13 files changed, 214 insertions, 0 deletions

diff --git a/3683/CH1/EX1.1/Ex1_1.sce b/3683/CH1/EX1.1/Ex1_1.sce
new file mode 100644
index 000000000..45338b80f
--- /dev/null
+++ b/3683/CH1/EX1.1/Ex1_1.sce
@@ -0,0 +1,14 @@
+//let the depth of neutral axis be x

+b=200//width, in mm

+d=350//effective depth, in mm

+m=18.66 //modular ratio

+sigma_cbc=5//in MPa

+sigma_st=140//in MPa

+x=d/(1+sigma_st/(m*sigma_cbc))//in mm

+mprintf("The depth of neutral axis = %f mm\n", x)

+//to find area of steel

+Ast=b*x*sigma_cbc/(2*sigma_st)//in sq mm

+mprintf("Area of steel = %f mm^2\n", Ast)

+//to find percentage steel

+pst=Ast*100/(b*d)//in %

+mprintf("Percentage of steel = %f percent\n", pst) 

diff --git a/3683/CH1/EX1.10/Ex1_10.sce b/3683/CH1/EX1.10/Ex1_10.sce
new file mode 100644
index 000000000..3c51a0e1d
--- /dev/null
+++ b/3683/CH1/EX1.10/Ex1_10.sce
@@ -0,0 +1,19 @@
+b=300//width, in mm

+D=700//overall depth, in mm

+Ast=4*.785*25^2//four 25mm dia bars, in sq mm

+cover=30//in mm

+d=D-cover//effective depth, in mm

+M=130*10^6//bending moment, in N-mm

+m=18.66//modular ratio

+//to find actual depth of neutral axis using b(x^2)/2=mAst(d-x), which becomes of the form px^2+qx+r=0

+p=b/2

+q=m*Ast

+r=-m*Ast*d

+x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm

+z=d-x/3//lever arm, in mm

+//assuming under-reinforced section, Mr=Ast*sigma_st(d-x/3) and equating Mr to M

+sigma_st=M/(Ast*z)//in MPa

+sigma_st=116//round-off, in MPa

+sigma_cbc=(sigma_st/m)*x/(d-x)//in MPa

+sigma_cbc=5//round-off, in MPa

+mprintf("Stress in steel=%d N/mm^2\nStress in concrete=%d N/mm^2",sigma_st,sigma_cbc)

diff --git a/3683/CH1/EX1.11/Ex1_11.sce b/3683/CH1/EX1.11/Ex1_11.sce
new file mode 100644
index 000000000..450118582
--- /dev/null
+++ b/3683/CH1/EX1.11/Ex1_11.sce
@@ -0,0 +1,19 @@
+b=350//width, in mm

+D=650//overall depth, in mm

+Ast=4*.785*22^2//four 22mm dia bars, in sq mm

+cover=25//in mm

+d=D-cover//effective depth, in mm

+W=20//UDL, in kN/m

+l=7//span, in m

+M=W*l^2/8*10^6//bending moment, in N-mm 

+m=13.33//modular ratio

+//to find actual depth of neutral axis using b(x^2)/2=mAst(d-x), which becomes of the form px^2+qx+r=0

+p=b/2

+q=m*Ast

+r=-m*Ast*d

+x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm

+z=d-x/3//lever arm, in mm

+//assuming under-reinforced section, Mr=Ast*sigma_st(d-x/3) and equating Mr to M

+sigma_st=M/(Ast*z)//in MPa

+sigma_cbc=(sigma_st/m)*x/(d-x)//in MPa

+mprintf("Stress in steel=%f N/mm^2\nStress in concrete=%f N/mm^2",sigma_st,sigma_cbc)

diff --git a/3683/CH1/EX1.12/Ex1_12.sce b/3683/CH1/EX1.12/Ex1_12.sce
new file mode 100644
index 000000000..bf05bff0d
--- /dev/null
+++ b/3683/CH1/EX1.12/Ex1_12.sce
@@ -0,0 +1,12 @@
+b=250//width, in mm

+sigma_cbc=5//in MPa

+sigma_st=190//in MPa

+m=280/(3*sigma_cbc)//modular ratio

+M=75*10^6//bending moment, in N-mm

+//critical depth of neutral axis, Xc=d/(1+sigma_st/(m*sigma_cbc))=a*d

+a=1/(1+sigma_st/(m*sigma_cbc))

+d=(M/(b*sigma_cbc*a*(1-a/3)/2))^0.5//in mm

+d=640//round-off, in mm

+Xc=a*d//in mm

+Ast=b*Xc*sigma_cbc/(2*sigma_st)//in sq mm

+mprintf("Effective depth=%d mm\nArea of steel=%f mm^2",round(d),Ast)

diff --git a/3683/CH1/EX1.13/Ex1_13.sce b/3683/CH1/EX1.13/Ex1_13.sce
new file mode 100644
index 000000000..b5de4b312
--- /dev/null
+++ b/3683/CH1/EX1.13/Ex1_13.sce
@@ -0,0 +1,14 @@
+//b=d/2 (given)

+sigma_cbc=5//in MPa

+sigma_st=140//in MPa

+m=18.66//modular ratio

+M=65*10^6//bending moment, in N-mm

+//critical depth of neutral axis, Xc=d/(1+sigma_st/(m*sigma_cbc))=a*d

+a=1/(1+sigma_st/(m*sigma_cbc))

+d=(M/(sigma_cbc*a*(1-a/3)/4))^(1/3)//in mm

+d=530//round-off, in mm

+Xc=a*d//in mm

+b=d/2//in mm

+Ast=M/sigma_st/0.87/d//in sq mm

+Ast=1007//round-off, in sq mm

+mprintf("Dimensions of section=%d x %d mm\nArea of steel=%d mm^2",b,d,Ast)

diff --git a/3683/CH1/EX1.2/Ex1_2.sce b/3683/CH1/EX1.2/Ex1_2.sce
new file mode 100644
index 000000000..483b1dd7c
--- /dev/null
+++ b/3683/CH1/EX1.2/Ex1_2.sce
@@ -0,0 +1,12 @@
+//let the depth of neutral axis be x

+b=150//width, in mm

+d=400//effective depth, in mm

+Ast=804//area of steel, in sq mm

+m=18.66//modular ratio

+//b(x^2)/2=mAst(d-x)-->this becomes a quadratic equation of form px^2+qx+r=0

+p=b/2

+q=m*Ast

+r=-m*Ast*d

+//solving the quadratic equation

+x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm

+mprintf("The depth of neutral axis = %f mm", x)

diff --git a/3683/CH1/EX1.3/Ex1_3.sce b/3683/CH1/EX1.3/Ex1_3.sce
new file mode 100644
index 000000000..533537c99
--- /dev/null
+++ b/3683/CH1/EX1.3/Ex1_3.sce
@@ -0,0 +1,12 @@
+//assume d = 400 mm and b = 200 mm

+b=200//in mm

+d=400//in mm

+sigma_cbc=5//in MPa

+sigma_st=140//in MPa

+m=18.66//modular ratio

+Xc=d/(1+sigma_st/m/sigma_cbc)//in mm

+z=d-Xc/3//in mm

+Mr=b*Xc*sigma_cbc/2*z//in N-mm

+Ast=b*Xc*sigma_cbc/2/sigma_st//in sq mm

+pt=Ast*100/b/d//in %

+mprintf("When d is assumed as 400 mm and b as 200 mm\n(a) Position of neutral axis=%f mm\n(b) Lever arm=%f mm\n(c) Moment of resistance=%f kN-m\n(d) Percentage of steel=%f percent",Xc,z,Mr/10^6,pt)

diff --git a/3683/CH1/EX1.4/Ex1_4.sce b/3683/CH1/EX1.4/Ex1_4.sce
new file mode 100644
index 000000000..0866ccd58
--- /dev/null
+++ b/3683/CH1/EX1.4/Ex1_4.sce
@@ -0,0 +1,10 @@
+b=250//width, in mm

+d=500//effective depth, in mm

+sigma_cbc=5//in MPa

+sigma_st=140//in MPa

+m=18.66//modular ratio

+//to find critical depth of neutral axis

+Xc=d/(1+sigma_st/(m*sigma_cbc))//in mm

+z=d-Xc/3//lever arm, in mm

+Mr=b*Xc*sigma_cbc*z/2//in N-mm

+mprintf("Moment of resistance of the beam = %f kN-m",Mr/10^6)

diff --git a/3683/CH1/EX1.5/Ex1_5.sce b/3683/CH1/EX1.5/Ex1_5.sce
new file mode 100644
index 000000000..6539b9de7
--- /dev/null
+++ b/3683/CH1/EX1.5/Ex1_5.sce
@@ -0,0 +1,18 @@
+b=250//width, in mm

+D=550//overall depth, in mm

+Ast=1521//area of steel, in sq mm

+cover=25//in mm

+d=D-cover//effective depth, in mm

+sigma_cbc=7//in MPa

+sigma_st=140//in MPa

+m=13.33//modular ratio

+//to find critical depth of neutral axis

+Xc=d/(1+sigma_st/(m*sigma_cbc))//in mm

+//to find actual depth of neutral axis using b(x^2)/2=mAst(d-x)--> this will become of the form px^2+qx+r=0

+p=b/2

+q=m*Ast

+r=-m*Ast*d

+x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm

+//x>Xc; hence beam is over-reinforced

+Mr=b*x*sigma_cbc/2*(d-x/3)//in N-mm

+mprintf("Moment of resistance of the beam=%f kN-m",Mr/10^6)

diff --git a/3683/CH1/EX1.6/Ex1_6.sce b/3683/CH1/EX1.6/Ex1_6.sce
new file mode 100644
index 000000000..9729b27b1
--- /dev/null
+++ b/3683/CH1/EX1.6/Ex1_6.sce
@@ -0,0 +1,16 @@
+b=200//width, in mm

+d=450//effective depth, in mm

+Ast=3*.785*16^2//three 16 dia bars, in sq mm

+sigma_cbc=5//in MPa

+sigma_st=140//in MPa

+m=18.66//modular ratio

+//to find critical depth of neutral axis

+Xc=d/(1+sigma_st/(m*sigma_cbc))//in mm

+//to find actual depth of neutral axis using b(x^2)/2=mAst(d-x), which becomes of form px^2+qx+r=0

+p=b/2

+q=m*Ast

+r=-m*Ast*d

+x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm

+//as x<Xc, beam is under-reinforced

+Mr=Ast*sigma_st*(d-x/3)//in N-mm

+mprintf("Moment of resistance of the beam = %f kN-m", Mr/10^6)

diff --git a/3683/CH1/EX1.7/Ex1_7.sce b/3683/CH1/EX1.7/Ex1_7.sce
new file mode 100644
index 000000000..3e9345b47
--- /dev/null
+++ b/3683/CH1/EX1.7/Ex1_7.sce
@@ -0,0 +1,24 @@
+b=300//width, in mm

+D=700//overall depth, in mm

+Ast=3*.785*20^2//3-20mm dia bars, in sq mm

+cover=50//in mm

+d=D-cover//effective depth, in mm

+sigma_cbc=7//in MPa

+sigma_st=190//in MPa

+m=13.33//modular ratio

+l=6//span, in m

+w=25//unit weight of concrete, in kN/m^3

+//to find critical depth of neutral axis

+Xc=d/(1+sigma_st/(m*sigma_cbc))//in mm

+//to find actual depth of neutral axis using b(x^2)/2=mAst(d-x), which becomes of the form px^2+qx+r=0

+p=b/2

+q=m*Ast

+r=-m*Ast*d

+//solving quadratic equation

+x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm

+//x<Xc, hence beam is under-reinforced

+Mr=sigma_st*Ast*(d-x/3)//in N-mm

+UDL=(Mr/10^6)*8/l^2//in kN/m

+self_weight=w*b*D/10^6//in kN/m

+net_weight=UDL-self_weight//in kN/m

+mprintf("Moment of resistance=%f kN-m\nSafe uniformly distributed load that the beam can carry=%f kN/m",Mr/10^6,net_weight)

diff --git a/3683/CH1/EX1.8/Ex1_8.sce b/3683/CH1/EX1.8/Ex1_8.sce
new file mode 100644
index 000000000..4d58db746
--- /dev/null
+++ b/3683/CH1/EX1.8/Ex1_8.sce
@@ -0,0 +1,22 @@
+b=250//width, in mm

+D=500//overall depth, in mm

+Ast=4*.785*22^2//four 22 mm dia bars, in sq mm

+cover=25//in mm

+d=D-cover//effective depth, in mm

+l=5//effective span, in m

+sigma_cbc=5//in MPa

+sigma_st=190//in MPa

+m=18.66//modular ratio

+//to find critical depth of neutral axis

+Xc=d/(1+sigma_st/(m*sigma_cbc))//in mm

+//to find actual depth of neutral axis using b(x^2)/2=mAst(d-x), which becomes of the form px^2+qx+r=0

+p=b/2

+q=m*Ast

+r=-m*Ast*d

+x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm

+//as x>Xc, beam is over-reinforced

+Mr=b*sigma_cbc*x/2*(d-x/3)//in N-mm

+self_weight=25*(b/10^3)*(D/10^3)//in kN/m

+M=Mr/10^6-self_weight*l^2/8//moment of resistance available for external load, in kN-m

+W=4*M/l//in kN

+mprintf("The concentrated load the beam can support at centre=%f kN",W)

diff --git a/3683/CH1/EX1.9/Ex1_9.sce b/3683/CH1/EX1.9/Ex1_9.sce
new file mode 100644
index 000000000..40a69ff7d
--- /dev/null
+++ b/3683/CH1/EX1.9/Ex1_9.sce
@@ -0,0 +1,22 @@
+d=120//effective depth of slab, in mm

+//consider 1 m strip of slab

+b=1000//in mm

+s=80//spacing of 12mm dia bars centre-to-centre, in mm

+Ast=1000*.785*12^2/s//in sq mm

+l=3.2//span, in m

+sigma_cbc=7//in MPa

+sigma_st=140//in MPa

+m=13.33//modular ratio

+//to find critical depth of neutral axis

+Xc=d/(1+sigma_st/(m*sigma_cbc))//in mm

+//to find actual depth of neutral axis using b(x^2)/2=mAst(d-x), which becomes of the form px^2+qx+r=0

+p=b/2

+q=m*Ast

+r=-m*Ast*d

+x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm

+//as x>Xc, the beam is over-reinforced

+Mr=b*sigma_cbc*x/2*(d-x/3)/10^6//in kN-m

+UDL=Mr*8/l^2//in kN/m

+self_weight=25*(d/10^3)*(b/10^3)//in kN/m

+W=UDL-self_weight//in kN/m

+mprintf("The safe load for slab=%f kN/m",W)