11 files changed, 480 insertions, 0 deletions
diff --git a/3864/CH9/EX9.1/Ex9_1.sce b/3864/CH9/EX9.1/Ex9_1.sce
new file mode 100644
index 000000000..aaad4d9c6
--- /dev/null
+++ b/3864/CH9/EX9.1/Ex9_1.sce
@@ -0,0 +1,23 @@
+clear
+//
+//
+
+//Initilization of Variables
+L=5000 //mm //Length of strut
+dell=10 //mm //Deflection
+W=10 //N //Load
+
+//Calculations
+
+//Central Deflection of a simply supported beam with central concentrated load is
+//dell=W*L**3*(48*E*I)**-1 
+
+//Let E*I=X
+X=W*L**3*(48*dell)**-1 //mm
+
+//Euler's Load
+//Let Euler's Load be P
+P=%pi**2*X*(L**2)**-1
+
+//Result
+printf("\n Critical Load of Bar is %0.2f  N",P)
diff --git a/3864/CH9/EX9.10/Ex9_10.sce b/3864/CH9/EX9.10/Ex9_10.sce
new file mode 100644
index 000000000..8bdea9929
--- /dev/null
+++ b/3864/CH9/EX9.10/Ex9_10.sce
@@ -0,0 +1,51 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+sigma=326 //N/mm**2 //stress
+E=2*10**5 //N/mm**2 //Modulus of Elasticity
+FOS=2 //Factor of safety
+a=1*7500**-1 //Rankine's constant
+D=350 //mm //Overall Depth 
+
+//Cover plates
+b1=500 //mm //width
+t1=10  //mm //Thickness
+
+d=220 //mm //Distance between two channels
+
+L=6000 //mm //Length of column
+
+A=5366 //mm**2 //Area of Column section 
+I_xx=100.08*10**6 //mm**4 //M.I of x-x axis
+I_yy=4.306*10**6 //mm**4 //M.I of y-y axis
+C_yy=23.6 //mm //Centroid at y-y axis
+
+//Calculations
+
+//Symmetric axes are the centroidal axes is
+
+//M.I of Channel at x-x axis
+I_xx_1=2*I_xx+2*(1*12**-1*b1*t1**3+b1*t1*(D*2**-1+t1*2**-1)**2)
+
+//M.I of Channel at y-y axis
+I_yy_1=2*(I_yy+A*(d*2**-1+C_yy)**2)+2*12**-1*t1*b1**3
+
+//As I_yy<I_xx
+//So
+I=I_yy_1 //mm**4 
+
+A2=2*A+2*t1*b1 //Area of channel
+
+k=(I*A2**-1)**0.5 //mm
+
+//Critical Load
+P=sigma*A2*(1+a*(L*k**-1)**2)**-1 
+
+//Safe Load
+S=P*2**-1*10**-3 //KN
+
+//Result
+printf("\n Safe Load carrying Capacity is %0.2f  KN",S)
diff --git a/3864/CH9/EX9.11/Ex9_11.sce b/3864/CH9/EX9.11/Ex9_11.sce
new file mode 100644
index 000000000..48212a800
--- /dev/null
+++ b/3864/CH9/EX9.11/Ex9_11.sce
@@ -0,0 +1,31 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+I=4.085*10**8 //mm**4 //M.I
+A=20732.0 //mm**2 //area of column
+f_y=250 //N/mm**2 
+L=6000 //mm //Length of column
+
+//Calculations
+
+k=(I*A**-1)**0.5 //mm
+lamda=L*k**-1 //Slenderness ratro
+
+//From Indian standard table
+lamda_1=40 
+sigma_a_c_1=139 //N/mm**2
+lamda_2=50 
+sigma_a_c_2=132 //N/mm**2 
+
+//Linearly interpolating between these values for lambda=42.744
+
+sigma_a_c_3=sigma_a_c_1-2.744*10**-1*(sigma_a_c_1-sigma_a_c_2)
+
+//Safe Load carrying capacity of column
+P=sigma_a_c_3*A*10**-3
+
+//Result
+printf("\n Safe Load carrying capacity is %0.2f  KN",P)
diff --git a/3864/CH9/EX9.2/Ex9_2.sce b/3864/CH9/EX9.2/Ex9_2.sce
new file mode 100644
index 000000000..2287a950a
--- /dev/null
+++ b/3864/CH9/EX9.2/Ex9_2.sce
@@ -0,0 +1,54 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+L=2000 //mm //Length of square column
+E=12*10**3 //N/mm**2 //Modulus of Elasticity
+sigma=12 //N/mm*2 //stress
+W1=95*10**3 //N //Load1
+W2=200*10**3 //N //Load2
+FOS=3
+
+//Calculations
+
+//From Euler's Formula
+//P=%pi**2*E*I*(L**2)**-1  .........(1)
+
+//Working Load
+//W=P*(FOS)**-1
+
+//Part-1
+
+//At W1=95*10**3 //N
+//W1=P*(3*L**2)**-1
+
+//Let 'a' be the side of the square
+//I=1*12**-1*a**4
+
+//sub value of I in Equation 1 and further rearranging we get
+a=(W1*3*12*L**2*(%pi**2*E)**-1)**0.25 //mm
+
+//From Consideration of direct crushing
+//sigma*a**2=W1
+//After Reaaranging the above equation we get
+a2=(W1*(sigma)**-1)**0.5 //mm
+
+//required size is 103.67*103.67 i.e a*a
+
+//Part-2
+
+//At W2=200*10**3 //N
+//W2=P*(3*L**2)**-1
+//After substituting values and further Rearranging the above equation we get
+a3=(W2*3*12*L**2*(%pi**2*E)**-1)**0.25 //mm
+
+//From consideration of direct compression,size required is
+a4=(W2*sigma**-1)**0.5
+
+//required size is 129.10*129.10 i.e a4*a4
+
+//Result
+printf("\n For W1 Load Required size is %0.2f  mm**2",a*a)
+printf("\n For W2 Load Required size is %0.2f  mm**2",a4*a4)
diff --git a/3864/CH9/EX9.3/Ex9_3.sce b/3864/CH9/EX9.3/Ex9_3.sce
new file mode 100644
index 000000000..522658e0f
--- /dev/null
+++ b/3864/CH9/EX9.3/Ex9_3.sce
@@ -0,0 +1,37 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+//Flange 
+b=100 //mm //Width
+
+D=80 //mm //Overall Depth
+t=10 //mm //Thickness of web and flanges
+L=3000 //mm //Length of strut
+E=200*10**3 //N/mm**2 //Modulus of Elasticity
+
+//Calculations
+
+//Let centroid be at depth y_bar from top fibre
+y_bar=(b*t*t*2**-1+(D-t)*t*((D-t)*2**-1+t))*(b*t+(D-t)*t)**-1 //mm 
+
+//M.I at x-x axis
+I_x=1*12**-1*b*t**3+b*t*(y_bar-t*2**-1)**2+1*12**-1*t*((D-t))**3+t*((D-t))*((((D-t)*2**-1)+t)-y_bar)**2
+
+//M.I at y-y axis
+I_y=1*12**-1*t*b**3+1*12**-1*(D-t)*t**3 //mm**3
+
+//Least M.I
+I=I_y
+
+//Since both ends are hinged
+//Feective Length=Actual Length
+L=3000 //mm
+l=3000 //mm
+//Buckling Load 
+P=%pi**2*E*I*(l**2)**-1*10**-3 //KN
+
+//Result
+printf("\n The Buckling Load for strut of tee section %0.2f  KN",P)
diff --git a/3864/CH9/EX9.4/Ex9_4.sce b/3864/CH9/EX9.4/Ex9_4.sce
new file mode 100644
index 000000000..ea72d26dd
--- /dev/null
+++ b/3864/CH9/EX9.4/Ex9_4.sce
@@ -0,0 +1,43 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+D=400 //mm //Overall Depth
+
+//Flanges
+b=300 //mm //Width
+t=50 //mm //Thickness
+
+t2=30 //mm //Web Thickness
+
+dell=10 //mm //Deflection
+w=40 //N/mm //Load
+FOS=1.75 //Factor of safety
+E=2*10**5 //N/mm**2
+
+//Calculations
+
+//M.I at x-x axis
+I_x=1*12**-1*(b*D**3-(b-t2)*b**3) //mm**4
+
+//Central Deflection
+//dell=5*w*L**4*(384*E*I)**-1
+//After sub values in above equation and further simplifying we get
+L=(dell*384*E*I_x*(5*w)**-1)**0.25
+
+//M.I aty-y axis
+I=1*12**-1*t*b**3+1*12**-1*b*t2**3+1*12**-1*t*b**3 //mm**4
+I_y=1*12**-1*t*b**3+1*12**-1*b*t2**3+1*12**-1*t*b**3 //mm**4
+
+//Both the Ends of column are hinged
+
+//Crippling Load
+P=%pi**2*E*I*(L**2)**-1 //N
+
+//Safe Load
+S=P*(FOS)**-1*10**-3 //N
+
+//Result
+printf("\n Safe Load if I-section is used as column with both Ends hhinged %0.2f  KN",S)
diff --git a/3864/CH9/EX9.5/Ex9_5.sce b/3864/CH9/EX9.5/Ex9_5.sce
new file mode 100644
index 000000000..b55ef7544
--- /dev/null
+++ b/3864/CH9/EX9.5/Ex9_5.sce
@@ -0,0 +1,42 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+D=200 //mm //External Diameter
+t=20 //mm //hickness
+d=200-2*t //mm //Internal Diameter
+E=1*10**5 //N/mm**2
+a=1*(1600)**-1 //Rankine's Constant
+L=4.5 //m //Length
+sigma=550 //N/mm**2 //Stress
+FOS=2.5
+
+//Calculations
+
+//Moment of Inertia
+I=%pi*D**4*64**-1-%pi*d**4*64**-1
+
+//Both Ends are fixed
+
+//Effective Length
+l=1*2**-1*L*10**3 //mm
+
+//Euler's Critical Load
+P_E=%pi**2*E*I*(l**2)**-1
+
+A=%pi*4**-1*(D**2-d**2) //mm*2
+
+k=(I*A**-1)**0.5
+
+//Rankine's Critical Load
+P_R=sigma*A*(1+a*(l*k**-1)**2)**-1
+
+X=P_E*P_R**-1 
+
+//Safe Load using Rankine's Formula
+S=P_R*(FOS)**-1*10**-3 //KN
+
+//Result
+printf("\n Safe Load by Rankines Formula is %0.2f  KN",S)
diff --git a/3864/CH9/EX9.6/Ex9_6.sce b/3864/CH9/EX9.6/Ex9_6.sce
new file mode 100644
index 000000000..cc66b9a26
--- /dev/null
+++ b/3864/CH9/EX9.6/Ex9_6.sce
@@ -0,0 +1,59 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+L=3000 //mm //Length of column
+W=800*10**3 //N //Load
+a=1*1600**-1 //Rankine's constant
+FOS=4 //Factor of safety
+sigma=550 //N/mm**2 //stress
+
+//Calculations
+
+//Effective Length
+l=L*2**-1 //mm 
+
+//Let d1=outer diameter & d2=inner diameter
+//d1=5*8**-1*d2
+
+//M.I
+//I=%pi*64**-1*(d1**4-d2**4) //mm**4
+
+//Area of section
+//A=pi4**-1*(d1**2-d2**2) //mm**2
+
+//k=(I*A**-1) 
+//substituting values in above equation 
+//k=1*16**-1*(d1**2-d2**2)
+//after simplifying further we get
+//k=0.2948119.d1
+
+//X=l*k**-1
+//substituting values in above equation and after simplifying further we get
+//X=5087.9898*d1**-1
+
+//Crtitcal Load
+P=W*FOS //N
+
+//From Rankine's Load
+//P2=sigma*A*(1+a*(X)**2)**-1
+//substituting values in above equation and after simplifying further we get
+//d1**4-12156618*d1**4-1.96691*10**8=0
+//Solving Quadratic Equation we get
+//d1**2-12156618*d1-196691000=0
+a=1
+b=-12156.618
+c=-196691000
+
+Y=b**2-4*a*c
+
+d1_1=((-b+Y**0.5)*(2*a)**-1)**0.5 //mm
+d1_2=((-b-Y**0.5)*(2*a)**-1) //mm
+
+d2=5*8**-1*d1_1
+
+//Result
+printf("\n Section of cast iron hollow cylindrical column is:d1_1 %0.2f  mm",d1_1)
+printf("\n                                                  :d2   %0.2f  mm",d2)
diff --git a/3864/CH9/EX9.7/Ex9_7.sce b/3864/CH9/EX9.7/Ex9_7.sce
new file mode 100644
index 000000000..1793b5f17
--- /dev/null
+++ b/3864/CH9/EX9.7/Ex9_7.sce
@@ -0,0 +1,65 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+//Let X=(P*A**-1) //Average Stress at Failure 
+Lamda_1=70 //Slenderness Ratio
+Lamda_2=170 //Slenderness Ratio
+X1=200 //N/mm**2 
+X2=69 //N/mm**2 
+
+//Rectangular section
+b=60 //mm //width
+t=20 //mm //Thickness
+
+L=1250 //mm //Length of strut
+FOS=4 //Factor of safety
+
+//Calculations
+
+//Slenderness ratio
+//Lamda=L*k**-1
+
+//The Rankine's Formula for strut
+//P=sigma*A*(1+a*(L*k**-1)**-1
+
+//From test result 1,
+//After sub values in above equation we get and further simplifying we get
+//sigma_1=200+980000*a   ...................(1)
+
+//From test result 2,
+//After sub values in above equation we get and further simplifying we get
+//sigma_2=69+1994100*a   ...................(2)
+
+//Substituting it in equation (1) we get
+a=131*1014100**-1   
+
+//Substituting a in equation 1
+sigma_1=200+980000*a //N/mm**2
+
+//Effective Length 
+l=1*2**-1*L //mm
+
+//Least of M.I
+I=1*12**-1*b*t**3 //mm**4
+
+//Area 
+A=b*t //mm**2 
+
+k=(I*A**-1)**0.5
+
+//Slenderness ratio
+Lamda=l*k**-1
+
+//From Rankine's Ratio
+P=sigma_1*A*(1+a*(Lamda)**2)**-1
+
+//Safe Load
+S=P*(FOS)**-1*10**-3 //N
+
+//Result
+printf("\n Constant in the Formula is:a       %0.6f  ",a)
+printf("\n                           :sigma_1 %0.2f  ",sigma_1)
+printf("\n Safe Load is %0.2f  KN",S)
diff --git a/3864/CH9/EX9.8/Ex9_8.sce b/3864/CH9/EX9.8/Ex9_8.sce
new file mode 100644
index 000000000..cd2e3d419
--- /dev/null
+++ b/3864/CH9/EX9.8/Ex9_8.sce
@@ -0,0 +1,45 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+D=200 //mm //Depth
+b=140 //mm //width
+
+//Plate
+b2=160 //mm //Width
+t2=10 //mm //Thickness
+
+L=4000 //mm #Length
+l=4000 //mm #Length
+FOS=4 //Factor of safety
+sigma=315 //N/mm**2 //stress
+a2=1*7500**-1 
+I_xx=26.245*10**6 //mm**4 //M.I at x-x
+I_yy=3.288*10**6 //mm**4 //M.I at y-y
+a=3671 //mm**2 //Area
+k_x=84.6//mm
+k_y=29.9 //mm
+
+//Calculations
+
+//Total Area
+A=a+2*t2*b2 //mm**2
+
+//M.I
+I=I_yy+2*12**-1*t2*b2**3 //mm**4
+
+k=(I*A**-1)**0.5 //mm
+
+//Let X=L*k**-1
+X=L*k**-1
+
+//Appliying Rankine's Formula
+P=sigma*A*(1+a2*(X)**2)**-1 //N
+
+//Safe Load
+S=P*(FOS)**-1*10**-3 //KN
+
+//Result
+printf("\n Safe axial Load is %0.2f  KN",S)
diff --git a/3864/CH9/EX9.9/Ex9_9.sce b/3864/CH9/EX9.9/Ex9_9.sce
new file mode 100644
index 000000000..5d64122bd
--- /dev/null
+++ b/3864/CH9/EX9.9/Ex9_9.sce
@@ -0,0 +1,30 @@
+clear
+//
+//
+
+//Initilization of Variables
+
+E=200*10**3 //N/mm**2 //Modulus of elasticity
+sigma=330 //N/mm**2 //Stress
+a=1*7500**-1 //Rankine's constant
+A=5205 //mm**2 //area of column
+I_xx=59.431*10**6 //mm**4 //M.I at x-x axis
+I_yy=8.575*10**6 //mm**24//M.I at y-y axis
+
+//Calculations
+
+//Total M.I
+I=I_xx+I_yy //mm**4
+
+//Area of compound Section 
+A2=2*A //mm**2
+
+k=(I*A2**-1)**0.5 //mm
+
+//Equating Euler's Load to Rankine's Load we get
+//%pi**2*E*I*(L**2)**-1=sigma*A*(1+a*(L*k)**2)**-1
+//After Substitt=uting values and further simplifying we get
+L=(39076198*(1-0.7975432)**-1)**0.5*10**-3 //m
+
+//Result
+printf("\n Length of column for which Rankines formula and Eulers Formula give the same result is %0.2f  m",L)