diff options
Diffstat (limited to '3864/CH2')
38 files changed, 1519 insertions, 0 deletions
diff --git a/3864/CH2/EX2.1/Ex2_1.sce b/3864/CH2/EX2.1/Ex2_1.sce new file mode 100644 index 000000000..573580d97 --- /dev/null +++ b/3864/CH2/EX2.1/Ex2_1.sce @@ -0,0 +1,21 @@ +clear +// +// + +//Initilization of Variables +P=45*10**3 //N //Load +E=200*10**3 //N/mm**2 //Modulus of elasticity of rod +L=500 //mm //Length of rod +d=20 //mm //Diameter of rod + +//Calculations + +A=%pi*d**2*4**-1 //mm**2 //Area of circular rod +p=P*A**-1 //N/mm**2 //stress +e=p*E**-1 //strain +dell_l=(P*L)*(A*E)**-1 + +//Result +printf("\n The stress in bar due to Load is %0.5f N/mm",p) +printf("\n The strain in bar due to Load is %0.5f N/mm",e) +printf("\n The Elongation in bar due to Load is %0.2f mm",dell_l) diff --git a/3864/CH2/EX2.11/Ex2_11.sce b/3864/CH2/EX2.11/Ex2_11.sce new file mode 100644 index 000000000..e3deff5c9 --- /dev/null +++ b/3864/CH2/EX2.11/Ex2_11.sce @@ -0,0 +1,26 @@ +clear +// +// + +//Initilization of Variables + +t=10 //mm //Thickness of steel +b1=60 //mm //width of plate1 +b2=40 //mm //width of plate2 +P=60*10**3 //Load +L=600 //mm //Length of plate +E=2*10**5 //N/mm**2 + +//Calculations + +//Extension of taperong bar of rectangular section +dell_l=P*L*(t*E*(b1-b2))**-1*log(b1*b2**-1) + +A_av=(b1*t+b2*t)*2**-1 //Average Area //mm**2 +dell_l2=P*L*(A_av*E)**-1 + +//PErcentage Error +e=(dell_l-dell_l2)*(dell_l)**-1*100 + +//Result +printf("\n The Percentage Error is %0.2f ",e) diff --git a/3864/CH2/EX2.12/Ex2_12.sce b/3864/CH2/EX2.12/Ex2_12.sce new file mode 100644 index 000000000..acb225448 --- /dev/null +++ b/3864/CH2/EX2.12/Ex2_12.sce @@ -0,0 +1,29 @@ +clear +// +// + +//Initilization of Variables + +L=1.5 //m //Length of steel bar +L1=1000 //m0 //Length of steel bar 1 +L2=500 //m //Length of steel bar 2 +d1=40 //Diameter of steel bar 1 +d2=20 //diameter of steel bar 2 +E=2*10**5 //N/mm**2 //Modulus of Elasticity +P=160*10**3 //N //Load + +//Calculations + +A1=%pi*4**-1*d1**2 //Area of Portion 1 + +//Extension of uniform Portion 1 +dell_l1=P*L1*(A1*E)**-1 //mm + +//Extension of uniform Portion 2 +dell_l2=4*P*L2*(%pi*d1*d2*E)**-1 //mm + +//Total Extension of Bar +dell_l=dell_l1+dell_l2 + +//Result +printf("\n The Elongation of the Bar is %0.2f mm",dell_l) diff --git a/3864/CH2/EX2.14/Ex2_14.sce b/3864/CH2/EX2.14/Ex2_14.sce new file mode 100644 index 000000000..b654e813d --- /dev/null +++ b/3864/CH2/EX2.14/Ex2_14.sce @@ -0,0 +1,51 @@ +clear +// +// + +//Initilization of Variables + +//Portion AB +L_AB=600 //mm //Length of AB +A_AB=40*40 //mm**2 //Cross-section Area of AB + +//Portion BC +L_BC=800 //mm //Length of BC +A_BC=30*30 //mm //Length of BC + +//Portion CD +L_CD=1000 //mm //Length of CD +A_CD=20*20 //mm //Area of CD + +P1=80*10**3 //N //Load1 +P2=60*10**3 //N //Load2 +P3=40*10**3 //N //Load3 + +E=2*10**5 //Modulus of Elasticity + +//Calculations + +P4=P1-P2+P3 //Load4 + +//Now Force in AB +F_AB=P1 + +//Force in BC +F_BC=P1-P2 + +//Force in CD +F_CD=P4 + +//Extension of AB +dell_l_AB=F_AB*L_AB*(A_AB*E)**-1 + +//Extension of BC +dell_l_BC=F_BC*L_BC*(A_BC*E)**-1 + +//Extension of CD +dell_l_CD=F_CD*L_CD*(A_CD*E)**-1 + +//Total Extension +dell_l=dell_l_AB+dell_l_BC+dell_l_CD + +//Result +printf("\n The Total Extension in Bar is %0.2f mm",dell_l) diff --git a/3864/CH2/EX2.15/Ex2_15.sce b/3864/CH2/EX2.15/Ex2_15.sce new file mode 100644 index 000000000..e93ab1cf5 --- /dev/null +++ b/3864/CH2/EX2.15/Ex2_15.sce @@ -0,0 +1,71 @@ +clear +// +// + +//Initilization of Variables + +L=800 //mm //Length of bar +F1=30*10**3 //N //Force acting on the bar +F2=60*10**3 //N //force acting on the bar +L=800 //mm //Length of bar +d=25 //mm //diameter of bar +L_AC=275 //mm //Length of AC +L_CD=150 //mm //Length of CD +L_DB=375 //mm //Length of DB +E=2*10**5 //Pa //Modulus of elasticity + +//Calculations + +//Let P be the Reaction on tne Bar from support at A + +//Shortening of Portion AC +//dell_l_AC1=P*L_AC*(A*E)**-1 + +//Shortening of Portion CD +//dell_l_CD1=(30+P)*L_CD*(A*E)**-1 + +//Extension of Portion DB +//dell_l_DB1=(30-P)*L_DB*(A*E)**-1 + +//Total Extensions=1*(A*E)**-1*(P*L_AC-(30+P)*L_CD+(30-P)*L_DB) +//As Supports are unyielding,Total Extensions=0 + +//After substituting values in above equation and Further simplifying we get +P=(30*375-150*30)*800**-1 + +//Reaction of support A +R_A=P + +//Reaction of support B +R_B=30-P + +//Cross-sectional Area +A=%pi*4**-1*d**2 + +//Stress in Portion AC +sigma1=P*10**3*A**-1 //N/mm**2 + +//Stress in Portion CD +sigma2=(30+P)*10**3*A**-1 //N/mm**2 + +//Stress in Portion DB +sigma3=(30-P)*10**3*A**-1 //N/mm**2 + +//Shortening of Portion AC +dell_l_AC2=P*10**3*L_AC*(A*E)**-1 //mm + +//Shortening of Portion CD +dell_l_CD2=(30+P)*10**3*L_CD*(A*E)**-1 //mm + +//Extension of Portion DB +dell_l_DB2=(30-P)*10**3*L_DB*(A*E)**-1 //mm + +//result +printf("\n The Reactios at two Ends are:R_A %0.2f KN",R_A) +printf("\n :R_B %0.2f KN",R_B) +printf("\n Stress in Portion AC %0.2f N/mm**2",sigma1) +printf("\n Stress in Portion CD %0.2f N/mm**2",sigma2) +printf("\n Stress in Portion DB %0.2f N/mm**2",sigma3) +printf("\n Shortening of Portion AC %0.3f mm",dell_l_AC2) +printf("\n Shortening of Portion CD %0.3f mm",dell_l_CD2) +printf("\n Shortening of Portion DB %0.3f mm",dell_l_DB2) diff --git a/3864/CH2/EX2.2/Ex2_2.sce b/3864/CH2/EX2.2/Ex2_2.sce new file mode 100644 index 000000000..b255a81fa --- /dev/null +++ b/3864/CH2/EX2.2/Ex2_2.sce @@ -0,0 +1,19 @@ +clear +// + +//Initilization of Variables + +A=15*0.75 //mm**2 //area of steel tape +P=100 //N //Force apllied +L=30*10**3 //mm //Length of tape +E=200*10**3 //N/m**2 //Modulus of Elasticity of steel tape +AB=150 //m //Measurement of Line AB + +//Calculations + +dell_l=P*L*(A*E)**-1 //mm //Elongation +l=L+dell_l*10**-3 //mm //Actual Length +AB1=AB*l*L**-1 //m Actual Length of AB + +//Result +printf("\n The Actual Length of Line AB is %0.2f m",AB1) diff --git a/3864/CH2/EX2.20/Ex2_20.sce b/3864/CH2/EX2.20/Ex2_20.sce new file mode 100644 index 000000000..9d5785310 --- /dev/null +++ b/3864/CH2/EX2.20/Ex2_20.sce @@ -0,0 +1,56 @@ +clear +// +// + +//Initilization of Variables + +sigma=150 //N/mm**2 //Stress +P=40*10**3 //N //Load + +//Calculations + +//LEt P_A.P_B,P_C,P_D be the forces developed in wires A,B,C,D respectively + +//Let sum of all Vertical Forces=0 +//P_A+P_B+P_C+P_D=40 ..........................(1) + +//Let x be the distance between each wires +//sum of all moments=0 +//P_B*x+P_C*2*x+P_D*3*x=40*2*x + +//After further simplifying we get +//P_B+2*P_C+3*P_D=80 ..........................(2) + +//As the equations of statics ae not enough to find unknowns,Consider compatibilit Equations + +//Let dell_l be the increse in elongation of wire + +//dell_l_B=dell_l_A+dell_l +//dell_l_C=dell_l_A+2*dell_l +//dell_l_D=dell_l_A+3*dell_l + +//Let P1 be the force required for the Elongation of wires,then +//P_B=P_A+P1 ] +//P_C=P_A+2*P1 ] +//P_D=P_A+3*P1 ] ................................(3) + +//from Equation (3) and (1) we get +//2*P_A+3*P1=20 ................................(4) + +//from Equation (3) and (2) we get +//6*P_A+14*P1=80 + +//subtracting 3 times equation (4) from (3) we get +P1=20*5**-1 + +//from Equation 4 we get +P_A=(80-14*P1)*6**-1 +P_B=P_A+P1 +P_C=P_A+2*P1 +P_D=P_A+3*P1 + +//Let d be the diameter required,then +d=(P_D*10**3*4*(%pi*150)**-1)**0.5 + +//result +printf("\n The Required Diameter is %0.2f mm",d) diff --git a/3864/CH2/EX2.21/Ex2_21.sce b/3864/CH2/EX2.21/Ex2_21.sce new file mode 100644 index 000000000..678fe0d54 --- /dev/null +++ b/3864/CH2/EX2.21/Ex2_21.sce @@ -0,0 +1,52 @@ +clear +// +// + +//Initilization of Variables + +P=20*10**3 //N //Load +d=6 //mm //diameter of wire +E=2*10**5 //N/mm**2 +L_BO=4000 //mm //Length of BO + +//Calculations + +//Let theta be the angle between OA and OB and also between OC and OB +theta=30 + +//Let P_OA,P_OB,P_OC be the Forces introduced in wires OA,OB,OC respectively +//Due to symmetry P_OA=P_OC (same angles) + +//Sum of all Vertical Forces=0 +//P_OA*cos(theta)+P_OB+P_OC*cos(theta)=P + +//After further simplifyinf we get +//2*P_OA*cos(theta)+P_OB=20 ...............(1) + +//Let oo1 be the extension of BO +//oo1=L_A1o1*(cos(theta))**-1 + +//From relation we get +//P_OB*L_BO=P_OA*L_AO*(cos(theta))**-1 + +//But L_AO=L_BO*(cos(theta))**-1 + +//After substituting value of L_AO in above equation we get +//P_OB=0.75*P_OA .......................(2) + +//substituting in Equation 1 we get +//2*P_OA*cos(theta)+0.75*P_OA=20 + +P_OA=20*(2*cos(theta*%pi*180**-1)+0.75)**-1 + +P_OB=0.75*P_OA + +A=%pi*4**-1*d**2 + +//Vertical displacement of Load +dell_l_BO=P_OB*10**3*L_BO*(A*E)**-1 + +//Result +printf("\n Forces in each wire is:P_OA %0.2f KN",P_OA) +printf("\n :P_OB %0.2f KN",P_OB) +printf("\n Vertical displacement of Loadis %0.2f mm",dell_l_BO) diff --git a/3864/CH2/EX2.22/Ex2_22.sce b/3864/CH2/EX2.22/Ex2_22.sce new file mode 100644 index 000000000..0949e768e --- /dev/null +++ b/3864/CH2/EX2.22/Ex2_22.sce @@ -0,0 +1,39 @@ +clear +// + +//Initilization of Variables + +A_a=50*20 //mm //Area of aluminium strip +A_s=50*15 //mm //Area of steel strip +P=50*10**3 //N //Load +E_a=1*10**5 //N/mm**2 //Modulus of aluminium +E_s=2*10**5 //N/mm**2 //Modulus of steel + +//Calculations + +//Let P_a and P_s br the Load shared by aluminium and steel strip +//P_a+P_s=P ..................(1) + +//For compatibility condition,dell_l_a=dell_l_s +//P_a*L_a*(A_a*E_a)**-1=P_s*L_s*(A_s*E_s)**-1 .....(2) + +//As L_a=L_s we get +//P_s=1.5*P_a .................(3) + +//From Equation 1 and 2 we get +P_a=P*2.5**-1 + +//Substituting in equation 1 we get +P_s=P-P_a + +//stress in aluminium strip +sigma_a=P_a*A_a**-1 + +//stress in steel strip +sigma_s=P_s*A_s**-1 + +//Now from the relation we get + +//result +printf("\n Stress in Aluminium strip is %0.2f N/mm**2",sigma_a) +printf("\n Stress in steel strip is %0.2f N/mm**2",sigma_s) diff --git a/3864/CH2/EX2.23/Ex2_23.sce b/3864/CH2/EX2.23/Ex2_23.sce new file mode 100644 index 000000000..b1ee4ddd9 --- /dev/null +++ b/3864/CH2/EX2.23/Ex2_23.sce @@ -0,0 +1,43 @@ +clear +// +// + +//Initilization of Variables + +D_s=20 //mm //Diameter of steel +D_Ci=20 //mm //Internal Diameter of Copper +t=5 //mm //THickness of copper bar +P=100*10**3 //N //Load +E_s=2*10**5 //N/mm**2 //modulus of elasticity of steel +E_c=1.2*10**5 //N/mm**2 //Modulus of Elasticity of Copper + +//Calculations + +A_s=%pi*4**-1*D_s**2 //mm**2 //Area of steel +D_Ce=D_s+2*t //mm //External Diameterof Copper Tube + +A_c=%pi*4**-1*(D_Ce**2-D_Ci**2) //mm**2 //Area of Copper + +//From static Equilibrium condition +//Let P_s and P_c be the Load shared by steel and copper in KN +//P_s+P_c=100 ....................................(1) + +//From compatibility Equation,dell_l_s=dell_l_c +//P_s*L*(A_s*E_s)**-1=P_c*L*(A_c*E_c)**-1 + +//Substituting values in above Equation we get +//P_s=1.3333*P_C + +//Now Substituting value of P_s in Equation (1),we get +P_c=100*2.3333**-1 //KN +P_s=100-P_c //KN + +//Stress in steel +sigma_s=P_s*10**3*A_s**-1 //N/mm**2 + +//Stress in copper +sigma_c=P_c*10**3*A_c**-1 //N/mm**2 + +//Result +printf("\n Stresses Developed in Two material are:sigma_s %0.2f N/mm**2",sigma_s) +printf("\n :sigma_c %0.2f N/mm**2",sigma_c) diff --git a/3864/CH2/EX2.24/Ex2_24.sce b/3864/CH2/EX2.24/Ex2_24.sce new file mode 100644 index 000000000..b75582839 --- /dev/null +++ b/3864/CH2/EX2.24/Ex2_24.sce @@ -0,0 +1,39 @@ +clear +// +// + +//Initilization of Variables + +A_C=230*400 //mm //Area of column +D_s=12 //mm //Diameter of steel Bar +P=600*10**3 //N //Axial compression +//E_s*E_c=18.67 +n=8 //number of steel Bars + +//Calculations + +A_s=%pi*4**-1*D_s**2*n //Area of steel //mm**2 +A_c=A_C-A_s //mm**2 //Area of concrete + +//From static Equilibrium condition +//P_s+P_c=600 .........(1) + +//Now from compatibility Equation dell_l_s=dell_l_c we get, +//P_s*L*(A_s*E_s)**-1=P_c*L*(A_c*E_c)**-1 + +//Substituting values in above Equation we get +//P_s=0.1854*P_c + +//Now Substituting value of P_s in Equation (1),we get +P_c=600*1.1854**-1 +P_s=600-P_c + +//Stress in steel +sigma_s=P_s*10**3*A_s**-1 //N/mm**2 + +//Stress in copper +sigma_c=P_c*10**3*A_c**-1 //N/mm**2 + +//Result +printf("\n Stresses Developed in Two material are:sigma_s %0.2f N/mm**2",sigma_s) +printf("\n :sigma_c %0.2f N/mm**2",sigma_c) diff --git a/3864/CH2/EX2.25/Ex2_25.sce b/3864/CH2/EX2.25/Ex2_25.sce new file mode 100644 index 000000000..8b3b0923d --- /dev/null +++ b/3864/CH2/EX2.25/Ex2_25.sce @@ -0,0 +1,56 @@ +clear +// + +//Initilization of Variables + +P=200*10**3 //N //Load +A_a=1000 //mm**2 //Area of Aluminium +A_s=800 //mm**2 //Area of steel +E_a=1*10**5 //N/mm**2 //Modulus of Elasticity of Aluminium +E_s=2*10**5 //N/mm**2 //Modulus of ELasticity of steel +sigma_a1=65 //N/mm**2 //stress in aluminium +sigma_s1=150 //N/mm**2 //Stress in steel + +//Calculations + +//Let P_a and P_s be the force in aluminium and steel pillar respectively + +//Now,sum of forces in Vertical direction we get +//2*P_a+P_s=200 .........................................(1) + +//By compatibility Equation dell_l_s=dell_l_a we get +//P_s=1.28*P_a ..........................................(2) + +//Now substituting value of P_s in Equation 1 we get +P_a=200*3.28**-1 //KN +P_s=200-2*P_a //KN + +//Stress developed in aluminium +sigma_a=P_a*10**3*A_a**-1 //N/mm**2 + +//Stress developed in steel +sigma_s=P_s*10**3*A_s**-1 //N/mm**2 + +//Part-2 + +//Let sigma_a1 and sigma_s1 be the stresses in Aluminium and steel due to Additional LOad + +P_a1=sigma_a1*A_a //Load carrying capacity of aluminium +P_s1=1.28*P_a1 + +//Total Load carrying capacity +P1=2*P_a1+P_s1 //N + +P_s2=sigma_s1*A_s //Load carrying capacity of steel +P_a2=P_s2*1.28**-1 + +//Total Load carrying capacity +P2=2*P_a2+P_s2 + +//Additional Load +P3=P1-P + +//Result +printf("\n Stresses Developed in Each Pillar is:sigma_a %0.2f N/mm**2",sigma_a) +printf("\n :sigma_s %0.2f N/mm**2",sigma_s) +printf("\n Additional Load taken by pillars is %0.2f N",P3) diff --git a/3864/CH2/EX2.26/Ex2_26.sce b/3864/CH2/EX2.26/Ex2_26.sce new file mode 100644 index 000000000..448652caf --- /dev/null +++ b/3864/CH2/EX2.26/Ex2_26.sce @@ -0,0 +1,38 @@ +clear +// +// + +//Initilization of Variables + +L=500 //mm //Length of assembly +D=16 //mm //Diameter of steel bolt +Di=20 //mm //internal Diameter of copper tube +Do=30 //mm //External Diameter of copper tube +E_s=2*10**5 //N/mm**2 //Modulus of Elasticity of steel +E_c=1.2*10**5 //N/mm**2 //Modulus of Elasticity of copper +p=2 //mm //Pitch of nut + +//Calculations + +//Let P_s be the Force in bolt and P_c be the FOrce in copper tube +//P_s=-P_s + +dell=1*4**-1*2 //Quarter turn of nut total movement + +//dell=dell_s+dell_c + +//Area of steel +A_s=%pi*4**-1*D**2 + +//Area of copper +A_c=%pi*4**-1*(Do**2-Di**2) + +//dell=P*L*(A_s*E_s)**-1+P*L*(A_c*E_c)**-1 +P=dell*(1*(A_s*E_s)**-1+1*(A_c*E_c)**-1)**-1*L**-1 //LOad + +P_s=P*A_s**-1 +P_c=P*A_c**-1 + +//result +printf("\n stress introduced in bolt is %0.2f N/mm**2",P_s) +printf("\n stress introduced in tube is %0.2f N/mm**2",P_c) diff --git a/3864/CH2/EX2.27/Ex2_27.sce b/3864/CH2/EX2.27/Ex2_27.sce new file mode 100644 index 000000000..d02f8430d --- /dev/null +++ b/3864/CH2/EX2.27/Ex2_27.sce @@ -0,0 +1,42 @@ +clear +// +// + +//Initilization of Variables + +D=20 //mm //Diameter of Bolts +Di=25 //m //internal Diameter +t=10 //mm //Thickness of bolt +E_s=2*10**5 //N/mm**2 //Modulus of Elasticity +E_c=1.2*10**5 //N/mm**2 //Modulus of copper +p=3 //mm //Pitch +theta=30 //degree +L_c=500 //Lengh of copper +L_s=600 //Length of steel + +//Calculations + +//Let P_s be the Force in each bolt and P_c be the FOrce in copper tube +//From Static Equilibrium condition +//P_c=2*P_s + +//As nut moves by 60 degree.If nut moves by 360 degree its Longitudinal movement is by 3 mm +dell=theta*360**-1*p + +//From Compatibility Equaton we get +//dell=dell_c+dell_s + + +A_s=%pi*4**-1*Di**2 //mm**2 //Area of steel +A_c=%pi*4**-1*(45**2-Di**2) //mm**2 //Area of copper + +//Force introduced in steel +P_s=0.5*(2*L_c*(A_c*E_c)**-1+L_s*(A_s*E_s)**-1)**-1 //N +P_s2=P_s*A_s**-1 + +//Force introduced in copper +P_c=2*P_s*A_c**-1 //N + +//Result +printf("\n Stress introduced in bolt is %0.2f N/mm**2",P_s2) +printf("\n stress introduced in tube is %0.2f N/mm**2",P_c) diff --git a/3864/CH2/EX2.28/Ex2_28.sce b/3864/CH2/EX2.28/Ex2_28.sce new file mode 100644 index 000000000..a89771447 --- /dev/null +++ b/3864/CH2/EX2.28/Ex2_28.sce @@ -0,0 +1,29 @@ +clear +// + +//Initilization of Variables + +L=9 //m //Length of rigid bar +L_b=3000 //Length of bar +A_b=1000 //mm**2 //Area of bar +E_b=1*10**5 //N/mm**2 //Modulus of Elasticity of brasss bar +L_s=5000 //mm //Length of steel bar +A_s=445 //mm**2 //Area of steel bar +E_s=2*10**5 //N/mm**2 //Modulus of elasticity of steel bar +P=3000 //N //Load + +//Calculations + +//From static equilibrium Equation of the rod after appliying Load is +//P_b+P_s=P ......................(1) + +//P_b=1.8727*P_s ..................(2) + +//NOw substituting equation 2 in equation 1 we get +P_s=P*2.8727**-1 +P_b=P-P_s + +d=P_s*L*P**-1 + +//Result +printf("\n Distance at which Load applied even after which bar remains horizontal is %0.2f m",d) diff --git a/3864/CH2/EX2.3/Ex2_3.sce b/3864/CH2/EX2.3/Ex2_3.sce new file mode 100644 index 000000000..9ef330004 --- /dev/null +++ b/3864/CH2/EX2.3/Ex2_3.sce @@ -0,0 +1,25 @@ +clear +// +// + +//Initilization of Variables + +//Let y be the yield stress + +y=250 //N/mm**2 //yield stress +FOS=1.75 //Factor of safety +P=140*10**3 //N //compressive Load +D=101.6 //mm //External diameter + +//Calculations + +p=y*(FOS)**-1 //N/mm**2 //Permissible stress +A=P*p**-1 //mm**2 //Area of hollow tube + +//Let d be the internal diameter of tube +d=-((A*4*(%pi)**-1)-D**2) +X=d**0.5 +t=(D-X)*2**-1 //mm //Thickness of steel tube + +//result +printf("\n The thickness of steel tube is %0.2f mm",t) diff --git a/3864/CH2/EX2.30/Ex2_30.sce b/3864/CH2/EX2.30/Ex2_30.sce new file mode 100644 index 000000000..494f7c86a --- /dev/null +++ b/3864/CH2/EX2.30/Ex2_30.sce @@ -0,0 +1,35 @@ +clear +// + +//Initilization of Variables + +L=12.6 //m //Length of rail +t1=24 //Degree celsius +t2=44 //degree celsius +alpha=12*10**-6 //Per degree celsius +E=2*10**5 //N/mm**2 //Modulus of ELasticity +gamma=2 //mm //Gap provided for Expansion +sigma=20 //N/mm**2 //Stress + +//Calculations + +t=t2-t1 //Temperature Difference + +//Free Expansion of the rails +dell=alpha*t*L*1000 //mm + +//When no expansion joint is provided then +p=dell*E*(L*10**3)**-1 + +//When a gap of 2 mm is provided,then free expansion prevented is +dell_1=dell-gamma +p2=dell_1*E*(L*10**3)**-1 + +//When stress is developed,then gap left is +gamma2=-(sigma*L*10**3*E**-1-dell) + +//Result +printf("\n The minimum gap between the two rails is %0.2f mm",dell) +printf("\n Thermal Developed in the rials if:No expansionn joint is provided:p %0.2f N/mm**2",p) +printf("\n :If a gap of is provided then :p2 %0.2f N/mm**2",p2) +printf("\n When stress is developed gap left between the rails is %0.2f mm",gamma2) diff --git a/3864/CH2/EX2.31/Ex2_31.sce b/3864/CH2/EX2.31/Ex2_31.sce new file mode 100644 index 000000000..8a95fa359 --- /dev/null +++ b/3864/CH2/EX2.31/Ex2_31.sce @@ -0,0 +1,26 @@ +clear +// + +//Initilization of Variables + +t=20 //degree celsius +E_a=70*10**9 //N/mm**2 //Modulus of Elasticicty of aluminium +alpha_a=11*10**-6 //per degree celsius //Temperature coeff of aluminium +alpha_s=12*10**-6 //Per degree celsius //Temperature coeff of steel +L_a=1000 //mm //Length of aluminium +L_s=3000 //mm //Length of steel +E_a=7*10**4 //N/mm**2 //Modulus of Elasticity of aluminium +E_s=2*10**5 //N/mm*2 //Modulus of Elasticity of steel +A_a=600 //mm**2 //Area of aluminium +A_s=300 //mm**2 //Area of steel + +//Calculations + +//Free Expansion +dell=alpha_a*t*L_a+alpha_s*t*L_s + +//support Reaction +P=dell*(L_a*(A_a*E_a)**-1+L_s*(A_s*E_s)**-1)**-1 + +//Result +printf("\n Reaction at support is %0.2f N",P) diff --git a/3864/CH2/EX2.33/Ex2_33.sce b/3864/CH2/EX2.33/Ex2_33.sce new file mode 100644 index 000000000..4baa8d7d1 --- /dev/null +++ b/3864/CH2/EX2.33/Ex2_33.sce @@ -0,0 +1,50 @@ +clear +// +// + +//Initilization of Variables + +D=25 //mm //Diameter of Brass +De=50 //mm //External Diameter of steel tube +Di=25 //mm //Internal Diameter of steel tube +L=1.5 //m //Length of both bars +t1=30 //degree celsius //Initial Temperature +t2=100 //degree celsius //final Temperature +E_s=2*10**5 //N/mm**2 //Modulus of ELasticity of steel bar +E_b=1*10**5 //N/mm**2 //Modulus of Elasticity of brass bar +alpha_s=11.6*10**-6 //Temperature Coeff of steel +alpha_b=18.7*10**-6 //Temperature coeff of brass bar +d=20 //mm //diameter of pins + +//Calculations + +t=t2-t1 //Temperature Difference +A_s=%pi*4**-1*(De**2-Di**2) //mm**2 //Area of steel +A_b=%pi*4**-1*D**2 //mm**2 //Area of brass + +//Let P_b be the tensile force in brass bar and P_s be the compressive force in steel bar +//But from Equilibrium of Forces +//P_b=P_s=P + +//Let dell=dell_s+dell_b +dell=(alpha_b-alpha_s)*t*L*1000 + +P=dell*(1*(A_s*E_s)**-1+1*(A_b*E_b)**-1)**-1*(L*1000)**-1 +P_b=P +P_s=P +//Stress in steel +sigma_s=P*A_s**-1 + +//Stress in Brass +sigma_b=P_b*A_b**-1 + +//Area of Pins +A_p=%pi*4**-1*d**2 + +//Since,the force is resisted by two cross section of pins +tou=P*(2*A_p)**-1 + +//Result +printf("\n Stress in steel bar is %0.2f N/mm**2",sigma_s) +printf("\n Stress in Brass bar is %0.2f N/mm**2",sigma_b) +printf("\n Shear Stresss induced in pins is %0.2f N/mm**2",tou) diff --git a/3864/CH2/EX2.34/Ex2_34.sce b/3864/CH2/EX2.34/Ex2_34.sce new file mode 100644 index 000000000..9ce4dd115 --- /dev/null +++ b/3864/CH2/EX2.34/Ex2_34.sce @@ -0,0 +1,45 @@ +clear +// + +//Initilization of Variables + +b_s=60 //mm //width of steel Bar +t_s=10 //mm //thickness of steel Bar +b_c=40 //mm //width of copper bar +t_c=5 //mm //thickness of copper bar +E_s=2*10**5 //N/mm**2 //Modulus of Elasticity of steel bar +E_c=1*10**5 //N/mm**2 //Modulus of Elasticity of copper bar +alpha_s=12*10**-6 //Per degree celsius //Temperature coeff of steel bar +alpha_c=17*10**-6 //Per degree celsius //Temperature coeff of copper bar +L=1000 //mm //Length of bar +L_s=1000 //mm //Length of bar +t=80 //degree celsius + +//Calculations + +A_s=b_s*t_s //Area of steel bar +A_c=b_c*t_c //Area of copper bar + +//Let P_s be the tensile force in steel bar and P_c be the compressive force in copper bar +//The equilibrium of forces gives +//P_s=2*P_c + +//Let dell=dell_s+dell_b +dell=(alpha_c-alpha_s)*t + +P_c=dell*(2*(A_s*E_s)**-1+1*(A_c*E_c)**-1)**-1 +P_s=2*P_c + +//Stress in copper +sigma_c=P_c*A_c**-1 + +//Stress in steel +sigma_s=P_s*A_s**-1 + +//Change in Length of bar +dell_2=alpha_s*t*L+P_s*L_s*(A_s*E_s)**-1 + +//result +printf("\n Stress in copper is %0.2f N/mm**2",sigma_c) +printf("\n Stress in steel is %0.2f N/mm**2",sigma_s) +printf("\n the change in Length is %0.2f mm",dell_2) diff --git a/3864/CH2/EX2.35/Ex2_35.sce b/3864/CH2/EX2.35/Ex2_35.sce new file mode 100644 index 000000000..66abf1a79 --- /dev/null +++ b/3864/CH2/EX2.35/Ex2_35.sce @@ -0,0 +1,72 @@ +clear +// + +//Initilization of Variables + +A_c=500 //mm**2 //Area of each rod +A_s=500 +A=500 +P=2*10**5 //N //Weight +L=1 //m //Length of each rod +t=40 //degree celsius //temperature +E_s=2*10**5 //N/mm**2 //Modulus of Elasticity of steel rod +E_c=1*10**5 //N/mm**2 //modulus of Elastictiy of copper rod +alpha_s=1.2*10**-5 //Per degree Celsius //temp coeff of steel rod +alpha_c=1.8*10**-5 //Per degree Celsius //Temp coeff of copper rod + +//Calculations + +//Let P_s be the force in each one of the copper rods and P_s be the force in steel rod +//2*P_c+P_s=P .....................(1) + +//Extension of copper bar=Extension of steel bar +//P_s*L*(A_s*E_s)**-1=P_c*L*(A_c*E_c)**-1 +//after simplifying above equation we get +//P_s=2*P_c ........................(2) + +//Now substituting value of P_s in Equation 1 we get +P_c=P*4**-1 +P_s=2*P_c + +//Now EXtension due to copper Load +dell_1=P_c*L*1000*(A_c*E_c)**-1 + +//Part-2 + +//Due to rise of temperature of40 degree celsius + +//As bars are rigidly joined,let P_c1 be the compressive forccesdeveloped in copper bar and P_s1 be the tensile force in steel causing changes +//P_s1=2*P_c1 + +//dell_s+dell_c=(alpha_c-alpha_s)*t*L .......................................(3) +//P_s1*L*(A_s*E_s)**-1+P_c1*L*(A_c*E_c)**-1=(alpha_c-alpha_s)*t*L ................(4) +//After substituting values in above equation and further simplifying we get, +P_c1=(alpha_c-alpha_s)*t*L*(2*(A_s*E_s)**-1+1*(A_c*E_c)**-1)**-1 //.................(5) +P_s1=2*P_c1 + +//Extension of bar due to temperature rise +dell_2=alpha_s*t*L+P_s1*L*(A_s*E_s)**-1 + +//Amount by which bar will descend +dell_3=dell_1+dell_2 + +//Load carried by steel bar +P_S=P_s+P_s1 + +//Load carried by copper bar +P_C=P_c-P_c1 + +//Part-3 + +//Let P_c1_1=P_c //For convenience +//Rise in temperature if Load is to be carried out by steel rod alone +P_c1_1=P_c + +//From equation 5 +t=P_c1_1*(2*(A_s*E_s)**-1+1*(A_c*E_c)**-1)*(alpha_c-alpha_s)**-1 + +//result +printf("\n Extension Due top copper Load %0.2f mm",dell_1) +printf("\n Load carried by each rod:P_s %0.2f N",P_s) +printf("\n :P_c %0.2f N",P_c) +printf("\n Rise in Temperature of steel rod should be %0.2f degree Celsius",t) diff --git a/3864/CH2/EX2.36/Ex2_36.sce b/3864/CH2/EX2.36/Ex2_36.sce new file mode 100644 index 000000000..6f16a2cc0 --- /dev/null +++ b/3864/CH2/EX2.36/Ex2_36.sce @@ -0,0 +1,36 @@ +clear +// + +//Initilization of Variables + +t=40 //degree celsius //temperature +A_s=400 //mm**2 //Area of steel bar +A_c=600 //mm**2 //Area of copper bar +E_s=2*10**5 //N/mm**2 //Modulus of Elasticity of steel bar +E_c=1*10**5 //N/mm**2 //Modulus of Elasticity of copper bar +alpha_s=12*10**-6 //degree celsius //Temperature coeff of steel bar +alpha_c=18*10**-6 //degree celsius //Temperature coeff of copper bar +L_c=800 //mm //Length of copper bar +L_s=600 //mm //Length of steel bar + +//Calculations + +//Let P_s be the tensile force in steel bar and P_c be the compressive force in copper bar +//Static Equilibrium obtained by taking moment about A +//P_c=2*P_s + +//From property of similar triangles we get +//(alpha_c*Lc-dell_c)*1**-1=(alpha_s*L_s-dell_s)*2**-1 +//After substituting values in above equations and further simplifying we get +P_s=(2*alpha_c*L_c-alpha_s*L_s)*t*(L_s*(A_s*E_s)**-1+4*L_c*(A_c*E_c)**-1)**-1 +P_c=2*P_s + +//Stress in steel rod +sigma_s=P_s*A_s**-1 //N/mm**2 + +//Stress in copper rod +sigma_c=P_c*A_c**-1 //N/mm**2 + +//Result +printf("\n Stress in steel rod is %0.2f N/mm**2",sigma_s) +printf("\n STress in copper rod is %0.2f N/mm**2",sigma_c) diff --git a/3864/CH2/EX2.37/Ex2_37.sce b/3864/CH2/EX2.37/Ex2_37.sce new file mode 100644 index 000000000..155d3e6c4 --- /dev/null +++ b/3864/CH2/EX2.37/Ex2_37.sce @@ -0,0 +1,36 @@ +clear +// +// + +//Initilization of Variables + +d=20 //mm //Diameter of bar +P=37.7*10**3 //N //Load +L=200 //mm //Guage Length +dell=0.12 //mm //Extension +dell_d=0.0036 //mm //contraction in diameter + +//Calculations + +//Area of bar +A=%pi*4**-1*d**2 + +//Let s and dell_s be the Linear strain and Lateral strain +s=dell*L**-1 +dell_s=dell_d*d**-1 +mu=dell_s*s**-1 //Poissons ratio + +//dell=P*L*(A*E)**-1 +E=P*L*(dell*A)**-1 //N/mm**2 //Modulus of Elasticity of bar + +//Modulus of Rigidity +G=E*(2*(1+mu))**-1 //N/mm**2 + +//Bulk Modulus +K=E*(3*(1-2*mu))**-1 //N/mm**2 + +//result +printf("\n Poissons ratio is %0.2f ",mu) +printf("\n The Elastic constant are:E %0.2f ",E) +printf("\n :G %0.2f ",G) +printf("\n :K %0.2f ",K) diff --git a/3864/CH2/EX2.38/Ex2_38.sce b/3864/CH2/EX2.38/Ex2_38.sce new file mode 100644 index 000000000..86842b02d --- /dev/null +++ b/3864/CH2/EX2.38/Ex2_38.sce @@ -0,0 +1,38 @@ +clear +// +// + +//Initilization of Variables + +d=100 //mm //Diameter of circular rod +P=1*10**6 //N //Tensile Force +mu=0.3 //Poissons ratio +E=2*10**5 //N/mm**2 //Youngs Modulus +L=500 //mm //Length of rod + +//Calculations + +//Modulus of Rigidity +G=E*(2*(1+mu))**-1 //N/mm**2 + +//Bulk Modulus +K=E*(3*(1-2*mu))**-1 //N/mm**2 + +A=%pi*4**-1*d**2 //mm**2 //Area of Circular rod +//Let sigma be the Longitudinal stress +sigma=P*A**-1 //N/mm**2 + +s=sigma*E**-1 //Linear strain +e_x=s + +//Volumetric strain +e_v=e_x*(1-2*mu) + +v=%pi*4**-1*d**2*L +//Change in VOlume +dell_v=e_v*v + +//Result +printf("\n Bulk Modulus is %0.2f N/mm**2",E) +printf("\n Modulus of Rigidity is %0.2f N/mm**2",G) +printf("\n The change in Volume is %0.2f mm**3",dell_v) diff --git a/3864/CH2/EX2.39/Ex2_39.sce b/3864/CH2/EX2.39/Ex2_39.sce new file mode 100644 index 000000000..1a55112ed --- /dev/null +++ b/3864/CH2/EX2.39/Ex2_39.sce @@ -0,0 +1,36 @@ +clear +// + +//Initilization of Variables + +L=500 //mm //Length of rectangular cross section bar +A=20*40 //mm**2 //Area of rectangular cross section bar +P1=4*10**4 //N //Tensile Force on 20mm*40mm Faces +P2=2*10**5 //N //compressive force on 20mm*500mm Faces +P3=3*10**5 //N //Tensile Force on 40mm*500mm Faces +E=2*10**5 //N/mm**2 //Youngs Modulus +mu=0.3 //Poissons Ratio + +//Calculations + +//Let P_x,P_y,P_z be the forces n x,y,z directions + +P_x=P1*A**-1 +P_y=P2*A**-1 +P_z=P3*A**-1 + +//Let e_x,e_y,e_z be the strains in x,y,z directions +e_x=1*E**-1*(50+mu*20-15*mu) +e_y=1*E**-1*(-mu*50-20-mu*15) +e_z=1*E**-1*(-mu*50+mu*20+15) + +//Volumetric strain +e_v=e_x+e_y+e_z + +//Volume +V=20*40*500 //mm**3 +//Change in Volume +dell_v=e_v*V //mm**3 + +//Result +printf("\n The change in Volume is %0.2f mm**3",dell_v) diff --git a/3864/CH2/EX2.4/Ex2_4.sce b/3864/CH2/EX2.4/Ex2_4.sce new file mode 100644 index 000000000..d8c5efd5a --- /dev/null +++ b/3864/CH2/EX2.4/Ex2_4.sce @@ -0,0 +1,39 @@ +clear +// +// + +//Initilization of Variables + +d=25 //mm //diameter of steel +d2=18 //mm //Diameter at neck +L=200 //mm //length of stee +P=80*10**3 //KN //Load +P1=160*10**3 //N //Load at Elastic Limit +P2=180*10**3 //N //Max Load +L1=56 //mm //Total Extension +dell_l=0.16 //mm //Extension + + +//Calculations + +A=%pi*d**2*4**-1 //Area of steel //mm**2 + +p=P1*A**-1 //Stress at Elastic Limit //N/mm**2 +Y=P*L*(A*dell_l)**-1 //Modulus of elasticity + +//Let % elongation be x +x=L1*L**-1*100 + +//Percentage reduction in area +//Let % A be a +a=((%pi*4**-1*d**2)-(%pi*4**-1*d2**2))*(%pi*4**-1*d**2)**-1*100 + +//Ultimate tensile stress +sigma=P2*A**-1 //N/mm**2 + +//result +printf("\n Stress at Elastic limit is %0.2f N/mm**2",p) +printf("\n Youngs Modulus is %0.2f N/mm**2",Y) +printf("\n Percentage Elongation is %0.2f ",a) +printf("\n Percentage reduction in area is %0.2f ",P2) +printf("\n Ultimate tensile stress %0.2f N/mm**2",sigma) diff --git a/3864/CH2/EX2.41/Ex2_41.sce b/3864/CH2/EX2.41/Ex2_41.sce new file mode 100644 index 000000000..c7360546a --- /dev/null +++ b/3864/CH2/EX2.41/Ex2_41.sce @@ -0,0 +1,21 @@ +clear +// + +//Initilization of Variables + +E=2.1*10**5 //N/mm**2 //Youngs Modulus +G=0.78*10**5 //N/mm**2 //Modulus of Rigidity + +//Calculations + +//Now using the relation +//E=2*G*(1+mu) +mu=E*(2*G)**-1-1 //Poissons ratio + +//Bulk Modulus +K=E*(3*(1-2*mu))**-1 //N/mm**2 + + +//Result +printf("\n The Poissons Ratio is %0.2f ",mu) +printf("\n The modulus of Rigidity %0.2f N/mm**2",K) diff --git a/3864/CH2/EX2.42/Ex2_42.sce b/3864/CH2/EX2.42/Ex2_42.sce new file mode 100644 index 000000000..f11a803cd --- /dev/null +++ b/3864/CH2/EX2.42/Ex2_42.sce @@ -0,0 +1,20 @@ +clear +// + +//Initilization of Variables + +G=0.4*10**5 //N/mm**2 //Modulus of rigidity +K=0.75*10**5 //N/mm**2 //Bulk Modulus + +//Calculations + +//Youngs Modulus +E=9*G*K*(3*K+G)**-1 + +//Now from the relation +//E=2*G(1+2*mu) +mu=E*(2*G)**-1-1 //Poissons ratio + +//result +printf("\n Youngs modulus is %0.2f N/mm**2",E) +printf("\n Poissons ratio is %0.2f ",mu) diff --git a/3864/CH2/EX2.43/Ex2_43.sce b/3864/CH2/EX2.43/Ex2_43.sce new file mode 100644 index 000000000..31a051d8c --- /dev/null +++ b/3864/CH2/EX2.43/Ex2_43.sce @@ -0,0 +1,82 @@ +clear +// + +//Initilization of Variables + +b=60 //mm //width of bar +d=30 //mm //depth of bar +L=200 //mm //Length of bar +A=30*60 //mm**2 //Area of bar +A2=30*200 //mm**2 //Area of bar along which expansion is restrained +P=180*10**3 //N //Compressive force +E=2*10**5 //N/mm**2 //Youngs Modulus +mu=0.3 //Poissons ratio + +//Calculations + +//The bar is restrained from expanding in Y direction +P_z=0 +P_x=P*A**-1 //stress developed in x direction + +//Now taking compressive strain as positive +//e_x=P_x*E**-1-mu*P_y*E**-1 .......................(1) +//e_y=-mu*P_x*E**-1+P_y*E**-1 ....................(2) +//e_z=-mu*P_x*E**-1-mu*P_y*E**-1 ......................(3) + +//Part-1 +//When it is fully restrained +e_y=0 +P_y=30 //N/mm**2 +e_x=P_x*E**-1-mu*P_y*E**-1 +e_z=-mu*P_x*E**-1-mu*P_y*E**-1 + +//Change in Length +dell_l=e_x*L //mm + +//Change in width +dell_b=b*e_y + +//change in Depth +dell_d=d*e_z + +//Volume of bar +V=b*d*L //mm**3 +//Change in Volume +e_v=(e_x+e_y+e_z)*V //mm**3 + +//Part-2 +//When 50% is restrained + +//Free strain in Y direction +e_y1=mu*P_x*E**-1 + +//As 50% is restrained,so +e_y2=-50*100**-1*e_y1 + +//But form Equation 2 we have e_y=-mu*P_x*E**-1+P_y*E**-1 +//After substituting values in above equation and furthe simplifying we get +P_y=e_y2*E+d + +e_x2=P_x*E**-1-mu*P_y*E**-1 +e_z2=-mu*P_x*E**-1-mu*P_y*E**-1 + +//Change in Length +dell_l2=e_x2*L //mm + +//Change in width +dell_b2=b*e_y2 + +//change in Depth +dell_d2=d*e_z2 + +//Change in Volume +e_v2=(e_x2+e_y2+e_z2)*V //mm**3 + +//REsult +printf("\n Change in Dimension of bar is:dell_l %0.2f mm",dell_l) +printf("\n :dell_b %0.4f mm",dell_b) +printf("\n :dell_d %0.2f mm",dell_d) +printf("\n Change in Volume is %0.2f mm**3",e_v) +printf("\n Changes in material when only 50% of expansion can be reatrained:dell_l2mm",dell_l2) +printf("\n :dell_b2 %0.4f mm",dell_b2) +printf("\n :dell_d2 %0.2f mm",dell_d2) diff --git a/3864/CH2/EX2.44/Ex2_44.sce b/3864/CH2/EX2.44/Ex2_44.sce new file mode 100644 index 000000000..8cd10f122 --- /dev/null +++ b/3864/CH2/EX2.44/Ex2_44.sce @@ -0,0 +1,32 @@ +clear +// +// + +//Initilization of Variables + +P=10*10**3 //N //Load +E=2*10**5 //N/mm**2 //Youngs Modulus +d2=12 //mm //Diameter of bar1 +d1=16 //mm //diameter of bar2 +L1=200 //mm //Length of bar1 +L2=500 //mm //Length of bar2 + +//Calculations + +//Let A1 and A2 be the cross Area of Bar1 & bar2 respectively +A1=%pi*4**-1*d1**2 //mm**2 +A2=%pi*4**-1*d2**2 //mm**2 + +//Let p1 and p2 be the stress in Bar1 nad bar2 respectively +p1=P*A1**-1 //N/mm**2 +p2=P*A2**-1 //N/mm**2 + +//Let V1 nad V2 be the Volume of of Bar1 and Bar2 +V1=A1*(L1+L1) +V2=A2*L2 + +//Let E be the strain Energy stored in the bar +E=p1**2*(2*E)**-1*V1+p2**2*V2*(2*E)**-1 + +//result +printf("\n The Strain Energy stored in Bar is %0.2f N-mm",E) diff --git a/3864/CH2/EX2.45/Ex2_45.sce b/3864/CH2/EX2.45/Ex2_45.sce new file mode 100644 index 000000000..bcb78b03e --- /dev/null +++ b/3864/CH2/EX2.45/Ex2_45.sce @@ -0,0 +1,66 @@ +clear +// +// + +//Initilization of Variables + +//Bar-A +d1=30 //mm //Diameter of bar1 +L=600 //mm //length of bar1 + +//Bar-B +d2=30 //mm //Diameter of bar2 +d3=20 //mm //Diameter of bar2 +L2=600 //mm //length of bar2 + +//Calculations + +//Area of bar-A +A1=%pi*4**-1*d1**2 + +//Area of bar-B +A2=%pi*4**-1*d2**2 +A3=%pi*4**-1*d3**2 + +//let SE be the Strain Energy +//Strain Energy stored in Bar-A +//SE=p**2*(2*E)**-1*V +//After substituting values and simolifying further we get +//SE=P**2*E**-1*0.4244 + +//Strain Energy stored in Bar-B +//SE2=p1**2*V1*(2*E)**-1+p2**2*V2*(2*E)**-1 +//After substituting values and simolifying further we get +//SE2=0.6897*P**2*E**-1 + +//Let X be the ratio of SE in Bar-B and SE in Bar-A +X=0.6897*0.4244**-1 + +//Part-2 + +//When Max stress is produced is same:Let p be the max stress produced + +//Stress in bar A is p throughout +//In bar B:stress in 20mm dia.portion=p2=p + +//Stress in 30 mm dia.portion +//p1=P*A2*A3**-1 +//After substituting values and simolifying further we get +//p1=4*9**-1*p + +//Strain Energy in bar A +//SE_1=p**2*(2*E)**-1*A1*L1 +//After substituting values and simolifying further we get +//SE_1=67500*p**2*%pi*E**-1 + +//Strain Energy in bar B +//SE_2=p1**2*V1*(2*E)**-1+p2**2*V2*(2*E)**-1 +//After substituting values and simolifying further we get +//SE_2=21666.67*%pi*p**2*E**-1 + +//Let Y be the Ratio of SE in bar B and SE in bar A +Y=21666.67*67500**-1 + +//result +printf("\n Gradually applied Load is %0.2f ",X) +printf("\n Gradually applied Load is %0.2f ",Y) diff --git a/3864/CH2/EX2.46/Ex2_46.sce b/3864/CH2/EX2.46/Ex2_46.sce new file mode 100644 index 000000000..11d592824 --- /dev/null +++ b/3864/CH2/EX2.46/Ex2_46.sce @@ -0,0 +1,34 @@ +clear +// +// + +//Initilization of Variables + +W=100 //N //Load +E=2*10**5 //N/mm**2 //Youngs Modulus +h=60 //mm //Height through Load falls down +L=400 //mm //Length of collar +d=30 //mm //diameter of bar + +//Calculations + +A=%pi*4**-1*d**2 //mm**2 //Area of bar + +//Instantaneous stress produced is +p=W*A**-1*(1+(1+(2*A*E*h*(W*L)**-1))**0.5) + +//Now the EXtension of the bar is neglected in calculating work doneby the Load,then +P=(2*E*h*W*(A*L)**-1)**0.5 + +//Let percentage error be denoted by E1 +//Percentage error in approximating is +E1=(p-P)*p**-1*100 + +//Instantaneous Extension produced is +dell_l=(P)*E**-1*L + + +//Result +printf("\n The Instantaneous stress is %0.2f N/mm",p) +printf("\n Percentage Error is %0.2f ",E1) +printf("\n The Instantaneous extension is %0.2f mm",dell_l) diff --git a/3864/CH2/EX2.47/Ex2_47.sce b/3864/CH2/EX2.47/Ex2_47.sce new file mode 100644 index 000000000..2ffb85808 --- /dev/null +++ b/3864/CH2/EX2.47/Ex2_47.sce @@ -0,0 +1,44 @@ +clear +// +// + +//Initilization of Variables + +d=20 //mm //Diameter of steel bar +L=1000 //mm //Length of bar +E=2*10**5 //N/mm**2 //Youngs Modulus +p=300 //N/mm**2 //max Permissible stress +h=50 //mm //Height through which weight will fall +w=600 //N //Load + +//Calculations + +//ARea of steel bar +A=%pi*4**-1*d**2 + +//Instantaneous extension is +dell_l=p*L*E**-1 //mm + +//Work done by Load +//W=W1*(h+dell_l) + +//Volume of bar +V=(A)*L + +//Let E1 be the strain Energy +E1=p**2*(2*E)**-1*V + +//Answer in Book for Strain Energy is Incorrect + +//Now Equating Workdone by Load to strain Energy +W1=E1*51.5**-1 + +//Now when w=600 N +//Let W2 be the Work done by the Load +//W2=w(h2*dell_l) + +h=E1*w**-1-dell_l + +//Result +printf("\n The Max Lodad which can Fall from a height of 50 mm on the collar is %0.2f N",W1) +printf("\n the Max Height from which a 600 N Load can fall on the collar is %0.2f mm",h) diff --git a/3864/CH2/EX2.48/Ex2_48.sce b/3864/CH2/EX2.48/Ex2_48.sce new file mode 100644 index 000000000..e5a667a1b --- /dev/null +++ b/3864/CH2/EX2.48/Ex2_48.sce @@ -0,0 +1,35 @@ +clear +// +// + +//Initilization of Variables + +D_s=30 //mm //Diameter of steel rod +d=30 //mm //Internal Diameter of copper tube +D=40//mm //External Diameter of copper tube +E_s=2*10**5 //N/mm**2 //Youngs Modulus of Steel rod +E_c=1*10**5//N/mm**2 //Youngs Modulus of copper tube +P=100 //N //Load +h=40 //mm //height from which Load falls +L=800 //mm //Length + +//Calculations + +//Area of steel rod +A_s=%pi*4**-1*D_s**2 + +//Area of copper tube +A_c=%pi*4**-1*(D**2-d**2) + +//But Dell_s=dell_c=dell +//p_s*E_s**-1*L=p_c*L*E_c +//After simplifying furthe we get +//p_s=2*p_c + +//Now Equating internal Energy to Workdone we get +p_c=(2*P*h*L**-1*(4*A_s*E_s**-1+A_c*E_c**-1))**0.5 +p_s=2*p_c + +//Result +printf("\n STress produced in steel is %0.2f N/mm**2",p_s) +printf("\n STress produced in copper is %0.2f N/mm**2",p_c) diff --git a/3864/CH2/EX2.49/Ex2_49.sce b/3864/CH2/EX2.49/Ex2_49.sce new file mode 100644 index 000000000..15102ddaf --- /dev/null +++ b/3864/CH2/EX2.49/Ex2_49.sce @@ -0,0 +1,63 @@ +clear +// +// + +dell=0.25 //mm //Instantaneous Extension + +//Bar-A +b1=25 //mm //width of bar +D1=500 //mm //Depth of bar + +//Bar-B +b2_1=25 //mm //width of upper bar +b2_2=15 //mm //Width of Lower Bar +L2=200 //mm //Length of upper bar +L1=300 //mm //Length of Lower bar + +E=2*10**5 //N/mm**2 //Youngs Modulus of bar + +//Calculations + +//Strain +e=dell*D1**-1 + +//Load +p=e*E + +//Area of bar-A +A=%pi*4**-1*25**2 + +//Volume of bar-A +V=A*D1 + +//Let E1 be the Energy of Blow +//Energy of Blow +E1=p**2*(E)**-1*V + +//Let p2 be the Max stress in bar B When this blow is applied. +//the max stress occurs in the 15mm dia. portion,Hence, the stress in 25 mm dia.portion is +//p2*%pi*4**-1*b2_2**2*(%pi*4**-1*b2_2**2=0.36*p + +//Strain Energy of bar B +//E2=p**2*(2*E)**-1*v1+1*(2*E)**-1*(0.36*p2)**2*v2 +//After substituting values and Further substituting values we get +//E2=0.1643445*p2**2 + +//Equating it to Energy of applied blow,we get +p2=(12271.846*0.1643445**-1)**0.5 + +//Stress in top portion +sigma=0.36*p2 + +//Extension in Bar-1 +dell_1=p2*E**-1*L1 + +//Extension in Bar-2 +dell_2=0.36*p2*E**-1*L2 + +//Extension of bar +dell_3=dell_1+dell_2 + +//Result +printf("\n Instantaneous Max stress is %0.2f N/mm**2",sigma) +printf("\n extension in Bar is %0.2f mm",dell_3) diff --git a/3864/CH2/EX2.6/Ex2_6.sce b/3864/CH2/EX2.6/Ex2_6.sce new file mode 100644 index 000000000..06fbd1663 --- /dev/null +++ b/3864/CH2/EX2.6/Ex2_6.sce @@ -0,0 +1,21 @@ +clear +// +// + +//Initilization of Variables + +P=40*10**3 //N //Load +L1=160 //mm //Length of Bar1 +L2=240 //mm //Length of bar2 +L3=160 //mm //Length of bar3 +d1=25 //mm //Diameter of Bar1 +d2=20 //mm //diameter of bar2 +d3=25 //mm //diameter of bar3 +dell_l=0.285 //mm //Total Extension of bar + +//Calculations + +E=P*4*(dell_l*%pi)**-1*(L1*(d1**2)**-1+L2*(d2**2)**-1+L3*(d3**2)**-1) + +//Result +printf("\n The Youngs Modulus of the material %0.2f N/mm**2",E) diff --git a/3864/CH2/EX2.7/Ex2_7.sce b/3864/CH2/EX2.7/Ex2_7.sce new file mode 100644 index 000000000..89129ffa2 --- /dev/null +++ b/3864/CH2/EX2.7/Ex2_7.sce @@ -0,0 +1,27 @@ +clear +// + +//Initilization of Variables + +E1=2*10**5 //N/mm**2 //modulus of Elasticity of material1 +E2=1*10**5 //N/mm**2 //modulus of Elasticity of material2 +P=25*10**3 //N //Load +t=20 //mm //thickness of material +b1=40 //mm //width of material1 +b2=30 //mm //width of material2 +L1=500 //mm //Length of material1 +L2=750 //mm //Length of material2 + +//Calculations + +A1=b1*t //mm**2 //Area of materila1 +A2=b2*t //mm**2 //Area of material2 + +dell_l1=P*L1*(A1*E1)**-1 //Extension of Portion1 +dell_l2=P*L2*(A2*E2)**-1 //Extension of portion2 + +//Total Extension of Bar is +dell_l=dell_l1+dell_l2 + +//Result +printf("\n The Total Extension of the Bar is %0.2f mm",dell_l) diff --git a/3864/CH2/EX2.8/Ex2_8.sce b/3864/CH2/EX2.8/Ex2_8.sce new file mode 100644 index 000000000..4d18eb885 --- /dev/null +++ b/3864/CH2/EX2.8/Ex2_8.sce @@ -0,0 +1,25 @@ +clear +// +// + +//Initilization of Variables + +L=1000 //mm //Length of Bar +l=400 //mm //Length upto which bire is drilled +D=30 //mm //diameter of bar +d1=10 //mm //diameter of bore +P=25*10**3 //N //Load +dell_l=0.185 //mm //Extension of bar + +//Calculations + +L1=L-l //Length of bar above the bore +L2=400 //mm //Length of bore + +A1=%pi*4**-1*D**2 //Area of bar +A2=%pi*4**-1*(D**2-d1**2) //Area of bore + +E=P*dell_l**-1*(L1*A1**-1+L2*A2**-1) + +//Result +printf("\n The Modulus of ELasticity is %0.2f N/mm**2",E) |