diff options
Diffstat (limited to '3705/CH2')
| -rw-r--r-- | 3705/CH2/EX2.1/Ex2_1.sce | 31 | ||||
| -rw-r--r-- | 3705/CH2/EX2.10/Ex2_10.sce | 21 | ||||
| -rw-r--r-- | 3705/CH2/EX2.11/Ex2_11.sce | 32 | ||||
| -rw-r--r-- | 3705/CH2/EX2.12/Ex2_12.sce | 16 | ||||
| -rw-r--r-- | 3705/CH2/EX2.3/Ex2_3.sce | 21 | ||||
| -rw-r--r-- | 3705/CH2/EX2.4/Ex2_4.sce | 24 | ||||
| -rw-r--r-- | 3705/CH2/EX2.5/Ex2_5.sce | 19 | ||||
| -rw-r--r-- | 3705/CH2/EX2.6/Ex2_6.sce | 22 | ||||
| -rw-r--r-- | 3705/CH2/EX2.7/Ex2_7.sce | 17 | ||||
| -rw-r--r-- | 3705/CH2/EX2.8/Ex2_8.sce | 31 | ||||
| -rw-r--r-- | 3705/CH2/EX2.9/Ex2_9.sce | 31 |
11 files changed, 265 insertions, 0 deletions
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)
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