summaryrefslogtreecommitdiff
path: root/3772/CH13
diff options
context:
space:
mode:
Diffstat (limited to '3772/CH13')
-rw-r--r--3772/CH13/EX13.10/Ex13_10.sce58
-rw-r--r--3772/CH13/EX13.2/Ex13_2.sce34
-rw-r--r--3772/CH13/EX13.3/Ex13_3.sce51
-rw-r--r--3772/CH13/EX13.4/Ex13_4.sce37
-rw-r--r--3772/CH13/EX13.5/Ex13_5.sce73
-rw-r--r--3772/CH13/EX13.6/Ex13_6.sce33
-rw-r--r--3772/CH13/EX13.7/Ex13_7.sce42
-rw-r--r--3772/CH13/EX13.8/Ex13_8.sce36
-rw-r--r--3772/CH13/EX13.9/Ex13_9.sce36
9 files changed, 400 insertions, 0 deletions
diff --git a/3772/CH13/EX13.10/Ex13_10.sce b/3772/CH13/EX13.10/Ex13_10.sce
new file mode 100644
index 000000000..6c381ddd9
--- /dev/null
+++ b/3772/CH13/EX13.10/Ex13_10.sce
@@ -0,0 +1,58 @@
+// Problem no 13.10,Page No.309
+
+clc;clear;
+close;
+
+b=25 //cm //width of top FLange
+t=5 //cm //thickness of top Flange
+D=35 //cm //Depth of overall section
+w_d=25 //cm //depth of web
+w_t=5 //cm //thickness of web
+t_1=5 //cm //thickness of bottom Flange
+b_1=15 //cm //width of bottom Flange
+sigma=17.5*10**6
+F=100*10**3 //N //S.F
+
+//Calculations
+
+a_1=b*t //area of top flange
+a_2=w_d*w_t //area of web
+a_3=b_1*t_1 //area of bottom Flange
+y_1=t*2**-1 //C.G of top flange
+y_3=D-(t_1*2**-1) //C.G of bottom Flange
+y_2=D*2**-1 //c.G of Web
+
+Y=(a_1*y_1+a_2*y_2+a_3*y_3)*(a_1+a_2+a_3)**-1
+
+I=b*t**3*12**-1+b*t*(Y-y_1)**2+w_t*w_d**3*12**-1+w_t*w_d*(D*2**-1-Y)**2+b_1*t_1**3*12**-1+b_1*t_1*(y_3-Y)**2
+
+M=sigma*I*10**-8*(Y*10**-2)**-1 //B.M
+
+//Shear Stress in upper Flange at the junction with web
+S_1=F*b*t*(Y-y_1)*10**-6*(I*10**-8*b*10**-2)**-1*10**-3
+
+//Shear Stress in web at the junction with upper Flange
+S_2=S_1*b*t**-1
+
+//Max shear stress at the N.A
+S=F*(b*t*(Y-y_1)+w_t*(Y-t)*(Y-t)*2**-1)*10**-6*(I*10**-8*w_t*10**-2)**-1*10**-3
+
+//Shear Stress in Lower Flange at the junction with web
+S_3=F*(a_3*(D-Y-t_1*2**-1))*10**-6*(I*10**-8*b_1*10**-2)**-1*10**-3
+
+//Shear Stress in web at the junction with Lower Flange
+S_4=S_3*b_1*t_1**-1
+
+//Result
+printf("The Bending Moment section can take is %.2f",M);printf(" N-m")
+printf("\n The shear stress Distribution Diagram")
+
+//Plotting the Shear stress distribution Diagram
+
+X_1=[0,5,5,15.19,30,30,35]
+Y_1=[0,S_1,S_2,S,S_3,S_4,0]
+Z_1=[0,0,0,0,0,0,0]
+plot(X_1,Y_1,X_1,Z_1)
+xlabel("Length x in m")
+ylabel("Shear Stress in kN/m**2")
+
diff --git a/3772/CH13/EX13.2/Ex13_2.sce b/3772/CH13/EX13.2/Ex13_2.sce
new file mode 100644
index 000000000..c4bb3ac8d
--- /dev/null
+++ b/3772/CH13/EX13.2/Ex13_2.sce
@@ -0,0 +1,34 @@
+// Problem no 13.2,Page No.301
+
+clc;clear;
+close;
+//W=10*w //KN/m //u.d.l
+sigma=805*10**6 //Pa //Bending stress
+Tou=0.85*10**6 //Pa //Shear stress
+
+//Calculations
+
+//M=W*L**2*10**-4*8**-1 //Max B.M
+//F=W*L*10**-2*2**-1 //Max S.F
+//y=h*2**-1 //depth
+//A-b*h //Area of c/s
+
+//Now using relation we get
+//sigma=M*h*(2*I)**-1 //Bending stress
+
+//AFter substituitng values we get
+//805*10**6=w*l**2*h*(16*10**5*I)**-1 //Equation 1
+
+//Again using the relation we get
+//tou=F*A*y_bar*(I*b)**-1 //shear atress
+
+//AFter substituitng values we get
+//0.85*10**6=w*L*h**2*(16*10**5*I)**-1 //Equation 2
+
+//Dividing equation 1 & 2 we get
+//L*h**-1=10
+//Let L*h**-1=Z
+z=10
+
+//Result
+printf("The Ratio of span to depth ratio is %.2f",z)
diff --git a/3772/CH13/EX13.3/Ex13_3.sce b/3772/CH13/EX13.3/Ex13_3.sce
new file mode 100644
index 000000000..04abb8e8d
--- /dev/null
+++ b/3772/CH13/EX13.3/Ex13_3.sce
@@ -0,0 +1,51 @@
+// Problem no 13.3,Page No.302
+
+clc;clear;
+close;
+
+L=2 //m //span
+w=20*10**3 //N/m //u.d.L
+b=12.5 //cm //width of Flange
+t=2.5 //cm //flange thickness
+w_t=2.5 //cm //web thickness
+D=20 //cm //Overall depth
+w_d=17.5 //m //Depth of web
+
+//Calculations
+
+F=w*L*2**-1 //N //Max S.F
+a_1=b*t //Area of flange
+a_2=w_d*w_t //Area of web
+y_1=t*2**-1 //C.G of flange
+y_2=w_d*2**-1+t //C.G of web
+
+//C.G of c/s
+Y=(a_1*y_1+a_2*y_2)*(a_1+a_2)**-1
+
+//M.I about N.A
+I=b*t**3*12**-1+b*t*(Y-y_1)**2+w_t*w_d**3*12**-1+w_t*w_d*(y_2-Y)**2
+
+//Shear Stress in flange at the junction with web
+//Let tou(Shear stress)=S
+//Change in the notifications of Shear Stress For convenience
+S_1=(F*a_1*(Y-y_1)*10**-6)*(I*10**-8*b*10**-2)**-1*10**-3
+
+//Shear Stress in web at the junction with flange
+S_2=(F*a_1*(Y-y_1)*10**-6)*(I*10**-8*w_t*10**-2)**-1*10**-3
+
+//Max Shear Stres at N.A
+S_max=(F*(a_1*(Y-y_1)+(w_t*(Y-t))*((Y-t)*2**-1))*10**-6)*(I*10**-8*w_t*10**-2)**-1*10**-3
+
+//Result
+printf("The Max shear stress in the beam is %.2f",S_max);printf(" KN/m**2")
+
+printf("\n\n Shear stress distribution Diagram")
+
+//Plotting the Shear stress distribution Diagram
+
+X_1=[0,2.5,2.5,4.58,15.42]
+Y_1=[0,S_1,S_2,S_max,0]
+Z_1=[0,0,0,0,0]
+plot(X_1,Y_1,X_1,Z_1)
+xlabel("Length x in m")
+ylabel("Shear Stress in kN/m**2")
diff --git a/3772/CH13/EX13.4/Ex13_4.sce b/3772/CH13/EX13.4/Ex13_4.sce
new file mode 100644
index 000000000..0cc8d1ef0
--- /dev/null
+++ b/3772/CH13/EX13.4/Ex13_4.sce
@@ -0,0 +1,37 @@
+// Problem no 13.4,Page No.303
+
+clc;clear;
+close;
+
+F=100*10**3 //N //Shear Force
+I=11340*10**-8 //m**4 //M.I
+b=20 //cm //width of Flange
+t=5 //cm //thickness of flange
+w_d=20 //cm //Depth of web
+w_t=5 //cm //thickness of web
+
+//Calculations
+
+a_1=b*t //cm**2 //Area of flange
+a_2=w_d*w_t //cm**2 //Area of web
+y_1=t*2**-1 //cm //C.G of flange
+y_2=t+w_d*2**-1
+
+//C.G of C/s
+Y=(a_1*y_1+a_2*y_2)*(a_1+a_2)**-1
+
+//Shear Stress in flange at the junction with web
+//Let tou(Shear stress)=S
+//Change in the notifications of Shear Stress For convenience
+S_1=(F*a_1*(Y-y_1)*10**-6)*(I*b*10**-2)**-1*10**-3
+
+//Shear Stress in web at the junction with flange
+S_2=(F*a_1*(Y-y_1)*10**-6)*(I*w_t*10**-2)**-1*10**-3
+
+//Max Shear Stres at N.A
+S_max=(F*(a_1*(Y-y_1)+(w_t*(Y-t))*((Y-t)*2**-1))*10**-6)*(I*w_t*10**-2)**-1*10**-3
+
+//Result
+printf("Shear Stress in flange at the junction with web %.2f",S_1);printf(" KN/m**2")
+printf("\n Shear Stress in web at the junction with flange %.2f",S_2);printf(" KN/m**2")
+printf("\n Max Shear Stress at N.A %.2f",S_max);printf(" KN/m**2")
diff --git a/3772/CH13/EX13.5/Ex13_5.sce b/3772/CH13/EX13.5/Ex13_5.sce
new file mode 100644
index 000000000..25c1ecc9b
--- /dev/null
+++ b/3772/CH13/EX13.5/Ex13_5.sce
@@ -0,0 +1,73 @@
+// Problem no 13.5,Page No.304
+
+clc;clear;
+close;
+
+D=50 //cm //Overall depth
+b=19 //cm //width of flange
+t=2.5 //cm //Thickness of Flange
+w_t=1.5 //cm //Web thickness
+w_d=45 //cm //web thickness
+F=400*10**3 //N //Shear Force
+I=64500*10**-8 //m**4 //M.I
+
+//Calculations (Part-1)
+
+a_1=b*t //cm**2 //Area of flange
+a_2=w_d*w_t //cm**2 //Area of web
+y_1=t*2**-1 //cm //C.G of flange
+y_2=t+w_d*2**-1
+
+//As section is symmetrical
+Y=D*2**-1 //cm
+
+//Shear Stress in flange at the junction with web
+//Let tou(Shear stress)=S
+//Change in the notifications of Shear Stress For convenience
+S_1=(F*a_1*(Y-y_1)*10**-6)*(I*b*10**-2)**-1*10**-3
+
+//Shear Stress in web at the junction with flange
+S_2=(F*a_1*(Y-y_1)*10**-6)*(I*w_t*10**-2)**-1*10**-3
+
+//Max Shear Stres at N.A
+S_max=(F*(a_1*(Y-y_1)+(w_t*(Y-t))*((Y-t)*2**-1))*10**-6)*(I*w_t*10**-2)**-1*10**-3 //kPa
+
+//Calculations (Part-2)
+
+//consider a strip in the flange of thickness dy at a distance y from N.A
+
+//S=F*(b*(Y-y)*(Y+y)*2**-1*10**-6)*(I*b*10**-2)**-1
+//after substituting values we get
+//S=625-y**2*(3225*10**-8)**-1
+
+//shear force carried by small strip
+//F_1=625-y**2*(3225*10**-8)**-1*b*dy*10**-4
+
+//Now Integrating above Equation we get
+a =625
+b =-1
+I = integrate('625-y**2','y', 22.5, 25)//, args=(a,b))
+//Shear force carried by one flange
+F_1=19*3225**-1*10**4*I
+
+//Shear force carried by two flange
+F_2=2*F_1
+
+//Shear force carried by web
+F_3=F-F_2
+
+//Result
+printf("The shear Force int the section is %.2f",S_max);printf(" kPa")
+printf("\n Total Shear Force in the web is %.2f",F_3);printf(" N")
+
+
+printf("\n Shear stress distribution Diagram")
+
+//Plotting the Shear stress distribution Diagram
+
+X_1=[0,2.5,2.5,25,47.5,47.5,50]
+Y_1=[0,S_1,S_2,S_max,S_2,S_1,0]
+Z_1=[0,0,0,0,0,0,0]
+plot(X_1,Y_1,X_1,Z_1)
+xlabel("Length x in m")
+ylabel("Shear Stress in kN/m**2")
diff --git a/3772/CH13/EX13.6/Ex13_6.sce b/3772/CH13/EX13.6/Ex13_6.sce
new file mode 100644
index 000000000..ff945c0eb
--- /dev/null
+++ b/3772/CH13/EX13.6/Ex13_6.sce
@@ -0,0 +1,33 @@
+// Problem no 13.6,Page No.305
+
+clc;clear;
+close;
+
+F=5*10**3 //N //shea Force
+b=20 //cm //width of Flange
+t=6 //cm //Thickness of flange
+w_d=20 //cm //depth of web
+w_t=6 //cm //thickness of web
+X=700 //N //Shear Looad
+
+//Calculations
+
+a_1=b*t //cm**2 //Area ofFlange
+a_2=w_d*w_t //cm**2 //Area of web
+y_1=t*2**-1 //cm //C.G of Flange
+y_2=t+w_d*2**-1 //cm //C.G of Web
+
+Y=(a_1*y_1+a_2*y_2)*(a_1+a_2)**-1
+
+//M.I about N.A
+I=b*t**3*12**-1+b*t*(Y-y_1)**2+w_t*w_d**3*12**-1+w_t*w_d*(y_2-Y)**2
+
+//Shear Force per metre Length in Plane of contact of two Planks
+//Let Shear Force per metre Length=F_1
+F_1=(F*a_1*(Y-y_1)*10**-6)*(I*10**-8)**-1
+
+//Spacing of nails
+s=X*F_1**-1*100
+
+//Result
+printf("The spacing of nails along the Length of beam is %.2f",s);printf(" cm")
diff --git a/3772/CH13/EX13.7/Ex13_7.sce b/3772/CH13/EX13.7/Ex13_7.sce
new file mode 100644
index 000000000..9dc2647cc
--- /dev/null
+++ b/3772/CH13/EX13.7/Ex13_7.sce
@@ -0,0 +1,42 @@
+// Problem no 13.7,Page No.306
+
+clc;clear;
+close;
+
+L=3 //m //span
+d=5 //cm //depth of each plank
+b=15 //cm //width of plank
+d_1=1.9 //cm //Diameter of bolt
+s=12.5 //cm //spacing of bolt
+w=3.3*10**3 //N.m //u.d.l
+
+//Calculations
+
+//Shear Force at 1.5m from support
+F=w*1.5
+
+I=b*(5*d)**3*12**-1 //M.I
+A=%pi*4**-1*d_1**2 //area of Bolt
+Y=5*d*2**-1 //C.G of beam
+y_1=d*2**-1 //c.G of top plank
+
+//Shear Force per metre Length
+F_1=F*b*d*(Y-y_1)*10**-6*(I*10**-8)**-1
+
+//Load carried by bolt
+W_1=F_1*s*10**-2
+
+//shear stress
+X_1=W_1*A**-1*10**+4
+
+//Shear Force per metre Length
+F_2=F*b*2*d*((d+y_1)-Y*10**-6)*(I*10**-8)**-1*10**-6
+
+//Load carried by bolt
+W_2=F_2*s*10**-2
+
+//shear stress
+X_2=W_2*(A*10**-4)**-1*10**-3
+
+//Reult
+printf("Shear stress in a bolt Located at 1.5 m from support is %.2f",X_2);printf(" KN/m**2")
diff --git a/3772/CH13/EX13.8/Ex13_8.sce b/3772/CH13/EX13.8/Ex13_8.sce
new file mode 100644
index 000000000..8ba8f6c7b
--- /dev/null
+++ b/3772/CH13/EX13.8/Ex13_8.sce
@@ -0,0 +1,36 @@
+// Problem no 13.8,Page No.307
+
+clc;clear;
+close;
+
+b=15 //cm //width of plank
+t=2.5 //cm //thickness of planf
+F_1=1250 //N //Shear Force
+F_2=5*10**3 //shaear force transmitted by screw
+d=15 //cm //Depth of plank
+D=20 //cm //Overall depth
+
+//Calculations
+
+Y=D*2**-1 //C.G of beam
+y_1=t*2**-1 //C.G of flange
+
+I=((b*D**3)-(D*2**-1*b**3))*12**-1 //cm**4 //M.I
+
+//Shear Stress in the Flange at 7.5 cm from N.A
+X_1=F_2*b*t*(Y-y_1)*10**-6*(I*10**-8*d*10**-2)**-1*10**-3
+
+//Shear Stress in the web at 7.5 cm from N.A
+X_2=X_1*d*(2*t)**-1
+
+//shear stress at N.A
+X_max=F_2*(b*t*(Y-y_1)+2*t*d*2**-1*d*4**-1)*10**-6*(I*10**-8*2*t*10**-2)**-1*10**-3
+
+//horizontal shear force per %pitch length to the shearing strength of two bolts we have
+//X_h=X_2*10**3*2*t*10**-2*p
+
+//Equating horizontal shear force per %pitch length to the shearing strength of two bolts we have
+p=F_1*2*(X_2*10**3*2*t*10**-2)**-1*10**2
+
+//Result
+printf("The Min spacing of screw along the beam is %.2f",p);printf(" cm")
diff --git a/3772/CH13/EX13.9/Ex13_9.sce b/3772/CH13/EX13.9/Ex13_9.sce
new file mode 100644
index 000000000..60f3477de
--- /dev/null
+++ b/3772/CH13/EX13.9/Ex13_9.sce
@@ -0,0 +1,36 @@
+// Problem no 13.9,Page No.308
+
+clc;clear;
+close;
+
+L=4 //m //span
+w=80*10**3 //N/m //u.d.l
+D=35 //cm //Overall depth
+b=15 //cm //width of Flange
+t=2.5 //cm //Thickness of flange
+w_d=30 //cm //Depth of web
+w_t=1.2 //cm //thickness of web
+
+//Calculations
+
+R_a=160;R_b=160 //KN //Reactions at supports
+
+//Shear FOrce at 1m from left support
+F=R_a*10**3-w
+
+M=R_a*10**3-w*2**-1 //B.M at 1m From support
+
+I=(b*D**3-((b-w_t)*w_d**3))*12**-1 //cm**4
+
+y=w_d*2**-1
+sigma=M*I**-1*y //N/m**2
+
+//Shear stress in Flange at the junction with web
+X_1=w*b*t*(w_d*2**-1+t*2**-1)*10**-6*(I*10**-8*b*10**-2)**-1*10**-3
+
+//Shear stress in web at the junction with Flange
+X_2=X_1*15*1.2**-1
+
+//Result
+printf("The Magnitude of Bending is %.2f",sigma);printf(" N/m**2")
+printf("\n Shear stress in web at the junction with Flange %.2f",X_1);printf(" KN/m**2")
generated by cgit (git 2.34.1) at 2024-12-19 12:48:20 +0000