diff options
Diffstat (limited to '2732/CH9')
| -rwxr-xr-x | 2732/CH9/EX9.1/Ex9_1.sce | 20 | ||||
| -rwxr-xr-x | 2732/CH9/EX9.10/Ex9_10.sce | 36 | ||||
| -rwxr-xr-x | 2732/CH9/EX9.11/Ex9_11.sce | 50 | ||||
| -rwxr-xr-x | 2732/CH9/EX9.12/Ex9_12.sce | 21 | ||||
| -rwxr-xr-x | 2732/CH9/EX9.13/Ex9_13.sce | 28 | ||||
| -rwxr-xr-x | 2732/CH9/EX9.14/Ex9_14.sce | 21 | ||||
| -rwxr-xr-x | 2732/CH9/EX9.15/Ex9_15.sce | 22 | ||||
| -rwxr-xr-x | 2732/CH9/EX9.3/Ex9_3.sce | 26 | ||||
| -rwxr-xr-x | 2732/CH9/EX9.4/Ex9_4.sce | 17 | ||||
| -rwxr-xr-x | 2732/CH9/EX9.5/Ex9_5.sce | 23 | ||||
| -rwxr-xr-x | 2732/CH9/EX9.6/Ex9_6.sce | 25 | ||||
| -rwxr-xr-x | 2732/CH9/EX9.7/Ex9_7.sce | 27 | ||||
| -rwxr-xr-x | 2732/CH9/EX9.8/Ex9_8.sce | 41 | ||||
| -rwxr-xr-x | 2732/CH9/EX9.9/Ex9_9.sce | 67 |
14 files changed, 424 insertions, 0 deletions
diff --git a/2732/CH9/EX9.1/Ex9_1.sce b/2732/CH9/EX9.1/Ex9_1.sce new file mode 100755 index 000000000..5fa09e4b6 --- /dev/null +++ b/2732/CH9/EX9.1/Ex9_1.sce @@ -0,0 +1,20 @@ +clc
+//initialization of variables
+clear
+//case (a)
+A=72.9 //cm^2
+Iy=633 //cm^4
+Ix=1199 //cm^4
+t=24/(5*Ix)+13.5/(5*Iy)
+r=1/(A*t)
+printf('case (a) \n r = %.3f cm',r)
+// case (b)
+t=24/(5*Ix)-13.5/(5*Iy)
+r=1/(A*t)
+printf('\n case (b) \n r = %.1f cm',r)
+//case (c)
+t=-24/(5*Ix)+13.5/(5*Iy)
+r=1/(A*t)
+printf('\n case (a) \n r = %.1f cm',r)
+printf('\n So the load is to be placed on the leg OD, at a distance of %.1f cm from O',r )
+
diff --git a/2732/CH9/EX9.10/Ex9_10.sce b/2732/CH9/EX9.10/Ex9_10.sce new file mode 100755 index 000000000..b8bda9bba --- /dev/null +++ b/2732/CH9/EX9.10/Ex9_10.sce @@ -0,0 +1,36 @@ +clc
+//initialization of variables
+clear
+b=2 //cm
+h=2 //cm
+T=2000 //kg-cm
+V=250 //kg
+M=2000 //kg-cm
+// calculations
+Mmax=M*6/(b*h*b)
+Vmax=3*V/(2*b*h)
+Zt=0.208*b^2*h
+Tmax=T/(Zt)
+
+sigma=Mmax
+printf('points A,B,')
+printf('\n sigma=%d kg/cm^2 (tension)',sigma)
+printf('\n points C,D,')
+printf('\n sigma=%d kg/cm^2 (cmpression)',sigma)
+tau=Vmax+Tmax
+printf('\n point E')
+printf('\n tau=%.2f kg/cm^2 shear',tau)
+tau=Vmax-Tmax
+printf('\n tau=%.2f kg/cm^2 shear',tau)
+// at G
+sigma_x=sigma
+sigma_y=0
+tau_xy=Tmax
+sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)
+sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)
+// results
+printf('\n at point G')
+printf('\n sigma_1 = %d kg/cm^2 (tension)',sigma_1)
+printf('\n sigma_2 = %d kg/cm^2 (compression)',sigma_2)
+
+// Question was asked only to find out at A,B,C,D,E,F and G
diff --git a/2732/CH9/EX9.11/Ex9_11.sce b/2732/CH9/EX9.11/Ex9_11.sce new file mode 100755 index 000000000..7efe34041 --- /dev/null +++ b/2732/CH9/EX9.11/Ex9_11.sce @@ -0,0 +1,50 @@ +clc
+//initialization of variables
+clear
+w=10 //cm
+s=2.8 //m
+P=1 //tonne
+Ft=1.4 //cm
+Wt=0.8 //cm
+Ix=13989.5 //cm^4
+Z=699.5 //cm^3
+// calculations
+BM= 2.8
+T=P*1000*8.21
+SF=P*1000
+BS=BM*10^5/(Z)
+sigmaXA=BS*18.6/20
+K=w*Ft*19.3+18.6*Wt*9.3
+tau_xy_C=SF/(Ix*Wt)*K
+tau_xy_A=tau_xy_C*(w*Ft*19.3)/K
+tau_xy_B=tau_xy_A*0.5*Wt/w
+sigmaXB=sigmaXA*19.3/20
+
+tau_max=3*Ft*8210/(w*Ft^3+37.2*Wt^3)
+tau_A=3*Wt*8210/(w*Ft^3+37.2*Wt^3)
+
+//For point A
+Shear=tau_xy_A-tau_A
+sigma_x=sigmaXA
+sigma_y=0
+tau_xy=Shear
+sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)
+sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)
+
+printf('For point A')
+printf('\n Total shear= %.1f kg/cm^2 ',Shear)
+printf('\n Bending stress = %d kg/cm^2 (Compr.)',sigma_x)
+printf('\n Principal stresses are %d (tension), %d (comp.) kg/cm^2 ',sigma_1,sigma_2)
+
+//For point B
+printf('\n FOr point B')
+printf('\n Bending shear stress is %.2f k/cm^2',tau_xy_B)
+sigmaXB=BS*19.3/20
+sigma_x=sigmaXB
+sigma_y=0
+tau_xy=tau_max
+sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)
+sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)
+printf('\n Principal stresses are %d (tension), %d (comp.) kg/cm^2 ',sigma_1,sigma_2)
+
+// Answers in the text are approximations
diff --git a/2732/CH9/EX9.12/Ex9_12.sce b/2732/CH9/EX9.12/Ex9_12.sce new file mode 100755 index 000000000..8d16ba009 --- /dev/null +++ b/2732/CH9/EX9.12/Ex9_12.sce @@ -0,0 +1,21 @@ +clc
+//initialization of variables
+clear
+b=10 //cm
+h=10 //cm
+P=5 //tonne
+e=1 //cm
+E=12*10^4 //kg/cm^2
+str=130 // kg/cm^2
+n=3
+L=2 //m
+// calculations
+L=L*100 //cm
+Pcr=%pi^2*E*b*h^3/(12*L^2)
+Pcr=Pcr/1000
+Smax=-P*1000/(b*h)-(P*1000*1*5*12/10^4)*1/(1-(n*P/Pcr))
+// results
+printf('permissible stress = %d kg/cm^2',str)
+printf('\n develoed stress = %.1f kg/cm^2',Smax)
+printf('\n Since it is below the permissible stress, the design is safe')
+
diff --git a/2732/CH9/EX9.13/Ex9_13.sce b/2732/CH9/EX9.13/Ex9_13.sce new file mode 100755 index 000000000..19e54268a --- /dev/null +++ b/2732/CH9/EX9.13/Ex9_13.sce @@ -0,0 +1,28 @@ +clc
+//initializatio of variables
+clear
+// linked to 9.13
+b=10 //cm
+h=10 //cm
+P=5 //tonne
+e=1 //cm
+E=12*10^4 //kg/cm^2
+str=130 // kg/cm^2
+n=3
+L=2 //m
+// calculations
+L=L*100 //cm
+Pcr=%pi^2*E*b*h^3/(12*L^2)
+Pcr=Pcr/1000
+Smax=-P*1000/(b*h)-(P*1000*1*5*12/10^4)*1/(1-(n*P/Pcr))
+Smax=abs(Smax)
+
+rr=b*h^3/(12*100)
+Smax_se=P*1000/(b*h)*(1+e*5/rr*sec(%pi/2*sqrt(n*P/Pcr)))
+Perror=(Smax-Smax_se)/Smax
+Perror=Perror*100
+Perror=abs(Perror)
+// results
+printf('Using secent formula, stress obtained is %d kg/cm^2',Smax_se)
+printf('\n hence, the percentage error %.2f',Perror)
+// approximate answees in the text
diff --git a/2732/CH9/EX9.14/Ex9_14.sce b/2732/CH9/EX9.14/Ex9_14.sce new file mode 100755 index 000000000..1adf4b700 --- /dev/null +++ b/2732/CH9/EX9.14/Ex9_14.sce @@ -0,0 +1,21 @@ +clc
+//initialization of variables
+clear
+P=400 //kg/m
+L=10 //m
+F=10 //tonne
+n=3
+Ixx=5943.1 //cm^4
+A=52.03 //cm^2
+rx=10.69 //cm
+E=2*10^6 //kg/cm^2
+// calculations
+Pcr=%pi^2*E*Ixx/((L*100)^2)
+Pcr=Pcr/1000
+e=P*L^2/(8*F*1000)
+g=e*12.5*100/rx^2
+Smax=F*1000/A*(1+g*1/(1-n*(F/Pcr)))
+// results
+printf('The maximum stress developed is %d kg/cm^2',Smax)
+
+// approximate calculations involved in the text book
diff --git a/2732/CH9/EX9.15/Ex9_15.sce b/2732/CH9/EX9.15/Ex9_15.sce new file mode 100755 index 000000000..962070e6d --- /dev/null +++ b/2732/CH9/EX9.15/Ex9_15.sce @@ -0,0 +1,22 @@ +clc
+//initialization of variables
+clear
+// linked to 9_14
+// calculations
+P=400 //kg/m
+L=10 //m
+F=10 //tonne
+n=3
+Ixx=5943.1 //cm^4
+A=52.03 //cm^2
+rx=10.69 //cm
+E=2*10^6 //kg/cm^2
+Pcr=%pi^2*E*Ixx/((L*100)^2)
+Pcr=Pcr/1000
+e=P*L^2/(8*F*1000)
+g=e*12.5*100/rx^2
+Smax=F*1000/A*(1+g*1/(1+n*(F/Pcr)))
+// results
+printf('The maximum stress developed is %d kg/cm^2',Smax)
+
+// approximate answer in the text
diff --git a/2732/CH9/EX9.3/Ex9_3.sce b/2732/CH9/EX9.3/Ex9_3.sce new file mode 100755 index 000000000..678cfbcc2 --- /dev/null +++ b/2732/CH9/EX9.3/Ex9_3.sce @@ -0,0 +1,26 @@ +clc
+//initialization of variables
+clear
+b=14 //cm
+d=20 //cm
+rx=8.46 //cm
+ry=2.99 //cm
+// calculations
+ex=2*rx^2/d
+ey=2*ry^2/b
+h=2*ex
+w=2*ey
+// results
+printf('for steel height=%.3f cm and width=%.3f cm',h,w)
+// ISHB 225
+b=22.5 //cm
+d=22.5 //cm
+rx=9.8 //cm
+ry=4.96 //cm
+// calculations
+ex=2*rx^2/d
+ey=2*ry^2/b
+h=2*ex
+w=2*ey
+// results
+printf('\n for an ISHB height=%.3f cm and width=%.3f cm',h,w)
diff --git a/2732/CH9/EX9.4/Ex9_4.sce b/2732/CH9/EX9.4/Ex9_4.sce new file mode 100755 index 000000000..4733f8514 --- /dev/null +++ b/2732/CH9/EX9.4/Ex9_4.sce @@ -0,0 +1,17 @@ +clc
+//initialization of variables
+clear
+t=280 //kg/cm^2
+c=840 //kg/cm^2
+xbar=7.5 //cm from AB
+A=210 //cm^2
+// calculations
+e=50+xbar //cm
+Iyy=7433 //cm^2
+k=(1/210+e*xbar/Iyy)
+P=t/k
+k1=(-1/210+e*(xbar+5)/Iyy)
+P1=c/k1
+P_safe=min(P1,P)
+// results
+printf('The safe load is %d kg',P_safe)
diff --git a/2732/CH9/EX9.5/Ex9_5.sce b/2732/CH9/EX9.5/Ex9_5.sce new file mode 100755 index 000000000..aa0398435 --- /dev/null +++ b/2732/CH9/EX9.5/Ex9_5.sce @@ -0,0 +1,23 @@ +clc
+//initialization of the variables
+clear
+s=1.6 //m
+s1=4 //m
+pi=28 //degrees
+w=16 //kg/m^2
+p=100 //kg/m^2
+pl=20 //cm
+pb=10 //cm
+r=500 //kg/m^3
+// calculations
+pi=pi*%pi/180 //radians
+W=w*s+(r*pl*pb/(100*100))
+P=p*s
+L=P+W*cos(pi)
+Mx=L*s1^2*100/8
+sigma_1=Mx*6/(pb*pl^2)
+My=W*sin(pi)*s1^2*100/8
+sigma_2=My*6/(pl*pb^2)
+sigma=sigma_1+sigma_2
+// results
+printf('Due to bending in the noth the planes, D experiences maximum \n compression of %.2f kg/cm^2 and B has maximum tension of %.2f kg/cm^2',sigma,sigma)
diff --git a/2732/CH9/EX9.6/Ex9_6.sce b/2732/CH9/EX9.6/Ex9_6.sce new file mode 100755 index 000000000..0cc8351b4 --- /dev/null +++ b/2732/CH9/EX9.6/Ex9_6.sce @@ -0,0 +1,25 @@ +clc
+//initialization of the problems
+clear
+s=1.6 //m
+s1=4 //m
+pi=28 //degrees
+w=16 //kg/m^2
+p=100 //kg/m^2
+pl=20 //cm
+pb=10 //cm
+r=500 //kg/m^3
+Zx=54.8 //cm^3
+Zy=3.9 //cm^3
+// calculations
+pi=pi*%pi/180 //radians
+W=w*s+8.1
+P=p*s
+L=P+W*cos(pi)
+Mx=L*s1^2*100/8
+sigma_1=Mx/Zx
+My=W*sin(pi)*s1^2*100/8
+sigma_2=My/Zy
+sigma=sigma_1+sigma_2
+// results
+printf('Maximum stresses are %d kg/cm^2, tension or compression',sigma)
diff --git a/2732/CH9/EX9.7/Ex9_7.sce b/2732/CH9/EX9.7/Ex9_7.sce new file mode 100755 index 000000000..e413e5f13 --- /dev/null +++ b/2732/CH9/EX9.7/Ex9_7.sce @@ -0,0 +1,27 @@ +clc
+//initialization of variables
+clear
+s=1.6 //m
+s1=4 //m
+pi=28 //degrees
+w=16 //kg/m^2
+p=100 //kg/m^2
+pl=20 //cm
+pb=10 //cm
+r=500 //kg/m^3
+sg=5 //cm
+E=12*10^4
+pi=pi*%pi/180 //radians
+// calculations
+W=w*s+(r*pl*pb/(100*100))
+P=p*s
+L=P+W*cos(pi)
+Mx=L*s1^2*100/8
+sigma_1=Mx*6/(pb*pl^2)
+My=W*sin(pi)*s1^2*100/8
+sigma_2=My*6/(pl*pb^2)
+st=sigma_1*sg/10
+Ts=st-sigma_2
+ez=Ts/E
+// results
+printf('The strain gauge, aligned to the z axis will give compression strain of %.1e',ez)
diff --git a/2732/CH9/EX9.8/Ex9_8.sce b/2732/CH9/EX9.8/Ex9_8.sce new file mode 100755 index 000000000..858797a26 --- /dev/null +++ b/2732/CH9/EX9.8/Ex9_8.sce @@ -0,0 +1,41 @@ +clc
+//initialization of variables
+clear
+P=3 //tonne/m
+s=6 //m
+l=50 //cm
+b=20 //cm
+k=0.5 //m
+//calculations
+R=P*s/2
+sf=R-k*P
+bm=R*k-P*k^2/2
+tau_xy=1.5*sf*1000/(l*b)
+tau_max=tau_xy
+str=bm*s*10^5/(b*l*l)
+
+// consider the line a-a
+
+sigma_x=str*12.5/25
+sigma_y=0
+tau_xy=tau_xy*(1-(12.5/25)^2)
+
+sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)
+sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)
+
+printf('For the line a-a the bending stress and shearing stress are \n respectively %.2f kg/cm^2, %.2f kg/cm^2 ',sigma_x,tau_xy)
+printf('\n The principal stresses are %.2f kg/cm^2 (tension) %.2f kg/cm^2 (compression) ',sigma_1,sigma_2)
+
+//consider the line c-c
+printf('\n For the line c-c the bending stress and shearing stress are \n respectively %.2f kg/cm^2, %.2f kg/cm^2 ',sigma_x,tau_xy)
+printf('\n The principal stresses are %.2f kg/cm^2 (compression) %.2f kg/cm^2 (tension) ',sigma_2,sigma_1)
+
+//for the line b-b
+tau_xy=tau_max
+sigma_x=0
+sigma_y=0
+sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)
+sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)
+// results
+printf('\n For the line b-b the bending stress and shearing stress are \n respectively %.2f kg/cm^2, %.2f kg/cm^2 ',sigma_x,tau_xy)
+printf('\n The principal stresses are %.2f kg/cm^2 (tension) %.2f kg/cm^2 (compression) ',sigma_1,sigma_2)
diff --git a/2732/CH9/EX9.9/Ex9_9.sce b/2732/CH9/EX9.9/Ex9_9.sce new file mode 100755 index 000000000..48071caae --- /dev/null +++ b/2732/CH9/EX9.9/Ex9_9.sce @@ -0,0 +1,67 @@ +clc
+//initialization of variables
+clear
+P=3 //tonne/m
+s=6 //m
+l=50 //cm
+b=20 //cm
+k=0.5 //m
+//calculations
+R=P*s/2
+sf=R-k*P
+bm=R*k-P*k^2/2
+tau_xy=1.5*sf*1000/(l*b) //max shear stress
+tau_max=tau_xy
+str=bm*s*10^5/(b*l*l) //max bending stress
+
+// consider the line a-a
+
+sigma_x=str*12.5/25
+sigma_y=0
+tau_xy=tau_xy*(1-(12.5/25)^2)
+
+sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)
+sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)
+
+theta=1/2*atan(2*tau_xy/(sigma_x-sigma_y))
+sigma_p=sigma_1/cos(theta)
+P=sigma_p*2*l*b/(3*1000)
+printf('A prestressing force of %.2f Tonne must be applied to balance the tension at a-a',P)
+
+//At bottom point D or C
+pre_str=P*2*1000/(l*b)
+net=str-pre_str
+printf('\n At bottom point D or C')
+printf('\n Net tension = %.2f kg/cm^2 ',net)
+
+//consider the line b-b
+pre_str=P
+sigma_x=pre_str
+sigma_y=0
+tau_xy=tau_max
+sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)
+sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)
+printf('\n At section b-b')
+printf('\n pre-stress=%.2f kg/cm^2',pre_str)
+printf('\n principal stresses are %.2f, %.2f kg/cm^2 ',sigma_1,sigma_2)
+
+//for the line c-c
+sigma_x=str*12.5/25
+sigma_y=0
+tau_xy=tau_xy*(1-(12.5/25)^2)
+sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)
+sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)
+pre_str=pre_str/2
+net=sigma_1+pre_str
+sigma_x=net
+sigma_y=0
+sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)
+sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)
+// results
+printf('\n At section c-c')
+printf('\n the direct stress is %.2f kg/cm^2',net)
+printf('\n pre-stress = %.2f kg/cm^2',pre_str)
+printf('\n principal stresses are %.2f, %.2f kg/cm^2 ',sigma_1,sigma_2)
+
+// wrong calculations in the thext for some parts
+
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