +1,11 @@ +clear +//Given +//Variable declaration +tau=50 //Shear stress in N/sq.mm +C=8e4 //Modulus of rigidity in N/sq.mm + +//Calculation +ste=(tau**2)/(2*C) //Strain energy per unit volume in N/sq.mm + +//Result +printf("\n Strain energy per unit volume = %0.3f N/mm^2",ste) diff --git a/3863/CH4/EX4.3/Ex4_3.sce b/3863/CH4/EX4.3/Ex4_3.sce new file mode 100644 index 000000000..2ed022d16 --- /dev/null +++ b/3863/CH4/EX4.3/Ex4_3.sce @@ -0,0 +1,15 @@ +clear +//Given +//Variable declaration +A=10*10**2 //Area of bar in sq.mm +L=3*10**3 //Length of bar in mm +x=1.5 //Extension due to suddenly applied load in mm +E=2e5 //Youngs Modulus in N/sq.mm + +//Calculation +sigma=int(x*E/L) //Instantaneous stress due to sudden load in N/sq.mm +P=int((sigma*A)/2*1e-3) //Suddenly applied load in kN + +//Result +printf("\n Instantaneous stress produced by a sudden load = %0.3f N/mm^2",sigma) +printf("\n Suddenly applied load = %0.3f kN",P) diff --git a/3863/CH4/EX4.4/Ex4_4.sce b/3863/CH4/EX4.4/Ex4_4.sce new file mode 100644 index 000000000..44a89a633 --- /dev/null +++ b/3863/CH4/EX4.4/Ex4_4.sce @@ -0,0 +1,19 @@ +clear +// + +//Given +//Variable declaration +L=2*10**3 //Length in mm +d=50 //Diameter in mm +P=100*10**3 //Suddenly applied load in N +E=200e3 //Youngs Modulus in N/sq.mm + +//Calculation +A=(%pi/4)*d**2 //Area in sq.mm +sigma=(2*P/A) //Instantaneous stress induced in N/sq.mm + +dL=(sigma*L)/E //Elongation in mm + +//Result +printf("\n Instantaneous stress induced = %0.3f N/mm^2",sigma) +printf("\n Instantaneous elongation = %0.3f mm",dL) diff --git a/3863/CH4/EX4.5/Ex4_5.sce b/3863/CH4/EX4.5/Ex4_5.sce new file mode 100644 index 000000000..21736ce34 --- /dev/null +++ b/3863/CH4/EX4.5/Ex4_5.sce @@ -0,0 +1,19 @@ +clear +//Given +//Variable declaration +A=700 //Area in sq.mm +L=1.5*10**3 //Length of a metal bar in mm +sigma=160 //Stress at elastic limit in N/sq.mm +E=2e5 //Youngs Modulus in N/sq.mm + + +//Calculation +V=A*L //Volume of bar in sq.mm +Pr=(sigma**2/(2*E)*V)*1e-3 //Proof resilience in N-m +P=int(sigma*A/2*1e-3) //Suddenly applied load in kN +P1=int(sigma*A*1e-3) //gradually applied load in kN + +//Result +printf("\n Proof resilience = %0.3f N-m",Pr) +printf("\n Suddenly applied load = %0.3f kN",P) +printf("\n Gradually applied load = %0.3f kN",P1) diff --git a/3863/CH4/EX4.9/Ex4_9.sce b/3863/CH4/EX4.9/Ex4_9.sce new file mode 100644 index 000000000..0e07d3505 --- /dev/null +++ b/3863/CH4/EX4.9/Ex4_9.sce @@ -0,0 +1,18 @@ +clear +// + +//Given +//Variable declaration +P=10*10**3 //Falling weight in N +h=30 //Falling height in mm +L=4*10**3 //Length of bar in mm +A=1000 //Area of bar in sq.m +E=2.1e5 //Youngs modulus in N/sq.mm + +//Calculation +sigma=((P/A)*(1+(sqrt(1+((2*E*A*h)/(P*L)))))) +delL=(sigma*L/E) + + +//Result +printf("\n Instantaneous elongation due to falling weight = %0.3f mm",delL) diff --git a/3863/CH7/EX7.1/Ex7_1.sce b/3863/CH7/EX7.1/Ex7_1.sce new file mode 100644 index 000000000..38268b64a --- /dev/null +++ b/3863/CH7/EX7.1/Ex7_1.sce @@ -0,0 +1,18 @@ +clear +//Given +//Variable declaration +b=120 //Width of plate in mm +t=20 //Thickness of plate in mm +R=10*10**3 //Radius of curvature in mm +E=2e5 //Youngs modulus in N/sq.mm + +//Calculation +I=b*t**3/12 //Moment of inertia in mm^4 +y_max=t/2 //Maximum distance in mm +sigma_max=int((E/R)*y_max) //Maximum stress in N/sq.mm +M=((E/R*I)*(10**-6)) //Bending moment in kNm + + +//Result +printf("\n Maximum stress = %0.3f N/mm^2",sigma_max) +printf("\n Bending moment = %0.3f kNm",M) diff --git a/3863/CH7/EX7.8/Ex7_8.sce b/3863/CH7/EX7.8/Ex7_8.sce new file mode 100644 index 000000000..97695e9bd --- /dev/null +++ b/3863/CH7/EX7.8/Ex7_8.sce @@ -0,0 +1,29 @@ +clear +// +// + +//Given +//Variable declaration +W=20*1000 //Total load in N +L=3.6 //Span in m +sigma_max=7 //Maximum stress in N/sq.mm + +//Calculation +M1=W*L/8*1e3 //Maximum Bending moment in Nmm +b1=((M1*3/(sigma_max*2))**(1/3)) //Breadth of the beam in mm + +d1=int((2*b1)) //depth of the beam in mm + +M2=W*L/4*1e3 //Maximum Bending moment in Nmm +b2=(((M2*3/(sigma_max*2))**(1/3))) //Breadth of the beam in mm + +d2=2*b2 //depth of the beam in mm + +//Result +printf("\n Dimensions of the cross-section:") +printf("\n Breadth of beam = %0.3f mm",b1) +printf("\n Depth of beam %0.3f mm",d1) + +printf("\n Dimensions of the cross-section when the beam carries a point load at the centre:") +printf("\n Breadth of beam = %0.3f mm",b2) +printf("\n Depth of beam %0.3f mm",d2) diff --git a/3863/CH8/EX8.12/Ex8_12.sce b/3863/CH8/EX8.12/Ex8_12.sce new file mode 100644 index 000000000..43cebdacd --- /dev/null +++ b/3863/CH8/EX8.12/Ex8_12.sce @@ -0,0 +1,18 @@ +clear +// +// + +//Given +//Variable declaration +F=50*10**3 //Shear force in N +b=250 //Base width in mm +h=200 //height in mm + +//Calculation +tau_max=int((3*F)/(b*h)) //Maximum shear stress in N/sq.mm +tau=((8*F)/(3*b*h)) //Shear stress at N.A. in N/sq.mm + + +//Result +printf("\n Maximum shear stress = %0.3f N/mm^2",tau_max) +printf("\n Shear stress at N.A. = %0.3f N/mm^2",tau) diff --git a/3863/CH8/EX8.6/Ex8_6.sce b/3863/CH8/EX8.6/Ex8_6.sce new file mode 100644 index 000000000..0af86c38f --- /dev/null +++ b/3863/CH8/EX8.6/Ex8_6.sce @@ -0,0 +1,26 @@ +clear +// +// +//Given +//Variable declaration +D=100 //Diameter in mm +R=D/2 //Radius in mm +F=5*10**3 //Shear force in N +y=40 //given distance from N.A. in mm + +//Calculation +//case(i):Average shear stress +A=%pi*R**2 +tau_avg=(F/A) + +//case(ii):Maximum shear stress for a circular section +tau_max=(4/3*tau_avg) + +//case(iii):Shear stress at a distance 40mm from N.A. +I=%pi/64*D**4 +tau=((F/(3*I)*(R**2-y**2))) + +//Result +printf("\n Average shear stress = %0.3f N/mm^2",tau_avg) +printf("\n Maximum shear stress = %0.3f N/mm^2",tau_max) +printf("\n Shear stress at a distance 40mm from N.A. = %0.3f N/mm^2",tau) |