23 files changed, 834 insertions, 0 deletions
diff --git a/3864/CH6/EX6.1/Ex6_1.sce b/3864/CH6/EX6.1/Ex6_1.sce
new file mode 100644
index 000000000..13d455f14
--- /dev/null
+++ b/3864/CH6/EX6.1/Ex6_1.sce
@@ -0,0 +1,25 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+L=10000 //mm //Length of solid shaft
+d=100 //mm //Diameter of shaft
+n=150     //rpm
+P=112.5*10**6 //N-mm/sec //Power Transmitted
+G=82*10**3 //N/mm**2 //modulus of Rigidity
+
+//Calculations
+
+J=%pi*d**4*(32)**-1  //mm**3 //Polar Modulus
+T=P*60*(2*%pi*n)**-1 //N-mm //Torsional moment
+
+r=50 //mm //Radius
+
+q_s=T*r*J**-1 //N/mm**2 //Max shear stress intensity
+Theta=T*L*(G*J)**-1 //angle of twist
+
+//Result
+printf("\n Max shear stress intensity %0.2f  N/mm**2",q_s)
+printf("\n Angle of Twist %0.3f  radian",Theta)
diff --git a/3864/CH6/EX6.11/Ex6_11.sce b/3864/CH6/EX6.11/Ex6_11.sce
new file mode 100644
index 000000000..a3f927997
--- /dev/null
+++ b/3864/CH6/EX6.11/Ex6_11.sce
@@ -0,0 +1,45 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+P=250*10**6 //N-mm/sec //Power transmitted
+n=100 //rpm
+q_s=75 //N/mm**2 //Shear stress
+
+//Calculations
+
+//From Equation of Power we have
+T=P*60*(2*%pi*n)**-1 //N-mm //Torsional moment
+
+//Now from torsional moment equation we have
+//T=j*q_s*(d/2**-1)**-1
+//After substituting values in above equation and further simplifying we get
+//T=%pi*16**-1**d**3*q_s
+d=(T*16*(%pi*q_s)**-1)**0.3333 //mm //Diameter of solid shaft
+
+//PArt-2
+
+//Let d1 and d2 be the outer and inner diameter of hollow shaft
+//d2=0.6*d1
+
+//Again from torsional moment equation we have
+//T=%pi*32**-1*(d1**4-d2**4)*q_s*(d1/2)**-1
+d1=(T*16*(%pi*(1-0.6**4)*q_s)**-1)**0.33333
+d2=0.6*d1
+
+//Cross sectional area of solid shaft
+A1=%pi*4**-1*d**2 //mm**2
+
+//cross sectional area of hollow shaft
+A2=%pi*4**-1*(d1**2-d2**2)
+
+//Now percentage saving in weight
+//Let W be the percentage saving in weight
+W=(A1-A2)*100*A1**-1
+
+//Result
+printf("\n Size of shaft is:solid shaft:d %0.3f  mm",d)
+printf("\n                :Hollow shaft:d1 %0.3f  mm",d1)
+printf("\n                :            :d2 %0.3f  mm",d2)
diff --git a/3864/CH6/EX6.12/Ex6_12.sce b/3864/CH6/EX6.12/Ex6_12.sce
new file mode 100644
index 000000000..a38b0a948
--- /dev/null
+++ b/3864/CH6/EX6.12/Ex6_12.sce
@@ -0,0 +1,43 @@
+clear
+//
+//
+
+//Initilization of Variables
+d=100 //mm //Diameter of solid shaft
+d1=100 //mm //Outer Diameter of hollow shaft
+d2=50  //mm //Inner Diameter of hollow shaft
+
+//Calculations
+
+//Torsional moment of solid shaft
+//T_s=J*q_s*(d*2**-1)**-1 
+//After substituting values in above equation and further simplifying we get
+//T_s=%pi*16*d**3*q_s ...............(1)
+
+//torsional moment for hollow shaft is
+//T_h=J*q_s*(d1**4-d2**4)**-1*(d1*2**-1)
+//After substituting values in above equation and further simplifying we get
+//T_h=%pi*32**-1*2*d1**-1*(d1**4-d2**4)*q_s  ...........(2)
+
+//Dividing Equation 2 by 1 we get
+//Let the ratio of T_h*T_s**-1 Be X
+X=1-0.5**4
+
+//Loss in strength 
+//Let s be the loss in strength
+//s=T_s*T_h*100*T_s**-1
+//After substituting values in above equation and further simplifying we get
+s=(1-0.9375)*100
+
+//Weight Ratio 
+//Let w be the Weight ratio
+//w=W_h*W_s**-1
+
+A_h=%pi*32**-1*(d1**2-d2**2) //mm**2 //Area of Hollow shaft
+A_s=%pi*32**-1*d**2 //mm**2 //Area of solid shaft
+
+w=A_h*A_s**-1 
+
+//Result
+printf("\n Loss in strength is %0.2f  ",s)
+printf("\n Weight ratio is %0.2f  ",w)
diff --git a/3864/CH6/EX6.13/Ex6_13.sce b/3864/CH6/EX6.13/Ex6_13.sce
new file mode 100644
index 000000000..12f36afcd
--- /dev/null
+++ b/3864/CH6/EX6.13/Ex6_13.sce
@@ -0,0 +1,36 @@
+clear
+//
+//
+
+//Initilization of Variables
+T=8 //KN-m //Torque 
+d=100 //mm //Diameter of portion AB
+d1=100 //mm //External Diameter of Portion BC
+d2=75 //mm //Internal Diameter of Portion BC
+G=80 //KN/mm**2 //Modulus of Rigidity
+L1=1500 //mm //Radial Distance of Portion AB
+L2=2500 //mm //Radial Distance ofPortion BC
+
+//Calculations
+
+R=d*2**-1 //mm //Radius of shaft
+
+//For Portion AB,Polar Modulus
+J1=%pi*32**-1*d**4 //mm**4 
+
+//For Portion BC,Polar modulus 
+J2=%pi*32**-1*(d1**4-d2**4) //mm**4
+
+//Now Max stress occurs in portion BC since max radial Distance is sme in both cases
+q_max=T*J2**-1*R*10**6 //N/mm**2 
+
+//Let theta1 be the rotation in Portion AB and theta2 be the rotation in portion BC
+theta1=T*L1*(G*J1)**-1 //Radians
+theta2=T*L2*(G*J2)**-1 //Radians
+
+//Total Rotational at end C
+theta=(theta1+theta2)*10**3 //Radians
+
+//Result
+printf("\n Max stress induced is %0.2f  N/mm**2",q_max)
+printf("\n Angle of Twist is %0.3f  radians",theta)
diff --git a/3864/CH6/EX6.14/Ex6_14.sce b/3864/CH6/EX6.14/Ex6_14.sce
new file mode 100644
index 000000000..62b0e8876
--- /dev/null
+++ b/3864/CH6/EX6.14/Ex6_14.sce
@@ -0,0 +1,40 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+q_b=80 //N/mm**2 //Shear stress in Brass
+q_s=100 //N/mm**2 //Shear stress in Steel
+G_b=40*10**3 //N/mm**2 
+G_s=80*10**3 
+L_b=1000 //mm //Length of brass shaft
+L_s=1200 //mm //Length of steel shaft
+d1=80 //mm //Diameter of brass shaft
+d2=60 //mm //Diameter of steel shaft
+
+//Calculations
+
+//Polar modulus of brass rod
+J_b=%pi*32**-1*d1**4 //mm**4 
+
+//Polar modulus of steel rod
+J_s=%pi*32**-1*d2**4 //mm**4
+
+//Considering bras Rod:AB
+T1=J_b*q_b*(d1*2**-1)**-1 //N-mm 
+
+//Considering Steel Rod:BC
+T2=J_s*q_s*(d2*2**-1)**-1 //N-mm
+
+//Max Torque that can be applied
+T2
+
+//Let theta_b and theta_s be the rotations in Brass and steel respectively
+theta_b=T2*L_b*(G_b*J_b)**-1 //Radians
+theta_s=T2*L_s*(G_s*J_s)**-1 //Radians
+
+theta=theta_b+theta_s //Radians //Rotation of free end
+
+//Result
+printf("\n Total of free end is %0.3f  Radians",theta)
diff --git a/3864/CH6/EX6.15/Ex6_15.sce b/3864/CH6/EX6.15/Ex6_15.sce
new file mode 100644
index 000000000..a96281897
--- /dev/null
+++ b/3864/CH6/EX6.15/Ex6_15.sce
@@ -0,0 +1,55 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+G=80*10**3 //N/mm**2 //Modulus of Rigidity
+d1=100 //mm //Outer diameter of hollow shft
+d2=80  //mm //Inner diameter of hollow shaft
+d=80   //mm //diameter of Solid shaft
+d3=60  //mm //diameter of Solid shaft having L=0.5m
+L1=300 //mm //Length of Hollow shaft
+L2=400 //mm //Length of solid shaft
+L3=500 //mm //LEngth of solid shaft of diameter 60mm
+T1=2*10**6 //N-mm //Torsion in Shaft AB
+T2=1*10**6 //N-mm //Torsion in shaft BC
+T3=1*10**6 //N-mm //Torsion in shaft CD
+
+//Calculations
+
+//Now Polar modulus of section AB
+J1=%pi*32**-1*(d1**4-d2**4) //mm**4 
+
+//Polar modulus of section BC
+J2=%pi*32**-1*d**4 //mm**4
+
+//Polar modulus of section CD
+J3=%pi*32**-1*d3**4 //mm**4
+
+//Now angle of twist of AB
+theta1=T1*L1*(G*J1)**-1 //radians
+
+//Angle of twist of BC
+theta2=T2*L2*(G*J2)**-1 //radians
+
+//Angle of twist of CD
+theta3=T3*L3*(G*J3)**-1 //radians
+
+//Angle of twist
+theta=theta1-theta2+theta3 //Radians
+
+//Shear stress in AB From Torsion Equation
+q_s1=T1*(d1*2**-1)*J1**-1 //N/mm**2 
+
+//Shear stress in BC
+q_s2=T2*(d*2**-1)*J2**-1 //N/mm**2 
+
+//Shear stress in CD
+q_s3=T3*(d3*2**-1)*J3**-1 //N-mm**2
+
+//As max shear stress occurs in portion CD,so consider CD
+
+//Result
+printf("\n Angle of twist at free end is %0.5f  Radian",theta)
+printf("\n Max Shear stress %0.2f  N/mm**2",q_s3)
diff --git a/3864/CH6/EX6.16/Ex6_16.sce b/3864/CH6/EX6.16/Ex6_16.sce
new file mode 100644
index 000000000..76268c16b
--- /dev/null
+++ b/3864/CH6/EX6.16/Ex6_16.sce
@@ -0,0 +1,52 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+L=1000 //mm //Length of bar
+L1=600 //mm //Length of Bar AB
+L2=400 //mm //Length of Bar BC
+d1=60  //mm //Outer Diameter of bar BC
+d2=30  //mm //Inner Diameter of bar BC
+d=60   //mm //Diameter of bar AB
+T=2*10**6 //N-mm //Total Torque
+
+//Calculations
+
+//Polar Modulus of Portion AB
+J1=%pi*32**-1*d**4 //mm*4
+
+//Polar Modulus of Portion BC
+J2=%pi*32**-1*(d1**4-d2**4) //mm**4
+
+//Let T1 be the torque resisted by bar AB and T2 be torque resisted by Bar BC
+//Let theta1 and theta2 be the rotation of shaft in portion AB & BC
+
+//theta1=T1*L1*(G*J1)**-1 //radians
+//After substituting values and further simplifying we get 
+//theta1=32*600*T1*(%pi*60**4*G)**-1
+
+//theta2=T2*L*(J2*G)**-1 //Radians
+//After substituting values and further simplifying we get 
+//theta2=32*400*T2*(%pi*60**4*(1-0.5**4)*G)**-1 
+
+//Now For consistency of Deformation,theta1=theta2
+//After substituting values and further simplifying we get 
+//T1=0.7111*T2  ..................................................(1)
+
+//But T1+T2=T=2*10**6   ...........................................(2)
+//Substituting value of T1 in above equation
+
+T2=T*(0.7111+1)**-1
+T1=0.71111*T2
+
+//Max stress in Portion AB
+q_s1=T1*(d*2**-1)*(J1)**-1 //N/mm**2
+
+//Max stress in Portion BC
+q_s2=T2*(d1*2**-1)*J2**-1 //N/mm**2 
+
+//Result
+printf("\n Stresses Developed in Portion:AB %0.2f  N/mm**2",q_s1)
+printf("\n                              :BC %0.2f  N/mm**2",q_s2)
diff --git a/3864/CH6/EX6.17/Ex6_17.sce b/3864/CH6/EX6.17/Ex6_17.sce
new file mode 100644
index 000000000..7012e6601
--- /dev/null
+++ b/3864/CH6/EX6.17/Ex6_17.sce
@@ -0,0 +1,45 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+d1=80 //mm //External Diameter of Brass tube
+d2=50 //mm //Internal Diameter of Brass tube
+d=50  //mm //Diameter of steel Tube
+G_b=40*10**3 //N/mm**2 //Modulus of Rigidity of brass tube
+G_s=80*10**3 //N/mm**2 //Modulus of rigidity of steel tube
+T=6*10**6 //N-mm //Torque
+L=2000 //mm //Length of Tube
+
+//Calculations
+
+//Polar Modulus of brass tube
+J1=%pi*32**-1*(d1**4-d2**4) //mm**4 
+
+//Polar modulus of steel Tube
+J2=%pi*32**-1*d**4 //mm**4
+
+//Let T_s & T_b be the torque resisted by steel and brass respectively
+//Then, T_b+T_s=T   ............................................(1)
+
+//Since the angle of twist will be the same
+//Theta1=Theta2
+//After substituting values and further simplifying we get 
+//Ts=0.360*Tb     ...........................................(2)
+
+//After substituting value of Ts in eqn 1 and further simplifying we get 
+T_b=T*(0.36+1)**-1 //N-mm
+T_s=0.360*T_b
+
+//Let q_s and q_b be the max stress in steel and brass respectively
+q_b=T_b*(d1*2**-1)*J1**-1 //N/mm**2
+q_s=T_s*(d2*2**-1)*J2**-1 //N/mm**2
+
+//Since angle of twist in brass=angle of twist in steel
+theta_s=T_s*L*(J2*G_s)**-1
+
+//Result
+printf("\n Stresses Developed in Materials are:Brass %0.2f  N/mm**2",q_b)
+printf("\n                                    :Steel %0.2f  N/mm**2",q_s)
+printf("\n Angle of Twist in 2m Length %0.3f  Radians",theta_s)
diff --git a/3864/CH6/EX6.18/Ex6_18.sce b/3864/CH6/EX6.18/Ex6_18.sce
new file mode 100644
index 000000000..cf2139d10
--- /dev/null
+++ b/3864/CH6/EX6.18/Ex6_18.sce
@@ -0,0 +1,39 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+d1=60 //mm //External Diameter of aluminium Tube
+d2=40 //mm //Internal Diameter of aluminium Tube
+d=40  //mm //Diameter of steel tube
+q_a=60 //N/mm**2 //Permissible stress in aluminium
+q_s=100 //N/mm**2 //Permissible stress in steel tube
+G_a=27*10**3 //N/mm**2 
+G_s=80*10**3 //N/mm**2 
+
+//Calculations
+
+//Polar modulus of aluminium Tube
+J_a=%pi*32**-1*(d1**4-d2**4) //mm**4
+
+//Polar Modulus of steel Tube
+J_s=%pi*32**-1*d**4 //mm**4
+
+//Now the angle of twist of steel tube = angle of twist of aluminium tube
+//T_s*L_s*(J_s*theta_s)**-1=T_a*L_a*(J_a*theta_a)**-1
+//After substituting values in above Equation and Further simplifyin we get
+//T_s=0.7293*T_a   .....................(1)
+
+//If steel Governs the resisting capacity
+T_s1=q_s*J_s*(d*2**-1)**-1 //N-mm
+T_a1=T_s1*0.7293**-1  //N-mm
+T1=(T_s1+T_a1)*10**-6 //KN-m //Total Torque in steel Tube
+
+//If aluminium Governs the resisting capacity 
+T_a2=q_a*J_a*(d1*2**-1) //N-mm
+T_s2=T_a2*0.7293 //N-mm
+T2=(T_s2+T_a2)*10**-6 //KN-m //Total Torque in aluminium tube
+
+//Result
+printf("\n Steel Governs the torque carrying capacity %0.2f  KN-m",T1)
diff --git a/3864/CH6/EX6.2/Ex6_2.sce b/3864/CH6/EX6.2/Ex6_2.sce
new file mode 100644
index 000000000..2c4184559
--- /dev/null
+++ b/3864/CH6/EX6.2/Ex6_2.sce
@@ -0,0 +1,26 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+P=440*10**6 //N-m/sec //Power transmitted
+n=280 //rpm
+theta=%pi*180**-1 //radian //angle of twist
+L=1000 //mm //Length of solid shaft
+q_s=40 //N/mm**2 //Max torsional shear stress
+G=84*10**3 //N/mm**2 //Modulus of rigidity
+
+//Calculations
+
+//P=2*%pi*n*T*(60)**-1  //Equation of Power transmitted
+T=P*60*(2*%pi*n)**-1 //N-mm //torsional moment
+
+//From Consideration of shear stress
+d1=(T*16*(%pi*40)**-1)**0.333333  
+
+//From Consideration of angle of twist
+d2=(T*L*32*180*(%pi*84*10**3*%pi)**-1)**0.25
+
+//result
+printf("\n Diameter of solid shaft is %0.2f  mm",d1)
diff --git a/3864/CH6/EX6.20/Ex6_20.sce b/3864/CH6/EX6.20/Ex6_20.sce
new file mode 100644
index 000000000..b8f895881
--- /dev/null
+++ b/3864/CH6/EX6.20/Ex6_20.sce
@@ -0,0 +1,31 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+T=2*10**6 //N-mm //Torque transmitted
+G=80*10**3 //N/mm**2 //Modulus of rigidity
+d1=40 //mm 
+d2=80 //mm
+r1=20 //mm
+r2=40 //mm
+L=2000 //mm //Length of shaft
+
+//Calculations
+
+//Angle of twist 
+theta=2*T*L*(r1**2+r1*r2+r2**2)*(3*%pi*G*r2**3*r1**3)**-1 //radians
+
+//If the shaft is treated as shaft of average Diameter
+d_avg=(d1+d2)*2**-1 //mm
+
+theta1=T*L*(G*%pi*32**-1*d_avg**4)**-1 //Radians
+
+//Percentage Error
+//Let Percentage Error be E
+X=theta-theta1
+E=(X*theta**-1)*100 
+
+//Result
+printf("Percentage Error is %0.3f",E)
diff --git a/3864/CH6/EX6.21/Ex6_21.sce b/3864/CH6/EX6.21/Ex6_21.sce
new file mode 100644
index 000000000..031493439
--- /dev/null
+++ b/3864/CH6/EX6.21/Ex6_21.sce
@@ -0,0 +1,29 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+G=80*10**3 //N/mm**2 
+P=1*10**9 //N-mm/sec //Power
+n=300 
+d1=150 //mm //Outer Diameter
+d2=120 //mm //Inner Diameter
+L=2000 //mm //Length of circular shaft
+
+//Calculations
+
+T=P*60*(2*%pi*n)**-1 //N-mm
+
+//Polar Modulus 
+J=%pi*32**-1*(d1**4-d2**4) //mm**4
+
+q_s=T*J**-1*(d1*2**-1) //N/mm**2 
+
+
+//Strain ENergy
+U=q_s**2*(4*G)**-1*%pi*4**-1*(d1**2-d2**2)*L
+
+//Result
+printf("\n Max shear stress is %0.2f  N/mm**2",q_s)
+printf("\n Strain Energy stored in the shaft is %0.2f  N-mm",U)
diff --git a/3864/CH6/EX6.22/Ex6_22.sce b/3864/CH6/EX6.22/Ex6_22.sce
new file mode 100644
index 000000000..573d185e2
--- /dev/null
+++ b/3864/CH6/EX6.22/Ex6_22.sce
@@ -0,0 +1,32 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+d=12 //mm //Diameter of helical spring
+D=150 //mm //Mean Diameter
+R=D*2**-1 //mm //Radius of helical spring
+n=10 //no.of turns
+G=80*10**3 //N/mm**2 
+W=450 //N //Load
+
+//Calculations
+
+//Max shear stress 
+q_s=16*W*R*(%pi*d**3)**-1 //N/mm**2
+
+//Strain Energy stored
+U=32*W**2*R**3*n*(G*d**4)**-1 //N-mm
+
+//Deflection Produced
+dell=64*W*R**3*n*(G*d**4)**-1 //mm
+
+//Stiffness Spring
+k=W*dell**-1 //N/mm
+
+//Result
+printf("\n Max shear stress is %0.2f  N/mm**2",q_s)
+printf("\n Strain Energy stored is %0.2f  N-mm",U)
+printf("\n Deflection Produced is %0.2f  mm",dell)
+printf("\n Stiffness spring is %0.2f  N/mm",k)
diff --git a/3864/CH6/EX6.23/Ex6_23.sce b/3864/CH6/EX6.23/Ex6_23.sce
new file mode 100644
index 000000000..d93dc86f7
--- /dev/null
+++ b/3864/CH6/EX6.23/Ex6_23.sce
@@ -0,0 +1,35 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+K=5 //N/mm //Stiffness
+L=100 //mm //Solid Length
+q_s=60 //N/mm**2 //Max shear stress
+W=200 //N //Max Load
+G=80*10**3 //N/mm**2
+
+//Calculations
+
+//K=W*dell**-1
+//After substituting values and further simplifying we get
+//d=0.004*R**3*n   ........(1) //mm //Diameter of wire
+//n=L*d**-1         ........(2)
+
+//From Shearing stress
+//q_s=16*W*R*(%pi*d**3)**-1 
+//After substituting values and further simplifying we get
+//d**4=0.004*R**3*n    .................(4)
+
+//From Equation 1,2,3
+//d**4=0.004*(0.0785*d**3)**3*100*d**-1
+//after further simplifying we get
+d=5168.101**0.25
+n=100*d**-1
+R=(d**4*(0.004*n)**-1)**0.3333
+
+//Result
+printf("\n Diameter of Wire is %0.2f  mm",d)
+printf("\n No.of turns is %0.2f  ",n)
+printf("\n Mean Radius of spring is %0.2f  mm",R)
diff --git a/3864/CH6/EX6.24/Ex6_24.sce b/3864/CH6/EX6.24/Ex6_24.sce
new file mode 100644
index 000000000..54c23cd26
--- /dev/null
+++ b/3864/CH6/EX6.24/Ex6_24.sce
@@ -0,0 +1,30 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+m=5*10**5 //Wagon Weighing
+v=18*1000*36000**-1 
+d=300 //mm //Diameter of Beffer springs
+n=18 //no.of turns
+G=80*10**3 //N/mm**2
+dell=225
+R=100 //mm //Mean Radius
+
+//Calculations
+
+//Energy of Wagon
+E=m*v**2*(9.81*2)**-1 //N-mm
+
+//Load applied
+W=dell*G*d**4*(64*R**3*n)**-1 //N 
+
+//Energy each spring can absorb is
+E2=W*dell*2**-1 //N-mm
+
+//No.of springs required to absorb energy of Wagon
+n2=E*E2**-1 *10**7
+
+//Result
+printf("\n No.of springs Required for Buffer is %0.2f  ",n2)
diff --git a/3864/CH6/EX6.25/Ex6_25.sce b/3864/CH6/EX6.25/Ex6_25.sce
new file mode 100644
index 000000000..a1b4c1ee4
--- /dev/null
+++ b/3864/CH6/EX6.25/Ex6_25.sce
@@ -0,0 +1,27 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+b=180 //mm //width of flange
+d=10 //mm //Depth of flange
+t=10 //mm //Thickness of flange
+D=400 //mm //Overall Depth 
+
+//Calculations
+
+I_xx=1*12**-1*(b*D**3-(b-t)*(D-2*d)**3)
+I_yy=1*12**-1*((D-2*d)*t**3+2*t*b**3)
+
+//If warping is neglected
+J=I_xx+I_yy //mm**4
+
+//Since b/d>1.6,we get
+J2=1*3**-1*d**3*b*(1-0.63*d*b**-1)*2+1*3**-1*t**3*(D-2*d)*(1-0.63*t*b**-1)
+
+//Over Estimation of torsional Rigidity would have been 
+T=J*J2**-1
+
+//Result
+printf("\n Error in assessing torsional Rigidity if the warping is neglected is %0.2f  ",T)
diff --git a/3864/CH6/EX6.26/Ex6_26.sce b/3864/CH6/EX6.26/Ex6_26.sce
new file mode 100644
index 000000000..4f3185b4c
--- /dev/null
+++ b/3864/CH6/EX6.26/Ex6_26.sce
@@ -0,0 +1,36 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+d1=100 //mm //Outer Diameter
+d2=95 //mm //Inner Diameter
+T=2*10**6 //N-mm //Torque
+
+//Calculations
+
+J=%pi*32**-1*(d1**4-d2**4) //mm**4 //Polar Modulus
+
+//Shear stress
+q_max=T*J**-1*d1*2**-1 //N/mm**2 
+
+//Now theta*L**-1=T*(G*J)**-1
+//After substituting values and further simplifying we get
+//Let theta*L**-1=X
+X=T*J**-1
+
+//Now Treating it as very thin walled tube
+d=(d1+d2)*2**-1 //mm
+
+r=d*2**-1 
+t=(d1-d2)*2**-1
+q_max2=T*(2*%pi*r**2*t)**-1 //N/mm**2
+
+X2=T*(2*%pi*r**3*t)**-1 
+
+//Result
+printf("\n When it is treated as hollow shaft:Max shear stress %0.2f  N/mm**2",q_max)
+printf("\n                                   :Angle of Twist per unit Length %0.3f  ",X)
+printf("\n When it is very thin Walled Tube  :Max shear stress %0.2f  N/mm**2",q_max2)
+printf("\n                                   :Angle of twist per Unit Length %0.3f  ",X2)
diff --git a/3864/CH6/EX6.3/Ex6_3.sce b/3864/CH6/EX6.3/Ex6_3.sce
new file mode 100644
index 000000000..5d5ac6967
--- /dev/null
+++ b/3864/CH6/EX6.3/Ex6_3.sce
@@ -0,0 +1,27 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+G=80*10**3 //N/mm**2 //Modulus of rigidity
+q_s=80 //N/mm**2 //Max sheare stress
+P=736*10**6 //N-mm/sec //Power transmitted
+n=200
+
+//Calculations
+
+T=P*60*(2*%pi*n)**-1 //N-mm //Torsional moment
+
+//Now From consideration of angle of twist
+theta=%pi*180**-1
+//L=15*d
+
+d=(T*32*180*15*(%pi**2*G)**-1)**0.33333
+
+//Now corresponding stress at the surface is
+q_s2=T*32*d*(%pi*2*d**4)**-1
+
+//Result
+printf("\n Max diameter required is %0.2f  mm",d)
+printf("\n Corresponding shear stress is %0.2f  N/mm**2",q_s2)
diff --git a/3864/CH6/EX6.4/Ex6_4.sce b/3864/CH6/EX6.4/Ex6_4.sce
new file mode 100644
index 000000000..0c51b1470
--- /dev/null
+++ b/3864/CH6/EX6.4/Ex6_4.sce
@@ -0,0 +1,28 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+d=25 //mm //Diameter of steel bar
+p=50*10**3 //N //Pull
+dell_1=0.095 //mm //Extension of bar
+l=200 //mm //Guage Length
+T=200*10**3 //N-mm //Torsional moment
+theta=0.9*%pi*180**-1 //angle of twist
+L=250 //mm Length of steel bar
+
+//Calculations
+
+A=%pi*4**-1*d**2 //Area of steel bar //mm**2
+E=p*l*(dell_1*A)**-1 //N/mm**2 //Modulus of elasticity 
+
+J=%pi*32**-1*d**4 //mm**4 //Polar modulus
+
+G=T*L*(theta*J)**-1 //Modulus of rigidity //N/mm**2
+
+//Now from the relation of Elastic constants
+mu=E*(2*G)**-1-1
+
+//result
+printf("\n The Poissons ratio is %0.3f  ",mu)
diff --git a/3864/CH6/EX6.5/Ex6_5.sce b/3864/CH6/EX6.5/Ex6_5.sce
new file mode 100644
index 000000000..0ee4239e2
--- /dev/null
+++ b/3864/CH6/EX6.5/Ex6_5.sce
@@ -0,0 +1,26 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+L=6000 //mm //Length of circular shaft
+d1=100 //mm //Outer Diameter
+d2=75 //mm //Inner Diameter
+R=100*2**-1 //Radius of shaft
+T=10*10**6 //N-mm //Torsional moment
+G=80*10**3 //N/mm**2 //Modulus of Rigidity
+
+//Calculations
+
+J=%pi*32**-1*(d1**4-d2**4) //mm**4 //Polar Modulus 
+
+//Max Shear stress produced
+q_s=T*R*J**-1 //N/mm**2
+
+//Angle of twist
+theta=T*L*(G*J)**-1 //Radian
+
+//Result
+printf("\n MAx shear stress produced is %0.2f  N/mm**2",q_s)
+printf("\n Angle of Twist is %0.2f  Radian",theta)
diff --git a/3864/CH6/EX6.6/Ex6_6.sce b/3864/CH6/EX6.6/Ex6_6.sce
new file mode 100644
index 000000000..f16af5a6e
--- /dev/null
+++ b/3864/CH6/EX6.6/Ex6_6.sce
@@ -0,0 +1,30 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+d1=200 //mm //External Diameter of shaft
+t=25 //mm //Thickness of shaft
+n=200 //rpm
+theta=0.5*%pi*180**-1 //Radian //angle of twist
+L=2000 //mm //Length of shaft
+G=84*10**3 //N/mm**2
+d2=d1-2*t //mm //Internal Diameter of shaft
+
+//Calculations
+
+J=%pi*32**-1*(d1**4-d2**4) //mm**4 //Polar Modulus 
+
+//Torsional moment
+T=G*J*theta*L**-1 //N/mm**2 
+
+//Power Transmitted
+P=2*%pi*n*T*60**-1*10**-6 //N-mm
+
+//Max shear stress transmitted
+q_s=G*theta*(d1*2**-1)*L**-1 //N/mm**2 
+
+//Result
+printf("\n Power Transmitted is %0.2f  N-mm",P)
+printf("\n Max Shear stress produced is %0.2f  N/mm**2",q_s)
diff --git a/3864/CH6/EX6.7/Ex6_7.sce b/3864/CH6/EX6.7/Ex6_7.sce
new file mode 100644
index 000000000..70abac79a
--- /dev/null
+++ b/3864/CH6/EX6.7/Ex6_7.sce
@@ -0,0 +1,33 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+P=3750*10**6 //N-mm/sec
+n=240 //Rpm
+q_s=160 //N/mm**2 //Max shear stress
+
+//Calculations
+
+//d2=0.8*d2 //mm //Internal Diameter of shaft
+
+//J=%pi*32**-1*(d1**4-d2**4) //mm**4 //Polar modulus
+//After substituting value in above Equation we get
+//J=0.05796*d1**4
+
+T=P*60*(2*%pi*n)**-1 //N-mm //Torsional moment
+
+//Now from Torsion Formula
+//T*J**-1=q_s*R**-1    ......................................(1)
+
+//But R=d1*2**-1 
+
+//Now substituting value of R and J in Equation (1) we get
+d1=(T*(0.05796*q_s*2)**-1)**0.33333
+
+d2=d1*0.8
+
+//Result
+printf("\n The size of the Shaft is:d1 %0.3f  mm",d1)
+printf("\n                         :d2 %0.3f  mm",d2)
diff --git a/3864/CH6/EX6.8/Ex6_8.sce b/3864/CH6/EX6.8/Ex6_8.sce
new file mode 100644
index 000000000..51b52d047
--- /dev/null
+++ b/3864/CH6/EX6.8/Ex6_8.sce
@@ -0,0 +1,64 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+P=245*10**6 //N-mm/sec //Power transmitted
+n=240 //rpm
+q_s=40 //N/mm**2 //Shear stress
+theta=%pi*180**-1 //radian //Angle of twist
+L=1000 //mm //Length of shaft
+G=80*10**3 //N/mm**2
+
+//Tmax=1.5*T
+
+//Calculations
+
+T=P*60*(2*%pi*n)**-1 //N-mm //Torsional Moment
+Tmax=1.5*T
+
+//Now For Solid shaft
+//J=%pi*32*d**4
+
+//Now from the consideration of shear stress we get
+//T*J**-1=q_s*(d*2**-1)**-1
+//After substituting value in above Equation we get
+//T=%pi*16**-1*d**3*q_s
+
+//Designing For max Torque
+d=(Tmax*16*(%pi*40)**-1)**0.33333 //mm //Diameter of shaft
+
+//For max Angle of Twist
+//Tmax*J**-1=G*theta*L**-1 
+//After substituting value in above Equation we get
+d2=(Tmax*32*180*L*(%pi**2*G)**-1)**0.25
+
+//For Hollow Shaft
+
+//d1_2=Outer Diameter
+//d2_2=Inner Diameter
+
+//d2_2=0.5*d1_2
+
+// Polar modulus
+//J=%pi*32**-1*(d1_2**4-d2_2**4)
+//After substituting values we get
+//J=0.092038*d1_2**4
+
+//Now from the consideration of stress
+//Tmax*J**-1=q_s*(d1_2*2**-1)**-1
+//After substituting values and further simplifying we get
+d1_2=(Tmax*(0.092038*2*q_s)**-1)**0.33333
+
+//Now from the consideration of angle of twist
+//Tmax*J**-1=G*theta*L**-1
+//After substituting values and further simplifying we get
+d1_3=(Tmax*180*L*(0.092038*G*%pi)**-1)**0.25
+
+d2_2=0.5*d1_2
+
+//result
+printf("\n Diameter of shaft is:For solid shaft:d %0.2f  mm",d)
+printf("\n                     :For Hollow shaft:d1_2 %0.3f  mm",d1_2)
+printf("\n                     :                :d2_2 %0.3f  mm",d2_2)