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| author | prashantsinalkar | 2017-10-10 12:27:19 +0530 |
|---|---|---|
| committer | prashantsinalkar | 2017-10-10 12:27:19 +0530 |
| commit | 7f60ea012dd2524dae921a2a35adbf7ef21f2bb6 (patch) | |
| tree | dbb9e3ddb5fc829e7c5c7e6be99b2c4ba356132c /3705 | |
| parent | b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b (diff) | |
| download | Scilab-TBC-Uploads-7f60ea012dd2524dae921a2a35adbf7ef21f2bb6.tar.gz Scilab-TBC-Uploads-7f60ea012dd2524dae921a2a35adbf7ef21f2bb6.tar.bz2 Scilab-TBC-Uploads-7f60ea012dd2524dae921a2a35adbf7ef21f2bb6.zip | |
initial commit / add all books
Diffstat (limited to '3705')
77 files changed, 1999 insertions, 0 deletions
diff --git a/3705/CH1/EX1.1/Ex1_1.sce b/3705/CH1/EX1.1/Ex1_1.sce new file mode 100644 index 000000000..d86a5575b --- /dev/null +++ b/3705/CH1/EX1.1/Ex1_1.sce @@ -0,0 +1,22 @@ + +clear//
+
+//NOTE:The notation has been changed to simplify the coding process
+
+//Variable Declaration
+P_AB=4000 //Axial Force at section 1 in lb
+P_BC=5000 //Axial Force at section 2 in lb
+P_CD=7000 //Axial Force at section 3 in lb
+A_1=1.2 //Area at section 1 in in^2
+A_2=1.8 //Area at section 2 in in^2
+A_3=1.6 //Area at section 3 in in^2
+
+//Calculation
+//S indicates sigma here
+S_AB=P_AB/A_1 //Stress at section 1 in psi (T)
+S_BC=P_BC/A_2 //Stress at section 2 in psi (C)
+S_CD=P_CD/A_3 //Stress at section 3 in psi (C)
+
+//Result
+printf("\n The stress at the three sections is given as")
+printf("\n Stress at section 1= %0.0f psi/in^2 section 2= %0.0f psi/in^2 section 3= %0.3f psi/in^2",S_AB,S_BC,S_CD)
diff --git a/3705/CH1/EX1.2/Ex1_2.sce b/3705/CH1/EX1.2/Ex1_2.sce new file mode 100644 index 000000000..f083daa4e --- /dev/null +++ b/3705/CH1/EX1.2/Ex1_2.sce @@ -0,0 +1,29 @@ + +clear//
+
+//Variable Declaration
+Ay=40 //Vertical Reaction at A in kN
+Hy=60 //Vertical Reaction at H in kN
+Hx=0 //Horizontal Reaction at H in kN
+y=3 //Height in m
+x=5 //Distance in m
+p=4 //Panel distance in m
+A=900 //Area of the member in mm^2
+P_C=30 //Force at point C in kN
+
+//Calculation
+//Part 1
+//Applying summation of forces in the x and y direction and equating to zero
+P_AB=(-Ay)*(x*y**-1) //Force in member AB in kN
+P_AC=-(p*x**-1*P_AB) //Force in member AC in kN
+//Using stress=force/area
+S_AC=(P_AC/A)*10**3 //Stress in member AC in MPa (T)
+
+//Part 2
+//Sum of moments about point E to zero
+P_BD=(Ay*p*2-(P_C*p))*y**-1 //Force in memeber AB in kN (C)
+S_BD=(P_BD/A)*10**3 //Stress in member in MPa (C)
+
+//Result
+printf("\n The Stress in member AC is %0.1f MPa (T)",S_AC)
+printf("\n The Stress in member BD is %0.1f MPa (C)",S_BD)
diff --git a/3705/CH1/EX1.3/Ex1_3.sce b/3705/CH1/EX1.3/Ex1_3.sce new file mode 100644 index 000000000..e3daf96df --- /dev/null +++ b/3705/CH1/EX1.3/Ex1_3.sce @@ -0,0 +1,28 @@ + +clear//
+//
+
+//Variable Declaration
+A_AB=800 //Area of member AB in m^2
+A_AC=400 //Area of member AC in m^2
+W_AB=110 //Safe value of stress in Pa for AB
+W_AC=120 //Safe value of stress in Pa for AC
+theta1=60*3.14*180**-1 //Angle in radians
+theta2=40*3.14*180**-1 //Angle in radians
+
+//Calculations
+//Applying sum of forces
+//Solving by matrix method putting W as 1
+A =[-cos(theta1),cos(theta2);sin(theta1),sin(theta2)]
+
+B = [1;1]
+C=inv(A)
+D=C
+
+//Using newtons third law
+//Two values of W hence the change in the notation
+W1=(W_AB*A_AB)*D(2,2)**-1 //Weight W in N
+W2=(W_AC*A_AC)*D(1,2)**-1 //Weight W in N
+
+//Result
+printf("\n The maximum value of W allowable is %0.1f kN",W2*1000**-1)
diff --git a/3705/CH1/EX1.4/Ex1_4.sce b/3705/CH1/EX1.4/Ex1_4.sce new file mode 100644 index 000000000..3b1200aad --- /dev/null +++ b/3705/CH1/EX1.4/Ex1_4.sce @@ -0,0 +1,17 @@ + +clear//
+
+//Variable Declaration
+d=3*4**-1 //Rivet diameter in inches
+t=7*8**-1 //Thickness of the plate in inches
+tau=14000 //Shear stress limit in psi
+sigma_b=18000 //Normal stress limit in psi
+
+//Calculations
+//Design Shear Stress in Rivets
+V=tau*(d**2*(%pi/4))*4 //Shear force maximum allowable in lb
+//Design for bearing stress in plate
+Pb=sigma_b*t*d*4 //lb
+
+//Result
+printf("\n The maximum load that the joint can carry is %0.0f lb",V)
diff --git a/3705/CH10/EX10.1/Ex10_1.sce b/3705/CH10/EX10.1/Ex10_1.sce new file mode 100644 index 000000000..d2637d4a7 --- /dev/null +++ b/3705/CH10/EX10.1/Ex10_1.sce @@ -0,0 +1,28 @@ + +clear//
+
+//Variable Declaration
+Le=7 //Effective length in m
+P=450 //Applied axial Load in kN
+FOS=3 //Factor of safety
+sigma_pl=200*10**6 //Stress allowable in Pa
+E=200*10**9 //Youngs Modulus in Pa
+end_cond=0.7 //End Condition factor to be multiplied
+
+//Calculations
+Pcr=P*FOS //Critical Load in kN
+A=Pcr*sigma_pl**-1*10**9 //Area in mm^2
+
+//Part 1
+I1=10**15*(Pcr*Le**2)*(%pi**2*E)**-1 //Moment of Inertia Required in mm^4
+//From table selecting appropriate Section W250x73
+
+//Part 2
+I2=10**15*(Pcr*end_cond**2*Le**2)*(%pi**2*E)**-1 //Moment of Inertia Required in mm^4
+//From table selecting appropriate Section W200x52
+
+//Lightest Section that meets these criterion is W250x58 section
+
+
+//Result
+printf("\n From the above computation we select W250x58 section")
diff --git a/3705/CH10/EX10.2/Ex10_2.sce b/3705/CH10/EX10.2/Ex10_2.sce new file mode 100644 index 000000000..a320e3bbe --- /dev/null +++ b/3705/CH10/EX10.2/Ex10_2.sce @@ -0,0 +1,39 @@ + +clear//
+
+//Variable Declaration
+E=200*10**9 //Youngs Modulus in Pa
+sigma_yp=380*10**6 //Stress allowable in Pa
+Le=10 //Length in m
+end_cond=0.5 //Support condition factor to be ,ultiplied to length
+A=15.5*10**-3 //Area in m^2
+
+//Calculations
+Cc=sqrt((2*%pi**2*E)*sigma_yp**-1) //Slenderness Ratio
+
+//Part 1
+S_R1=142.9 //Slenderness ratio
+sigma_w=(12*%pi**2*E)/(23*S_R1**2) //Allowable Working Stress in Pa
+P=sigma_w*A //Maximum Allowable Load in kN
+
+//Part 2
+S_R2=79.37 //Slenderness ratio
+N=5*3**-1+((3*S_R2)/(8*Cc))-(S_R2**3*(8*Cc**3)**-1) //Factor Of Safety
+
+sigma_w2=(1-(S_R2**2*0.5*Cc**-2))*(sigma_yp*N**-1) //Allowable working Stress in Pa
+P2=sigma_w2*A //Allowable Load in kN
+
+//Part 3
+S_R3=55.56 //Slenderness Ratio
+N3=5*3**-1+((3*S_R3)/(8*Cc))-(S_R3**3*(8*Cc**3)**-1) //Factor Of Safety
+
+sigma_w3=(1-(S_R3**2*0.5*Cc**-2))*(sigma_yp*N3**-1) //Allowable working Stress in Pa
+P3=sigma_w3*A //Allowable Load in kN
+
+//Result
+printf("\n The results for Part 1 are")
+printf("\n Maximum Allowable Load P= %0.0f kN",P*10**-3)
+printf("\n Part 2")
+printf("\n Maximum Allowable Load P= %0.0f kN",P2*10**-3)
+printf("\n Part 3")
+printf("\n Maximum Allowable Load P= %0.0f kN",P3*10**-3)
diff --git a/3705/CH10/EX10.3/Ex10_3.sce b/3705/CH10/EX10.3/Ex10_3.sce new file mode 100644 index 000000000..2f4065870 --- /dev/null +++ b/3705/CH10/EX10.3/Ex10_3.sce @@ -0,0 +1,31 @@ + +clear//
+//
+
+//Variable Declaration
+E=29*10**6 //Youngs Modulus in psi
+sigma_yp=36*10**3 //Stress in psi
+L=25 //Length in ft
+A=17.9 //Area in in^2
+Iz=640 //Moment of inertia in in^4
+Sz=92.2 //Sectional Modulus in in^3
+P=150*10**3 //Load in lb
+e=4 //Eccentricity in inches
+
+//Calculations
+
+//Part 1
+a=1.09836
+sigma_max=P*A**-1+(P*e*Sz**-1)*a //Maximum Stress in psi
+
+//Part 2
+//After simplification we get the equation to compute N
+N=2.19 //Trial and Error yields
+
+//Part 3
+v_max=e*((cos(sqrt((P*L**2*12**2)*(4*E*Iz)**-1)))**-1-1)
+
+//Result
+printf("\n The maximum compressive stress in the Column is %0.2f psi",sigma_max)
+printf("\n The factor of safety is %0.3f ",N)
+printf("\n The maximum lateral dfelection is %0.3f in",v_max)
diff --git a/3705/CH10/EX10.4/Ex10_4.sce b/3705/CH10/EX10.4/Ex10_4.sce new file mode 100644 index 000000000..9a1ca8516 --- /dev/null +++ b/3705/CH10/EX10.4/Ex10_4.sce @@ -0,0 +1,29 @@ + +clear//
+
+//Variable Declaration
+Le=7 //Effective Length in m
+N=2 //Factor of Safety
+h_max=400 //Maximum depth in mm
+E=200 //Youngs Modulus in GPa
+sigma_yp=250 //Maximum stress in yielding in MPa
+P1=400 //Load 1 in kN
+P2=900 //Load 2 in kN
+x1=75 //Distance in mm
+x2=125 //Distance in mm
+
+//Calculations
+e=(P2*x2-P1*x1)*(P1+P2)**-1 //Eccentricity in mm
+P=N*(P1+P2) //Applied load after factor of safety is considered in kN
+
+//Part 1 is not computable
+I=415*10**-6 //Moment of inertia from the table in mm^4
+
+//Part 2
+P_cr=%pi**2*E*10**9*I*Le**-2 //Critical load for buckling in kN
+FOS=P_cr*10**-3/(P1+P2) //Factor of safety against buckling in y-axis
+
+
+//Result
+printf("\n The critical load for buckling is %0.0f kN",P_cr*10**-3)
+printf("\n The factor of safety is %0.1f ",FOS)
diff --git a/3705/CH11/EX11.1/Ex11_1.sce b/3705/CH11/EX11.1/Ex11_1.sce new file mode 100644 index 000000000..c5a223e21 --- /dev/null +++ b/3705/CH11/EX11.1/Ex11_1.sce @@ -0,0 +1,28 @@ + +clear//
+
+//Variable Declaration
+V=1000 //Force acting on he section in lb
+t=0.5 //Thickness in inches
+//Dimensions
+d=8 //Depth of the section in inches
+wf=12 //Width of the flange in inches
+wbf=8 //Width of the bottom flange in inches
+
+//Calculations
+y_bar=((d*t*0)+wbf*t*4+wf*t*8)/(d*t+wbf*t+wf*t) //Location of Neutral Axis in inches
+I=d*t*y_bar**2+t*d**3*12**-1+d*t*(d*t-y_bar)**2+wf*t*(8-y_bar)**2 //Moment of Inertia in in^4
+
+//Top Flange
+q1=V*t*t*wf*(8-y_bar)*I**-1 //Shear flow in lb/in
+//Bottom Flange
+q2=V*t*t*d*y_bar*I**-1 //Shear Flow in lb/in
+//Web
+qB=2*q1 //Shear Flow in lb/in
+qF=2*q2 //Shear Flow in lb/in
+
+//Max Shear Flow
+qMAX=qB+V*t*(8-y_bar)**2*0.5*I**-1 //Maximum Shear Flow in lb/in
+
+//Result
+printf("\n The Maximum Shear Flow is %0.0f lb/in",qMAX)
diff --git a/3705/CH11/EX11.2/Ex11_2.sce b/3705/CH11/EX11.2/Ex11_2.sce new file mode 100644 index 000000000..dccd269c2 --- /dev/null +++ b/3705/CH11/EX11.2/Ex11_2.sce @@ -0,0 +1,26 @@ + +clear//
+
+//Variable Declaration
+V=1000 //Shear Force in lb
+t=0.5 //Thickness in inches
+wf=12 //Width of the flange in inches
+d=8 //Depth of the section in inches
+//Rest ALL DATA is similar to previous problem
+
+//Calcualtions
+I=t*wf**3*12**-1+t*d**3*12**-1 //Moment of Inertia
+
+//Part 1
+q1=V*t*t*wf*3*I**-1 //Shear Flow in lb/in
+q2=V*t*t*d*2*I**-1 //Shear FLow in lb/in
+V1=2*3**-1*q1*wf //Shear force carried in lb
+V2=2*3**-1*q2*d //Shear force carried in lb
+
+//Part 2
+e=8*V2*V**-1 //Eccentricity in inches
+
+//Result
+printf("\n The Shear Force carried by Flanges is")
+printf("\n Top Flange= %0.1f lb Bottom Flange= %0.1f lb",V1,V2)
+printf("\n The eccentricity is %0.3f in",e)
diff --git a/3705/CH11/EX11.3/Ex11_3.sce b/3705/CH11/EX11.3/Ex11_3.sce new file mode 100644 index 000000000..08382169c --- /dev/null +++ b/3705/CH11/EX11.3/Ex11_3.sce @@ -0,0 +1,25 @@ + +clear//
+//
+
+//Variable Declaration
+M=32 //Moment in kN.m
+Iy=4.73*10**6 //Moment of inertia in y-axis in mm^4
+Iz=48.9*10**6 //Moment of inertia in z-axis in mm^4
+Sy=64.7*10**3 //Sectional Modulus in y-axis in mm^3
+Sz=379*10**3 //Sectional Modulus in z-axis in mm^3
+theta=16.2 //Angle between moment and z-axis in degrees
+
+//Calculations
+//Part 1
+alpha=atan((Iz*Iy**-1)*tan(theta*%pi*180**-1))*180*%pi**-1 //Angle between NA and z-axis in degrees
+
+//Part 2
+My=-M*sin(theta*%pi*180**-1) //Bending Moment in y in kN.m
+Mz=-M*cos(theta*%pi*180**-1) //Bending Moment in z in kN.m
+
+sigma_max=My*Sy**-1+Mz*Sz**-1 //Largest Bending Stress in MPa
+
+//Result
+printf("\n The angle between the Neutral Axis and Z-Axis is %0.1f degrees",alpha)
+printf("\n The maximum Bending Moment is %0.0f MPa",-sigma_max*10**6)
diff --git a/3705/CH11/EX11.4/Ex11_4.sce b/3705/CH11/EX11.4/Ex11_4.sce new file mode 100644 index 000000000..8ea44dbb4 --- /dev/null +++ b/3705/CH11/EX11.4/Ex11_4.sce @@ -0,0 +1,37 @@ + +clear//
+
+//Variable Declaration
+A=4.75 //Area in inches^2
+Iy_dash=6.27 //Moment of inertia in in^4
+Iz_dash=17.4 //Moment of inertia in in^4
+ry=0.87 //Radius of Gyration in inches
+tan_theta=0.44
+P=1 //Force in kips
+L=48 //Length in inches
+y_dash_B=-4.01 //Y coordinate of point B in inches
+z_dash_B=-0.487 //Z coordinate of point B in inches
+
+//Calcualtions
+theta=atan(tan_theta) //Angle in radians
+Iy=A*ry**2 //Moment of inertia in y in in^4
+Iz=Iy_dash+Iz_dash-Iy //Moment of inertia in y in in^4
+
+//Part 1
+alpha=atan(Iz*Iy**-1*tan_theta)*180*%pi**-1 //Angle in radians
+beta=alpha-(theta*180*%pi**-1) //Angle in degrees
+
+//Part 2
+M=P*L*4**-1 //Moment in kip.in
+My=M*sin(theta) //Moment in y in kip.in
+Mz=M*cos(theta) //Moment in z in kip.in
+
+y_B=y_dash_B*cos(theta)+z_dash_B*sin(theta) //Y coordinate in inches
+z_B=z_dash_B*cos(theta)-y_dash_B*sin(theta) //Z coordinate in inches
+
+//Maximum Bending Stress
+sigma_max=My*z_B*Iy**-1-Mz*y_B*Iz**-1 //Maximum Bending Stress in ksi
+
+//Result
+printf("\n The angle of inclination of the Neutral axis to the z-axis is %0.1f degrees",beta)
+printf("\n The maximum Bending Stress is %0.2f ksi",sigma_max)
diff --git a/3705/CH11/EX11.5/Ex11_5.sce b/3705/CH11/EX11.5/Ex11_5.sce new file mode 100644 index 000000000..bfe4bfc74 --- /dev/null +++ b/3705/CH11/EX11.5/Ex11_5.sce @@ -0,0 +1,28 @@ + +clear//
+
+//Variable Declaration
+A1=4 //Area in in^2
+A2=6 //Area in in^2
+r1=7.8 //Radius in inches
+r2=14.8 //Radius in inches
+t=0.5 //Thickness in inches
+d=4 //Depth in inches
+sigma_w=18 //Maximum allowable stress in kips
+
+//Calculations
+A=A1+A2 //Area in in^2
+r_bar=(A1*(r1+t)+A2*(r2+d))*(A1+A2)**-1 //Centroidal Axis in inches
+//Simplfying the computation
+a=(r1+2*t)/r1
+b=r2/(r1+t*2)
+integral=d*log(a)+2*t*log(b) //
+R=A/integral //Radius of neutral Surface in inches
+
+//Maximum Stress
+//Answers are in variable terms hence not computable
+
+P=sigma_w/0.7847 //Maximum Allowable load in kips
+
+//Result
+printf("\n The maximum allowable load is %0.1f kips",P)
diff --git a/3705/CH12/EX12.1/Ex12_1.sce b/3705/CH12/EX12.1/Ex12_1.sce new file mode 100644 index 000000000..f168f9c28 --- /dev/null +++ b/3705/CH12/EX12.1/Ex12_1.sce @@ -0,0 +1,20 @@ + +clear//
+
+//Variable Declaration
+W=24*10**3 //Load in kips
+E=29*10**6 //Youngs Modulus in psi
+L=72 //length in inches
+theta=30 //Angle in degrees
+
+//Calculations
+L_ab=L/sin(theta*%pi*180**-1) //Length of AB in inches
+L_ac=L/sin((90-theta)*%pi*180**-1) //Length of AC in inches
+
+//Applying the forces in x and y sum to zero
+//Applying the follows energy formula
+//Applying Castiglinos theorem
+delta_A=91.16*W*E**-1 //Displacement in inches
+
+//Result
+printf("\n The displacement of point A is %0.4f in",delta_A)
diff --git a/3705/CH12/EX12.4/Ex12_4.sce b/3705/CH12/EX12.4/Ex12_4.sce new file mode 100644 index 000000000..b47cf530a --- /dev/null +++ b/3705/CH12/EX12.4/Ex12_4.sce @@ -0,0 +1,23 @@ + +clear//
+//
+
+//NOTE:The figure mentions the unit of length as ft which is incorrect
+//Variable Declaration
+L=30 //Length in m
+m=2000 //Mass in kg
+v=2 //Velocity in m/s
+E=10**5 //Youngs Modulus in MPa
+A=600 //Area in mm^2
+g=9.81 //Acceleration due to gravity in m/s^2
+
+//Calculations
+k=E*A*L**-1 //Stifness of the cable in N/m
+
+//Applying the Work-Energy principle
+delta_max=sqrt((0.5*m*v**2)*(0.5*k)**-1) //Maximum Displacement in m
+
+P_max=k*delta_max+m*g //Maximum force in N
+
+//Result
+printf("\n The maximum force is %0.1f kN",P_max*10**-3)
diff --git a/3705/CH12/EX12.5/Ex12_5.sce b/3705/CH12/EX12.5/Ex12_5.sce new file mode 100644 index 000000000..69ce31f2f --- /dev/null +++ b/3705/CH12/EX12.5/Ex12_5.sce @@ -0,0 +1,27 @@ + +clear//
+
+//Variable Declaration
+b=0.060 //Breadth of the section in mm
+d=0.03 //Depth of the section in mm
+L=1.2 //Length in m
+m=80 //Mass in kg
+g=9.81 //Acceleration due to gravity in m/s^2
+E=200*10**9 //Youngs Modulus in Pa
+e=0.015
+h=0.01 //height in m
+
+//Calculations
+//Part 1
+I=b*d**3*12**-1 //Moment of Inertia in m^4
+delta_st=m*g*L**3/(48*E*I) //Mid-span Displacement in m
+n=1+sqrt(1+(2*h/delta_st)) //Impact Factor
+
+//Part 2
+P_max=n*m*g //Maximum dynamic load in N at midspan
+M_max=P_max*0.5*L*0.5 //Maximum moment in N.m
+sigma_max=M_max*e/I //Maximum dynamic Bending Stress in Pa
+
+//Result
+printf("\n The impact factor is %0.3f ",n)
+printf("\n The maximum dynamic Bending Moment is %0.1f MPa",sigma_max*10**-6)
diff --git a/3705/CH12/EX12.7/Ex12_7.sce b/3705/CH12/EX12.7/Ex12_7.sce new file mode 100644 index 000000000..b73033b48 --- /dev/null +++ b/3705/CH12/EX12.7/Ex12_7.sce @@ -0,0 +1,20 @@ + +clear//
+
+//Variable Declaration
+M=2.21 //Applied moment in kip.ft
+d=3 //Diameter of the bar in inches
+sigma_y=40 //Yield strength of the of steel in ksi
+
+//Calculations
+//Part 1
+sigma=32*M*12*(%pi*d**3)**-1 //Maximum Bending Stress in ksi
+T1=sqrt((sigma_y*0.5)**2-5**2)/(12*0.18863) //Maximum Allowable torque in kip.ft
+
+//Part 2
+R=sqrt((sigma_y**2-5**2)*3**-1) //Maximum shear stress in ksi
+T2=sqrt(R**2-5**2)/(12*0.18863) //Maximum safe torque in kpi.ft
+
+//Result
+printf("\n Using the maximum shear stress theory T= %0.2f kip.ft",T1)
+printf("\n Using the maximum sitrotion energy theory T= %0.2f kip.ft",T2)
diff --git a/3705/CH12/EX12.8/Ex12_8.sce b/3705/CH12/EX12.8/Ex12_8.sce new file mode 100644 index 000000000..9b7ebee9d --- /dev/null +++ b/3705/CH12/EX12.8/Ex12_8.sce @@ -0,0 +1,24 @@ + +clear//
+
+//Variable Declaration
+D=250 //Wideness in mm
+b=20 //Thickness of the plate in mm
+r=50 //Radius of the hole in mm
+e=50 //Eccentricity in mm
+sigma_max=150 //Maximum normal stress at the hole in MPa
+kb=2 //Stress Concentraion factor
+
+//Calculations
+A=b*(D-2*r)*10**-6 //Area in m^2
+I=10**-12*(b*D**3*12**-1-(b*2**3*r**3*12**-1)) //Moment of inertia in m^4
+//Simplfying computation
+a=2*r*D**-1
+kt=3-3.13*a+3.66*a**2-1.53*a**3 //Stress Concentration factor
+//Simplfying computation
+b=kt*A**-1
+c=kb*r*r*10**-6*I**-1
+P=10**3*sigma_max*(b+c)**-1 //Maximum Load in N
+
+//Result
+printf("\n The maximum value of P is %0.1f kN",P)
diff --git a/3705/CH13/EX13.1/Ex13_1.sce b/3705/CH13/EX13.1/Ex13_1.sce new file mode 100644 index 000000000..caa62df4c --- /dev/null +++ b/3705/CH13/EX13.1/Ex13_1.sce @@ -0,0 +1,26 @@ + +clear//
+
+//Variable Declaration
+d=150 //Depth of the web in mm
+wf=100 //Width of the flange in mm
+df=20 //Depth of the flange in mm
+t=20 //Thickness of the web in mm
+
+//Calculations
+y_bar=10**-3*(((wf*df*(d+df*0.5))+(d*t*d*0.5))/(wf*df+d*t)) //Distance of Neutral Axis in m
+//Simplfying the computation
+a=wf*df**3*12**-1
+b=wf*df*((d+df*0.5)-y_bar*10**3)**2
+c=t*d**3*12**-1
+f=t*d*((d*0.5)-y_bar*10**3)**2
+I=(a+b+c+f)*10**-12 //Moment of inertia in mm^3
+
+//Limit Moment
+yp=(wf*df+d*t)/(2*t) //Plastic Neutral Axis in mm
+Myp=I/y_bar //Yielding will start at moment without the stress term to ease computation
+mom=10**-9*((t*yp**2*0.5)+(wf*df*(d-yp+10))+(t*25**2*0.5)) //Sum of 1st moments
+Ml_Myp=mom*Myp**-1 //Ratio
+
+//Result
+printf("\n The ratio ML/Myp= %0.3f ",Ml_Myp)
diff --git a/3705/CH13/EX13.2/Ex13_2.sce b/3705/CH13/EX13.2/Ex13_2.sce new file mode 100644 index 000000000..051a9aaa2 --- /dev/null +++ b/3705/CH13/EX13.2/Ex13_2.sce @@ -0,0 +1,36 @@ + +clear//
+//
+
+//Variable Declaration
+E_st=200 //Youngs Modulus of Steel in GPa
+sigma_st_yp=290 //Yielding Stress in MPa
+E_al=70 //Youngs Modulus of Aluminium in GPa
+sigma_al_yp=330 //Yielding Stresss of Aluminium in MPa
+A_st=900 //Area of steel rod in mm^2
+A_al=600 //Area of Aluminium rod in mm^2
+L_st=350 //Length of the steel rod in mm
+L_al=250 //Length of the aluminium rod in mm
+
+//Calculations
+//Limit Load
+P_st=sigma_st_yp*A_st*10**-3 //Load in limiting condition in kN
+P_al=sigma_al_yp*A_al*10**-3 //Load in limiting condition in kN
+P_L=P_st+2*P_al //Total Loading in kN
+
+//Elastic Unloading
+//Solving for Pst and Pal using matri approach
+A=([[1,2;L_st*(E_st*A_st)**-1,-L_al*(E_al*A_al)**-1]])
+B=([P_L;0])
+C=linsolve(A,B) //Loading in kN
+
+//Residual Stresses
+P_res_st=-C(1)-P_st //Residual Load in kN
+P_res_al=-C(2)-P_al //Residual Load in kN
+sigma_st=P_res_st/A_st //residual Stress in Steel in MPa
+sigma_al=P_res_al/A_al //residual Stress in Aluminium in MPa
+
+
+//Result
+printf("\n The Residual stresses are as follows")
+printf("\n Sigma_st= %0.1f MPa and sigma_al= %0.1f MPa",sigma_st*10**3,sigma_al*10**3)
diff --git a/3705/CH14/EX14.1/Ex14_1.sce b/3705/CH14/EX14.1/Ex14_1.sce new file mode 100644 index 000000000..1dcedf9b5 --- /dev/null +++ b/3705/CH14/EX14.1/Ex14_1.sce @@ -0,0 +1,16 @@ + +clear//
+
+//Variable Declaration
+A=2000 //Area of the plane in mm^2
+Ix=40*10**6 //Momnet of Inertia in mm^4
+d1=90 //Distance in mm
+d2=70 //Distance in mm
+
+//Calculations
+Ix_bar=Ix-(A*d1**2) //Moment of Inertia along x_bar axis in mm^4
+Iu=Ix_bar+A*d2**2 //Moment of Inertia along U-axis in mm^4
+
+//Result
+printf("\n Ix_bar")
+printf("\n The moment of inertia along u-axis is %0.1f mm^4",Iu)
diff --git a/3705/CH14/EX14.2/Ex14_2.sce b/3705/CH14/EX14.2/Ex14_2.sce new file mode 100644 index 000000000..33f4e0e3b --- /dev/null +++ b/3705/CH14/EX14.2/Ex14_2.sce @@ -0,0 +1,41 @@ + +clear//
+
+//Variable Declaration
+R=45 //Radius of the circle in mm
+r=20 //Radius of the smaller circle in mm
+h=100 //Depth of the straight section in mm
+
+//Calculations
+//Part 1
+
+//Triangle
+b=2*R //Breadth in mm
+A_t=b*h*0.5 //Area in mm^2
+Ix_bar_t=b*h**3*36**-1 //Moment of inertia in mm^4
+y_bar1=2*3**-1*h //centroidal axis in mm
+Ix_t=Ix_bar_t+A_t*y_bar1**2 //moment of inertia in mm^4
+
+//Semi-circle
+A_sc=%pi*R**2*0.5 //Area of the semi-circle in mm^2
+Ix_bar_sc=0.1098*R**4 //Moment of inertia in mm^4
+y_bar2=h+(4*R*(3*%pi)**-1) //Distance of centroid in mm
+Ix_sc=Ix_bar_sc+A_sc*y_bar2**2 //Moment of inertia in mm^4
+
+//Circle
+A_c=%pi*r**2 //Area of the circle in mm^2
+Ix_bar_c=%pi*r**4*4**-1 //Moment of inertia in mm^4
+y_bar3=h //Distance of centroid in mm
+Ix_c=Ix_bar_c+A_c*y_bar3**2 //Moment of inertia in mm^4
+
+//Composite Area
+A=A_t+A_sc-A_c //Total area in mm^2
+Ix=Ix_t+Ix_sc-Ix_c //Moment of inertia in mm^4
+
+//Part 2
+y_bar=(A_t*y_bar1+A_sc*y_bar2-A_c*y_bar3)/(A) //Location of centroid in mm
+Ix_bar=Ix-A*y_bar**2 //Moment of inertia in mm^4
+
+//Result
+printf("\n Moment of inertia about x-axis is %0.0f mm^4",Ix)
+printf("\n Moment of inertia about the centroidal axis is %0.0f mm^4",Ix_bar)
diff --git a/3705/CH14/EX14.3/Ex14_3.sce b/3705/CH14/EX14.3/Ex14_3.sce new file mode 100644 index 000000000..55c316531 --- /dev/null +++ b/3705/CH14/EX14.3/Ex14_3.sce @@ -0,0 +1,15 @@ + +clear//
+
+//Variable Declaration
+t=20 //Thickness in mm
+h=140 //Depth in mm
+w=180 //Width in mm
+
+//Calculations
+Ixy_1=0+(h*t*t*0.5*h*0.5) //product of inertia in mm^4
+Ixy_2=0+((w-t)*t*(w+t)*0.5*t*0.5) //Product of inertia in mm^4
+Ixy=Ixy_1+Ixy_2 //Product of inertia in mm^4
+
+//Result
+printf("\n The Product of inertia is %0.0f mm^4",Ixy)
diff --git a/3705/CH14/EX14.4/Ex14_4.sce b/3705/CH14/EX14.4/Ex14_4.sce new file mode 100644 index 000000000..e6028d7f9 --- /dev/null +++ b/3705/CH14/EX14.4/Ex14_4.sce @@ -0,0 +1,58 @@ + +clear//
+
+//Variable Declaration
+t=30 //Thickness in mm
+h=200 //Depth of the section in mm
+w=160 //Width in mm
+the=50 //Angle in degrees
+
+
+//Calculations
+A1=t*h //Area of the web portion in mm^2
+A2=(w-t)*t //Area of the flange portion in mm^2
+x_bar=(A1*t*0.5+A2*(t+(w-t)*0.5))/(A1+A2) //Location of x_bar in mm
+y_bar=(A1*h*0.5+A2*t*0.5)/(A1+A2) //Location of y_bar in mm
+
+//Simplfying the computation
+a=t*h**3*12**-1
+b=A1*(200*0.5-y_bar)**2
+c=(w-t)*t**3*12**-1
+d=A2*(t*0.5-y_bar)**2
+Ix_bar=a+b+c+d //Moment of inertia about x-axis in mm^4
+
+//Simplifying the computation
+p=h*t**3*12**-1
+q=A1*(t*0.5-x_bar)**2
+r=t*(w-t)**3*12**-1
+s=A2*((w-t)*0.5+t-x_bar)**2
+Iy_bar=p+q+r+s //Moment of inertia about y-axis in mm^4
+
+//Simplfying the computation
+a1=(t*0.5-x_bar)*(h*0.5-y_bar)
+a2=(t*0.5-y_bar)*((w-t)*0.5+t-x_bar)
+Ixy_bar=A1*a1+A2*a2 //Moment of inertia in mm^4
+
+//Part 1
+//Simplfying the computation
+a3=(Ix_bar+Iy_bar)*0.5
+a4=(0.5*(Ix_bar-Iy_bar))**2
+a5=Ixy_bar**2
+I1=a3+sqrt(a4+a5) //Moment of inertia in mm^4
+I2=a3-sqrt(a4+a5) //Moment of inertia in mm^4
+
+ThetaRHS=-(2*Ixy_bar)/(Ix_bar-Iy_bar) //RHS of the tan term
+theta1=atan(ThetaRHS)*0.5*180*%pi**-1 //Angle in degrees
+theta2=theta1+90 //Angle in degrees
+
+//Part 2
+Iu=a3+sqrt(a4)*cos(2*the*%pi*180**-1)-(Ixy_bar)*sin(2*the*%pi*180**-1) //Moment of inertia in mm^4
+Iv=a3-sqrt(a4)*cos(2*the*%pi*180**-1)+(Ixy_bar)*sin(2*the*%pi*180**-1) //Moment of inertia in mm^4
+Iuv=sqrt(a4)*sin(2*the*%pi*180**-1)+(Ixy_bar)*cos(2*the*%pi*180**-1) //Moment of inertia in mm^4
+
+
+//Result
+printf("\n The Principal Moment of inertias are as follows")
+printf("\n I1= %0.0f mm^4 and I2= %0.0f mm^4",I1,I2)
+printf("\n Princial direction are theta1= %0.1f degrees theta2= %0.1f degrees",theta1,theta2)
+printf("\n The moment of inertia along the uv-axis is %0.0f mm^4" ,Iuv)
diff --git a/3705/CH14/EX14.5/Ex14_5.sce b/3705/CH14/EX14.5/Ex14_5.sce new file mode 100644 index 000000000..799cc3e53 --- /dev/null +++ b/3705/CH14/EX14.5/Ex14_5.sce @@ -0,0 +1,31 @@ + +clear//
+
+//Variable Declaration
+Ix_bar=37.37*10**6 //Moment of inertia in mm^4
+Iy_bar=21.07*10**6 //Moment of inertia in mm^4
+Ixy_bar=-16.073*10**6 //Moment of inertia in mm^4
+
+//Calculations
+b=(Ix_bar+Iy_bar)*0.5 //Parameter for the circle in mm^4
+R=sqrt(((Ix_bar-Iy_bar)*0.5)**2+Ixy_bar**2) //Radius of the Mohr's Circle in mm^4
+
+//Part 1
+I1=b+R //MI in mm^4
+I2=b-R //MI in mm^4
+theta1=asin(abs(Ixy_bar)/R)*180*%pi**-1*0.5 //Angle in degrees
+theta2=theta1+90 //Angle in degrees
+
+//Part 2
+alpha=(100-theta1*2)*0.5 //Angle in degrees
+Iu=(b)+R*(cos(alpha*%pi*180**-1)) //MI in mm^4
+
+Iv=(b)-R*(cos(alpha*%pi*180**-1)) //MI in mm^4
+
+Iuv=R*sin(2*alpha*%pi*180**-1) //MI in mm^4
+
+//Result
+printf("\n The Principal Moment of inertias are as follows")
+printf("\n I1= %0.0f mm^4 and I2= %0.0f mm^4",I1,I2)
+printf("\n Princial direction are theta1= %0.1f degrees theta2= %0.1f degrees" ,theta1,theta2)
+printf("\n The moment of inertia along the uv-axis is %0.0f mm^4" ,Iuv)
diff --git a/3705/CH2/EX2.1/Ex2_1.sce b/3705/CH2/EX2.1/Ex2_1.sce new file mode 100644 index 000000000..0a3263ff0 --- /dev/null +++ b/3705/CH2/EX2.1/Ex2_1.sce @@ -0,0 +1,31 @@ + +clear//
+
+//Variable Declaration
+//Axial Forces in lb in member AB, BC and CD
+P_AB=2000
+P_BC=2000
+P_CD=4000
+//Other Variables
+E=29*10**6 //Modulus of Elasticity in psi
+//Length of each member in inches
+L_AB=5*12
+L_BC=4*12
+L_CD=4*12
+//Diameter of each member in inches
+D_AB=0.5
+D_BC=0.75
+D_CD=0.75
+
+//Calculation
+//Area Calculation of each member in square inches
+A_AB=(%pi*D_AB**2)/4
+A_BC=(%pi*D_BC**2)/4
+A_CD=(%pi*D_CD**2)/4
+
+//Using relation delta=(PL/AE) to compute strain
+//As stress in Member CD is compression
+delta=(E**-1)*((P_AB*L_AB*A_AB**-1)+(P_BC*L_BC*A_BC**-1)-(P_CD*L_CD*A_CD**-1))
+
+//Result
+printf("\n The elongation in the total structure is %0.5f in",delta)
diff --git a/3705/CH2/EX2.10/Ex2_10.sce b/3705/CH2/EX2.10/Ex2_10.sce new file mode 100644 index 000000000..2d7dee6b1 --- /dev/null +++ b/3705/CH2/EX2.10/Ex2_10.sce @@ -0,0 +1,21 @@ + +clear//
+
+//Variable Declaration
+L=2.5 //Length in m
+A=1200 //Cross sectional Area in mm^2
+delta_T=40 //Temperature drop in degree C
+delta=0.5*10**-3 //Movement of the walls in mm
+alpha=11.7*10**-6 //Coefficient of thermal expansion in /degreeC
+E=200*10**9 //Modulus of elasticity in Pa
+
+//Calculation
+//Part(1)
+sigma_1=alpha*delta_T*E //Stress in the rod in Pa
+
+//Part(2)
+//Using Hookes Law
+sigma_2=E*((alpha*delta_T)-(delta*L**-1)) //Stress in the rod in Pa
+
+printf("\n The Stress in part 1 in the rod is %0.1f MPa",sigma_1*10**-6)
+printf("\n The Stress in part 2 in the rod is %0.1f MPa",sigma_2*10**-6)
diff --git a/3705/CH2/EX2.11/Ex2_11.sce b/3705/CH2/EX2.11/Ex2_11.sce new file mode 100644 index 000000000..ec18a18c6 --- /dev/null +++ b/3705/CH2/EX2.11/Ex2_11.sce @@ -0,0 +1,32 @@ + +clear//
+
+//Variable Declaration
+delta=100 //Increase in the temperature in degreeF
+Load=12000 //Load on the beam in lb
+//Length in inch
+Ls=2*12 //Steel
+Lb=3*12 //Bronze
+//Area in sq.in
+As=0.75 //Steel
+Ab=1.5 //Bronze
+//Modulus of elasticity in psi
+Es=29*10**6 //Steel
+Eb=12*10**6 //Bronze
+//Coefficient of thermal expansion in /degree C
+alpha_s=6.5*10**-6 //Steel
+alpha_b=10**-5 //Bronze
+
+//Calculations
+//Applying the Hookes Law and equilibrium we get two equations
+a=([[Ls*(Es*As)**-1,-Lb*(Eb*Ab)**-1;2,1]])
+b=([(alpha_b*delta*Lb-alpha_s*delta*Ls);Load])
+y=linsolve(a,b)
+
+//Stresses
+sigma_st=-y(1)*As**-1 //Stress in steel in psi (T)
+sigma_br=-y(2)*Ab**-1 //Stress in bronze in psi (C)
+
+//Result
+printf("\n The Stress in steel and bronze are as follows")
+printf("\n %0.3f psi (T) and %0.3f psi(C)",sigma_st,sigma_br)
diff --git a/3705/CH2/EX2.12/Ex2_12.sce b/3705/CH2/EX2.12/Ex2_12.sce new file mode 100644 index 000000000..072603d85 --- /dev/null +++ b/3705/CH2/EX2.12/Ex2_12.sce @@ -0,0 +1,16 @@ + +clear//
+
+//Variable Declaration
+P=6000 //Force in lb
+Est=29*10**6 //Modulus of elasticity of steel in psi
+L1=24 //Length in inches
+L2=36 //Length in inches
+alpha_1=6.5*10**-6 //coefficient of thermal expansion in /degree F of steel
+alpha_2=10**-5 //coefficient of thermal expansion in /degree F of bronze
+As=0.75 //Area os steel in sq.in
+
+//Calculations
+delta_T=((P*L1)/(Est*As))/(alpha_2*L2-alpha_1*L1) //Change in temperature in degree F
+
+printf("\n The change in the Temperature is %0.1f F",delta_T)
diff --git a/3705/CH2/EX2.3/Ex2_3.sce b/3705/CH2/EX2.3/Ex2_3.sce new file mode 100644 index 000000000..c6a5bb43d --- /dev/null +++ b/3705/CH2/EX2.3/Ex2_3.sce @@ -0,0 +1,21 @@ + +clear//
+
+//Variable Decelration
+A_AC=0.25 //Cross Sectional Area in square inch
+Load=2000 //Load at point C in lb
+E=29*10**6 //Modulus of elasticity in psi
+theta=(%pi*40)/180 //Angle in radians
+L_BC=8 //Length in ft
+
+//Calculations
+//Using sum of forces
+P_AC=Load/sin(theta) //Force in cable AC in lb
+L_AC=(L_BC*12)/cos(theta) //Length of cable AC in in
+
+delta_AC=(P_AC*L_AC)/(E*A_AC) //elongation in inches
+
+delta_C=delta_AC/sin(theta) //displacement of point C in inches
+
+//Result
+printf("\n The displacement of point C is %0.4f in",delta_C)
diff --git a/3705/CH2/EX2.4/Ex2_4.sce b/3705/CH2/EX2.4/Ex2_4.sce new file mode 100644 index 000000000..1eb211300 --- /dev/null +++ b/3705/CH2/EX2.4/Ex2_4.sce @@ -0,0 +1,24 @@ + +clear//
+
+//Variable Declaration
+d=0.05 //Diameter of the rod in mm
+P=8000 //Load on the bar in N
+E=40*10**6 //Modulus of elasticity in Pa
+v=0.45 //Poisson Ratio
+L=300 //Length of the rod in mm
+
+//Calculation
+A=((%pi*d**2)/4) //Area of the bar in mm^2
+sigma_x=-P/A //Axial Stress in the bar in Pa
+//As contact pressure resists the force
+p=(v*sigma_x)/(1-v)
+//Using Axial Strain formula
+e_x=(sigma_x-(v*2*p))/E
+//Corresponding change in length
+delta=e_x*L //contraction in mm
+//Without constrains of the wall
+delta_w=(-P*(L*10**-3))/(E*A) //Elongation in m
+
+//Result
+printf("\n The elongation in the bar is %0.2f mm contraction",delta)
diff --git a/3705/CH2/EX2.5/Ex2_5.sce b/3705/CH2/EX2.5/Ex2_5.sce new file mode 100644 index 000000000..b5b3417d6 --- /dev/null +++ b/3705/CH2/EX2.5/Ex2_5.sce @@ -0,0 +1,19 @@ + +clear//
+
+//Variable Declaration
+E=500 //Modulus of elasticity in psi
+v=0.48 //Poisson ratio
+V=600 //Force in lb
+w=5 //Width of the plate in inches
+l=9 //Length of the plate in inches
+t=1.75 //Thickness of the rubber layer in inches
+
+//Calculations
+tau=V*(w*l)**-1 //Shear stress in rubber in psi
+G=E/(2*(1+v)) //Bulk modulus in psi
+gamma=tau/G //Shear Modulus
+disp=t*gamma //Diplacement in inches
+
+//Result
+printf("\n The displacement of the rubber layer is %0.4f in",disp)
diff --git a/3705/CH2/EX2.6/Ex2_6.sce b/3705/CH2/EX2.6/Ex2_6.sce new file mode 100644 index 000000000..97cc0b4b0 --- /dev/null +++ b/3705/CH2/EX2.6/Ex2_6.sce @@ -0,0 +1,22 @@ + +clear//
+
+//Variable Declaration
+P=10**6 //Force on the member in N
+Es=200 //Modulus of elasticity of steel in GPa
+Ec=14 //Modulus of elasticity concrete in GPa
+As=900*10**-6 //Area of steel in m^2
+Ac=0.3**2 //Area of concrete block in m^2
+
+//Calculation
+//Cross Sectional Areas
+Ast=4*As //Cross Sectional Area in m^2 of Steel
+Act=Ac-Ast //Cross Sectional Area of Concrete in m^2
+
+//Applying equilibrium to the structure
+//Using the ratio of stress and modulii of elasticity we obtain the following eq
+sigma_ct=P/(((Es*Ec**-1)*Ast)+Act) //Stress in Concrete in Pa
+sigma_st=sigma_ct*Es*Ec**-1 //Stress in Steel in Pa
+
+//Result
+printf("\n The stress in steel and concrete is as follows %0.1f MPa and %0.3f Mpa respectively",sigma_st*10**-6,sigma_ct*10**-6)
diff --git a/3705/CH2/EX2.7/Ex2_7.sce b/3705/CH2/EX2.7/Ex2_7.sce new file mode 100644 index 000000000..9008e96b4 --- /dev/null +++ b/3705/CH2/EX2.7/Ex2_7.sce @@ -0,0 +1,17 @@ + +clear//
+
+//Variable Declaration
+//Say the ratio of stress in steel to concrete is R
+R=14.286
+sigma_co=6*10**6 //Stress in concrete in Pa
+Ast=3.6*10**-3 //Area of steel in m^2
+Aco=86.4*10**-3 //Area of Concrete in m^2
+
+//Calculation
+sigma_st=R*sigma_co //Stress in steel in Pa
+//Here stress is below the allowable hence safe
+P=sigma_st*Ast+sigma_co*Aco //Allowable force in N
+
+//Result
+printf("\n The maximum allowable force is %0.0f kN",P*10**-3)
diff --git a/3705/CH2/EX2.8/Ex2_8.sce b/3705/CH2/EX2.8/Ex2_8.sce new file mode 100644 index 000000000..6f0fac5eb --- /dev/null +++ b/3705/CH2/EX2.8/Ex2_8.sce @@ -0,0 +1,31 @@ + +clear//
+
+//NOTE:The NOtation has been changed to ease coding
+//Variable Declaration
+d=0.005 //difference in length in inch
+L=10 //Length in inch
+//Area of copper and aluminium in sq.in
+Ac=2 //Area of copper
+Aa=3 //Area of aluminium
+//Modulus of elasticity of copper and aluminium in psi
+Ec=17000000 //Copper
+Ea=10**7 //Aluminium
+//Allowable Stress in psi
+Sc=20*10**3 //Copper
+Sa=10*10**3 //Aluminium
+
+//Calculation
+//Equilibrium is Pc+Pa=P
+//Hookes Law is delta_c=delta_a+0.005
+//Simplfying the solution we have constants we can directly compute
+A=d*Ec*(L+d)**-1
+B=Ec*Ea**-1
+C=L*B*(L+d)**-1
+sigma_a=(Sc-A)*C**-1
+
+//Using equilibrium equation
+P=Sc*Ac+sigma_a*Aa //Safe load in lb
+
+//Result
+printf("\n The safe load on the structure is %0.0f lb",P)
diff --git a/3705/CH2/EX2.9/Ex2_9.sce b/3705/CH2/EX2.9/Ex2_9.sce new file mode 100644 index 000000000..e71d0274e --- /dev/null +++ b/3705/CH2/EX2.9/Ex2_9.sce @@ -0,0 +1,31 @@ + +clear//
+//
+
+//Variable Declaration
+P=50*10**3 //Load applied in N
+x1=0.6 //Length in m
+x2=1.6 //Length in m
+L1=1 //Length of steel cable in m
+L2=2 //Length of bronze cable in m
+L=2.4 //Length in m
+//Area in m^2
+Ast=600*10**-6 //Steel
+Abr=300*10**-6 //Bronze
+//Modulus of elasticity in GPa
+Est=200 //Steel
+Ebr=83 //Bronze
+
+//Calculations
+//Applying the equilibrium and Hookes law we solve by matrix method
+a=[x1,x2;1,-((x1*Est*Ast*L2)/(x2*Ebr*Abr))]
+b=([L*P;0])
+y=linsolve(a,b)
+
+//Stresses in Pa
+sigma_st=-y(1)*Ast**-1 //Stress in steel
+sigma_br=-y(2)/Abr //Stress in bronze
+
+//Result
+printf("\n The stresses in steel and bronze are as follows")
+printf("\n %0.1f MPa and %0.1f MPa respectively",sigma_st*10**-6,sigma_br*10**-6)
diff --git a/3705/CH3/EX3.1/Ex3_1.sce b/3705/CH3/EX3.1/Ex3_1.sce new file mode 100644 index 000000000..1888f20e2 --- /dev/null +++ b/3705/CH3/EX3.1/Ex3_1.sce @@ -0,0 +1,22 @@ + +clear//
+
+//Variable Declaration
+P=20*10**3 //Power in W
+f=2 //Frequency in Hz
+t_max=40*10**6 //Maximum shear stress in Pa
+G=83*10**9 //Bulk modulus in Pa
+theta=(6*%pi)/180 //Angle of twist in radians
+L=3 //Length in m
+
+//Calculations
+//Strength condition
+T=P/(2*%pi*f) //Torque in N.m
+d1=((16*T)/(%pi*t_max))**0.333 //Max allowable diameter in mm
+
+//Applying torque-twist relationship
+d2=((32*T*L)/(G*theta*%pi))**0.25 //Diameter in mm
+
+d=max(d1,d2)
+
+printf("\n To satisfy both strength and rigidity conditions d= %0.1f mm",d*1000)
diff --git a/3705/CH3/EX3.2/Ex3_2.sce b/3705/CH3/EX3.2/Ex3_2.sce new file mode 100644 index 000000000..18a7deeea --- /dev/null +++ b/3705/CH3/EX3.2/Ex3_2.sce @@ -0,0 +1,24 @@ + +clear//
+
+//Variable Declaration
+Ga=4*10**6 //Bulk modulus of Aluminium in psi
+Gs=12*10**6 //Bulk Modulus of Steel in psi
+T=10**4 //Torque in lb.in
+L1=3 //Length in ft of the Steel bar
+L2=6 //Length in ft of the Aluminium bar
+d1=3 //Diameter of the Aluminium bar in inches
+d2=2 //Diameter of the Steel bar in inches
+
+//Calculations
+//Using Compatibility and equlibrium conditions
+a=([[1,1;(L1*32)/(Gs*%pi*d2**4),-((L2*32)/(Ga*d1**4*%pi))]])
+b=([T;0])
+y=linsolve(a,b)
+
+//Stresses
+t_max_st=(16*-y(1))/(%pi*d2**3) //Max shear Stress in Steel in psi
+t_max_al=(16*-y(2))/(%pi*d1**3) //Max shear stress in aluminium in psi
+
+printf("\n The maximum values of Shear Stresses are as follows")
+printf("\n %0.1f psi in Steel and %0.1f psi in aluminium",(t_max_st),t_max_al)
diff --git a/3705/CH3/EX3.3/Ex3_3.sce b/3705/CH3/EX3.3/Ex3_3.sce new file mode 100644 index 000000000..e6cd078f9 --- /dev/null +++ b/3705/CH3/EX3.3/Ex3_3.sce @@ -0,0 +1,26 @@ + +clear//
+
+//Variable Declaration
+d=2 //Diameter in ft
+G=12*10**6 //Bulk Modulus in psi
+//Torque in lb.ft
+T1=500 //Torque 1
+T2=900 //Torque 2
+T3=1000 //Torque 3
+//Length in ft
+L1=4
+L2=3
+L3=5
+
+//Calculations
+//Applying the sum of torques we get
+Tab=T1 //Torque at section AB in lb.ft
+Tbc=-T2+T1 //Torque at section BC in lb.ft
+Tcd=T3-T2+T1 //Torque at Section CD in lb.ft
+
+//Summing the angle of twists
+theta_r=(((Tab*12*L3*12)+(Tbc*12*L2*12)+(Tcd*12*L1*12))*32)/(%pi*2**4*G)
+theta=(theta_r*180)/%pi //Angle in degrees
+
+printf("\n The angle of twist is %0.3f degrees",theta)
diff --git a/3705/CH3/EX3.4/Ex3_4.sce b/3705/CH3/EX3.4/Ex3_4.sce new file mode 100644 index 000000000..9382d9354 --- /dev/null +++ b/3705/CH3/EX3.4/Ex3_4.sce @@ -0,0 +1,28 @@ + +clear//
+
+//Variable Declaration
+L=1.5 //Length of the shaft in m
+t_B=200 //Torque per unit length in N.m/m
+d=0.025 //Diameter of the shaft in m
+G=80*10**9 //Bulk Modulus for steel in Pa
+
+
+//Calculations
+//Part(1)
+//After carrying out the variable integration
+T_A=0.5*t_B*L //Torque about point A in N.m
+//Using equation of max stress
+tau_Max=(16*T_A)*(%pi*d**3)**-1 //Maximum stress in the shaft in Pa
+
+//Part(2)
+J=(%pi*d**4)*32**-1 //Polar moment of inertia in m^4
+//After carrying out the computation for angle of twist we get
+theta_r=(t_B*L**2)*(3*G*J)**-1 //Angle of twist in radians
+theta=theta_r*(180*%pi**-1) //Angle of twist in degrees
+
+//Result
+printf("\n Result for part (1)")
+printf("\n Maximum Shear Stress in the shaft is %0.1f MPa",tau_Max/10**6)
+printf("\n Result for part (2)")
+printf("\n The angle of twist in the shaft is %0.2f degrees",theta)
diff --git a/3705/CH3/EX3.5/Ex3_5.sce b/3705/CH3/EX3.5/Ex3_5.sce new file mode 100644 index 000000000..7a9420cde --- /dev/null +++ b/3705/CH3/EX3.5/Ex3_5.sce @@ -0,0 +1,30 @@ + +clear//
+
+//Variable Declaration
+L=6 //Length of the tube in ft
+t=3*8**-1 //Constant wall thickness in inches
+G=12*10**6 //Bulk modulus of the tube in psi
+w1=6 //Width on the top in inches
+w2=4 //Width at the bottom in inches
+h=5 //Height in inches
+theta=0.5 //Angle of twist in radians
+
+//Calculations
+//Part(1)
+Ao=(w1+w2)*2**-1*h //Area enclosed by the median line in sq.in
+S=w1+w2+2*(sqrt(1**2+h**2)) //Length of the median line in inches
+//Using the torsional stifness formula we get
+k=4*G*Ao**2*t*(L*12*S)**-1*(%pi*180**-1) //tortional Stiffness in lb.in/rad
+
+//Part(2)
+T=k*theta //Torque required to produce an angle of twist of theta in lb.in
+q=T*(2*Ao)**-1 //Shear flow in lb/in
+tau=q/t //Shear stress in the wall in psi
+
+
+//Result
+printf("\n Part(1) results")
+printf("\n Torsional stiffness is %0.0f lb.in/deg",k)
+printf("\n Part(2) results")
+printf("\n The shear stress in the wall is %0.0f psi",tau)
diff --git a/3705/CH3/EX3.6/Ex3_6.sce b/3705/CH3/EX3.6/Ex3_6.sce new file mode 100644 index 000000000..0c743d44d --- /dev/null +++ b/3705/CH3/EX3.6/Ex3_6.sce @@ -0,0 +1,29 @@ + +clear//
+
+//Variable Declaration
+L=1.2 //Length of the tube in m
+tau=40*10**6 //MAximum shear stress in MPa
+t=0.002 //Thickness in m
+r=0.025 //Radius of the semicircle in m
+G=28*10**9 //Bulk Modulus in Pa
+t1=2 //Thickness in mm
+t2=3 //thickness in mm
+
+//Calculations
+//Part(1)
+q=tau*t //Shear flow causing the stress in N/m
+Ao=%pi*r**2*0.5 //Area of the semi-circle in m^2
+T=2*Ao*q //Torque causing the shear stress in N.m
+
+//Part(2)
+//After computing the median lines integration we get
+S=(%pi*25*t1**-1)+(2*25*t2**-1) //Length of median line
+theta_r=T*L*S*(4*G*Ao**2)**-1 //Angle of twist in radians
+theta=theta_r*(180*%pi**-1) //Angle of twist in degrees
+
+//Result
+printf("\n Result for part(1)")
+printf("\n The torque causing the stress of 40MPa is %0.2f N.m",T)
+printf("\n Result for part (2)")
+printf("\n The angle of twist is %0.1f degrees",theta)
diff --git a/3705/CH4/EX4.6/Ex4_6.sce b/3705/CH4/EX4.6/Ex4_6.sce new file mode 100644 index 000000000..e330f4f3c --- /dev/null +++ b/3705/CH4/EX4.6/Ex4_6.sce @@ -0,0 +1,36 @@ + +clear//
+
+//Variable Declaration
+P1=15 //Load in kN
+P2=25 //Load in kN
+P3=50 //Load in kN
+R=90 //Load in kN
+L1=3.5 //Length in m
+L2=2 //Length in m
+L3=3 //Length in m
+L=12 //Total span in m
+
+//Calculation
+//Part 1
+//Maximum Bending Moment at A
+R1=R*L1*L**-1 //Reaction 1 in kN
+M_A=R1*L1 //Moment about A in kN.m
+//Maximum Bending Moment at B
+R1_2=R*(L1+(L3-L2))*L**-1 //reaction 1 in kN
+M_B=R1_2*(L1+(L3-L2))-P1*L2 //Moment at B in kN.m
+
+//Maximum Moment at C
+R2=(P2+P3)*(L2+L3)*L**-1 //Reaction 2 in kN
+M_C=R2*(L2+L3) //Moment at C in kN.m
+
+[M_max] = (max(M_A,M_B,M_C))
+
+//Part 2
+R2_2=R*(L-L3)*L**-1 //Reaction 2 in kN
+
+[V_max] = (max(R1,R2,R1_2,R2_2))
+
+
+//Result
+printf("\n The maximum Shear force is %0.3f kN and the Maximum Bending Moment is %0.1f kN.m",V_max,M_max)
diff --git a/3705/CH5/EX5.10/Ex5_10.sce b/3705/CH5/EX5.10/Ex5_10.sce new file mode 100644 index 000000000..a2bf0f093 --- /dev/null +++ b/3705/CH5/EX5.10/Ex5_10.sce @@ -0,0 +1,24 @@ + +clear//
+
+//Variable Declaration
+sigma_w=1000 //Working Stress in Bending in psi
+tau_w=100 //Working stress in shear in psi
+//Dimensions
+b_out=8 //Width in inches
+h=10 //Depth in inches
+b_in=6 //Width in inches
+
+//Calculations
+I=((b_out*h**3)-(b_in*b_out**3))*12**-1 //Moment of inertia in in^4
+//Design for shear
+Q=(b_out*h*0.5*0.25*h)-(b_in*b_out*0.5*0.25*b_out) //First Moment about NA in in^3
+
+//Largest P
+P=(tau_w*I*2)/(1.5*Q) //P in shear in lb
+
+//Design for bending
+P1=(sigma_w*I)/(60*5) //P in bending in lb
+
+//Result
+printf("\n The maximum allowable P value is %0.0f lb",min(P,P1))
diff --git a/3705/CH5/EX5.11/Ex5_11.sce b/3705/CH5/EX5.11/Ex5_11.sce new file mode 100644 index 000000000..8497a6f3a --- /dev/null +++ b/3705/CH5/EX5.11/Ex5_11.sce @@ -0,0 +1,21 @@ + +clear//
+
+//Variable Declaration
+A=2630 //Area in mm^2
+y_bar=536.6 //Neutral Axis depth from top in mm
+tau_w=100 //Allowable stress in MPa
+sigma_b_w=280 //Allowable bending stress in MPa
+d=0.019 //Diameter of the rivet in m
+t_web=0.01 //Thickness of the web in m
+I=4140 //Moment of inertia in m^4
+V=450 //Max shear allowable in kN
+
+//Calculations
+Q=A*y_bar //first moment in mm^3
+Fw=(%pi*d**2)*tau_w*10**6 //Allowable force in N
+Fw_2=d*t_web*sigma_b_w*10**6*0.5 //Allowable force in N
+e=Fw_2*I*(V*10**3*Q*10**-3)**-1 //Allowable spacing in m
+
+//Result
+printf("\n The maximum spacing allowed is %0.1f mm",e*1000)
diff --git a/3705/CH5/EX5.2/Ex5_2.sce b/3705/CH5/EX5.2/Ex5_2.sce new file mode 100644 index 000000000..45506c5aa --- /dev/null +++ b/3705/CH5/EX5.2/Ex5_2.sce @@ -0,0 +1,48 @@ + +clear//
+
+//Variable Declaration
+wf=6 //Width of the top flange in inches
+df=0.8 //Depth of the top flange in inches
+dw=8 //Depth of the web portion in inches
+ww=0.8 //Width of the web portion in inches
+Ra=1600 //Reation at point A in lb
+Rb=3400 //Reaction at point B in lb
+w=400 //Load on the beam in lb/ft
+M_4=3200 //Moment at x=4 ft in lb.ft
+M_10=4000 //Moment at x=10 ft in lb.ft
+
+//Calculations
+//Preliminary Calculations
+//Area computation
+A1=dw*ww //Area of the web portion in sq.in
+A2=wf*df //Area of the top flange in sq.in
+y1=dw*0.5 //Centroid from the bottom of the web portion in inches
+y2=dw+df*0.5 //Centroid from the bottom of the flange portion in inches
+
+//y_bar computation
+y_bar=(A1*y1+A2*y2)/(A1+A2) //centroid of the section in inches from the bottom
+
+//Moment of Inertia computation
+I=(ww*dw**3*12**-1)+(A1*(y1-y_bar)**2)+(wf*df**3*12**-1)+(A2*(y2-y_bar)**2) //Moment of inertia in in^4
+
+//Maximum Bending Moment
+c_top=dw+df-y_bar //distance of top fibre in inches
+c_bot=y_bar //Distance of bottom fibre in inches
+
+//Stress at x=4 ft
+sigma_top=-(12*M_4*c_top)*I**-1 //Stress at top fibre in psi
+sigma_bot=12*M_4*c_bot*I**-1 //Stress at bottom fibre in psi
+
+//Stress at x=10 ft
+sigma_top2=M_10*12*c_top*I**-1 //Stress at the top fibre in psi
+sigma_bot2=-M_10*12*c_bot*I**-1 //Stress at the bottom fibre in psi
+
+//Maximum values
+[sigma_t] = (max(sigma_bot,sigma_bot2,sigma_top,sigma_top2))
+[sigma_c] = (min(sigma_top,sigma_top2,sigma_bot,sigma_bot2))
+
+//Result
+printf("\n The maximum values of stress are")
+printf("\n Maximum Tension= %0.0f psi at x=4ft",sigma_t)
+printf("\n Maximum Compression= %0.0f psi at x=10ft",-sigma_c)
diff --git a/3705/CH5/EX5.3/Ex5_3.sce b/3705/CH5/EX5.3/Ex5_3.sce new file mode 100644 index 000000000..b6b6448ce --- /dev/null +++ b/3705/CH5/EX5.3/Ex5_3.sce @@ -0,0 +1,24 @@ + +clear//
+
+//Variable Declaration
+L=4 //Length of each section in ft
+h_ab=4 //Thickness of the front section in inches
+h_bd=6 //Thickness of the back section in inches
+P=2000 //Point load acting at point A in lb
+M_B=8000 //Moment at 4ft in lb.ft
+M_D=16000 //Moment at x=8ft in lb.ft
+b=2 //Breadth in inches
+
+//Calculations
+S_ab=b*h_ab**2*6**-1 //Sectional Modulus of section AB in in^3
+S_bd=b*h_bd**2*6**-1 //Sectional Modulus of section BD in in^3
+sigma_B=12*M_B*S_ab**-1 //Maximum bending stress in psi
+sigma_D=12*M_D*S_bd**-1 //Maximum bending stress in psi
+
+//Maximum stress
+sigma_max=max(sigma_B,sigma_D) //Maximum stress in psi
+
+//Result
+printf("\n Comparing the two results we find that the maximum stress is")
+printf("\n Sigma_max= %0.0f psi",sigma_max)
diff --git a/3705/CH5/EX5.4/Ex5_4.sce b/3705/CH5/EX5.4/Ex5_4.sce new file mode 100644 index 000000000..94b980574 --- /dev/null +++ b/3705/CH5/EX5.4/Ex5_4.sce @@ -0,0 +1,12 @@ + +clear//
+
+//Variable Declaration
+M=15000 //Maximum bending moment in absolute values in lb.ft
+S=42 //Sectional Modulus in in^3
+
+//Calculations
+sigma_max=M*12*S**-1 //Maximum stress in the section in psi
+
+//Result
+printf("\n The maximum Bending Stress in the section is %0.0f psi",sigma_max)
diff --git a/3705/CH5/EX5.5/Ex5_5.sce b/3705/CH5/EX5.5/Ex5_5.sce new file mode 100644 index 000000000..ed515504c --- /dev/null +++ b/3705/CH5/EX5.5/Ex5_5.sce @@ -0,0 +1,22 @@ + +clear//
+
+//Variable Declaration
+M_max=60*10**3 //Maximum Bending Moment in kN.m
+sigma_w=120*10**6 //Maximum Bending Stress allowed in Pa
+M_max_2=61.52*10**3 //max bending moment computed in N.m
+
+//Section details
+mass=38.7 //Mass in kg/m
+g=9.81 //Acceleration due to gravity in m/s^2
+S=549*10**3 //Sectional modulus of the section in mm^3
+
+//Calculations
+S_min=M_max*sigma_w**-1*10**9 //Minimum Sectional Modulus required in mm^3
+
+//We selecet section W310x39
+w0=mass*g*10**-3 //Weight of the beam in kN/m
+sigma_max=M_max_2*S**-1*10**3 //Maximum stress in MPa
+
+//Result
+printf("\n The section chosen is W310x39 with maximum stress as %0.1f MPa",sigma_max)
diff --git a/3705/CH5/EX5.6/Ex5_6.sce b/3705/CH5/EX5.6/Ex5_6.sce new file mode 100644 index 000000000..80b492023 --- /dev/null +++ b/3705/CH5/EX5.6/Ex5_6.sce @@ -0,0 +1,23 @@ + +clear//
+
+//Variable Declaration
+V_max=24 //Maximum Shear in kN
+b=0.160 //Width of the beam in m
+h=0.240 //Depth of the beam in m
+
+//Calculations
+I=b*h**3*12**-1 //Moment of Inertia of the beam in m^4
+
+//Part 1
+Q=b*(h*3**-1)**2 //First moment of Area m^3
+tau_max=(V_max*Q)*(I*b)**-1 //Maximum Shear Stress in glue in kPa
+
+//Part 2
+tau_max_2=(3.0/2.0)*(V_max/(b*h)) //Shear Stress in kPa
+Q_1=b*h*0.5*h*0.25 //First moment about NA in m^3
+tau_maxx=(V_max*Q_1)/(I*b) //Shear stress in kPa
+
+//Result
+printf("\n The Results agree in both parts")
+printf("\n The maximum stress is %0.0f kPa",tau_max_2)
diff --git a/3705/CH5/EX5.7/Ex5_7.sce b/3705/CH5/EX5.7/Ex5_7.sce new file mode 100644 index 000000000..43c4cc5aa --- /dev/null +++ b/3705/CH5/EX5.7/Ex5_7.sce @@ -0,0 +1,32 @@ + +clear//
+
+//Variable Declaration
+I=310 //Moment of inertia in in^4
+V=160 //Shear Force in kips
+//Dimension defination
+tf=0.515 //Thickness of flange in inches
+de=11.94 //Effective depth in inches
+tw=0.295 //Thickness of web in inches
+wf=8.005 //Width of lange in inches
+
+//Calculations
+//Part 1
+Q=wf*tf*(de-tf)*0.5 //First moment about NA in inch^3
+tau_min=(V*Q*10**2)/(I*tw) //Minimum shear stress in web in psi
+
+//Part 2
+A_2=(de*0.5-tf)*tw //Area in in^3
+y_bar_2=0.5*(de*0.5-tf) //Depth in inches
+
+Q_2=Q+A_2*y_bar_2 //First Moment in inches^3
+
+tau_max=(V*Q_2*10**2)/(I*tw) //Maximum Shear Stress in psi
+
+//Part 3
+V_web=10.91*tw*(tau_min+((2*3**-1)*(tau_max-tau_min))) //Shear in the web in lb
+perV=(V_web/V)*100 //Percentage shear force in web in %
+t_max_final=V*10**3/(10.91*tw)
+
+//result
+printf("\n The final shear stress in the web portion is %0.0f psi",t_max_final)
diff --git a/3705/CH5/EX5.8/Ex5_8.sce b/3705/CH5/EX5.8/Ex5_8.sce new file mode 100644 index 000000000..fd5ca7985 --- /dev/null +++ b/3705/CH5/EX5.8/Ex5_8.sce @@ -0,0 +1,24 @@ + +clear//
+
+//Variable Declaration
+I=547 //Moment of inertia in inches^4
+d=8.9 //NA deoth in inches
+V=12 //Shear Force in kips
+h=7.3 //Depth of NA
+b=2 //Width in inches
+t=1.2 //Thickness in inches
+h2=7.5 //Depth in inches
+
+//Calculations
+//Shear Stress at NA
+Q=(b*h)*(h*0.5) //First Moment about NA in in^3
+tau=(V*10**3*Q)/(I*b) //Shear stress at NA in psi
+
+//Shear Stress at a-a
+Q_1=(t*h2)*(d-h2*0.5) //First moment about NA in in^3
+tau1=(V*Q_1)/(I*t) //Shear Stress in psi
+
+//Result
+printf("\n Comparing two stresses")
+printf("\n The maximum stress is %0.0f psi",max(tau,tau1))
diff --git a/3705/CH6/EX6.1/Ex6_1.sce b/3705/CH6/EX6.1/Ex6_1.sce new file mode 100644 index 000000000..7647b01cb --- /dev/null +++ b/3705/CH6/EX6.1/Ex6_1.sce @@ -0,0 +1,23 @@ + +clear//
+
+//Variable Declaration
+wo=400 //loading in lb/ft
+E=29*10**6 //Modulus of elasticity in psi
+I=285 //Moment of inertia in in^4
+S=45.6 //Sectional Modulus in in^3
+L=8 //Span in ft
+
+//Calculations
+//Part 1
+//Part1 is theoretical in nature hence not coded
+
+//Part 2
+delta_max=((wo*12**-1)*(L*12)**4)/(8*E*I) //maximum deflection in inches
+M_max=(wo*12**-1)*(L*12)**2 //Maximum moment
+sigma_max=M_max/(2*S) //Maximum bending stress in psi
+
+//Result
+printf("\n M_max")
+printf("\n The maximum deflection is %0.4f in",delta_max)
+printf("\n The maximum Bending Stress is %0.0f psi",sigma_max)
diff --git a/3705/CH6/EX6.10/Ex6_10.sce b/3705/CH6/EX6.10/Ex6_10.sce new file mode 100644 index 000000000..7aaafaa66 --- /dev/null +++ b/3705/CH6/EX6.10/Ex6_10.sce @@ -0,0 +1,23 @@ + +clear//
+
+//Variable Declaration
+P1=150 //Load in lb
+P2=30 //Load in lb
+R_A=78 //Reaction at A in lb
+R_C=102 //Reaction at C in lb
+L1=4 //Length in ft
+L2=6 //Length in ft
+M1=780 //Moment in lb.ft
+M2=900 //Moment in lb.ft
+M3=120 //Moment in lb.ft
+
+//Calculations
+EI_AC=0.5*(L1+L2)*M1*(2*3**-1)*(L1+L2)-(0.5*L2*M2*(L1+(2*3**-1)*L2)) //Deflection in lb.ft^3
+EI_thetaC=EI_AC/(L1+L2) //Deflection in lb.ft^2
+
+EI_DC=-0.5*L1*M3*2*3**-1*L1 //Deflection in lb.ft^3
+EI_deltaD=EI_thetaC*L1-(-EI_DC) //Deflection in lb.ft^2
+
+//Result
+printf("\n The deflection is %0.0f lb.ft^2 upwards",EI_deltaD)
diff --git a/3705/CH6/EX6.11/Ex6_11.sce b/3705/CH6/EX6.11/Ex6_11.sce new file mode 100644 index 000000000..16aa50af8 --- /dev/null +++ b/3705/CH6/EX6.11/Ex6_11.sce @@ -0,0 +1,17 @@ + +clear//
+
+//Variable Declaration
+P1=80 //Load in lb
+P2=100 //Load in lb
+b1=3 //Distance of load from end in ft
+b2=2 //Distance of load from end in ft
+L=9 //Span of the beam in ft
+
+//Calcualtions
+EI_delta1=(P1*b1*48**-1)*(3*L**2-4*b1**2) //Deflection in lb.ft^3
+EI_delta2=(P2*b2*48**-1)*(3*L**2-4*b2**2) //Deflection in lb.ft^3
+EI_delta=EI_delta1+EI_delta2 //Deflection at modspan in lb.ft^3
+
+//Result
+printf("\n The deflection at midspan is %0.0f lb.ft^3 downward",EI_delta)
diff --git a/3705/CH6/EX6.12/Ex6_12.sce b/3705/CH6/EX6.12/Ex6_12.sce new file mode 100644 index 000000000..ce78f3d18 --- /dev/null +++ b/3705/CH6/EX6.12/Ex6_12.sce @@ -0,0 +1,17 @@ + +clear//
+
+//Variable Declaration
+wo=600 //Load in N/m
+L=6 //Span of the beam in m
+b=2 //Distance of the load from end in m
+a=1 //Distance of the load from end in m
+
+//Calulations
+EI_delta1=wo*384**-1*(5*L**4-12*L**2*b**2+8*b**4) //Deflection in N.m^3
+EI_delta2=wo*96**-1*a**2*(3*L**2-2*a**2) //Deflection in N.m^3
+
+EI_delta=EI_delta1-EI_delta2 //Total Delfection at midspan in N.m^3
+
+//Result
+printf("\n The total Deflection at midpsan is %0.0f N.m^3 downwards",EI_delta)
diff --git a/3705/CH6/EX6.3/Ex6_3.sce b/3705/CH6/EX6.3/Ex6_3.sce new file mode 100644 index 000000000..d27f6f2fc --- /dev/null +++ b/3705/CH6/EX6.3/Ex6_3.sce @@ -0,0 +1,37 @@ + +clear//
+
+//Variable Declaration
+P=300 //Point Load in N
+R_a=100 //Reaction at A in N
+R_c=200 //Reaction at C in N
+E=12 //Youngs Modulus in GPa
+L1=2 //Length of the load from A in m
+L2=1 //Length of the load from C in m
+b=0.04 //Width of the CS of the beam in m
+h=0.08 //Depth of the CS of the beam in m
+
+//Claculations
+//Moment of inertia
+I=b*h**3*12**-1 //Moment of Inertia in m^4
+//Flexural Rigidity
+FR=E*10**9*I //FLexural rigidity in N.m^2
+
+//Moments in terms of x are
+//Given
+//After the variable Calculations we get
+C1=-400/3 //Constant
+C3=C1 //Constant
+C2=0 //Constant
+C4=0 //Constant
+
+//to get max displacement x we have
+x=(6.510/2.441)**0.5 //Length at which displacement is maximum in m
+v=(0.8138*x**3-6.510*x) //Displacement in mm
+
+//Largest slope
+theta=(2.441*(L1+L2)**2-(7.324*(L1+L2-L1)**2)-6.150)*10**-3//Angle in radians
+
+//Result
+printf("\n The maximum displacement is %0.2f mm downwards",-v)
+printf("\n The maximum angle is %0.3f degrees anticlockwise",theta*180*%pi**-1)
diff --git a/3705/CH6/EX6.4/Ex6_4.sce b/3705/CH6/EX6.4/Ex6_4.sce new file mode 100644 index 000000000..30a06d6be --- /dev/null +++ b/3705/CH6/EX6.4/Ex6_4.sce @@ -0,0 +1,16 @@ + +clear//
+
+//Variable Declaration
+//The computation is mostly variable based hence values will be directly declared
+C1=19.20*10**3 //lb.ft^2
+C2=-131.6*10**3 //lb.ft^2
+C3=14.7*10**3 //lb.ft^2
+C4=-112.7*10**3 //lb.ft^2
+EI=10**7 //Flexural Rigidity in psi
+
+//Calculations
+v=-(C2*12**3)/(EI*40) //Displacement in inches
+
+//Result
+printf("\n The maximum displacement is %0.3f in downwards",v)
diff --git a/3705/CH6/EX6.6/Ex6_6.sce b/3705/CH6/EX6.6/Ex6_6.sce new file mode 100644 index 000000000..c10a9808b --- /dev/null +++ b/3705/CH6/EX6.6/Ex6_6.sce @@ -0,0 +1,20 @@ + +clear//
+
+//Variable Declaration
+L1=3 //Length in m
+L2=1 //Length in m
+L3=8 //Length in m
+L4=4 //Length in m
+L5=6 //Length in m
+
+//Calculations
+//Deflection midway
+EIv=250*3**-1*L1**3-(50*3**-1*(L1-L2)**4)-(3925*3**-1*L1) //Deflection in N.m^3
+
+//Deflection at E
+EIv_E=250*3**-1*L3**3-(50*3**-1*(L3-L2)**4)+(50*3**-1*(L3-L4)**4)+(650*3**-1*(L3-L5)**3)-(3925*3**-1*L3) //Deflection in N.m^3
+
+//Result
+printf("\n The deflection at midspan is %0.0f N.m^3 downwards",-EIv)
+printf("\n The deflection at point E is %0.0f N.m^3 downwards",-EIv_E)
diff --git a/3705/CH6/EX6.8/Ex6_8.sce b/3705/CH6/EX6.8/Ex6_8.sce new file mode 100644 index 000000000..ff38e0796 --- /dev/null +++ b/3705/CH6/EX6.8/Ex6_8.sce @@ -0,0 +1,17 @@ + +clear//
+
+//Variable Declaration
+x1=16*3**-1 //Centroid of the triangle in ft
+x2=3 //Centroid of the lower parabola in ft
+x3=6 //Centroid of the rectangle in ft
+x4=20*3**-1 //Centroid of the triangle in ft
+//Moment values
+M1=4800 //Moment in lb.ft
+M2=14400 //Moment in lb.ft
+
+//Calcualtions
+P=((3**-1*4*M1*x2)+(4*M1*x3)+(0.5*4*M1*2*x4))*(x1*8*8*0.5)**-1 //Force P in lb
+
+//Result
+printf("\n The magnitude of force P is %0.1f lb",P)
diff --git a/3705/CH6/EX6.9/Ex6_9.sce b/3705/CH6/EX6.9/Ex6_9.sce new file mode 100644 index 000000000..f41c2bd7d --- /dev/null +++ b/3705/CH6/EX6.9/Ex6_9.sce @@ -0,0 +1,23 @@ + +clear//
+
+//Variable Declaration
+P=300 //Force in N
+L1=1 //Length in m
+L2=2 //Length in m
+R_a=100 //Reaction at A in N
+R_c=200 //Reaction at C in N
+EI=20.48*10**3 //Flexural Rigidity in N.m^2
+
+//Calculations
+//Part 1
+tC_A=(0.5*(L1+L2)*P*L1-(0.5*L1*P*(L1+L2)**-1))*EI**-1 //First Moment in m
+theta_A=tC_A/(L1+L2) //Angle in radians
+
+//Part 2
+tD_A=0.5*L1*R_a*(L1+L2)**-1*EI**-1 //First Moment in m
+delta_D=(theta_A*L1-tD_A) //Displacement in m
+
+//Result
+printf("\n The angle in part 1 is %0.3f Degrees",theta_A*180*%pi**-1)
+printf("\n The displacement in part 2 is %0.2f mm downward",delta_D*1000)
diff --git a/3705/CH7/EX7.4/Ex7_4.sce b/3705/CH7/EX7.4/Ex7_4.sce new file mode 100644 index 000000000..dbccb8b37 --- /dev/null +++ b/3705/CH7/EX7.4/Ex7_4.sce @@ -0,0 +1,18 @@ + +clear//
+//
+
+//Variable Declaration
+w=60 //Continous Load in lb/ft
+L1=3 //Length in ft
+L2=9 //Length in ft
+
+//Calculations
+//After carrying out the variable computations we get
+A=([[1,1,0,0;(L1+L2),0,1,1;0.5*(L1+L2)**2,0,-(L1+L2),0;6**-1*(L1+L2)**3,0,-0.5*(L1+L2)**2,0]])
+B=([w*L2;w*L2*0.5*L2;L2**3*10;L2**4*2.5])
+C=linsolve(A,B)
+
+//Result
+printf("\n The values are as follows")
+printf("\n Ra= %0.0f lb Ma= %0.0f lb.ft Rb= %0.0f lb and Mb= %0.0f lb.ft",-C(1),-C(2),-C(3),-C(4))
diff --git a/3705/CH8/EX8.1/Ex8_1.sce b/3705/CH8/EX8.1/Ex8_1.sce new file mode 100644 index 000000000..d62c4b00a --- /dev/null +++ b/3705/CH8/EX8.1/Ex8_1.sce @@ -0,0 +1,29 @@ + +clear//
+
+//Variable Declaration
+p=125 //Pressure in psi
+r=24 //Radius of the vessel in inches
+t=0.25 //Thickness of the vessel in inches
+E=29*10**6 //Modulus of Elasticity in psi
+v=0.28 //poisson ratio
+
+//Calcualtions
+//Part 1
+sigma_c=p*r*t**-1 //Circumferential Stress in psi
+sigma_l=sigma_c/2 //Longitudinat Stress in psi
+e_c=E**-1*(sigma_c-(v*sigma_l)) //Circumferential Strain using biaxial Hooke's Law
+delta_r=e_c*r //Change in the radius in inches
+
+//Part 2
+sigma=(p*r)*(2*t)**-1 //Stress in psi
+e=E**-1*(sigma-(v*sigma)) //Strain using biaxial Hooke's Law
+delta_R=e*r //Change inradius of end-cap in inches
+
+//Result
+printf("\n Part 1 Answers")
+printf("\n Stresses are sigma_c= %0.0f psi and sigma_l= %0.0f psi",sigma_c,sigma_l)
+printf("\n Change of radius of cylinder= %0.5f in",delta_r)
+printf("\n Part 2 Answers")
+printf("\n Stresses are sigma= %0.0f psi",sigma)
+printf("\n Change in radius of end cap= %0.5f in",delta_R)
diff --git a/3705/CH8/EX8.10/Ex8_10.sce b/3705/CH8/EX8.10/Ex8_10.sce new file mode 100644 index 000000000..f0042a5f9 --- /dev/null +++ b/3705/CH8/EX8.10/Ex8_10.sce @@ -0,0 +1,22 @@ + +clear//
+
+//Variable Declaration
+t=0.01 //Thickness of the shaft in m
+p=2 //Internal Pressure in MPa
+r=0.45 //Mean radius of the vessel in m
+tw=50 //Working shear stress in MPa
+
+//Calculation
+sigma_x=(p*r)/(2*t) //Stress in MPa
+sigma_y=(p*r)/t //Stress in MPa
+
+R=100-67.5 //From the diagram in MPa
+tau_xy=sqrt((R**2-(sigma_y-67.5)**2)) //Stress in MPa
+
+J=2*%pi*r**3*t //Polar Moment of inertia in mm^4
+
+T=1000*(tau_xy*J)/r //Maximum allowable Torque in kN.m
+
+//Result
+printf("\n The largest allowable Torque is %0.0f kN.m",T)
diff --git a/3705/CH8/EX8.11/Ex8_11.sce b/3705/CH8/EX8.11/Ex8_11.sce new file mode 100644 index 000000000..d763804e0 --- /dev/null +++ b/3705/CH8/EX8.11/Ex8_11.sce @@ -0,0 +1,32 @@ + +clear//
+
+//Variable Declaration
+L=15 //Length of the shaft in inches
+r=3.0/8.001 //Radius of the shaft in inches
+T=540 //Torque applied in lb.in
+
+//Calculations
+V=30 //Transverse Shear Force in lb
+M=15*V //Bending Moment in lb.in
+I=(%pi*r**4)/4.0 //Moment of Inertia in in^4
+J=2*I //Polar Moment Of Inertia in in^4
+
+//Part 1
+sigma=(M*r)/I //Bending Stress in psi
+tau_t=10**-3*(T*r)/J //Shear Stress in ksi
+
+sigma_max1=13.92 //From the Mohr Circle in ksi
+
+//Part 2
+Q=(2*r**3)/3.0 //First Moment in in^3
+b=2*r // in
+
+tau_V=10**-3*(V*Q)/(I*b) //Shear Stress in ksi
+tau=tau_t+tau_V //Total Shear in ksi
+
+sigma_max2=tau //Maximum stress in ksi
+
+//Result
+printf("\n The maximum normal stress in case 1 is %0.3f ksi",sigma_max1)
+printf("\n The Maximum normal stress in case 2 is %0.2f ksi",sigma_max2)
diff --git a/3705/CH8/EX8.12/Ex8_12.sce b/3705/CH8/EX8.12/Ex8_12.sce new file mode 100644 index 000000000..f4a0adade --- /dev/null +++ b/3705/CH8/EX8.12/Ex8_12.sce @@ -0,0 +1,28 @@ + +clear//
+
+//Variable Declaration
+ex=800*10**-6 //Strain in x (no units)
+ey=200*10**-6 //Strain in y(no units)
+y_xy=-600*10**-6 //Strain in xy(no units)
+
+//Calculations
+e_bar=(ex+ey)*0.5 //Strain
+R=sqrt(2*300**2)*10**-6 //Resultant
+
+//Part 1
+e1=e_bar+R //Strain in Principal Axis(no units)
+e2=e_bar-R //Strain in Principal Axis(no units)
+
+//Part 2
+alpha=15*180**-1*%pi //From the Mohr Circle in degrees
+e_xbar=e_bar-(R*cos(alpha)) //Strain in x (no units)
+e_ybar=e_bar+(R*cos(alpha)) //Strain in y(no units)
+
+shear_strain=2*R*sin(alpha) //Shear follows
+
+//Result
+printf("\n The principal Strains are")
+printf("\n e1= %0.6f e2= %0.6f ",e1,e2)
+printf("\n The follows components are")
+printf("\n ex= %0.6f ey= %0.6f y_xy= %0.6f ",e_xbar,e_ybar,shear_strain)
diff --git a/3705/CH8/EX8.13/Ex8_13.sce b/3705/CH8/EX8.13/Ex8_13.sce new file mode 100644 index 000000000..29735881b --- /dev/null +++ b/3705/CH8/EX8.13/Ex8_13.sce @@ -0,0 +1,24 @@ + +clear//
+
+//Variable Declaration
+e_x=800*10**-6 //Strain in x
+e_y=200*10**-6 //Strain in y
+y_xy=-600*10**-6 //Strain in xy
+v=0.30 //Poissons Ratio
+E=200 //Youngs Modulus in GPa
+R_e=424.3*10**-6 //Strain
+e_bar=500*10**-6 //Strain
+
+//Calculations
+//Part 1
+R_sigma=10**-6*R_e*(E*10**9/(1+v)) //Stress in MPa
+sigma_bar=10**-6*e_bar*(E*10**9/(1-v)) //Stress in MPa
+
+//Part 2
+sigma1=sigma_bar+R_sigma //Principal Stress in MPa
+sigma2=sigma_bar-R_sigma //Principal Stress in MPa
+
+//Result
+printf("\n The principal Stresses are as follows")
+printf("\n Sigma1= %0.0f MPa and Sigma2= %0.1f MPa",sigma1,sigma2)
diff --git a/3705/CH8/EX8.14/Ex8_14.sce b/3705/CH8/EX8.14/Ex8_14.sce new file mode 100644 index 000000000..5383e59be --- /dev/null +++ b/3705/CH8/EX8.14/Ex8_14.sce @@ -0,0 +1,29 @@ + +clear//
+
+//Variable Declaration
+e_a=100*10**-6 //Strain
+e_b=300*10**-6 //Strain
+e_c=-200*10**-6 //Strain
+E=180 //Youngs Modulus in GPa
+v=0.28 //Poissons Ratio
+
+//Calculations
+y_xy=(e_b-(e_a+e_c)*0.5) //Strain in xy
+e_bar=(e_a+e_c)*0.5 //Strain
+R_e=sqrt(y_xy**2+(150*10**-6)**2) //Resultant Strain
+
+//Corresponding Parameters from Mohrs Diagram
+sigma_bar=(E/(1-v))*e_bar*10**3 //Stress in MPa
+R_sigma=(E/(1+v))*R_e*10**3 //Resultant Stress in MPa
+
+//Principal Stresses
+sigma1=sigma_bar+R_sigma //MPa
+sigma2=sigma_bar-R_sigma //MPa
+
+theta=atan(y_xy/(150*10**-6))*180*%pi**-1*0.5 //Degrees
+
+//Result
+printf("\n The Principal Stresses are as follows")
+printf("\n Sigma1= %0.1f MPa and Sigma2= %0.2f MPa",sigma1,sigma2)
+printf("\n The plane orientation is %0.2f degrees",theta)
diff --git a/3705/CH8/EX8.3/Ex8_3.sce b/3705/CH8/EX8.3/Ex8_3.sce new file mode 100644 index 000000000..5e4560e43 --- /dev/null +++ b/3705/CH8/EX8.3/Ex8_3.sce @@ -0,0 +1,28 @@ + +clear//
+
+//Variable Declaration
+b=6 //Width in inches
+h=10 //Depth in inches
+P1=6000 //Force in lb
+P2=3000 //Force in lb
+L=4 //Length in ft
+P=-13400 //Load in lb
+M=6000 //Moment in lb.ft
+y=5 //Depth in inches
+P2=-9800 //Load in lb
+M2=-12000 //Moment in lb.ft
+
+//Calculations
+A=b*h //Area in in^2
+I=b*h**3*12**-1 //Moment of inertia in in^4
+T=(P1*L+P2*L*3)*(6)**-1 //Tension in the cable in lb
+
+//Computation of largest stress
+sigma_B=(P*A**-1)-(M*y*12*I**-1) //Maximum Compressive Stress caused by +ve BM in psi
+sigma_C=(P2*A**-1)-(M2*-y*12*I**-1) //Maximum Compressive Stress caused by -ve BM in psi
+
+sigma_max=max(-sigma_B,-sigma_C) //Maximum Compressive Stress in psi
+
+//Result
+printf("\n The maximum Stress is %0.0f psi",sigma_max)
diff --git a/3705/CH8/EX8.4/Ex8_4.sce b/3705/CH8/EX8.4/Ex8_4.sce new file mode 100644 index 000000000..ec1510039 --- /dev/null +++ b/3705/CH8/EX8.4/Ex8_4.sce @@ -0,0 +1,17 @@ + +clear//
+
+//Variable Declaration
+theta=(60*%pi)/180 //Angle in radians (Twice as declared)
+sigma_x=30 // Stress in x in MPa
+sigma_y=60 //Stress in y in MPa
+tau_xy=40 //Stress in MPa
+
+//Calcualtions
+sigma_xdash=0.5*(sigma_x+sigma_y)+0.5*(sigma_x-sigma_y)*cos(theta)+tau_xy*sin(theta) //Stress at x' axis in MPa
+sigma_ydash=0.5*(sigma_x+sigma_y)-0.5*(sigma_x-sigma_y)*cos(theta)-tau_xy*sin(theta) //Stress at y' axis in MPa
+tau_x_y=-0.5*(sigma_x-sigma_y)*sin(theta)+tau_xy*cos(theta) //Stress at x'y' in shear in MPa
+//Result
+printf("\n The new stresses at new axes are as follows")
+printf("\n sigma_x= %0.1f MPa sigma_y= %0.1f MPa",sigma_xdash,sigma_ydash)
+printf("\n And tau_xy= %0.0f MPa",tau_x_y)
diff --git a/3705/CH8/EX8.5/Ex8_5.sce b/3705/CH8/EX8.5/Ex8_5.sce new file mode 100644 index 000000000..39cad6526 --- /dev/null +++ b/3705/CH8/EX8.5/Ex8_5.sce @@ -0,0 +1,27 @@ + +clear//
+
+//Variable Declaration
+sigma_x=8000 //Stress in x in psi
+sigma_y=4000 //Stress in y in psi
+tau_xy=3000 //Stress in xy in psi
+
+//Calculations
+R=sqrt(((sigma_x-sigma_y)*0.5)**2+tau_xy**2) //Resultant Stress in psi
+
+//Principal Stresses
+sigma1=(sigma_x+sigma_y)*0.5+R //Principal Stress in psi
+sigma2=(sigma_x+sigma_y)*0.5-R //Principal Stress in psi
+
+//Principal Direction
+theta1=atan(2*tau_xy*(sigma_x-sigma_y)**-1)*0.5*180*%pi**-1 //Principal direction in degrees
+theta2=theta1+90 //Second pricnipal direction in degrees
+
+//Normal Stress
+sigma_xdash=0.5*(sigma_x+sigma_y)+0.5*(sigma_x-sigma_y)*cos(2*theta1*%pi*180**-1)+tau_xy*sin(2*theta1*%pi*180**-1)
+
+//Result
+printf("\n The principal stresses are as follows")
+printf("\n sigma1= %0.0f psi and sigma2= %0.0f psi",sigma1,sigma2)
+printf("\n The corresponding directions are")
+printf("\n Theta1= %0.1f degrees and Theta2= %0.1f degrees",theta1,theta2)
diff --git a/3705/CH8/EX8.6/Ex8_6.sce b/3705/CH8/EX8.6/Ex8_6.sce new file mode 100644 index 000000000..66c8e4b54 --- /dev/null +++ b/3705/CH8/EX8.6/Ex8_6.sce @@ -0,0 +1,23 @@ + +clear//
+
+//Variable Declaration
+sigma_x=40 //Stress in x in MPa
+sigma_y=-100 //Stress in y in MPa
+tau_xy=-50 //Shear stress in MPa
+
+//Calculations
+tau_max=sqrt(((sigma_x-sigma_y)*0.5)**2+tau_xy**2) //Maximum in-plane shear in MPa
+
+//Orientation of Plane
+theta1=atan(-((sigma_x-sigma_y)*(2*tau_xy)**-1))*180*%pi**-1*0.5 //Angle in Degrees
+theta2=theta1+90 //Angle in degrees
+
+//Plane of max in-plane shear
+tau_x_y=-0.5*(sigma_x-sigma_y)*sin(2*theta1*%pi*180**-1)+tau_xy*cos(2*theta1*%pi*180**-1)
+
+//Normal Stress
+sigma=(sigma_x+sigma_y)*0.5 //Stress in MPa
+
+//Result
+printf("\n The maximum in-plane Shear is %0.0f MPa",tau_x_y)
diff --git a/3705/CH8/EX8.7/Ex8_7.sce b/3705/CH8/EX8.7/Ex8_7.sce new file mode 100644 index 000000000..fefb67c2f --- /dev/null +++ b/3705/CH8/EX8.7/Ex8_7.sce @@ -0,0 +1,32 @@ + +clear//
+
+//Vairable Declaration
+sigma_x=40 //Stress in x in MPa
+sigma_y=20 //Stress in y in MPa
+tau_xy=16 //Shear in xy in MPa
+
+//Calculations
+sigma=(sigma_x+sigma_y)*0.5 //Normal Stress in MPa
+R=sqrt(((sigma_x-sigma_y)*0.5)**2+tau_xy**2) //Resultant Stress in MPa
+
+//Part 1
+sigma1=sigma+R //Principal Stress in MPa
+sigma2=sigma-R //Principal Stress in MPa
+theta=atan(tau_xy*((sigma_x-sigma_y)*0.5)**-1)*180*%pi**-1*0.5 //Orientation in degrees
+
+//Part 2
+tau_max=18.87 //From figure in MPa
+
+//Part 3
+sigma_xdash=sigma+tau_max*cos((100-theta*2)*%pi*180**-1) //Stress in MPa
+sigma_ydash=sigma-tau_max*cos((100-theta*2)*%pi*180**-1) //Stress in MPa
+tau_x_y=tau_max*sin((100-2*theta)*%pi*180**-1) //Shear stress in MPa
+
+//Result
+printf("\n The principal Stresses are")
+printf("\n Sigma1= %0.1f MPa and Sigma2= %0.1f MPa",sigma1,sigma2)
+printf("\n The Principal Plane is at %0.0f degrees",theta)
+printf("\n The Maximum Shear Stress is %0.3f MPa",tau_max)
+printf("\n Sigma_x= %0.0f MPa and Sigma_y= %0.2f MPa",sigma_xdash,sigma_ydash)
+printf("\n Tau_xy= %0.2f MPa",tau_x_y)
diff --git a/3705/CH8/EX8.9/Ex8_9.sce b/3705/CH8/EX8.9/Ex8_9.sce new file mode 100644 index 000000000..503b2ef6f --- /dev/null +++ b/3705/CH8/EX8.9/Ex8_9.sce @@ -0,0 +1,19 @@ + +clear//
+
+//Variable Declaration
+sigma_w=120 //Working Stress in MPa
+tau_w=70 //Working Shear in MPa
+
+//Calcualtions
+//Section a-a
+M=3750 //Applied moment at section a-a in N.m
+T=1500 //Applied Torque at section a-a in N.m
+
+//After carrying out the variable based computation we compute d
+d1=((124.62)/(sigma_w*10**3*%pi))**0.3333 //Diameter of the shaft in m
+d2=((65.6)/(tau_w*10**3*%pi))**0.3333 //Diameter of the shaft in m
+d=max(d1,d2) //Diameter of the shaft to be selected in m
+
+//Result
+printf("\n The diameter of the shaft to be selected is %0.1f mm",d*1000)
diff --git a/3705/CH9/EX9.1/Ex9_1.sce b/3705/CH9/EX9.1/Ex9_1.sce new file mode 100644 index 000000000..07b55e8aa --- /dev/null +++ b/3705/CH9/EX9.1/Ex9_1.sce @@ -0,0 +1,33 @@ + +clear//
+
+//Variable Declaration
+n=20 //Modular Ratio
+sigma_wd=8*10**6 //Maximum bending stress in wood in Pa
+sigma_st=120*10**6 //Maximum bending stress in steel in Pa
+
+//Cross Sectional Details
+Awd=45 //Area of wood in mm^2
+y_wd=160 //Neutral Axis of from bottom of the wooden section in mm
+Ast=15 //Area of steel in mm^2
+y_st=5 //Neutral Axis of the Steel section in mm
+//Dimensions
+ww=150 //width of wooden section in mm
+dw=300 //depth of wooden section in mm
+ws=75 //width of steel section in mm
+ds=10 //depth of steel section in mm
+
+//Calculations
+y_bar=(Awd*y_wd+Ast*y_st)*(Ast+Awd)**-1 //Location of Neutral axis from the bottom in mm
+//Moment of inertia
+I=(ww*dw**3*12**-1)+(ww*dw*(y_wd-y_bar)**2)+(n*ws*ds**3*12**-1)+(n*ws*ds*(y_bar-y_st)**2) //mm^4
+c_top=dw+ds-y_bar //Distance from NA to top fibre in mm
+c_bot=y_bar //Distance from NA to bottom fibre in mm
+
+//The solution will be in different order
+M1=sigma_wd*I*10**-12*c_top**-1 //Maximum Bending Moment in N.m
+M2=sigma_st*I*10**-12*c_bot**-1 //Maximum Bending Moment in N.m
+M=min(M1,M2) //Maximum allowable moment in N.m
+
+//Result
+printf("\n The Maximum Allowable moment that the beam can support is %0.1f kN.m",M)
diff --git a/3705/CH9/EX9.2/Ex9_2.sce b/3705/CH9/EX9.2/Ex9_2.sce new file mode 100644 index 000000000..b90500567 --- /dev/null +++ b/3705/CH9/EX9.2/Ex9_2.sce @@ -0,0 +1,28 @@ + +clear//
+
+//Variable Declaration
+dw=8 //Depth of wooden section in inches
+da=0.4 //Depth og aluminium section in inches
+w=2 //Width of the section in inches
+n=40*3**-1 //Modular Ratio
+Ewd=1.5*10**6 //Youngs modulus of wood in psi
+Eal=10**7 //Youngs Modulus of aluminium in psi
+V_max=4000 //Maximum shear in lb
+b=24 //Inches
+L=72 //Length in inches
+P=6000 //Load on the beam in lb
+
+//Calculations
+I=w*dw**3*12**-1+2*(n*w*da**3*12**-1+n*da*4.2**2) //Moment of Inertia in in^4
+
+//Part 1
+Q=(w*dw*0.5)*2+(n*da)*(dw*0.5+da*0.5) //First Moment in in^3
+tau_max=V_max*Q*I**-1*w**-1 //Maximum Shear Stress in psi
+
+//Part 2
+delta_mid=(P*b)*(48*Ewd*I)**-1*(3*L**2-4*b**2)
+
+//Result
+printf("\n The maximum shear stress allowable is %0.0f psi",tau_max)
+printf("\n The deflection at the mid-span is %0.4f in",delta_mid)
diff --git a/3705/CH9/EX9.4/Ex9_4.sce b/3705/CH9/EX9.4/Ex9_4.sce new file mode 100644 index 000000000..99ca2c8ef --- /dev/null +++ b/3705/CH9/EX9.4/Ex9_4.sce @@ -0,0 +1,23 @@ + +clear//
+
+//Variable Declaration
+sigma_co_w=12 //Maximum stress in compression in MPa
+sigma_st_w=140 //Maximum stress in steel in MPa
+M=90 //Moment in kN.m
+n=8 //Modular Ratio
+
+//Calculations
+//h=0.4068d
+//bd^2=0.04266
+b=(0.04266/(1.5**2))**0.3333 //Breadth in m
+d=1.5*b //Depth in m
+h=0.4068*d //Height in m
+
+//Area of steel
+Ast=((M*10**3)/((d-h*3**-1)*sigma_st_w*10**3))*10**3 //Area of steel in mm^2
+
+//Result
+printf("\n The dimensions of the beam are")
+printf("\n b= %0.0f mm and d= %0.0f mm",b*1000,d*1000)
+printf("\n Area of steel= %0.0f mm^2",Ast)
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