diff options
Diffstat (limited to '3683')
130 files changed, 4044 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)
diff --git a/3683/CH10/EX10.1/Ex10_1.sce b/3683/CH10/EX10.1/Ex10_1.sce new file mode 100644 index 000000000..e7d9e4374 --- /dev/null +++ b/3683/CH10/EX10.1/Ex10_1.sce @@ -0,0 +1,31 @@ +l=1//span, in m
+t=0.27//tread in m
+sigma_cbc=5//in MPa
+sigma_st=140//in MPa
+MF=1.6
+a=MF*7
+D=l*10^3/a//in mm
+D=100//assume, in mm
+W1=D/10^3*t*25//in kN/m
+M1=W1*l/2//in kN-m
+M2=t*3*l/2//in kN-m
+M3=1.3*l//in kN-m
+M=M1+max(M2,M3)//in kN-m
+d=sqrt(M*10^6/0.87/t/10^3)//in mm
+d=83//in mm
+//assume 8 mm dia bars
+dia=8//in mm
+D=d+dia/2+15//this is slightly more than assumed value, hence OK
+D=100//in mm
+z=0.87*d//in mm
+Ast=M*10^6/sigma_st/z//in sq mm
+n=Ast/0.785/8^2
+n=4//assume
+Ads=0.15/100*D*t*10^3//distribution steel, in sq mm
+//provide 6 mm dia bars
+s=1000*0.785*6^2/Ads//>5d=415 mm
+s=415//in mm
+Tbd=0.6//in MPa
+Ld=dia*sigma_st/4/Tbd//in mm
+Ld=470//assume, in mm
+mprintf("Summary of design\nThickness of steps=%d mm\nCover from top=15 mm\nMain steel = 8 mm dia, %d in each step with development length of %d mm\nDistribution steel = 6 mm dia @ %d mm c/c",D,n,Ld,s)
diff --git a/3683/CH10/EX10.2/Ex10_2.sce b/3683/CH10/EX10.2/Ex10_2.sce new file mode 100644 index 000000000..1365a39d9 --- /dev/null +++ b/3683/CH10/EX10.2/Ex10_2.sce @@ -0,0 +1,33 @@ +l=2.7+1//span, in m
+R=0.15//rise, in m
+t=0.27//tread, in m
+sigma_cbc=5//in MPa
+sigma_st=230//in MPa
+//assuming 50 mm per 1 m of span
+D=50*l//in mm
+D=200//assume, in mm
+W1=D/10^3*25*sqrt(R^2+t^2)/t//slab load on plan, in kN/m
+W2=1/2*R*t*25/t//load of step per metre, in kN/m
+W3=3//live load, in kN/m
+W=W1+W2+W3//in kN/m
+M=W*l^2/8//in kN-m
+d=sqrt(M*10^6/0.65/10^3)//in mm
+d=170//in mm
+//assume 10 mm dia bars
+dia=10//in mm
+D=d+dia/2+25//which is equal to assumed value, hence OK
+z=0.9*d//in mm
+Ast=M*10^6/sigma_st/z//in mm
+s1=1000*0.785*dia^2/Ast//spacing of 10 mm dia bars
+s1=150//assume, in mm
+Ads=0.12/100*D*10^3//distribution steel, in sq mm
+//provide 8 mm dia bars
+s2=1000*0.785*8^2/Ads//in mm
+s2=210//in mm
+//let span-to-depth ratio be 'a'
+a=l*10^3/D
+//for Fe415 grade steel and pt=.32
+MF=1.2
+b=20*MF//permissible span-to-depth ratio
+//as a<b, hence OK
+mprintf("Summary of design\nSlab thickness=%d mm\nCover = 25 mm\nMain steel = 10 mm dia bars @ %d mm c/c\nDistribution steel = 8 mm dia @ %d mm c/c",D,s1,s2)
diff --git a/3683/CH10/EX10.3/Ex10_3.sce b/3683/CH10/EX10.3/Ex10_3.sce new file mode 100644 index 000000000..d5caa30b5 --- /dev/null +++ b/3683/CH10/EX10.3/Ex10_3.sce @@ -0,0 +1,35 @@ +l=2.5+1.5//span, in m
+R=0.15//rise, in m
+t=0.25//tread in m
+sigma_cbc=7//in MPa
+sigma_st=275//in MPa
+//assuming 50 mm per 1 m of span
+D=50*l//in mm
+W1=D/10^3*25*1.5*sqrt(R^2+t^2)/t//slab load on plan, in kN/m
+W2=1/2*R*t*1.5*25/t//load of step per metre, in kN/m
+W3=1.5*5//live load, in kN/m
+W=W1+W2+W3//in kN/m
+M=W*l^2/8//in kN-m
+d=sqrt(M*10^6/0.81/1.5/10^3)//in mm
+d=177//in mm
+//assume 10 mm dia bars
+dia=10//in mm
+D=d+dia/2+25//which is slightly more than assumed value, hence OK
+D=200//in mm
+d=D-dia/2-25//in mm
+z=0.92*d//in mm
+Ast=M*10^6/sigma_st/z//in sq mm
+s1=1500*0.785*dia^2/Ast//spacing of 10 mm dia bars, in mm
+s1=130//assume, in mm
+Ads=0.12/100*D*1.5*10^3//distribution steel, in sq mm
+//provide 8 mm dia bars
+s2=1000*0.785*8^2/Ads//in mm
+s2=140//in mm
+//let span-to-depth ratio be 'a'
+a=l*10^3/D
+pt=Ast/1500/D*100//pt=0.3
+//for Fe500 grade steel and pt=.3
+MF=1.2
+b=20*MF//permissible span-to-depth ratio
+//as a<b, hence OK
+mprintf("Summary of design\nSlab thickness=%d mm\nCover = 25 mm\nMain steel = 10 mm dia bars @ %d mm c/c\nDistribution steel = 8 mm dia @ %d mm c/c",D,s1,s2)
diff --git a/3683/CH10/EX10.4/Ex10_4.sce b/3683/CH10/EX10.4/Ex10_4.sce new file mode 100644 index 000000000..2b0da9bc0 --- /dev/null +++ b/3683/CH10/EX10.4/Ex10_4.sce @@ -0,0 +1,54 @@ +R=0.15//rise, in m
+t=0.3//tread, in m
+sigma_cbc=5//in MPa
+sigma_st=230//in MPa
+l1=1.8+1.5//span for flight AB, in m
+l2=1.2+1.5+1.5//span for flight BC, in m
+l3=1.8+1.5//span for flight CD, in m
+//assuming 50 mm slab thickness per 1 m of span
+D=50*l2//slab thickness, in mm
+W1=D/10^3*25*1.5*sqrt(R^2+t^2)/t//slab load on plan, in kN/m
+W2=1/2*R*t*1.5*25/t//load of step per metre, in kN/m
+W3=1.5*5//live load, in kN/m
+W=W1+W2+W3//in kN/m
+//bending moment
+//(a) flight AB and CD, refer Fig. 10.9
+Rb=(W/2*1.5*(1.8+1.5/2)+W*1.8^2/2)/(1.5+1.8)//in kN
+Ra=W/2*1.5+W*1.8-Rb//in kN
+x=Ra/Rb//point of zero shear force from Ra, in m
+M1=Ra*x-W*x^2/2//maximum bending moment, in kN-m
+//(b) flight BC, refer Fig. 10.10
+Rb=(W/2*1.5^2/2+W*1.2*(1.2/2+1.5)+W/2*1.5*(1.5+1.2+1.5/2))/(1.5+1.2+1.5)//in kN
+Rc=Rb//in kN
+//maximum bending moment will be at centre
+M2=Rb*(1.5+1.2/2)-W/2*1.5*(1.5/2+1.2/2)-W*(1.2/2)^2/2//maximum bending moment, in kN-m
+M=max(M1,M2)//in kN/m
+d=sqrt(M*10^6/0.65/1.5/10^3)//in mm
+//assume 10 mm dia bars
+dia=10//in mm
+D=d+dia/2+25//< 210 mm (assumed value)
+D=210//in mm
+d=D-dia/2-25//in mm
+//steel
+//flight AB and CD
+z=0.9*d//in mm
+Ast=M1*10^6/sigma_st/z//in sq mm
+s1=1500*0.785*dia^2/Ast//spacing of 10 mm dia bars, in mm
+s1=210//round-off, in mm
+Ads=0.12/100*D*1.5*10^3//distribution steel, in sq mm
+//provide 6 mm dia bars
+s2=1000*0.785*6^2/Ads//in mm
+s2=70//round-off, in mm
+//flight BC
+Ast=M2*10^6/sigma_st/z//in sq mm
+s3=1500*0.785*dia^2/Ast//spacing of 10 mm dia bars, in mm
+s3=130//round-off, in mm
+//distribution steel is same as flights AB and CD
+//let span-to-depth ratio be 'a'
+a=l2*10^3/D
+//for Fe415 grade steel and pt=.32
+MF=1.2//modification factor
+b=20*MF//permissible span-to-depth ratio
+//as a < b, hence OK
+mprintf("Summary of design\nSlab thickness=%d mm\nCover = 25 mm\n(a)Flight AB and CD\nMain steel = 10 mm dia bars @ %d mm c/c\nDistribution steel = 6 mm dia @ %d mm c/c\n(b)Flight BC\nMain steel = 10 mm dia bars @ %d mm c/c\nDistribution steel = 6 mm dia @ %d mm c/c",D,s1,s2,s3,s2)
+//answer in textbook is incorrect
diff --git a/3683/CH11/EX11.1/Ex11_1.sce b/3683/CH11/EX11.1/Ex11_1.sce new file mode 100644 index 000000000..dc50b33f8 --- /dev/null +++ b/3683/CH11/EX11.1/Ex11_1.sce @@ -0,0 +1,46 @@ +b=0.2//column width in m
+D=0.3//column depth in m
+fck=15//in MPa
+sigma_cbc=5//in MPa
+sigma_st=230//in MPa
+P1=600//load on column in kN
+P2=0.05*P1//weight of footing, in kN
+P=P1+P2//in kN
+q=150//bearing capacity of soil in kN/sq m
+A=P/q//in sq m
+L=sqrt(A)//assuming footing to be square
+L=2.1//assume, in m
+p=P1/L^2//soil pressure, in kN/sq m
+p=136//assume, in sq m
+bc=b/D
+ks=0.5+bc//>1
+ks=1
+Tc=0.16*sqrt(fck)*10^3//in kN/sq m
+Tv=Tc
+//let d be the depth of footing in metres
+//case I: consider greater width of shaded portion in Fig. 11.3 of textbook
+d1=L*(L-b)/2*p/(Tc*L+L*p)//in m
+//case II: refer Fig. 11.4 of textbook; we get a quadratic equation of the form e d^2 + f d + g = 0
+e=p+4*Tc
+f=b*p+D*p+2*(b+D)*Tc
+g=-(L^2-b*D)*p
+d2=(-f+sqrt(f^2-4*e*g))/2/e//in m
+d2=0.362//assume, in m
+//bending moment consideration, refer Fig. 11.5 of textbook
+Mx=1*((L-b)/2)^2/2*p//in kN-m
+My=1*((L-D)/2)^2/2*p//in kN-m
+d3=sqrt(Mx*10^6/0.65/10^3)//<362 mm, hence OK
+z=0.9*d2*10^3//lever arm, in mm
+Ast1=(Mx*10^6/sigma_st/z)//in sq mm
+Ast=L*Ast1//steel required for full width of 2.1 m, in sq mm
+//provide 12 mm dia bars
+dia=12//in mm
+n=Ast/0.785/dia^2//no. of 12 mm dia bars
+n=16//assume
+Tbd=0.84//in MPa
+Ld=dia*sigma_st/4/Tbd//in mm
+Ld=825//assume, in mm
+c=50//side cover, in mm
+La=(L-D)/2*10^3-c//>Ld, hence OK
+D=d2*10^3+dia/2+100//in mm
+mprintf("Summary of design:\nOverall depth of footing=%d mm\nCover=100 mm bottom; 50 mm side\nSteel-%d bars of 12 mm dia both ways",D,n)
diff --git a/3683/CH11/EX11.2/Ex11_2.sce b/3683/CH11/EX11.2/Ex11_2.sce new file mode 100644 index 000000000..a242e5dcb --- /dev/null +++ b/3683/CH11/EX11.2/Ex11_2.sce @@ -0,0 +1,47 @@ +b=0.4//column width, in m
+D=0.4//column depth, in m
+fck=15//in MPa
+sigma_cbc=5//in MPa
+sigma_st=140//in MPa
+P1=1000//load on column, in kN
+P2=0.05*P1//weight of footing, in kN
+P=P1+P2//in kN
+q=200//bearing capacity of soil, in kN/sq m
+A=P/q//in sq m
+L=sqrt(A)//assuming footing to be square
+L=2.3//assume, in m
+p=P1/L^2//soil pressure, in kN/sq m
+p=189//assume, in kN/sq m
+bc=b/D
+ks=0.5+bc//>1
+ks=1
+Tc=0.16*sqrt(fck)*10^3//in kN/sq m
+Tv=Tc
+//let d be the depth of footing in metres
+//case I: consider greater width of shaded portion in Fig. 11.7 of textbook
+d1=L*(L-b)/2*p/(Tc*L+L*p)//in m
+//case II: refer Fig. 11.8 of textbook; we get a quadratic equation of the form e d^2 + f d + g = 0
+e=p+4*Tc
+f=b*p+D*p+2*(b+D)*Tc
+g=-(L^2-b*D)*p
+d2=(-f+sqrt(f^2-4*e*g))/2/e//in m
+d2=0.425//assume, in m
+d=max(d1,d2)//in m
+//bending moment consideration, refer Fig. 11.9 of textbook
+Mx=1*((L-b)/2)^2/2*p//in kN-m
+d3=sqrt(Mx*10^6/0.87/10^3)//<425 mm, hence OK
+z=0.87*d*10^3//lever arm, in mm
+Ast1=(Mx*10^6/sigma_st/z)//in sq mm
+Ast=L*Ast1//steel required for full width of 2.3 m, in sq mm
+//provide 18 mm dia bars
+dia=18//in mm
+n=Ast/0.785/dia^2//no. of 18 mm dia bars
+n=15//assume
+Tbd=0.6//in MPa
+Ld=dia*sigma_st/4/Tbd//in mm
+c=50//side cover, in mm
+La=(L-D)/2*10^3-c//in mm
+//providing hook at ends
+La=La+16*dia//>Ld, hence OK
+D=d2*10^3+dia/2+100//in mm
+mprintf("Summary of design:\nOverall depth of footing=%d mm\nCover=100 mm bottom; 50 mm side\nSteel-%d bars of 18 mm dia both ways",D,n)
diff --git a/3683/CH11/EX11.3/Ex11_3.sce b/3683/CH11/EX11.3/Ex11_3.sce new file mode 100644 index 000000000..13303fb88 --- /dev/null +++ b/3683/CH11/EX11.3/Ex11_3.sce @@ -0,0 +1,48 @@ +B=0.5//column diameter, in m
+fck=20//in MPa
+sigma_cbc=7//in MPa
+sigma_st=230//in MPa
+P1=1600//load on column, in kN
+P2=0.05*P1//weight of footing, in kN
+P=P1+P2//in kN
+q=300//bearing capacity of soil, in kN/sq m
+A=P/q//in sq m
+L=sqrt(A)//assuming footing to be square
+L=2.4//assume, in m
+p=P1/L^2//soil pressure, in kN/sq m
+p=278//assume, in kN/sq m
+bc=1
+ks=0.5+bc//>1
+ks=1
+Tc=0.16*sqrt(fck)*10^3//in kN/sq m
+Tv=Tc
+//let d be the depth of footing in metres
+//case I: refer Fig. 11.11 of textbook
+d1=L*(L-B)/2*p/(Tc*L+L*p)//in m
+//case II: refer Fig. 11.12 of textbook; we get a quadratic equation of the form e d^2 + f d + g = 0
+e=%pi/4*p+%pi*Tc
+f=2*%pi/4*B*p+%pi*B*Tc
+g=-(L^2-%pi/4*B^2)*p
+d2=(-f+sqrt(f^2-4*e*g))/2/e//in m
+d2=0.57//assume, in m
+d=max(d1,d2)//in m
+//bending moment consideration, refer Fig. 11.13 of textbook
+M=1*((L-B)/2)^2/2*p//in kN-m
+d3=sqrt(M*10^6/0.88/10^3)//<570 mm, hence OK
+z=0.9*d*10^3//lever arm, in mm
+Ast1=(M*10^6/sigma_st/z)//in sq mm
+Ast=L*Ast1//steel required for full width of 2.4 m
+//provide 20 mm dia bars
+dia=20//in mm
+n=Ast/0.785/dia^2//no. of 20 mm dia bars
+n=9//assume
+Tbd=1.12//in MPa
+Ld=dia*sigma_st/4/Tbd//in mm
+Ld=1030//assume, in mm
+c=50//side cover, in mm
+La=(L-B)/2*10^3-c//in mm
+//bend bar at right angle and provide length, l
+l=Ld-La//in mm
+D=d*10^3+dia/2+100//in mm
+mprintf("Summary of design:\nOverall depth of footing=%d mm\nCover:100 mm bottom; 50 mm side\nSteel:%d-20 mm dia bars both ways",D,n)
+//answer in textbook is incorrect
diff --git a/3683/CH11/EX11.4/Ex11_4.sce b/3683/CH11/EX11.4/Ex11_4.sce new file mode 100644 index 000000000..8b3220299 --- /dev/null +++ b/3683/CH11/EX11.4/Ex11_4.sce @@ -0,0 +1,70 @@ +b=0.3//column width in m
+c1=0.4//column depth in m
+fck=20//in MPa
+sigma_cbc=7//in MPa
+sigma_st=275//in MPa
+P1=1200//load on column, in kN
+P2=0.05*P1//weight of footing, in kN
+P=P1+P2//in kN
+q=200//bearing capacity of soil, in kN/sq m
+A=P/q//in sq m
+L1=2//in m
+L2=A/L1//assuming footing to be square
+L2=3.2//assume, in m
+p=P1/L1/L2//soil pressure, in kN/sq m
+bc=b/c1
+ks=0.5+bc//>1
+ks=1
+Tc=0.16*sqrt(fck)*10^3//in kN/sq m
+Tv=Tc
+//let d be the depth of footing in metres
+//case I, refer Fig. 11.15 of textbook
+//short direction
+d1=L1*(L2-c1)/2*p/(Tc*L1+L1*p)//in m
+//long direction
+d2=L2*(L1-b)/2*p/(Tc*L2+L2*p)//in m
+//case II: refer Fig. 11.16 of textbook; we get a quadratic equation of the form e d^2 + f d + g = 0
+e=p+4*Tc
+f=b*p+c1*p+2*(b+c1)*Tc
+g=-(L1*L2-b*c1)*p
+d3=(-f+sqrt(f^2-4*e*g))/2/e//in m
+d3=0.47//assume, in m
+d=max(d1,d2,d3)//in m
+//bending moment consideration, refer Fig. 11.17 of textbook
+Mx=1*((L1-b)/2)^2/2*p//in kN-m
+My=1*((L2-c1)/2)^2/2*p//in kN-m
+d4=sqrt(My*10^6/0.8/10^3)//in mm
+d4=480//>470 mm (provided for shear)
+d=d4//in mm
+z=0.92*d//lever arm, in mm
+//short direction
+Ast1=(Mx*10^6/sigma_st/z)//in sq mm
+Ast=L2*Ast1//steel required for full width of 3.2 m, in sq mm
+b1=L1//central band width, in m
+beta=L2/L1
+Astc=L1/(beta+1)*Ast//in sq mm
+//provide 12 mm dia bars
+dia=12//in mm
+n1=Astc/0.785/dia^2//no. of 12 mm dia bars
+n1=13//assume
+Astr=Ast-Astc//steel in remaining width, in sq mm
+n2=Astr/0.785/dia^2
+n2=4//assume
+n2=n2/2//on each side
+Tbd=1.12//in MPa
+Ld=dia*sigma_st/4/Tbd//in mm
+c=50//side cover, in mm
+La=(L1-b)/2*10^3-c//>Ld, hence OK
+//long direction
+Ast1=(My*10^6/sigma_st/z)//in sq mm
+Ast=L1*Ast1//steel required for full width of 2 m, in sq mm
+//provide 18 mm dia bars
+dia=18//in mm
+n=Ast/0.785/dia^2//no. of 18 mm dia bars
+n=12//assume
+Ld=dia*sigma_st/4/Tbd//in mm
+c=50//side cover, in mm
+La=(L2-c1)/2*10^3-c//>Ld, hence OK
+D=d+dia/2+100//in mm
+D=590//assume, in mm
+mprintf("Summary of design:\nOverall depth of footing=%d mm\nCover=100 mm bottom; 50 mm side\nSteel-long direction\n%d bars of 18 mm dia in %d m width equally spaced\nShort direction\nCentral band %d m:%d-12 mm dia bars equally spaced\nRemaining sides:%d-12 mm dia bars on each side",D,n,L1,L1,n1,n2)
diff --git a/3683/CH12/EX12.1/Ex12_1.sce b/3683/CH12/EX12.1/Ex12_1.sce new file mode 100644 index 000000000..c40e9f633 --- /dev/null +++ b/3683/CH12/EX12.1/Ex12_1.sce @@ -0,0 +1,77 @@ +sigma_cbc=5//in MPa
+sigma_st=230//in MPa
+phi=30//angle of repose, in degrees
+H=5//height of wall, in m
+B=0.6*H//assume, in m
+T=B/4//assume toe to base ratio as 1:4
+W=16//density of retained earth, in kN/cu m
+P=W*H^2/2*(1-sind(phi))/(1+sind(phi))//in kN
+P=67//assume, in kN
+M1=P*H/3//in kN-m
+M1=112//assume, in kN-m
+//bending moment at 2.5 m below the top
+h=2.5//in m
+M2=W*h^2/2*(1-sind(phi))/(1+sind(phi))*h/3//in kN-m
+M2=14//in kN-m
+//thickness of stem (at the base)
+d=sqrt(M1*10^6/0.65/1000)//in mm
+d=415//in mm
+dia=20//assume 20 mm dia bars
+D1=d+dia/2+25//in mm
+D2=200//thickness at top, in mm
+D3=D2+(D1-D2)*h/H//in mm
+d3=sqrt(M2*10^6/0.65/1000)//in mm
+D3=d3+dia/2+25//< 325 mm (provided), hence OK
+D3=325//in mm
+d3=D3-dia/2-25//in mm
+//main steel
+//(a) 5 m below the top
+Ast=M1*10^6/sigma_st/0.9/d//in sq mm
+//provide 20 mm dia bars
+s1=1000*0.785*20^2/Ast//in mm
+s1=240//assume, in mm
+//(b) 2.5 m below the top
+Ast=M2*10^6/sigma_st/0.9/d3//in sq mm
+Astmin=0.12/100*10^3*D3//in sq mm
+Ast=max(Ast,Astmin)//in sq mm
+//provide 12 mm dia bars
+s2=1000*0.785*12^2/Ast//in mm
+s2=290//assume, in mm
+//distribution steel
+Ads=0.12/100*10^3*D3//in sq mm
+//provide 8 mm dia bars
+s3=1000*0.785*8^2/Ads//in mm
+s3=125//assume, in mm
+//check for shear
+V=P//in kN
+Tv=V*10^3/10^3/d//in MPa
+//for M15 grade concrete and pt=0.31
+Tc=0.22//in MPa
+//as Tc > Tv, no shear reinforcement required
+//development length
+//(a) At the base of stem
+dia=20//in mm
+Tbd=0.84//in MPa
+Ld=dia*sigma_st/4/Tbd//in mm
+Ld=1370//assume, in mm
+//(b) At 2.5 m below the top
+dia=12//in mm
+Ld=dia*sigma_st/4/Tbd//in mm
+Ld=825//assume, in mm
+//check for stability
+D4=500//thickness of base, in mm (assume)
+V1=1/2*(D1-D2)/10^3*H*25//in kN
+V2=(D2/10^3)*H*25//in kN
+V3=(D4/10^3)*B*25//weight of base, in kN
+V4=(B-T-D1/10^3)*H*W//weight of soil, in kN
+V=V1+V2+V3+V4//in kN
+M=V1*(T+2/3*(D1-D2)/10^3)+V2*(T+(D1-D2)/10^3+D2/10^3/2)+V3*B/2+V4*(B-(B-T-D1/10^3)/2)//in kN-m
+x=M/V//in m
+x=1.8//assume, in m
+//factor of safety
+//for overturning
+F1=V*x/P/(H/3)//> 1.5, hence OK
+mu=0.5
+//for sliding
+F2=mu*V/P//> 1.5, hence OK
+mprintf("Summary of design:\nThickness of stem (at base) = %d mm\nThickness of stem at top = %d mm\nRefer Fig. 12.4 of textbook for reinforcement details",D1,D2)
diff --git a/3683/CH12/EX12.2/Ex12_2.sce b/3683/CH12/EX12.2/Ex12_2.sce new file mode 100644 index 000000000..9b2de709a --- /dev/null +++ b/3683/CH12/EX12.2/Ex12_2.sce @@ -0,0 +1,74 @@ +sigma_cbc=5//in MPa
+sigma_st=140//in MPa
+phi=35//angle of repose, in degrees
+H=6//height of wall, in m
+B=0.4*H//assume, in m
+T=B/4//assume toe to base ratio as 1:4
+W=18//density of retained earth, in kN/cu m
+P=W*H^2/2*(1-sind(phi))/(1+sind(phi))//in kN
+P=88//assume, in kN
+M1=P*H/3//in kN-m
+//bending moment at 3 m below the top
+h=3//in m
+M2=W*h^2/2*(1-sind(phi))/(1+sind(phi))*h/3//in kN-m
+M2=22//in kN-m
+//thickness of stem (at the base)
+d=sqrt(M1*10^6/0.87/1000)//in mm
+d=450//in mm
+dia=20//assume 20 mm dia bars
+D1=d+dia/2+25//in mm
+D2=200//thickness at top, in mm
+D3=D2+(D1-D2)*h/H//in mm
+d3=sqrt(M2*10^6/0.87/1000)//in mm
+D3=d3+dia/2+25//< 342.5 mm (provided), hence OK
+D3=342.5//in mm
+d3=D3-dia/2-25//in mm
+//main steel
+//(a) 6 m below the top
+Ast=M1*10^6/sigma_st/0.87/d//in sq mm
+//provide 20 mm dia bars
+s1=1000*0.785*20^2/Ast//in mm
+s1=95//assume, in mm
+//(b) 3 m below the top
+Ast=M2*10^6/sigma_st/0.87/d3//in sq mm
+//provide 10 mm dia bars
+s2=1000*0.785*10^2/Ast//in mm
+s2=130//assume, in mm
+//distribution steel
+Ads=0.15/100*10^3*D3//in sq mm
+//provide 10 mm dia bars
+s3=1000*0.785*10^2/Ads//in mm
+s3=150//assume, in mm
+//check for shear
+V=P//in kN
+Tv=V*10^3/10^3/d//in MPa
+//for M15 grade concrete and pt=0.71
+Tc=0.34//in MPa
+//as Tc > Tv, no shear reinforcement required
+//development length
+//(a) At the base of stem
+dia=20//in mm
+Tbd=0.6//in MPa
+Ld=dia*sigma_st/4/Tbd//in mm
+Ld=1170//assume, in mm
+//(b) At 3 m below the top
+dia=10//in mm
+Ld=dia*sigma_st/4/Tbd//in mm
+Ld=590//assume, in mm
+//check for stability
+D4=500//thickness of base, in mm (assume)
+V1=1/2*(D1-D2)/10^3*H*25//in kN
+V2=(D2/10^3)*H*25//in kN
+V3=(D4/10^3)*B*25//weight of base, in kN
+V4=(B-T-D1/10^3)*H*W//in kN
+V=V1+V2+V3+V4//in kN
+M=V1*(T+2/3*(D1-D2)/10^3)+V2*(T+(D1-D2)/10^3+D2/10^3/2)+V3*B/2+V4*(B-(B-T-D1/10^3)/2)//in kN-m
+x=M/V//in m
+//factor of safety
+//for overturning
+F1=V*x/P/(H/3)//> 1.5, hence OK
+mu=0.5
+//for sliding
+F2=mu*V/P//< 1.5, hence it is not safe against sliding
+mprintf("Summary of design:\nThickness of stem (at base) = %d mm\nThickness of stem at top = %d mm\nRefer Fig. 12.7 of textbook for reinforcement details",D1,D2)
+//answers in textbook for factor of safety against overturning and sliding are incorrect
diff --git a/3683/CH12/EX12.3/Ex12_3.sce b/3683/CH12/EX12.3/Ex12_3.sce new file mode 100644 index 000000000..ada5ef959 --- /dev/null +++ b/3683/CH12/EX12.3/Ex12_3.sce @@ -0,0 +1,68 @@ +sigma_cbc=5//in MPa
+sigma_st=230//in MPa
+phi=30//angle of repose, in degrees
+H=5//height of wall, in m
+B=0.6*H//assume, in m
+T=B/4//assume toe to base ratio as 1:4
+t=450//thickness of wall, in mm
+W=16//density of retained earth, in kN/cu m
+P=W*H^2/2*(1-sind(phi))/(1+sind(phi))//in kN
+P=67//assume, in kN
+y=1.8//in m
+P=67//in kN
+Wt=223//in kN
+D=0.5//thickness of base, in m
+x=1.8-P*(H/3+D/10^3)/Wt//in m
+x=1.15//in m
+e=B/2-x//in m
+q1=Wt/B+Wt*e/(1*B^2/6)//maximum pressure, in kN/sq m
+q2=Wt/B-Wt*e/(1*B^2/6)//minimum pressure, in kN/sq m
+Pa=q1-(q1-q2)/B*T//pressure at A, in kN/sq m
+Pa=100//assume, in kN/sq m
+Pb=q1-(q1-q2)/B*(T+t/10^3)//pressure at B, in kN/sq m
+Pb=85//assume, in kN/sq m
+Ma=Pa*T^2/2+1/2*(q1-Pa)*T*2/3*T-T*D*25*T/2//bending moment at A, in kN-m
+Ma=30//round-off, in kN-m
+Mb=(B-T-t/10^3)^2*H*W/2+(B-T-t/10^3)^2*D*25/2-q2*(B-T-t/10^3)^2/2-(Pb-q2)*1/3*(B-T-t/10^3)^2/2//bending moment at B, in kN-m
+Mb=80//in kN-m
+//design of toe
+d=sqrt(Ma*10^6/0.65/10^3)//in mm
+D=d+10/2+70//<500 mm (provided), hence OK
+D=500//in mm
+d=D-70//in mm
+Ast=Ma*10^6/sigma_st/0.9/d//in sq mm
+Astmin=0.12/100*10^3*D//in sq mm
+Ast=max(Ast,Astmin)//in sq mm
+s1=1000*0.785*10^2/Ast//in mm
+s1=130//assume, in mm
+//distribution steel is same as above
+//check for shear
+V=(q1+Pa)/2*T//in kN
+Tv=V*10^3/10^3/d//in MPa
+//for M15 grade concrete and pt=0.32
+Tc=0.2368//in MPa
+//as Tc > Tv, no shear reinforcement required
+//development length
+dia=10//in mm
+Tbd=0.84//in MPa
+Ld=dia*sigma_st/4/Tbd//in mm
+Ld=685//assume, in mm
+//design of heel
+d=sqrt(Mb*10^6/0.65/10^3)//< 430 mm (provided), hence OK
+d=430//in mm
+Ast=Mb*10^6/sigma_st/0.9/d//in sq mm
+s2=1000*0.785*10^2/Ast//in mm
+s2=85//assume, in mm
+//distribution steel: 0.12% of Ag, hence provide 10 mm dia bars @ 130 mm c/c
+V=(B-T-t/10^3)*H*W-(Pb+q2)/2*(B-T-t/10^3)//in kN
+Tv=V*10^3/10^3/d//in MPa
+//for M15 grade concrete and pt=0.32
+Tc=0.2368//in MPa
+//as Tc > Tv, no shear reinforcement required
+//development length
+dia=10//in mm
+Tbd=0.84//in MPa
+Ld=dia*sigma_st/4/Tbd//in mm
+Ld=685//assume, in mm
+mprintf("Summary of design:\nThickness of base slab=%d mm. Refer to Fig. 12.11 of textbook for reinforcement details.",D)
+//answer in textbook for spacing of 10 mm dia bars for main steel in toe and distribution steel is incorrect
diff --git a/3683/CH13/EX13.1/Ex13_1.sce b/3683/CH13/EX13.1/Ex13_1.sce new file mode 100644 index 000000000..cd92300f0 --- /dev/null +++ b/3683/CH13/EX13.1/Ex13_1.sce @@ -0,0 +1,34 @@ +sigma_cbc=7//in MPa
+sigma_ct=1.2//in MPa
+sigma_st=100//in MPa
+m=13.33//modular ratio
+V=200000//capacity, in L
+V=V/10^3//in cu m
+h=2.5//assumed depth of water in tank, in m
+A=V/h//area of tank, in sq m
+B=sqrt(4/%pi*A)//diameter, in m
+B=10.1//assume, in m
+H=h+0.5//including freeboard, in m
+w=10//unit weight of water, in kN/cu m
+T=w*H*B/2//hoop tension, in kN
+Ast=T*10^3/sigma_st//in sq mm
+s1=10^3*0.785*16^2/Ast//in mm
+s1=130//assume, in mm
+t=(T*10^3/sigma_ct-(m-1)*Ast)/1000//in mm
+t=110//assume, in mm
+//hoop tension steel at 1.5 m below top of wall
+h=1.5//in m
+T=w*h*B/2//in kN
+Ast=T*10^3/sigma_st//in sq mm
+s2=10^3*0.785*16^2/Ast//in mm
+s2=260//assume, in mm
+Ads=0.3/100*t*10^3//vertical steel as distribution steel, in sq mm
+s3=1000*0.785*10^2/Ads//in mm
+s3=235//in mm
+//design of tank floor
+D=150//in mm
+Ast=0.3/100*D*1000//in sq mm
+s4=1000*0.785*10^2/Ast//in mm
+s4=170//in mm
+mprintf("Summary of design\nDiameter of tank=%f m\nDepth of tank=%d m\nTank wall thickness=%d mm\nSteel-hoop steel; 3 m to 1.5 m below top=16 mm dia @ %d mm c/c\n1.5 m to 0 m below top=16 mm dia @ %d mm c/c\nvertical steel=10 mm dia @ %d mm c/c\nTank floor: Thickness %d mm\nSteel=10 mm dia @ %d mm c/c",B,H,t,s1,s2,s3,D,s4)
+//answer in textbook for spacing of 16 mm dia bars from 1.5 m to 0 m below top is incorrect
diff --git a/3683/CH13/EX13.2/Ex13_2.sce b/3683/CH13/EX13.2/Ex13_2.sce new file mode 100644 index 000000000..86af614f3 --- /dev/null +++ b/3683/CH13/EX13.2/Ex13_2.sce @@ -0,0 +1,33 @@ +sigma_cbc=7//in MPa
+sigma_ct=1.2//in MPa
+sigma_st=170//in MPa
+m=13.33//modular ratio
+V=400000//capacity, in L
+V=V/10^3//in cu m
+h=3//assumed depth of water in tank, in m
+A=V/h//area of tank, in sq m
+B=sqrt(4/%pi*A)//diameter, in m
+B=13//assume, in m
+H=h+0.5//including freeboard, in m
+w=10//unit weight of water, in kN/cu m
+T=w*H*B/2//hoop tension, in kN
+Ast=T*10^3/sigma_st//in sq mm
+s1=10^3*0.785*12^2/Ast//in mm
+s1=80//assume, in mm
+t=(T*10^3/sigma_ct-(m-1)*Ast)/1000//in mm
+t=175//assume, in mm
+//steel at 2 m below top of wall
+h=2//in m
+T=w*h*B/2//in kN
+Ast=T*10^3/sigma_st//in sq mm
+s2=10^3*0.785*12^2/Ast//in mm
+s2=145//assume, in mm
+Ads=0.3/100*t*10^3//vertical steel as distribution steel, in sq mm
+s3=1000*0.785*10^2/Ads//in mm
+s3=150//assume, in mm
+//design of tank floor
+D=190//in mm
+Ast=0.3/100*D*1000//in sq mm
+s4=1000*0.785*10^2/Ast//in mm
+s4=135//assume, in mm
+mprintf("Summary of design\nDiameter of tank=%d m\nDepth of tank=%f m\nTank wall thickness=%d mm\nSteel-hoop steel; 4 m to 2 m below top=12 mm dia @ %d mm c/c\n2 m to 0 m below top=12 mm dia @ %d mm c/c\nvertical steel=10 mm dia @ %d mm c/c\nTank floor: Thickness %d mm\nSteel=10 mm dia @ %d mm c/c both ways",B,H,t,s1,s2,s3,D,s4)
diff --git a/3683/CH14/EX14.1/Ex14_1.sce b/3683/CH14/EX14.1/Ex14_1.sce new file mode 100644 index 000000000..37602cbc6 --- /dev/null +++ b/3683/CH14/EX14.1/Ex14_1.sce @@ -0,0 +1,10 @@ +b=250//width, in mm
+d=500//effective depth, in mm
+Ast=4*0.785*20^2//four 20 mm dia bars, in sq mm
+fck=15//in MPa
+fy=250//in MPa
+Xu=round(0.87*fy*Ast/0.36/fck/b)//in mm
+Xc=0.531*d//in mm
+//as Xu<Xc, it is under-reinforced section, hence OK
+Mu=0.87*fy*Ast*(d-0.416*Xu)/10^6//in kN-m
+mprintf("Moment of resistance of the beam=%f kN-m", Mu)
diff --git a/3683/CH14/EX14.2/Ex14_2.sce b/3683/CH14/EX14.2/Ex14_2.sce new file mode 100644 index 000000000..b028b2fb0 --- /dev/null +++ b/3683/CH14/EX14.2/Ex14_2.sce @@ -0,0 +1,8 @@ +b=300//width, in mm
+d=600//effective depth, in mm
+fck=15//in MPa
+fy=500//in MPa
+Xc=0.456*d//in mm
+Mu=0.36*fck*b*Xc*(d-0.416*Xc)/10^6//in kN-m
+Ast=round(0.36*fck*b*Xc/0.87/fy)//in sq mm
+mprintf("Moment of resistance of the beam=%f kN-m\nSteel required=%d sq mm", Mu,Ast)
diff --git a/3683/CH14/EX14.3/Ex14_3.sce b/3683/CH14/EX14.3/Ex14_3.sce new file mode 100644 index 000000000..7a2b8d376 --- /dev/null +++ b/3683/CH14/EX14.3/Ex14_3.sce @@ -0,0 +1,9 @@ +b=300//width, in mm
+d=600//effective depth, in mm
+fck=20//in MPa
+fy=415//in MPa
+Xc=0.479*d//in mm
+Mu=0.36*fck*b*Xc*(d-0.416*Xc)/10^6//in kN-m
+Ast=round(0.36*fck*b*Xc/0.87/fy)//in sq mm
+mprintf("Moment of resistance of the beam=%f kN-m\nSteel required=%d sq mm", Mu,Ast)
+//answer does not match with textbook because of round-off error
diff --git a/3683/CH14/EX14.4/Ex14_4.sce b/3683/CH14/EX14.4/Ex14_4.sce new file mode 100644 index 000000000..b2b65924d --- /dev/null +++ b/3683/CH14/EX14.4/Ex14_4.sce @@ -0,0 +1,14 @@ +b=300//width, in mm
+d=650//effective depth, in mm
+Ast=942//in sq mm
+lef=6//in m
+fck=20//in MPa
+fy=340//in MPa
+Xu=round(0.87*fy*Ast/0.36/fck/b)//in mm
+Xc=0.5*d//in mm
+//as Xu<Xc, it is under-reinforced beam, hence OK
+Mu=0.87*fy*Ast*(d-0.416*Xu)/10^6//in kN-m
+Wu=Mu*8/lef^2//in kN/m
+self_weight=25*(b/1000)*(d/1000)//in kN/m
+W=Wu/1.5-self_weight//in kN/m
+mprintf("Safe load on the beam=%f kN/m",W)
diff --git a/3683/CH14/EX14.5/Ex14_5.sce b/3683/CH14/EX14.5/Ex14_5.sce new file mode 100644 index 000000000..ce7ac81ac --- /dev/null +++ b/3683/CH14/EX14.5/Ex14_5.sce @@ -0,0 +1,14 @@ +b=1000//width, in mm
+d=120//effective depth, in mm
+Ast=1412//in sq mm
+lef=3.2//in m
+fck=20//in MPa
+fy=250//in MPa
+Xu=0.87*fy*Ast/0.36/fck/b//in mm
+Xc=0.531*d//in mm
+//as Xu<Xc, it is under-reinforced section, hence OK
+Mu=0.87*fy*Ast*(d-0.416*Xu)/10^6//in kN-m
+Wu=Mu*8/lef^2//in kN/m
+self_weight=25*(b/1000)*(d/1000)//in kN/m
+W=Wu/1.5-self_weight//in kN/m
+mprintf("Safe load on the slab=%f kN/m",W)
diff --git a/3683/CH14/EX14.6/Ex14_6.sce b/3683/CH14/EX14.6/Ex14_6.sce new file mode 100644 index 000000000..e43eef4ce --- /dev/null +++ b/3683/CH14/EX14.6/Ex14_6.sce @@ -0,0 +1,12 @@ +fck=15//in MPa
+fy=250//in MPa
+//b=d/2
+M=65//in kN-m
+Mu=1.5*M//factored moment, in kN-m
+d=(Mu*10^6/(0.149*fck*0.5))^(1/3)//in mm
+d=445//approximately, in mm
+b=d/2//in mm
+Xc=0.531*d//in mm
+Ast=round(0.36*fck*b*Xc/0.87/fy)//in sq mm
+mprintf("b=%f mm\nd=%f mm\nAst=%f sq mm",b,d,Ast)
+//answer does not match with textbook because of round-off error
diff --git a/3683/CH14/EX14.7/Ex14_7.sce b/3683/CH14/EX14.7/Ex14_7.sce new file mode 100644 index 000000000..595c36bb4 --- /dev/null +++ b/3683/CH14/EX14.7/Ex14_7.sce @@ -0,0 +1,16 @@ +b=300//width, in mm
+d=500//effective depth, in mm
+fck=20//in MPa
+fy=500//in MPa
+Mu=175//in kN-m
+Mulim=0.133*fck*b*d^2/10^6//in kN-m
+//as Mu<Mulim, beam is under-reinforced
+//using Cu=Tu, Xu=0.87 fy Ast/(0.36 fck b); let Xu= a Ast
+a=0.87*fy/(0.36*fck*b)
+//Mu=0.87 fy Ast (d-0.416 Xu), putting Xu = a Ast, we get p Ast^2 + q Ast + r =0
+p=0.87*0.416*fy*a
+q=-0.87*fy*d
+r=Mu*10^6
+//solving the quadratic equation
+Ast=round((-q-sqrt(q^2-4*p*r))/2/p)//in sq mm
+mprintf("Area of steel required=%d sq mm",Ast)
diff --git a/3683/CH15/EX15.1/Ex15_1.sce b/3683/CH15/EX15.1/Ex15_1.sce new file mode 100644 index 000000000..61a601611 --- /dev/null +++ b/3683/CH15/EX15.1/Ex15_1.sce @@ -0,0 +1,12 @@ +b=300//width, in mm
+d=800//effective depth, in mm
+Ast=3940//in sq mm
+Asc=795//in sq mm
+top_cover=40//in mm
+fck=15//in MPa
+fy=250//in MPa
+Xc=0.531*d//in mm
+fcc=0.446*fck//in MPa
+fsc=0.87*fy//in MPa
+Mu=(0.36*fck*b*Xc*(d-0.416*Xc)+(fsc-fcc)*Asc*(d-top_cover))/10^6//in kN-m
+mprintf("Moment of resistance of the beam = %f kN-m",Mu)
diff --git a/3683/CH15/EX15.2/Ex15_2.sce b/3683/CH15/EX15.2/Ex15_2.sce new file mode 100644 index 000000000..faa60932f --- /dev/null +++ b/3683/CH15/EX15.2/Ex15_2.sce @@ -0,0 +1,13 @@ +b=230//width, in mm
+d=600//effective depth, in mm
+Asc=554//in sq mm
+Ast=1524//in sq mm
+top_cover=30//in mm
+fck=15//in MPa
+fy=415//in MPa
+Xc=0.479*d//in mm
+fcc=0.446*fck//in MPa
+//for d'/d=30/600=0.05 and Fe415 grade steel,
+fsc=355//in MPa
+Mu=(0.36*fck*b*Xc*(d-0.416*Xc)+(fsc-fcc)*Asc*(d-top_cover))/10^6//in kN-m
+mprintf("Moment of resistance of the beam = %f kN-m",Mu)
diff --git a/3683/CH15/EX15.3/Ex15_3.sce b/3683/CH15/EX15.3/Ex15_3.sce new file mode 100644 index 000000000..3e8e7fb71 --- /dev/null +++ b/3683/CH15/EX15.3/Ex15_3.sce @@ -0,0 +1,9 @@ +b=250//width, in mm
+d=550//effective depth, in mm
+fck=15//in MPa
+fy=250//in MPa
+M=95//in kN-m
+Mu=1.5*M//factored moment, in kN-m
+Mulim=0.149*fck*b*d^2/10^6//in kN-m
+//as Mu<Mulim, no steel required on compression side
+mprintf("As factored moment is less than limiting moment, no steel is required on compression side (as per LSM)")
diff --git a/3683/CH15/EX15.4/Ex15_4.sce b/3683/CH15/EX15.4/Ex15_4.sce new file mode 100644 index 000000000..c87a137ca --- /dev/null +++ b/3683/CH15/EX15.4/Ex15_4.sce @@ -0,0 +1,13 @@ +b=225//width, in mm
+d=500//effective depth, in mm
+Asc=125//in sq mm
+Ast=754//in sq mm
+top_cover=50//in mm
+fck=15//in MPa
+fy=500//in MPa
+Xc=0.456*d//in mm
+fcc=0.446*fck//in MPa
+//for d'/d=50/500=0.1 and Fe500 grade steel,
+fsc=412//in MPa
+Mu=(0.36*fck*b*Xc*(d-0.416*Xc)+(fsc-fcc)*Asc*(d-top_cover))/10^6//in kN-m
+mprintf("Moment of resistance of the beam = %f kN-m",Mu)
diff --git a/3683/CH15/EX15.5/Ex15_5.sce b/3683/CH15/EX15.5/Ex15_5.sce new file mode 100644 index 000000000..fba27015c --- /dev/null +++ b/3683/CH15/EX15.5/Ex15_5.sce @@ -0,0 +1,16 @@ +b=250//width, in mm
+d=500//effective depth, in mm
+Mu=165//in kN-m
+top_cover=50//in mm
+fck=15//in MPa
+fy=250//in MPa
+Xc=0.531*d//in mm
+Mulim=0.149*fck*b*d^2/10^6//in kN-m
+Ast1=round(0.36*fck*b*Xc/0.87/fy)//in sq mm
+M1=Mu-Mulim//in kN-m
+fcc=0.446*fck//in MPa
+fsc=0.87*fy//in MPa
+Asc=round(M1*10^6/(fsc-fcc)/(d-top_cover))//in sq mm
+Ast2=round((fsc-fcc)*Asc/0.87/fy)//in sq mm
+Ast=Ast1+Ast2//in sq mm
+mprintf("Compression steel = %d sq mm\nTension steel = %d sq mm",Asc,Ast)
diff --git a/3683/CH15/EX15.6/Ex15_6.sce b/3683/CH15/EX15.6/Ex15_6.sce new file mode 100644 index 000000000..9932bd465 --- /dev/null +++ b/3683/CH15/EX15.6/Ex15_6.sce @@ -0,0 +1,17 @@ +b=200//width, in mm
+d=300//effective depth, in mm
+Mu=74//in kN-m
+top_cover=30//in mm
+fck=20//in MPa
+fy=415//in MPa
+Xc=0.479*d//in mm
+Mulim=0.138*fck*b*d^2/10^6//in kN-m
+Ast1=round(0.36*fck*b*Xc/0.87/fy)//in sq mm
+M1=Mu-Mulim//in kN-m
+fcc=0.446*fck//in MPa
+//for d'/d=30/300=0.1 and Fe415 grade steel,
+fsc=353//in MPa
+Asc=round(M1*10^6/(fsc-fcc)/(d-top_cover))//in sq mm
+Ast2=round((fsc-fcc)*Asc/0.87/fy)//in sq mm
+Ast=Ast1+Ast2//in sq mm
+mprintf("Compression steel = %d sq mm\nTension steel = %d sq mm",Asc,Ast)
diff --git a/3683/CH15/EX15.7/Ex15_7.sce b/3683/CH15/EX15.7/Ex15_7.sce new file mode 100644 index 000000000..686e51616 --- /dev/null +++ b/3683/CH15/EX15.7/Ex15_7.sce @@ -0,0 +1,17 @@ +b=200//width, in mm
+d=200//effective depth, in mm
+Mu=32//in kN-m
+top_cover=30//in mm
+fck=20//in MPa
+fy=500//in MPa
+Xc=0.456*d//in mm
+Mulim=0.133*fck*b*d^2/10^6//in kN-m
+Ast1=round(0.36*fck*b*Xc/0.87/fy)//in sq mm
+M1=Mu-Mulim//in kN-m
+fcc=0.446*fck//in MPa
+//for d'/d=30/200=0.15 and Fe500 grade steel,
+fsc=395//in MPa
+Asc=round(M1*10^6/(fsc-fcc)/(d-top_cover))//in sq mm
+Ast2=round((fsc-fcc)*Asc/0.87/fy)//in sq mm
+Ast=Ast1+Ast2//in sq mm
+mprintf("Compression steel = %d sq mm\nTension steel = %d sq mm",Asc,Ast)
diff --git a/3683/CH16/EX16.1/Ex16_1.sce b/3683/CH16/EX16.1/Ex16_1.sce new file mode 100644 index 000000000..889e4805c --- /dev/null +++ b/3683/CH16/EX16.1/Ex16_1.sce @@ -0,0 +1,12 @@ +Df=120//in mm
+bf=1100//in mm
+bw=275//in mm
+d=450//in mm
+Ast=2700//in sq mm
+fy=500//in MPa
+fck=25//in MPa
+Asf=round(0.36*fck*bf*Df/0.87/fy)//area of steel required for flange, in sq mm
+//as Ast<Asf, Xu<Df
+Xu=0.87*fy*Ast/0.36/fck/bf//in mm
+Mu=0.36*fck*bf*Xu*(d-0.416*Xu)/10^6//in kN-m
+mprintf("Moment of resistance of T-beam=%f kN-m",Mu)
diff --git a/3683/CH16/EX16.2/Ex16_2.sce b/3683/CH16/EX16.2/Ex16_2.sce new file mode 100644 index 000000000..6da5a663e --- /dev/null +++ b/3683/CH16/EX16.2/Ex16_2.sce @@ -0,0 +1,14 @@ +Df=100//in mm
+bf=1500//in mm
+bw=300//in mm
+d=600//in mm
+Ast=4500//in sq mm
+fy=415//in MPa
+fck=20//in MPa
+Asf=round(0.36*fck*bf*Df/0.87/fy)//area of steel required for flange, in sq mm
+//as Ast>Asf, Xu>Df
+Xu=(0.87*fy*Ast-0.446*fck*(bf-bw)*Df)/0.36/fck/bw//in mm
+Xc=0.479*d//Xc>Xu; hence OK
+a=0.43*Xu//as Df<0.43 Xu, stress in flange is uniform
+Mu=(0.36*fck*bw*Xu*(d-0.416*Xu)+0.446*fck*(bf-bw)*Df*(d-Df/2))/10^6//in kN-m
+mprintf("Moment of resistance of T-beam=%f kN-m",Mu)
diff --git a/3683/CH16/EX16.3/Ex16_3.sce b/3683/CH16/EX16.3/Ex16_3.sce new file mode 100644 index 000000000..f87b75a2e --- /dev/null +++ b/3683/CH16/EX16.3/Ex16_3.sce @@ -0,0 +1,15 @@ +Df=100//in mm
+bf=1500//in mm
+bw=300//in mm
+d=700//in mm
+Ast=4510//in sq mm
+fy=250//in MPa
+fck=15//in MPa
+Asf=round(0.36*fck*bf*Df/0.87/fy)//area of steel required for flange, in sq mm
+//as Ast>Asf, Xu>Df
+Xu=round((0.87*fy*Ast-0.446*fck*(bf-bw)*Df)/0.36/fck/bw)//in mm
+Xc=0.531*d//Xc>Xu; hence OK
+a=0.43*Xu//as Df>0.43 Xu, stress in flange is not uniform
+yf=0.15*Xu+0.65*Df//in mm
+Mu=(0.36*fck*bw*Xu*(d-0.416*Xu)+0.446*fck*(bf-bw)*yf*(d-yf/2))/10^6//in kN-m
+mprintf("Moment of resistance of T-beam=%f kN-m",Mu)
diff --git a/3683/CH16/EX16.4/Ex16_4.sce b/3683/CH16/EX16.4/Ex16_4.sce new file mode 100644 index 000000000..cadee8158 --- /dev/null +++ b/3683/CH16/EX16.4/Ex16_4.sce @@ -0,0 +1,18 @@ +Df=100//in mm
+bf=1250//in mm
+bw=250//in mm
+d=650//in mm
+Ast=2800//in sq mm
+fy=415//in MPa
+fck=20//in MPa
+Asf=round(0.36*fck*bf*Df/0.87/fy)//area of steel required for flange, in sq mm
+//as Ast>Asf, Xu>Df
+Xu=round((0.87*fy*Ast-0.446*fck*(bf-bw)*Df)/0.36/fck/bw)//in mm
+//but Xu<Df; this indicates that stress in the flange is not uniform, hence replace Df by yf
+Xu=(0.87*fy*Ast-0.446*fck*(bf-bw)*0.65*Df)/(0.36*fck*bw+0.446*fck*(bf-bw)*0.15)//in mm
+Xc=0.479*d//Xc>Xu; hence OK
+a=0.43*Xu//as Df>0.43 Xu, stress in flange is not uniform
+yf=0.15*Xu+0.65*Df//in mm
+Mu=(0.36*fck*bw*Xu*(d-0.416*Xu)+0.446*fck*(bf-bw)*yf*(d-yf/2))/10^6//in kN-m
+mprintf("Moment of resistance of T-beam=%f kN-m",Mu)
+//answer in textbook is incorrect
diff --git a/3683/CH16/EX16.5/Ex16_5.sce b/3683/CH16/EX16.5/Ex16_5.sce new file mode 100644 index 000000000..8e4eecb8b --- /dev/null +++ b/3683/CH16/EX16.5/Ex16_5.sce @@ -0,0 +1,11 @@ +Df=100//in mm
+bf=1250//in mm
+bw=250//in mm
+d=660//in mm
+fy=250//in MPa
+fck=15//in MPa
+Xc=0.531*d//in mm
+a=0.43*Xc//Df<0.43 Xu, stress in entire flange is uniform
+Mu=(0.36*fck*bw*Xc*(d-0.416*Xc)+0.446*fck*(bf-bw)*Df*(d-Df/2))/10^6//in kN-m
+Ast=(0.36*fck*bw*Xc+0.446*fck*(bf-bw)*Df)/0.87/fy//in sq mm
+mprintf("Moment of resistance of T-beam=%f kN-m\nArea of steel required=%f sq mm",Mu,Ast)
diff --git a/3683/CH16/EX16.6/Ex16_6.sce b/3683/CH16/EX16.6/Ex16_6.sce new file mode 100644 index 000000000..486947a51 --- /dev/null +++ b/3683/CH16/EX16.6/Ex16_6.sce @@ -0,0 +1,20 @@ +Df=100//in mm
+bf=1250//in mm
+bw=250//in mm
+d=550//in mm
+Mu=400//in kN-m
+fy=415//in MPa
+fck=15//in MPa
+Asf=0.446*fck*(bf-bw)*Df/0.87/fy//in sq mm
+Muf=0.446*fck*(bf-bw)*Df*(d-Df/2)/10^6//in kN-m
+Muw=Mu-Muf//in kN-m
+//using Cu=Tu, 0.36 fck bw Xu = 0.87 fy Ast, Xu = a Asw
+a=0.87*fy/0.36/fck/bw
+//Muw=0.87 fy Asw (d-0.416 Xu)
+p=0.87*fy*0.416*a
+q=-0.87*fy*d
+r=Muw*10^6
+Asw=(-q-sqrt(q^2-4*p*r))/2/p//in sq mm
+Ast=Asw+Asf//in sq mm
+mprintf("Area of steel required=%f sq mm",Ast)
+
diff --git a/3683/CH17/EX17.1/Ex17_1.sce b/3683/CH17/EX17.1/Ex17_1.sce new file mode 100644 index 000000000..4b9d5be37 --- /dev/null +++ b/3683/CH17/EX17.1/Ex17_1.sce @@ -0,0 +1,16 @@ +b=230//width, in mm
+d=500//effective depth, in mm
+l=4.5//span, in m
+Ast=4*0.785*20^2//four 20 mm dia bars, in sq mm
+fck=20//in MPa
+W=24//in kN/m
+Wu=1.5*W//factored load, in kN/m
+Vu=Wu*l/2//in kN
+Tv=Vu*10^3/b/d//in MPa
+Tcmax=2.8//for M20, in MPa
+//Tv<Tcmax, hence OK
+p=Ast/b/d*100//p=1.1, approximately
+//for p=1.1 and M20 grade concrete
+Tc=0.64//in MPa
+//Tv>Tc, hence shear reinforcement required
+mprintf("Nominal shear stress=%f MPa\nShear strength of concrete=%f MPa",Tv,Tc)
diff --git a/3683/CH17/EX17.2/Ex17_2.sce b/3683/CH17/EX17.2/Ex17_2.sce new file mode 100644 index 000000000..6fd4923cd --- /dev/null +++ b/3683/CH17/EX17.2/Ex17_2.sce @@ -0,0 +1,23 @@ +b=300//width, in mm
+d=1010//effective depth, in mm
+l=7//span, in m
+Ast=round(6*0.785*22^2)//six 22 mm dia bars, in sq mm
+fck=15//in MPa
+fy=250//in MPa
+W=45//in kN/m
+Wu=1.5*W//factored load, in kN/m
+Vu=Wu*l/2//in kN
+Tv=Vu*10^3/b/d//in MPa
+//Tv<Tcmax, hence OK
+p=Ast/b/d*100//p=0.75, approximately
+//for p=0.75 and M15 grade concrete
+Tc=0.54//in MPa
+//Tv>Tc, hence shear reinforcement required
+Vus=Vu-Tc*b*d/10^3//in kN
+//provide 6 mm dia stirrups
+Sv=0.87*fy*2*0.785*6^2*d/Vus/10^3//in mm
+Sv=171//approximately, in mm
+Svmin=2*0.785*6^2*fy/b/0.4//in mm
+Svmin=118//approximately, in mm
+Sv=min(Sv,Svmin)//in mm
+mprintf("Provide 6 mm dia stirrups at %d mm c/c as shear reinforcement",Sv)
diff --git a/3683/CH18/EX18.1/Ex18_1.sce b/3683/CH18/EX18.1/Ex18_1.sce new file mode 100644 index 000000000..e64a26f30 --- /dev/null +++ b/3683/CH18/EX18.1/Ex18_1.sce @@ -0,0 +1,12 @@ +Pu=3000//in kN
+fck=20//in MPa
+fy=415//in MPa
+l=3//unsupported length, in m
+//assume 1% steel
+Ag=Pu*10^3/(0.4*fck*0.99+0.67*fy*0.01)//in sq mm
+L=sqrt(Ag)//assuming a square column
+L=530//in mm
+Asc=0.01*L^2//in sq mm
+emin=l*10^3/500+L/30//in mm
+ep=0.05*L//>emin, hence OK
+mprintf("Column size - %d x %d mm",L,L)
diff --git a/3683/CH18/EX18.2/Ex18_2.sce b/3683/CH18/EX18.2/Ex18_2.sce new file mode 100644 index 000000000..3e3856ed2 --- /dev/null +++ b/3683/CH18/EX18.2/Ex18_2.sce @@ -0,0 +1,15 @@ +Pu=1500//in kN
+fck=15//in MPa
+fy=250//in MPa
+l=2.75//unsupported length, in m
+//assume 1% steel
+Ag=Pu*10^3/(0.4*fck*0.99+0.67*fy*0.01)//in sq mm
+L1=225//assuming a square column
+L2=Ag/L1//in mm
+L2=880//in mm
+Asc=0.01*L1*L2//in sq mm
+e1=l*10^3/500+L1/30//in mm
+e2=l*10^3/500+L2/30//in mm
+ep1=0.05*L1//<e1
+ep2=0.05*L2//>e2, hence Ok
+mprintf("The column is safe on long dimension side but not on short dimension side. As such, the column be checked for eccentricity in short direction.")
diff --git a/3683/CH18/EX18.3/Ex18_3.sce b/3683/CH18/EX18.3/Ex18_3.sce new file mode 100644 index 000000000..3f73c91ac --- /dev/null +++ b/3683/CH18/EX18.3/Ex18_3.sce @@ -0,0 +1,35 @@ +b=225//in mm
+D=500//in mm
+c=45//cover, in mm
+Asc=2463//in sq mm
+Ast=Asc
+fck=15//in MPa
+fy=250//in MPa
+fcc=0.446*fck//in MPa
+//(i)
+xu=1.1*D//in mm
+m=0.43*D//in mm
+esc1=0.002*(xu-c)/(xu-m)
+esc2=0.002*(xu-D+c)/(xu-m)
+//by interpolation
+fsc1=217.5//in MPa
+fsc2=217.5*esc2/0.0010875//in MPa
+//stress block parameters for xu / D = 1.1
+n=0.384
+l=0.443
+A=n*fck*D//area of stress block
+r=l*D//distance of c.g., in mm
+Pu=(A*b+Asc*(fsc1-fcc)+Ast*fsc2)/10^3
+Mu=(A*b*(D/2-r)+Asc*(fsc1-fcc)*(D/2-c)-Ast*fsc2*(D/2-c))/10^6
+mprintf("(i) For xu = 1.1 D\nP=%f kN\nMu=%f kN-m\n",Pu,Mu)
+//answer in textbook is incorrect
+//(ii)
+xu=330//in mm
+esc=0.0035*(xu-c)/xu
+est=0.0035*(D-c-xu)/xu
+//by interpolation
+fsc=217.5//in MPa
+fst=217.5//in MPa
+Pu=(0.36*fck*b*xu+Asc*(fsc-fcc)-Ast*fst)/10^3//in kN
+Mu=(0.36*fck*b*xu*(D/2-0.416*xu)+Asc*(fsc-fcc)*(D/2-c)+Ast*fst*(D/2-c))/10^6//in kN-m
+mprintf("(ii) For xu = 330 mm\nP=%f kN\nMu=%f kN-m",Pu,Mu)
diff --git a/3683/CH18/EX18.4/Ex18_4.sce b/3683/CH18/EX18.4/Ex18_4.sce new file mode 100644 index 000000000..b2960c1f4 --- /dev/null +++ b/3683/CH18/EX18.4/Ex18_4.sce @@ -0,0 +1,33 @@ +b=300//in mm
+D=400//in mm
+c=30//cover, in mm
+Asc=452//in sq mm
+Ast=Asc
+fck=15//in MPa
+fy=415//in MPa
+fcc=0.446*fck//in MPa
+//(i)
+xu=1.4*D//in mm
+m=0.43*D//in mm
+esc1=0.002*(xu-c)/(xu-m)
+esc2=0.002*(xu-D+c)/(xu-m)
+//by interpolation
+fsc1=356.8//in MPa
+fsc2=238.68//in MPa
+//stress block parameters for xu / D = 1.4
+n=0.417
+l=0.475
+A=n*fck*D//area of stress block
+r=l*D//distance of c.g., in mm
+Pu=(A*b+Asc*(fsc1-fcc)+Ast*fsc2)/10^3//in kN
+Mu=(A*b*(D/2-r)+Asc*(fsc1-fcc)*(D/2-c)-Ast*fsc2*(D/2-c))/10^6//in kN-m
+mprintf("(i) For xu = 1.4 D\nP=%f kN\nMu=%f kN-m\n",Pu,Mu)
+//(ii)
+xu=370//in mm
+esc=0.0035*(xu-c)/xu
+est=0.0035*(D-c-xu)/xu
+//by interpolation
+fsc=355.8//in MPa
+Pu=(0.36*fck*b*xu+Asc*(fsc-fcc))/10^3//in kN
+Mu=(0.36*fck*b*xu*(D/2-0.416*xu)+Asc*(fsc-fcc)*(D/2-c))/10^6//in kN-m
+mprintf("(ii) For xu = 370 mm\nP=%f kN\nMu=%f kN-m",Pu,Mu)
diff --git a/3683/CH18/EX18.5/Ex18_5.sce b/3683/CH18/EX18.5/Ex18_5.sce new file mode 100644 index 000000000..b6c66e42d --- /dev/null +++ b/3683/CH18/EX18.5/Ex18_5.sce @@ -0,0 +1,35 @@ +b=225//in mm
+D=500//in mm
+c=50//cover, in mm
+Asc=1520//in sq mm
+Ast=Asc
+fck=20//in MPa
+fy=500//in MPa
+fcc=0.446*fck//in MPa
+//(i)
+xu=1.3*D//in mm
+m=0.43*D//in mm
+esc1=0.002*(xu-c)/(xu-m)
+esc2=0.002*(xu-D+c)/(xu-m)
+//by interpolation
+fsc1=412.515//in MPa
+fsc2=183.794//in MPa
+//stress block parameters for xu / D = 1.3
+n=0.409
+l=0.468
+A=n*fck*D//area of stress block
+r=l*D//distance of c.g., in mm
+Pu=(A*b+Asc*(fsc1-fcc)+Ast*fsc2)/10^3//in kN
+Mu=(A*b*(D/2-r)+Asc*(fsc1-fcc)*(D/2-c)-Ast*fsc2*(D/2-c))/10^6//in kN-m
+mprintf("(i) For xu = 1.3 D\nP=%f kN\nMu=%f kN-m\n",Pu,Mu)
+//(ii)
+xu=400//in mm
+esc=0.0035*(xu-c)/xu
+est=0.0035*(D-c-xu)/xu
+//by interpolation
+fsc=422.11//in MPa
+fst=87.45//in MPa
+Pu=(0.36*fck*b*xu+Asc*(fsc-fcc)-Ast*fst)/10^3//in kN
+Mu=(0.36*fck*b*xu*(D/2-0.416*xu)+Asc*(fsc-fcc)*(D/2-c)+Ast*fst*(D/2-c))/10^6//in kN-m
+mprintf("(ii) For xu = 400 mm\nP=%f kN\nMu=%f kN-m",Pu,Mu)
+//answer in textbook for Mu in (ii) is incorrect
diff --git a/3683/CH18/EX18.6/Ex18_6.jpeg b/3683/CH18/EX18.6/Ex18_6.jpeg Binary files differnew file mode 100644 index 000000000..01971b3cb --- /dev/null +++ b/3683/CH18/EX18.6/Ex18_6.jpeg diff --git a/3683/CH18/EX18.6/Ex18_6.sce b/3683/CH18/EX18.6/Ex18_6.sce new file mode 100644 index 000000000..cf18fb256 --- /dev/null +++ b/3683/CH18/EX18.6/Ex18_6.sce @@ -0,0 +1,328 @@ +b=250//width, in mm
+D=450//depth, in mm
+c=50//cover, in mm
+Asc=1472//in sq mm
+Ast=Asc
+fck=15//in MPa
+fcc=0.446*fck//in MPa
+fy=250//in MPa
+Es=2*10^5//in MPa
+ey=0.87*fy/Es//strain in mild steel at yield point
+fs=0.87*fy//stress in mild steel at yield point, in MPa
+
+//xu=infinity
+Pu1=(0.446*fck*(b*D-Asc-Ast)+(Asc+Ast)*fs)/10^3//in kN
+Mu1=0//in kN-m
+
+//xu=1.5 D
+xu=1.5*D//in mm
+m=0.43*D//in mm
+esc1=0.002*(xu-c)/(xu-m)
+if(esc1<=ey)
+ fsc1=esc1/ey*fs
+else
+ fsc1=fs
+end
+esc2=0.002*(xu-D+c)/(xu-m)//>ey
+if(esc2<=ey)
+ fsc2=esc2/ey*fs
+else
+ fsc2=fs
+end
+//stress block parameters for xu / D = 1.5
+n=0.422
+l=0.48
+A=n*fck*D//area of stress block
+r=l*D//distance of c.g.
+Pu2=(A*b+Asc*fsc1+Ast*fsc2)/10^3//in kN
+Mu2=(A*b*(D/2-r)+Asc*fsc1*(D/2-c)-Ast*fsc2*(D/2-c))/10^6//in kN-m
+
+//xu=1.3 D
+xu=1.3*D//in mm
+m=0.43*D//in mm
+esc1=0.002*(xu-c)/(xu-m)
+if(esc1<=ey)
+ fsc1=esc1/ey*fs
+else
+ fsc1=fs
+end
+esc2=0.002*(xu-D+c)/(xu-m)//>ey
+if(esc2<=ey)
+ fsc2=esc2/ey*fs
+else
+ fsc2=fs
+end
+//stress block parameters for xu / D = 1.3
+n=0.409
+l=0.468
+A=n*fck*D//area of stress block
+r=l*D//distance of c.g.
+Pu3=(A*b+Asc*fsc1+Ast*fsc2)/10^3//in kN
+Mu3=(A*b*(D/2-r)+Asc*fsc1*(D/2-c)-Ast*fsc2*(D/2-c))/10^6//in kN-m
+
+//xu=1.2 D
+xu=1.2*D//in mm
+m=0.43*D//in mm
+esc1=0.002*(xu-c)/(xu-m)
+if(esc1<=ey)
+ fsc1=esc1/ey*fs
+else
+ fsc1=fs
+end
+esc2=0.002*(xu-D+c)/(xu-m)//>ey
+if(esc2<=ey)
+ fsc2=esc2/ey*fs
+else
+ fsc2=fs
+end
+//stress block parameters for xu / D = 1.2
+n=0.399
+l=0.458
+A=n*fck*D//area of stress block
+r=l*D//distance of c.g.
+Pu4=(A*b+Asc*fsc1+Ast*fsc2)/10^3//in kN
+Mu4=(A*b*(D/2-r)+Asc*fsc1*(D/2-c)-Ast*fsc2*(D/2-c))/10^6//in kN-m
+
+//xu=1.1 D
+xu=1.1*D//in mm
+m=0.43*D//in mm
+esc1=0.002*(xu-c)/(xu-m)
+if(esc1<=ey)
+ fsc1=esc1/ey*fs
+else
+ fsc1=fs
+end
+esc2=0.002*(xu-D+c)/(xu-m)//>ey
+if(esc2<=ey)
+ fsc2=esc2/ey*fs
+else
+ fsc2=fs
+end
+//stress block parameters for xu / D = 1.1
+n=0.384
+l=0.443
+A=n*fck*D//area of stress block
+r=l*D//distance of c.g.
+Pu5=(A*b+Asc*fsc1+Ast*fsc2)/10^3//in kN
+Mu5=(A*b*(D/2-r)+Asc*fsc1*(D/2-c)-Ast*fsc2*(D/2-c))/10^6//in kN-m
+
+//xu = D
+xu=D//in mm
+m=0.43*D//in mm
+esc1=0.002*(xu-c)/(xu-m)
+if(esc1<=ey)
+ fsc1=esc1/ey*fs
+else
+ fsc1=fs
+end
+esc2=0.002*(xu-D+c)/(xu-m)//>ey
+if(esc2<=ey)
+ fsc2=esc2/ey*fs
+else
+ fsc2=fs
+end
+//stress block parameters for xu / D = 1
+n=0.361
+l=0.416
+A=n*fck*D//area of stress block
+r=l*D//distance of c.g.
+Pu6=(A*b+Asc*fsc1+Ast*fsc2)/10^3//in kN
+Mu6=(A*b*(D/2-r)+Asc*fsc1*(D/2-c)-Ast*fsc2*(D/2-c))/10^6//in kN-m
+
+//xu=400 mm
+xu=400//in mm
+esc=0.0035*(xu-c)/xu
+if(esc<=ey)
+ fsc=esc/ey*fs
+else
+ fsc=fs
+end
+est=0.0035*(D-xu-c)/xu
+if(est<=ey)
+ fst=est/ey*fs
+else
+ fst=fs
+end
+Pu7=(0.36*fck*b*xu+Asc*fsc-Ast*fst)/10^3
+Mu7=(0.36*fck*b*xu*(D/2-0.416*xu)+Asc*fsc*(D/2-c)+Ast*fst*(D/2-c))/10^6
+
+//xu=375 mm
+xu=375//in mm
+esc=0.0035*(xu-c)/xu
+if(esc<=ey)
+ fsc=esc/ey*fs
+else
+ fsc=fs
+end
+est=0.0035*(D-xu-c)/xu
+if(est<=ey)
+ fst=est/ey*fs
+else
+ fst=fs
+end
+Pu8=(0.36*fck*b*xu+Asc*fsc-Ast*fst)/10^3
+Mu8=(0.36*fck*b*xu*(D/2-0.416*xu)+Asc*fsc*(D/2-c)+Ast*fst*(D/2-c))/10^6
+
+//xu=350 mm
+xu=350//in mm
+esc=0.0035*(xu-c)/xu
+if(esc<=ey)
+ fsc=esc/ey*fs
+else
+ fsc=fs
+end
+est=0.0035*(D-xu-c)/xu
+if(est<=ey)
+ fst=est/ey*fs
+else
+ fst=fs
+end
+Pu9=(0.36*fck*b*xu+Asc*fsc-Ast*fst)/10^3
+Mu9=(0.36*fck*b*xu*(D/2-0.416*xu)+Asc*fsc*(D/2-c)+Ast*fst*(D/2-c))/10^6
+
+//xu=325 mm
+xu=325//in mm
+esc=0.0035*(xu-c)/xu
+if(esc<=ey)
+ fsc=esc/ey*fs
+else
+ fsc=fs
+end
+est=0.0035*(D-xu-c)/xu
+if(est<=ey)
+ fst=est/ey*fs
+else
+ fst=fs
+end
+Pu10=(0.36*fck*b*xu+Asc*fsc-Ast*fst)/10^3
+Mu10=(0.36*fck*b*xu*(D/2-0.416*xu)+Asc*fsc*(D/2-c)+Ast*fst*(D/2-c))/10^6
+
+//xu=300 mm
+xu=300//in mm
+esc=0.0035*(xu-c)/xu
+if(esc<=ey)
+ fsc=esc/ey*fs
+else
+ fsc=fs
+end
+est=0.0035*(D-xu-c)/xu
+if(est<=ey)
+ fst=est/ey*fs
+else
+ fst=fs
+end
+Pu11=(0.36*fck*b*xu+Asc*fsc-Ast*fst)/10^3
+Mu11=(0.36*fck*b*xu*(D/2-0.416*xu)+Asc*fsc*(D/2-c)+Ast*fst*(D/2-c))/10^6
+
+//xu=275 mm
+xu=275//in mm
+esc=0.0035*(xu-c)/xu
+if(esc<=ey)
+ fsc=esc/ey*fs
+else
+ fsc=fs
+end
+est=0.0035*(D-xu-c)/xu
+if(est<=ey)
+ fst=est/ey*fs
+else
+ fst=fs
+end
+Pu12=(0.36*fck*b*xu+Asc*fsc-Ast*fst)/10^3
+Mu12=(0.36*fck*b*xu*(D/2-0.416*xu)+Asc*fsc*(D/2-c)+Ast*fst*(D/2-c))/10^6
+
+//xu=250 mm
+xu=250//in mm
+esc=0.0035*(xu-c)/xu
+if(esc<=ey)
+ fsc=esc/ey*fs
+else
+ fsc=fs
+end
+est=0.0035*(D-xu-c)/xu
+if(est<=ey)
+ fst=est/ey*fs
+else
+ fst=fs
+end
+Pu13=(0.36*fck*b*xu+Asc*fsc-Ast*fst)/10^3
+Mu13=(0.36*fck*b*xu*(D/2-0.416*xu)+Asc*fsc*(D/2-c)+Ast*fst*(D/2-c))/10^6
+
+//xu=225 mm
+xu=225//in mm
+esc=0.0035*(xu-c)/xu
+if(esc<=ey)
+ fsc=esc/ey*fs
+else
+ fsc=fs
+end
+est=0.0035*(D-xu-c)/xu
+if(est<=ey)
+ fst=est/ey*fs
+else
+ fst=fs
+end
+Pu14=(0.36*fck*b*xu+Asc*fsc-Ast*fst)/10^3
+Mu14=(0.36*fck*b*xu*(D/2-0.416*xu)+Asc*fsc*(D/2-c)+Ast*fst*(D/2-c))/10^6
+
+//xu=200 mm
+xu=200//in mm
+esc=0.0035*(xu-c)/xu
+if(esc<=ey)
+ fsc=esc/ey*fs
+else
+ fsc=fs
+end
+est=0.0035*(D-xu-c)/xu
+if(est<=ey)
+ fst=est/ey*fs
+else
+ fst=fs
+end
+Pu15=(0.36*fck*b*xu+Asc*fsc-Ast*fst)/10^3
+Mu15=(0.36*fck*b*xu*(D/2-0.416*xu)+Asc*fsc*(D/2-c)+Ast*fst*(D/2-c))/10^6
+
+//xu=150 mm
+xu=150//in mm
+esc=0.0035*(xu-c)/xu
+if(esc<=ey)
+ fsc=esc/ey*fs
+else
+ fsc=fs
+end
+est=0.0035*(D-xu-c)/xu
+if(est<=ey)
+ fst=est/ey*fs
+else
+ fst=fs
+end
+Pu16=(0.36*fck*b*xu+Asc*fsc-Ast*fst)/10^3
+Mu16=(0.36*fck*b*xu*(D/2-0.416*xu)+Asc*fsc*(D/2-c)+Ast*fst*(D/2-c))/10^6
+
+//xu=100 mm
+xu=100//in mm
+esc=0.0035*(xu-c)/xu
+if(esc<=ey)
+ fsc=esc/ey*fs
+else
+ fsc=fs
+end
+est=0.0035*(D-xu-c)/xu
+if(est<=ey)
+ fst=est/ey*fs
+else
+ fst=fs
+end
+Pu17=(0.36*fck*b*xu+Asc*fsc-Ast*fst)/10^3
+Mu17=(0.36*fck*b*xu*(D/2-0.416*xu)+Asc*fsc*(D/2-c)+Ast*fst*(D/2-c))/10^6
+
+//xu=0.531 d
+d=D-c
+xu=0.531*d
+Pu18=0//in kN
+Mu18=0.149*fck*b*d^2/10^6//in kN-m
+
+Pu=[Pu1 Pu2 Pu3 Pu4 Pu5 Pu6 Pu7 Pu8 Pu9 Pu10 Pu11 Pu12 Pu13 Pu14 Pu15 Pu16 Pu17 Pu18]
+Mu=[Mu1 Mu2 Mu3 Mu4 Mu5 Mu6 Mu7 Mu8 Mu9 Mu10 Mu11 Mu12 Mu13 Mu14 Mu15 Mu16 Mu17 Mu18]
+xtitle('P-M Interaction Diagram', 'Mu (kN-m)', 'Pu (kN)')
+plot(Mu,Pu)
diff --git a/3683/CH18/EX18.8/Ex18_8.sce b/3683/CH18/EX18.8/Ex18_8.sce new file mode 100644 index 000000000..1fa76e868 --- /dev/null +++ b/3683/CH18/EX18.8/Ex18_8.sce @@ -0,0 +1,31 @@ +b=250//column width in mm
+D=450//column depth in mm
+Asc=2*1472//in sq mm
+fck=15//in MPa
+fy=250//in MPa
+ex=200//in mm
+ey=150//in mm
+//from interaction curve
+//for ex=200 mm on x-axis
+Pum1=610//in kN
+Muy1=120//in kN-m
+//for ey=150 mm on y-axis
+Pum2=720//in kN
+Mux1=106//in kN-m
+//(i)
+Pu=300//in kN
+Mux=Pu*ey/10^3//in kN-m
+Muy=Pu*ex/10^3//in kN-m
+Puz=(0.45*fck*(b*D-Asc)+0.75*fy*Asc)/10^3//in kN
+a=Pu/Puz
+an=1+1/0.6*(a-0.2)
+b=(Mux/Mux1)^an+(Muy/Muy1)^an//<1
+mprintf("The column can take a load of 300 kN with ex=200 mm and ey=150 mm\n")
+//(ii)
+Pu=500//in kN
+Mux=Pu*ey/10^3//in kN-m
+Muy=Pu*ex/10^3//in kN-m
+a=Pu/Puz
+an=1+1/0.6*(a-0.2)
+b=(Mux/Mux1)^an+(Muy/Muy1)^an//>1
+mprintf("The section is not suitable for a load of 500 kN with ex=200 mm and ey=150 mm\n")
diff --git a/3683/CH18/EX18.9/Ex18_9.sce b/3683/CH18/EX18.9/Ex18_9.sce new file mode 100644 index 000000000..c8521f0e3 --- /dev/null +++ b/3683/CH18/EX18.9/Ex18_9.sce @@ -0,0 +1,23 @@ +b=250//column width, in mm
+D=500//column depth, in mm
+lex=4//in m
+ley=4//in m
+Pu=300//in kN
+Asc=1472//in sq mm
+Ast=1472//in sq mm
+fck=15//in MPa
+fy=250//in MPa
+c=50//cover, in mm
+Max=Pu*10^3*D/2000*(lex/(D/10^3))^2/10^6//in kN-m
+May=Pu*10^3*b/2000*(ley/(b/10^3))^2/10^6//in kN-m
+Puz=(0.45*fck*(b*D-(Asc+Ast))+0.75*fy*(Asc+Ast))/10^3//in kN
+//to find Pb
+xu=(D-c)/(1+0.002/0.0035)//in mm
+fsc=217.5//in MPa
+fst=217.5//in MPa
+Pb=(0.36*fck*b*xu+fsc*Asc-fst*Ast)/10^3//in kN
+k=(Puz-Pu)/(Puz-Pb)//>1
+k=1
+Max=k*Max//in kN-m
+May=k*May//in kN-m
+mprintf("Additional Moments are:\nMax=%f kN/m\nMay=%f kN-m", Max,May)
diff --git a/3683/CH19/EX19.1/Ex19_1.sce b/3683/CH19/EX19.1/Ex19_1.sce new file mode 100644 index 000000000..fcad6fe34 --- /dev/null +++ b/3683/CH19/EX19.1/Ex19_1.sce @@ -0,0 +1,41 @@ +fck=15//in MPa
+fy=250//in MPa
+l=4//span, in m
+MF=1.6
+a=MF*20
+D=l*10^3/a//in mm
+W1=(D/10^3)*25//self-weight, in kN/m
+W2=1//floor finish, in kN/m
+W3=2//live load, in kN/m
+W=W1+W2+W3//in kN/m
+Wu=1.5*W//in kN/m
+lef=4.125//in m
+Mu=Wu*lef^2/8//in kN-m
+d=sqrt(Mu*10^6/0.149/fck/10^3)//in mm
+dia=12//assume 12 mm dia bars
+D=d+dia/2+15//<125 mm (assumed value), hence OK
+D=125//in mm
+d=D-dia/2-15//in mm
+//steel
+//Xu=0.87*fy*Ast/0.36/fck/b = a*Ast
+a=0.87*fy/0.36/fck/10^3
+//using Mu=0.87 fy Ast (d-0.416 Xu), we get a quadratic equation
+p=0.87*fy*0.416*a
+q=-0.87*fy*d
+r=Mu*10^6
+Ast=(-q-sqrt(q^2-4*p*r))/2/p//in sq mm
+s1=1000*0.785*dia^2/Ast//in mm
+s1=105//in mm
+pt=1000*0.785*dia^2/s1/10^3/d*100//in %
+Ads=0.15/100*10^3*D//in sq mm
+//provide 8 mm dia bars
+s2=1000*0.785*8^2/Ads//in mm
+s2=265//in mm
+Vu=Wu*lef/2//in kN
+Tv=Vu*10^3/10^3/d//in MPa
+//for M15 and pt=1
+Tc=0.6//in MPa
+//for solid slabs
+Tc=1.3*Tc//in MPa
+//as Tc>Tv, no shear reinforcement required
+mprintf("Summary of design:\nSlab thickness= %d mm\nCover = 15 mm\nMain steel = 12 mm dia @ %d mm c/c\nDistribution steel = 8 mm dia @ %d mm c/c",D,s1,s2)
diff --git a/3683/CH19/EX19.10/Ex19_10.sce b/3683/CH19/EX19.10/Ex19_10.sce new file mode 100644 index 000000000..92ebaeca3 --- /dev/null +++ b/3683/CH19/EX19.10/Ex19_10.sce @@ -0,0 +1,52 @@ +b=0.2//column width, in m
+D=0.3//column depth, in m
+fck=15//in MPa
+fy=415//in MPa
+P1=600//load on column, in kN
+P2=0.05*P1//weight of footing, in kN
+P=P1+P2//in kN
+Pu=1.5*P//in kN
+q=150//bearing capacity of soil, in kN/sq m
+qu=2*q//ultimate bearing capacity of soil, in kN/sq m
+A=Pu/qu//in sq m
+L=sqrt(A)//assuming footing to be square, in m
+L=1.8//round-off, in m
+p=P1*1.5/L^2//soil pressure, in kN/sq m
+p=277.8//round-off, in kN/sq m
+bc=b/D
+ks=0.5+bc//>1
+ks=1
+Tc=0.25*sqrt(fck)*10^3//in kN/sq m
+Tv=Tc
+//let d be the depth of footing in metres
+//case I: consider greater width of shaded portion in Fig. 19.6 of textbook
+d1=L*(L-b)/2*p/(Tc*L+L*p)//in m
+//case II: refer Fig. 19.7 of textbook; we get a quadratic equation of the form e d^2 + f d + g = 0
+e=p+4*Tc
+f=b*p+D*p+2*(b+D)*Tc
+g=-(L^2-b*D)*p
+d2=(-f+sqrt(f^2-4*e*g))/2/e//in m
+d2=0.35//round-off, in m
+//bending moment consideration, refer Fig. 19.8 of textbook
+Mx=1*((L-b)/2)^2/2*p//in kN-m
+My=1*((L-D)/2)^2/2*p//in kN-m
+d3=sqrt(Mx*10^6/0.138/fck/10^3)//<350 mm, hence OK
+//steel
+//Xu=0.87*fy*Ast/0.36/fck/b = a*Ast
+a=0.87*fy/0.36/fck/10^3
+//using Mu=0.87 fy Ast (d-0.416 Xu), we get a quadratic equation
+p=0.87*fy*0.416*a
+q=-0.87*fy*d2*10^3
+r=Mx*10^6
+Ast=(-q-sqrt(q^2-4*p*r))/2/p//in sq mm
+Ast=L*Ast//steel required for full width of 1.8 m
+//provide 12 mm dia bars
+dia=12//in mm
+n=Ast/0.785/dia^2//no. of 12 mm dia bars
+n=12//round-off
+Tbd=1.6//in MPa
+Ld=dia*0.87*fy/4/Tbd//in mm
+Ld=677//assume, in mm
+//this length is available from the face of the column in both directions
+D=d2*10^3+dia/2+100//in mm
+mprintf("Summary of design:\nOverall depth of footing=%d mm\nCover=100 mm\nSteel-%d bars of 12 mm dia both ways",D,n)
diff --git a/3683/CH19/EX19.11/Ex19_11.sce b/3683/CH19/EX19.11/Ex19_11.sce new file mode 100644 index 000000000..72a08499b --- /dev/null +++ b/3683/CH19/EX19.11/Ex19_11.sce @@ -0,0 +1,74 @@ +fck=15//in MPa
+fy=415//in MPa
+phi=30//angle of repose, in degrees
+H=5//height of wall, in m
+B=0.6*H//assume, in m
+T=B/4//assume toe to base ratio as 1:4, in m
+W=16//density of retained earth, in kN/cu m
+Wu=1.5*W//factored load, in kN/cu m
+P=Wu*H^2/2*(1-sind(phi))/(1+sind(phi))//in kN
+M1=P*H/3//in kN-m
+M1=167//round-off, in kN-m
+//bending moment at 2.5 m below the top
+h=2.5//in m
+M2=Wu*h^2/2*(1-sind(phi))/(1+sind(phi))*h/3//in kN-m
+M2=21//round-off, in kN-m
+//thickness of stem (at the base)
+d=sqrt(M1*10^6/0.138/fck/1000)//in mm
+d=285//round-off, in mm
+dia=20//assume 20 mm dia bars
+D1=d+dia/2+25//in mm
+D2=200//thickness at top, in mm
+D3=D2+(D1-D2)*h/H//thickness at 2.5 m below top, in mm
+d3=sqrt(M2*10^6/0.138/fck/1000)//in mm
+D3=d3+dia/2+25//< 260 mm (provided), hence OK
+D3=260//in mm
+d3=D3-dia/2-25//in mm
+//main steel
+//(a) 5 m below the top
+//Xu=0.87*fy*Ast/0.36/fck/b = a*Ast
+a=0.87*fy/0.36/fck/10^3
+//using Mu=0.87 fy Ast (d-0.416 Xu), we get a quadratic equation
+p=0.87*fy*0.416*a
+q=-0.87*fy*d
+r=M1*10^6
+Ast=(-q-sqrt(q^2-4*p*r))/2/p//in sq mm
+pt=Ast/1000/d*100//in %
+//provide 20 mm dia bars
+s1=1000*0.785*20^2/Ast//in mm
+s1=155//round-off, in mm
+//(b) 2.5 m below the top
+//Xu=0.87*fy*Ast/0.36/fck/b = a*Ast
+a=0.87*fy/0.36/fck/10^3
+//using Mu=0.87 fy Ast (d-0.416 Xu), we get a quadratic equation
+p=0.87*fy*0.416*a
+q=-0.87*fy*d3
+r=M2*10^6
+Ast=(-q-sqrt(q^2-4*p*r))/2/p//in sq mm
+Astmin=0.12/100*10^3*D3//in sq mm
+Ast=max(Ast,Astmin)//in sq mm
+//provide 12 mm dia bars
+s2=1000*0.785*12^2/Ast//in mm
+s2=360//round-off, in mm
+//distribution steel
+Ads=0.12/100*10^3*D3//in sq mm
+//provide 8 mm dia bars
+s3=1000*0.785*8^2/Ads//in mm
+s3=160//round-off, in mm
+//check for shear
+Vu=P//in kN
+Tv=Vu*10^3/10^3/d//in MPa
+//for M15 grade concrete and pt=0.71
+Tc=0.54//in MPa
+//as Tc > Tv, no shear reinforcement required
+//development length
+//(a) At the base of stem
+dia=20//in mm
+Tbd=1.6//in MPa
+Ld=dia*0.87*fy/4/Tbd//in mm
+Ld=1130//round-off, in mm
+//(b) At 2.5 m below the top
+dia=12//in mm
+Ld=dia*0.87*fy/4/Tbd//in mm
+Ld=680//round-off, in mm
+mprintf("Summary of design:\nThickness of stem (at base) = %d mm\nThickness of stem at top = %d mm\nRefer Fig. 19.10 of textbook for reinforcement details",D1,D2)
diff --git a/3683/CH19/EX19.12/Ex19_12.sce b/3683/CH19/EX19.12/Ex19_12.sce new file mode 100644 index 000000000..9a201893b --- /dev/null +++ b/3683/CH19/EX19.12/Ex19_12.sce @@ -0,0 +1,15 @@ +P=1000//in kN
+Pu=1.5*P//in kN
+fck=15//in MPa
+fy=415//in MPa
+l=3.5//unsupported length, in m
+//assume 1% steel
+Ag=Pu*10^3/(0.4*fck*0.99+0.67*fy*0.01)//in sq mm
+L=sqrt(Ag)//assuming a square column
+L=420//in mm
+emin=l*10^3/500+L/30//in mm
+ep=0.05*L//=emin, hence OK
+Asc=0.01*L^2//in sq mm
+//provide 6-20 mm dia bars
+Asc=6*0.785*20^2//in sq mm
+mprintf("Summary of design:\nColumn size - %d x %d mm\nSteel-main = 6-20 mm dia bars",L,L)
diff --git a/3683/CH19/EX19.13/Ex19_13.sce b/3683/CH19/EX19.13/Ex19_13.sce new file mode 100644 index 000000000..6c782e0bb --- /dev/null +++ b/3683/CH19/EX19.13/Ex19_13.sce @@ -0,0 +1,23 @@ +P=500//in kN
+Pu=1.5*P//in kN
+fck=15//in MPa
+fy=250//in MPa
+l=3//unsupported length, in m
+//assume 1% steel
+Ag=Pu*10^3/(0.4*fck*0.99+0.67*fy*0.01)//in sq mm
+L=sqrt(Ag)//assuming a square column
+L=315//in mm
+emin=l*10^3/500+L/30//<20
+emin=20//in mm
+ep=0.05*L//<emin, hence the column is to be checked for bending
+Mu=Pu*10^3*emin//in N-mm
+a=Pu*10^3/fck/L/L
+b=Mu/fck/L/L^2//b=0.032
+d1=40//cover(assume), in mm
+c=d1/L//c=d'/D
+//for d'/D = 0.15
+p=0.07*fck//in %
+Asc=p/100*L^2//in sq mm
+//provide 4-20 mm dia bars
+Asc=4*0.785*20^2//in sq mm
+mprintf("Summary of design:\nColumn size - %d x %d mm\nSteel-main = 4-20 mm dia bars",L,L)
diff --git a/3683/CH19/EX19.14/Ex19_14.sce b/3683/CH19/EX19.14/Ex19_14.sce new file mode 100644 index 000000000..063d07d44 --- /dev/null +++ b/3683/CH19/EX19.14/Ex19_14.sce @@ -0,0 +1,30 @@ +P=500//in kN
+Pu=1.5*P//in kN
+fck=15//in MPa
+fy=250//in MPa
+l=3//unsupported length, in m
+//assume 1% steel
+Ag=Pu*10^3/(0.4*fck*0.99+0.67*fy*0.01)//in sq mm
+b=250//in mm
+D=Ag/b//in mm
+D=400//round-off, in mm
+emin1=l*10^3/500+D/30//in direction of Y axis, in mm, < 20 mm
+emin1=20//in mm
+ep1=0.05*D//=emin, hence no moment is required to be considered in this direction
+emin2=l*10^3/500+b/30//in direction of X axis, in mm, < 20 mm
+emin2=20//in mm
+ep2=0.05*b//<emin, hence moment in this direction needs to be considered
+//interaction diagram
+b=400//in mm
+D=250//in mm
+Mu=Pu*10^3*emin2//in N-mm
+m=Pu*10^3/fck/b/D
+n=Mu/fck/b/D^2//b=0.032
+d1=40//cover(assume), in mm
+c=d1/D//c=d'/D
+//referring to Fig. 19.12
+p=0.08*fck//in %
+Asc=p/100*b*D//in sq mm
+//provide 6-16 dia bars
+Asc=6*0.785*16^2//in sq mm
+mprintf("Summary of design:\nColumn size - %d x %d mm\nSteel-main = 6-16 mm dia bars",D,b)
diff --git a/3683/CH19/EX19.15/Ex19_15.sce b/3683/CH19/EX19.15/Ex19_15.sce new file mode 100644 index 000000000..b57d28ca9 --- /dev/null +++ b/3683/CH19/EX19.15/Ex19_15.sce @@ -0,0 +1,32 @@ +P=500//in kN
+Pu=1.5*P//in kN
+fck=15//in MPa
+fy=250//in MPa
+l=5//effective length, in m
+lex=5//in m
+ley=5//in m
+L=315//column dimension in mm (square column)
+Asc=1256//in sq mm
+m=lex*10^3/L//>12
+n=ley*10^3/L//>12
+//hence the column is slender on both the axes
+Max=Pu*10^3*L/2000*(lex/(L/10^3))^2/10^6//in kN-m
+May=Max
+Puz=(0.45*fck*(L^2-Asc)+0.75*fy*Asc)/10^3//in kN
+c=40//cover, in mm
+//to find Pb
+xu=(L-c)/(1+0.002/0.0035)//in mm
+Pb=0.36*fck*L*xu/10^3//in kN
+k=(Puz-Pu)/(Puz-Pb)//>1
+Max=k*Max//in kN-m
+Mu=15//in kN-m
+Mu=Mu+Max//in kN-m
+a=Pu*10^3/fck/L/L
+b=Mu*10^6/fck/L/L^2//b=0.047
+d1=c/L//d1=d'/D
+//for d'/D = 0.1
+p=0.095*fck//in %
+Asc=p/100*L^2//in sq mm
+//provide 4-18 mm + 4-12 mm dia bars
+Asc=4*0.785*18^2+4*0.785*12^2//in sq mm
+mprintf("Summary of design:\nColumn size - %d x %d mm\nSteel-main = 4-18 mm + 4-12 mm dia bars",L,L)
diff --git a/3683/CH19/EX19.16/Ex19_16.sce b/3683/CH19/EX19.16/Ex19_16.sce new file mode 100644 index 000000000..8e3a75cf6 --- /dev/null +++ b/3683/CH19/EX19.16/Ex19_16.sce @@ -0,0 +1,37 @@ +Pu=2000//in kN
+Mux=50//in kN-m
+Muy=Mux
+fck=20//in MPa
+fy=415//in MPa
+//assume 2% steel
+p=2//in %
+Ag=Pu*10^3/(0.4*fck*(1-p/100)+0.67*fy*p/100)//in sq mm
+L=sqrt(Ag)//assuming a square column
+L=400//in mm
+m=Pu*10^3/fck/L/L
+n=p/fck
+c=50//cover (assume), in mm
+d1=c/L//d1=d'/D
+//from Fig. 19.21, for d'/D = 0.15 and Pu / fck b D = 0.625
+f=0.046
+Mux1=f*fck*L*L^2/10^6//in kN-m
+Muy1=Mux1
+Puz=(0.45*fck*(1-p/100)*L^2+0.75*fy*p/100*L^2)/10^3//in kN
+a=Pu/Puz//>0.8
+an=2
+b=(Mux/Mux1)^an+(Muy/Muy1)^an//>1
+//assume 2.5% steel
+p=2.5//in %
+n=p/fck
+//from Fig. 19.21, for d'/D = 0.15 and Pu / fck b D = 0.625
+f=0.08
+Mux1=f*fck*L*L^2/10^6//in kN-m
+Muy1=Mux1
+Puz=(0.45*fck*(1-p/100)*L^2+0.75*fy*p/100*L^2)/10^3//in kN
+a=Pu/Puz//<0.8
+an=1+1/0.6*(a-0.2)
+b=(Mux/Mux1)^an+(Muy/Muy1)^an//<1, hence OK
+Asc=p/100*L^2//in sq mm
+//provide 12-22 mm dia bars
+Asc=12*0.785*22^2//in sq mm
+mprintf("Summary of design:\nColumn size - %d x %d mm\nSteel-main = 12-22 mm dia bars placed equally on four faces of the column",L,L)
diff --git a/3683/CH19/EX19.17/Ex19_17.sce b/3683/CH19/EX19.17/Ex19_17.sce new file mode 100644 index 000000000..c6a8814da --- /dev/null +++ b/3683/CH19/EX19.17/Ex19_17.sce @@ -0,0 +1,33 @@ +b=400//in mm
+D=500//in mm
+Pu=1600//in kN
+Mux=90//in kN-m
+Muy=50//in kN-m
+fck=15//in MPa
+fy=415//in MPa
+p=1.5//assume 1.5% steel, placed on four sides
+m=p/fck
+c=50//cover (assume), in mm
+//to find Mux1
+n=c/D//n=d'/D
+l=Pu*10^3/fck/b/D
+//referring to Fig.19.20, for Pu/ fck/ b/ D = 0.53 and p/ fck = 0.1
+f=0.09
+Mux1=f*fck*b*D^2/10^6//in kN-m
+//to find Muy1
+b=500//in mm
+D=400//in mm
+n=c/D//n=d'/D
+l=Pu*10^3/fck/b/D
+//referring to Fig.19.21, for Pu/ fck/ b/ D = 0.53 and p/ fck = 0.1
+f=0.08
+Muy1=f*fck*b*D^2/10^6//in kN-m
+Puz=(0.45*fck*(1-p/100)*b*D+0.75*fy*p/100*b*D)/10^3//in kN
+a=Pu/Puz//<0.8
+an=1+1/0.6*(a-0.2)
+r=(Mux/Mux1)^an+(Muy/Muy1)^an//<1
+Asc=p/100*b*D//in sq mm
+//provide 6-16 mm + 6-20 mm dia bars
+Asc=6*0.785*16^2+6*0.785*20^2//in sq mm
+mprintf("Summary of design:\nColumn size - %d x %d mm\nSteel-main = 6-16 mm + 6-20 mm dia bars",D,b)
+//answer in textbook is incorrect
diff --git a/3683/CH19/EX19.18/Ex19_18.sce b/3683/CH19/EX19.18/Ex19_18.sce new file mode 100644 index 000000000..27dd70c0a --- /dev/null +++ b/3683/CH19/EX19.18/Ex19_18.sce @@ -0,0 +1,73 @@ +b=300//in mm
+Pu=1500//in kN
+Mux=100//in kN-m
+Muy=70//in kN-m
+fck=15//in MPa
+fy=250//in MPa
+p=1.5//assume 1.5% steel, placed on four sides
+Ag=Pu*10^3/(0.4*fck*(1-p/100)+0.67*fy*p/100)//in sq mm
+D=Ag/b//in mm
+D=600//assume, in mm
+m=p/fck
+c=60//cover (assume), in mm
+//to find Mux1
+n=c/D//n=d'/D
+l=Pu*10^3/fck/b/D
+//referring to Fig.19.17, for Pu/ fck/ b/ D = 0.56 and p/ fck = 0.1
+f=0.038
+Mux1=f*fck*b*D^2/10^6//in kN-m
+//to find Muy1
+b=600//in mm
+D=300//in mm
+n=c/D//n=d'/D
+l=Pu*10^3/fck/b/D
+//referring to Fig.19.19, for Pu/ fck/ b/ D = 0.56 and p/ fck = 0.1
+f=0.038
+Muy1=f*fck*b*D^2/10^6//in kN-m
+Puz=(0.45*fck*(1-p/100)*b*D+0.75*fy*p/100*b*D)/10^3//in kN
+a=Pu/Puz//>0.8
+an=2
+r=(Mux/Mux1)^an+(Muy/Muy1)^an//>1
+p=4//assume 4% steel, second trial
+m=p/fck
+//to find Mux1
+b=300//in mm
+D=600//in mm
+//referring to Fig.19.17, for Pu/ fck/ b/ D = 0.56 and p/ fck = 0.26
+f=0.15
+Mux1=f*fck*b*D^2/10^6//in kN-m
+//to find Muy1
+b=600//in mm
+D=300//in mm
+n=c/D//n=d'/D
+//referring to Fig.19.19, for Pu/ fck/ b/ D = 0.56 and p/ fck = 0.26
+f=0.15
+Muy1=f*fck*b*D^2/10^6//in kN-m
+Puz=(0.45*fck*(1-p/100)*b*D+0.75*fy*p/100*b*D)/10^3//in kN
+a=Pu/Puz//<0.8
+an=1+1/0.6*(a-0.2)
+r=(Mux/Mux1)^an+(Muy/Muy1)^an//<1, hence OK
+//but steel can be reduced
+p=3//assume 3% steel, second trial
+m=p/fck
+//to find Mux1
+b=300//in mm
+D=600//in mm
+//referring to Fig.19.17, for Pu/ fck/ b/ D = 0.56 and p/ fck = 0.2
+f=0.12
+Mux1=f*fck*b*D^2/10^6//in kN-m
+//to find Muy1
+b=600//in mm
+D=300//in mm
+n=c/D//n=d'/D
+//referring to Fig.19.19, for Pu/ fck/ b/ D = 0.56 and p/ fck = 0.2
+f=0.12
+Muy1=f*fck*b*D^2/10^6//in kN-m
+Puz=(0.45*fck*(1-p/100)*b*D+0.75*fy*p/100*b*D)/10^3//in kN
+a=Pu/Puz//<0.8
+an=1+1/0.6*(a-0.2)
+r=(Mux/Mux1)^an+(Muy/Muy1)^an//<1, hence OK
+Asc=p/100*b*D//in sq mm
+//provide 12-25 dia bars
+Asc=12*0.785*25^2//in sq mm
+mprintf("Summary of design:\nColumn size - %d x %d mm\nSteel-main = 12-25 mm dia bars",D,b)
diff --git a/3683/CH19/EX19.3/Ex19_3.sce b/3683/CH19/EX19.3/Ex19_3.sce new file mode 100644 index 000000000..33876dac8 --- /dev/null +++ b/3683/CH19/EX19.3/Ex19_3.sce @@ -0,0 +1,43 @@ +fck=15//in MPa
+fy=415//in MPa
+l=4.5//span, in m
+MF=1.4
+a=MF*20
+D=l*10^3/a//in mm
+D=160//in mm
+W1=(D/10^3)*25//self-weight, in kN/m
+W2=1//floor finish, in kN/m
+W3=1//partitions, in kN/m
+W4=4//live load, in kN/m
+W=W1+W2+W3+W4//in kN/m
+Wu=1.5*W//in kN/m
+lef=l+0.16//in m
+Mu=Wu*lef^2/8//in kN-m
+d=sqrt(Mu*10^6/0.138/fck/10^3)//in mm
+dia=12//assume 12 mm dia bars
+D=d+dia/2+15//=160 mm(assumed value), approximately
+D=160//in mm
+d=140//in mm
+//steel
+//Xu=0.87*fy*Ast/0.36/fck/b = a*Ast
+a=0.87*fy/0.36/fck/10^3
+//using Mu=0.87 fy Ast (d-0.416 Xu), we get a quadratic equation
+p=0.87*fy*0.416*a
+q=-0.87*fy*d
+r=Mu*10^6
+Ast=(-q-sqrt(q^2-4*p*r))/2/p//in sq mm
+s1=1000*0.785*dia^2/Ast//in mm
+s1=112//in mm
+pt=Ast/10^3/d*100//in %
+Ads=0.12/100*10^3*D//in sq mm
+//provide 8 mm dia bars
+s2=1000*0.785*8^2/Ads//in mm
+s2=260//in mm
+Vu=Wu*lef/2//in kN
+Tv=Vu*10^3/10^3/d//in MPa
+//for M15 and pt=0.718
+Tc=0.53//in MPa
+//for solid slabs
+Tc=1.25*Tc//in MPa
+//as Tc>Tv, no shear reinforcement required
+mprintf("Summary of design:\nSlab thickness= %d mm\nCover = 15 mm\nMain steel = 12 mm dia @ %d mm c/c\nDistribution steel = 8 mm dia @ %d mm c/c",D,s1,s2)
diff --git a/3683/CH19/EX19.4/Ex19_4.sce b/3683/CH19/EX19.4/Ex19_4.sce new file mode 100644 index 000000000..430eca029 --- /dev/null +++ b/3683/CH19/EX19.4/Ex19_4.sce @@ -0,0 +1,48 @@ +fck=15//in MPa
+fy=415//in MPa
+MF=1.4//modification factor
+//let a be span to depth ratio
+l=1//span, in m
+a=MF*7
+D=l*1000/a//in mm
+D=105//assume, in mm
+//to calculate loading
+W1=25*(D/10^3)*1.5//self-weight, in kN/m
+W2=0.5*1.5//finish, in kN/m
+W3=0.75*1.5//live load, in kN/m
+W=W1+W2+W3//in kN/m
+Wu=1.5*W//in kN/m
+lef=l+0.23/2//effective span, in m
+Mu=Wu*lef/2//in kN-m
+//check for depth
+d=sqrt(Mu*10^6/(0.138*fck*1500))//in mm
+dia=12//assume 12 mm dia bars
+D=d+12/2+15//<105, hence OK
+D=100//assume, in mm
+d=D-dia/2-15//in mm
+//steel
+//Xu=0.87*fy*Ast/0.36/fck/b = a*Ast
+a=0.87*fy/0.36/fck/1.5/10^3
+//using Mu=0.87 fy Ast (d-0.416 Xu), we get a quadratic equation
+p=0.87*fy*0.416*a
+q=-0.87*fy*d
+r=Mu*10^6
+Ast=(-q-sqrt(q^2-4*p*r))/2/p//in sq mm
+//provide 8 mm dia bars
+dia=8//in mm
+s1=1500*0.785*dia^2/Ast//>3d=3x79=237 mm
+s1=235//in mm
+Ads=0.12/100*1000*D//distribution steel, in sq mm
+//assume 6 mm dia bars
+s2=1000*0.785*6^2/Ads//in mm
+s2=235//round-off, in mm
+Tbd=1.6//in MPa
+Ld=dia*0.87*fy/4/Tbd//in mm
+Ld=452//in mm
+Tv=Wu*10^3/1500/d//in MPa
+Ast=1500*0.785*8^2/235//in sq mm
+pt=Ast/1500/d*100//in %
+//for M15 and pt=0.26
+Tc=0.35//in MPa
+//as Tc>Tv, no shear reinforcement required
+mprintf("Summary of design\nThickness of slab = %d mm\nCover = 15 mm\nMain steel = 8 mm dia @ %d mm c/c\nDevelopment length = %d mm\nDistribution steel = 6 mm dia @ %d mm c/c",D,s1,Ld,s2)
diff --git a/3683/CH19/EX19.5/Ex19_5.sce b/3683/CH19/EX19.5/Ex19_5.sce new file mode 100644 index 000000000..6c01260cc --- /dev/null +++ b/3683/CH19/EX19.5/Ex19_5.sce @@ -0,0 +1,43 @@ +lx=3.5//in m
+ly=4//in m
+fck=15//in MPa
+fy=250//in MPa
+D=lx*10^3/35//in mm
+W1=(D/10^3)*25//self-weight, in kN/m
+W2=1.5//live load, in kN/m
+W=W1+W2//in kN/m
+Wu=1.5*W//in kN/m
+a=ly/lx
+Ax=0.078
+Ay=0.0602
+Mx=Ax*Wu*lx^2//in kN-m
+My=Ay*Wu*lx^2//in kN-m
+d=sqrt(Mx*10^6/0.149/fck/10^3)//in mm
+d=51//round-off, in mm
+//assume 10 mm dia bars
+dia=10//in mm
+D=d+dia/2+15//<100 mm assumed value
+D=100//in mm
+d=D-dia/2-15//in mm
+//steel - short span
+//Xu=0.87*fy*Ast/0.36/fck/b = a*Ast
+a=0.87*fy/0.36/fck/10^3
+//using Mu=0.87 fy Ast (d-0.416 Xu), we get a quadratic equation
+p=0.87*fy*0.416*a
+q=-0.87*fy*d
+r=Mx*10^6
+Ast=(-q-sqrt(q^2-4*p*r))/2/p//in sq mm
+s1=1000*0.785*dia^2/Ast//in mm
+s1=220//round-off, in mm
+//long span
+d=d-dia/2-dia/2//in mm
+//Xu=0.87*fy*Ast/0.36/fck/b = a*Ast
+a=0.87*fy/0.36/fck/10^3
+//using Mu=0.87 fy Ast (d-0.416 Xu), we get a quadratic equation
+p=0.87*fy*0.416*a
+q=-0.87*fy*d
+r=My*10^6
+Ast=(-q-sqrt(q^2-4*p*r))/2/p//in sq mm
+s2=1000*0.785*dia^2/Ast//in mm
+s2=250//round-off, in mm
+mprintf("Summary of design\nSlab thickness=%d mm\nCover=15 mm\nSteel-\n(i)Short span = 10 mm dia @ %d mm c/c\n(ii)Long span = 10 mm dia @ %d mm c/c",D,s1,s2)
diff --git a/3683/CH19/EX19.6/Ex19_6.sce b/3683/CH19/EX19.6/Ex19_6.sce new file mode 100644 index 000000000..c9f8bea98 --- /dev/null +++ b/3683/CH19/EX19.6/Ex19_6.sce @@ -0,0 +1,79 @@ +b=225//width in mm
+D=300//depth in mm
+fck=15//in MPa
+fy=415//in MPa
+l=4.2//span, in m
+W1=(b/10^3)*(D/10^3)*25//self-weight, in kN/m
+W2=6//live load, in kN/m
+W=W1+W2//in kN/m
+Wu=1.5*W//in kN/m
+Mu=Wu*l^2/8//in kN-m
+d=270//assume, in mm
+Mulim=0.138*fck*b*d^2/10^6//in kN-m
+//as Mulim > Mu, it will be a singly reinforced beam
+//Xu=0.87*fy*Ast/0.36/fck/b = a*Ast
+a=0.87*fy/0.36/fck/b
+//using Mu=0.87 fy Ast (d-0.416 Xu), we get a quadratic equation
+p=0.87*fy*0.416*a
+q=-0.87*fy*d
+r=Mu*10^6
+Ast=(-q-sqrt(q^2-4*p*r))/2/p//in sq mm
+//provide 12 mm dia bars
+n=Ast/0.785/12^2
+n=3//assume
+Ast=n*0.785*12^2//in sq mm
+Vu=Wu*l/2//in kN
+Tv=Vu*10^3/b/d//in MPa
+pt=Ast/b/d*100//pt=0.56
+//for M15 and pt=0.56
+Tc=0.46//in MPa
+//as Tc>Tv, no shear reinforcement required
+//provide nominal stirrups and provide 6 mm stirrups
+Asv=2*0.785*6^2//in sq mm
+Sv=Asv*fy/0.4/b//in mm
+Sv=260//assume, in mm
+Svmax=0.75*d//in mm
+Svmax=200//round-off, in mm
+Sv=min(Sv,Svmax)//in mm
+mprintf("Summary of design:\nBeam size - %d x %d mm\nCover - 25 mm\nSteel - %d-12 mm dia bars\nStirrups - 6 mm dia @ %d mm c/c",b,D,n,Sv)
+//deflection check
+Ec=5700*sqrt(fck)//in MPa
+Es=2*10^5//in MPa
+m=Es/Ec
+fcr=0.7*sqrt(fck)//in MPa
+//using b x x/2 = m Ast (d-x), we get a quadratic equation
+//solving the quadratic equation
+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//in mm
+Ir=b*x^3/12+b*x*(x/2)^2+m*Ast*(d-x)^2//in mm^4
+Igr=b*D^3/12//in mm^4
+yt=D/2//in mm
+Mr=fcr*Igr/yt//in N-mm
+M=W*l^2/8*10^6//in N-mm
+Ieff=Ir/(1.2-Mr/M*z/d*(1-x/d)*b/b)//in mm^4
+//Ir<Ieff<Igr, hence OK
+W1=W*l//in kN
+u1=5/384*(W1*10^3)*(l*10^3)^3/Ec/Ieff//short-term deflection, in mm
+//long-term deflection
+//(i) deflection due to shrinkage
+k3=0.125//for simply supported beam
+pt=0.56//in %
+pc=0//in %
+k4=0.72*(pt-pc)/sqrt(pt)
+phi=k4*0.0003/D
+u2=k3*phi*(l*10^3)^2//in mm
+//(ii) deflection due to creep
+Ecc=Ec/(1+1.6)//in MPa
+//assuming a permanent load of 60%
+W2=0.6*W*l//in kN
+u3=5/384*(W2*10^3)*(l*10^3)^3/Ecc/Ieff//in mm
+u4=5/384*(W2*10^3)*(l*10^3)^3/Ec/Ieff//in mm
+u5=u3-u4//in mm
+u=u1+u2+u5//total deflection, in mm
+v1=l*10^3/250//permissible deflection, in mm
+v2=l*10^3/350//in mm
+//assuming half the shrinkage strain occurs within the first 28 days, the deflection occurring after this time
+v3=u2/2+u5//< permissible value, hence OK
diff --git a/3683/CH19/EX19.7/Ex19_7.sce b/3683/CH19/EX19.7/Ex19_7.sce new file mode 100644 index 000000000..de5c0cd3e --- /dev/null +++ b/3683/CH19/EX19.7/Ex19_7.sce @@ -0,0 +1,89 @@ +l=7//span, in m
+fck=15//in MPa
+fy=250//in MPa
+b=300//assume, in mm
+W=35//live load, in kN/m
+Wu=1.5*W//in kN/m
+Mu=Wu*l^2/8//in kN-m
+d=(Mu*10^6/0.149/fck/b)^0.5//in mm
+d=1.1*d//increase depth by 10% for self-weight
+d=750//assume, in mm
+c=50//cover, in mm
+D=d+c//in mm
+W1=(b/10^3)*(D/10^3)*25//self-weight, in kN/m
+W2=35//live load, in kN/m
+W=W1+W2//in kN/m
+Wu=1.5*W//in kN/m
+Mu=Wu*l^2/8//in kN-m
+d=(Mu*10^6/0.149/fck/b)^0.5//<750 mm, hence OK
+d=750//in mm
+//steel
+//Xu=0.87*fy*Ast/0.36/fck/b = a*Ast
+a=0.87*fy/0.36/fck/b
+//using Mu=0.87 fy Ast (d-0.416 Xu), we get a quadratic equation
+p=0.87*fy*0.416*a
+q=-0.87*fy*d
+r=Mu*10^6
+Ast=(-q-sqrt(q^2-4*p*r))/2/p//in sq mm
+//provide 20 mm dia bars
+n=Ast/0.785/20^2
+//provide 8-20 mm + 2-18 mm dia bars
+Ast=8*0.785*20^2+2*0.785*18^2//in sq mm
+pt=Ast/b/d*100//pt=1.34
+Vu=Wu*l/2//in kN
+Tv=Vu*10^3/b/d//in MPa
+//for M15 and pt=1.34
+Tc=0.65//in MPa
+//as Tv>Tc, shear reinforcement required
+//provide 6 mm stirrups
+Vus=Vu-Tc*b*d/10^3//in kN
+Asv=2*0.785*6^2//in sq mm
+Sv=Asv*0.87*fy*d/Vus/10^3//in mm
+Sv=130//assume, in mm
+Svmin=Asv*fy/0.4/b//in mm
+Svmin=115//assume, in mm
+Sv=min(Sv,Svmin)//in mm
+mprintf("Summary of design:\nBeam size - %d x %d mm\nCover - 50 mm\nSteel - 8-20 mm + 2-18 mm dia bars\nStirrups - 6 mm dia @ %d mm c/c",b,D,Sv)
+//deflection check
+Ec=5700*sqrt(fck)//in MPa
+Es=2*10^5//in MPa
+m=Es/Ec
+fcr=0.7*sqrt(fck)//in MPa
+//using b x x/2 = m Ast (d-x), we get a quadratic equation
+//solving the quadratic equation
+p=b/2
+q=m*Ast
+r=-m*Ast*d
+x=(-q+sqrt(q^2-4*p*r))/2/p//in mm
+x=290//assume, in mm
+z=d-x/3//in mm
+Ir=b*x^3/12+b*x*(x/2)^2+m*Ast*(d-x)^2//in mm^4
+Igr=b*D^3/12//in mm^4
+yt=D/2//in mm
+Mr=fcr*Igr/yt//in N-mm
+M=W*l^2/8*10^6//in N-mm
+Ieff=Ir/(1.2-Mr/M*z/d*(1-x/d)*b/b)//in mm^4
+//Ir>Ieff
+Ieff=Ir//in mm^4
+W1=W*l//in kN
+u1=5/384*(W1*10^3)*(l*10^3)^3/Ec/Ieff//short-term deflection, in mm
+//long-term deflection
+//(i) deflection due to shrinkage
+k3=0.125//for simply supported beam
+pt=1.34//in %
+pc=0//in %
+k4=0.65*(pt-pc)/sqrt(pt)
+phi=k4*0.0003/D
+u2=k3*phi*(l*10^3)^2//in mm
+//(ii) deflection due to creep
+Ecc=Ec/(1+1.6)//in MPa
+//assuming a permanent load of 60%
+W2=0.6*W*l//in kN
+u3=5/384*(W2*10^3)*(l*10^3)^3/Ecc/Ieff//in mm
+u4=5/384*(W2*10^3)*(l*10^3)^3/Ec/Ieff//in mm
+u5=u3-u4//in mm
+u=u1+u2+u5//total deflection, in mm
+v1=l*10^3/250//permissible deflection, in mm
+v2=l*10^3/350//in mm
+//assuming half the shrinkage strain occurs within the first 28 days, the deflection occurring after this time
+v3=u2/2+u5//< permissible value, hence OK
diff --git a/3683/CH19/EX19.8/Ex19_8.sce b/3683/CH19/EX19.8/Ex19_8.sce new file mode 100644 index 000000000..c9609ce52 --- /dev/null +++ b/3683/CH19/EX19.8/Ex19_8.sce @@ -0,0 +1,86 @@ +l=10//span, in m
+fck=15//in MPa
+fy=250//in MPa
+Df=100//slab thickness, in mm
+D=l*10^3/15//depth of beam, in mm
+D=600//assume, in mm
+d=D-50//cover=50 mm
+bw=300//beam width, in mm
+bf=l*10^3/6+bw+6*Df//>2500 mm c/c distance of beams
+bf=2500//in mm
+W1=(bw/10^3)*(D-Df)/10^3*25//web, in kN/m
+W2=(Df/10^3)*(bf/10^3)*25//slab, in kN/m
+W3=(bf/10^3)*5//imposed load, in kN/m
+W=W1+W2+W3//in kN/m
+Wu=1.5*W//in kN/m
+Mu=Wu*l^2/8//in kN-m
+Vu=Wu*l/2//in kN
+Asf=0.36*fck*bf*Df/0.87/fy//steel required only for flange, in sq mm
+Asf=6210//round-off, in sq mm
+//verification of trial section
+xu=100//assume, in mm
+Ast=Asf//in sq mm
+Mulim=0.87*fy*Ast*(d-0.416*xu)/10^6//in kN-m
+//Mulim > Mu, hence OK
+//keeping the assumed trial section, work out the steel required
+//Xu=0.87*fy*Ast/0.36/fck/b = a*Ast
+a=0.87*fy/0.36/fck/bf
+//using Mu=0.87 fy Ast (d-0.416 Xu), we get a quadratic equation
+p=0.87*fy*0.416*a
+q=-0.87*fy*d
+r=Mu*10^6
+Ast=(-q-sqrt(q^2-4*p*r))/2/p//in sq mm
+//provide 5-25 mm dia + 3-22 mm dia bars
+pt=Ast*100/(bw*d+(bf-bw)*Df)//pt=1%, approximately
+//check for shear
+Tv=Vu*10^3/bw/d//in MPa
+//for M15 grade concrete and pt=1%
+Tc=0.6//in MPa
+//as Tv > Tc, shear reinforcement required
+Vus=Vu-Tc*bw*d/10^3//in kN
+//provide 6 mm dia stirrups
+Asv=2*0.785*6^2//in sq mm
+Sv=Asv*0.87*fy*d/Vus/10^3//in mm
+Sv=90//round-off, in mm
+mprintf("T beam:bf=%d mm\nDf=%d mm\nd=%d mm\nD=%d mm\nCover = 50 mm\nSteel= 5-25 mm dia + 3-22 mm dia bars\nStirrups = 6 mm dia @ %d mm c/c throughout",bf,Df,d,D,Sv)
+//answer in textbook for spacing of stirrups is incorrect
+//deflection check
+Ec=5700*sqrt(fck)//in MPa
+Es=2*10^5//in MPa
+m=Es/Ec//modular ratio
+fcr=0.7*sqrt(fck)//in MPa
+//using bf Df (x-Df/2) = m Ast (d-x), we get a quadratic equation
+x=(m*Ast*d+bf*Df^2/2)/(bf*Df+m*Ast)//in mm
+z=0.87*d//assume, in mm
+//refer Fig. 19.5 of textbook
+Ir=bf*x^3/12+bf*Df*(x/2)^2+m*Ast*(d-x)^2//in mm^4
+y=(bf*Df*Df/2+(D-Df)*bw*((D-Df)/2+Df))/(bf*Df+(D-Df)*bw)//c.g. from top, in mm (neglecting steel)
+Igr=bf*Df^3/12+bf*Df*(Df/2-y)^2+bw*(D-Df)^3/12+bw*(D-Df)*((D-Df)/2+Df-y)^2//in mm^4
+yt=d/2//in mm
+Mr=fcr*Igr/yt//in N-mm
+M=W*l^2/8*10^6//in N-mm
+Ieff=Ir/(1.2-Mr/M*z/d*(1-x/d)*bw/bf)//in mm^4
+//Ir > Ieff
+Ieff=Ir//in mm^4
+W1=W*l//in kN
+u1=5/384*(W1*10^3)*(l*10^3)^3/Ec/Ieff//short term deflection, in mm
+//deflection due to shrinkage
+k3=0.125//for simply supported beam
+pt=1//in %
+pc=0//in %
+k4=0.65*(pt-pc)/sqrt(pt)
+phi=k4*0.0003/D
+u2=k3*phi*(l*10^3)^2//in mm
+//deflection due to creep
+Ecc=Ec/(1+1.6)//in MPa
+//assuming a permanent load of 60%
+W2=0.6*W*l//in kN
+u3=5/384*(W2*10^3)*(l*10^3)^3/Ecc/Ieff//in mm
+u4=5/384*(W2*10^3)*(l*10^3)^3/Ec/Ieff//in mm
+u5=u3-u4//in mm
+u=u1+u2+u5//total deflection, in mm
+v1=l*10^3/250//permissible deflection, in mm
+v2=l*10^3/350//>20 mm
+v2=20//in mm
+//assuming half the shrinkage strain occurs within the first 28 days, the deflection occurring after this time
+v3=u2/2+u5//< permissible value, hence OK
diff --git a/3683/CH19/EX19.9/Ex19_9.sce b/3683/CH19/EX19.9/Ex19_9.sce new file mode 100644 index 000000000..39a5c515b --- /dev/null +++ b/3683/CH19/EX19.9/Ex19_9.sce @@ -0,0 +1,36 @@ +l=2.7+1//span, in m
+R=0.15//rise, in m
+t=0.27//tread, in m
+fck=15//in MPa
+fy=415//in MPa
+D=200//assume, in mm
+W1=D/10^3*25*sqrt(R^2+t^2)/t//slab load on plan, in kN/m
+W2=1/2*R*t*25/t//load of step per metre, in kN/m
+W3=3//live load, in kN/m
+W=W1+W2+W3//in kN/m
+Wu=1.5*W//in kN/m
+Mu=Wu*l^2/8//in kN-m
+d=sqrt(Mu*10^6/0.138/fck/10^3)//in mm
+d=115//round-off, in mm
+//assume 10 mm dia bars
+dia=10//in mm
+D=d+dia/2+25//< 200 mm, hence OK
+D=l*10^3/24//depth required for deflection, in mm
+D=155//round-off, in mm
+d=D-dia/2-25//in mm
+//steel
+//Xu=0.87*fy*Ast/0.36/fck/b = a*Ast
+a=0.87*fy/0.36/fck/10^3
+//using Mu=0.87 fy Ast (d-0.416 Xu), we get a quadratic equation
+p=0.87*fy*0.416*a
+q=-0.87*fy*d
+r=Mu*10^6
+Ast=(-q-sqrt(q^2-4*p*r))/2/p//in sq mm
+s1=1000*0.785*dia^2/Ast//spacing of 10 mm dia bars
+s1=110//round-off, in mm
+Ads=0.12/100*D*10^3//distribution steel, in sq mm
+//provide 8 mm dia bars
+s2=1000*0.785*8^2/Ads//in mm
+s2=270//round-off, in mm
+mprintf("Summary of design\nSlab thickness=%d mm\nCover = 25 mm\nMain steel = 10 mm dia bars @ %d mm c/c\nDistribution steel = 8 mm dia @ %d mm c/c",D,s1,s2)
+//answer in textbook for spacing of 10 mm dia bars is incorrect
diff --git a/3683/CH2/EX2.1/Ex2_1.sce b/3683/CH2/EX2.1/Ex2_1.sce new file mode 100644 index 000000000..4cf74c248 --- /dev/null +++ b/3683/CH2/EX2.1/Ex2_1.sce @@ -0,0 +1,14 @@ +b=200//width, in mm
+D=400//overall depth, in mm
+m=18.66//modular ratio
+Ast=4*0.785*22^2//four 22 mm dia bars at bottom, in sq mm
+Asc=3*0.785*20^2//three 20 mm dia bars at top, in sq mm
+bottom_cover=30//in mm
+top_cover=25//in mm
+d=D-bottom_cover//effective depth, in mm
+//to find x using b(x^2)/2 + (1.5m-1)Asc(x-d')=mAst(d-x), which becomes of the form px^2+qx+r=0
+p=b/2
+q=(1.5*m-1)*Asc+m*Ast
+r=-(1.5*m-1)*Asc*top_cover-m*Ast*d
+x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm
+mprintf("Depth of neutral axis=%f mm",x)
diff --git a/3683/CH2/EX2.2/Ex2_2.sce b/3683/CH2/EX2.2/Ex2_2.sce new file mode 100644 index 000000000..96c43be64 --- /dev/null +++ b/3683/CH2/EX2.2/Ex2_2.sce @@ -0,0 +1,24 @@ +b=280//width, in mm
+D=540//overall depth, in mm
+Ast=5*0.785*22^2//five 22 mm dia bars on tension side, in sq mm
+Asc=4*0.785*20^2//four 20 mm dia bars on compression side, in sq mm
+bottom_cover=40//in mm
+top_cover=30//in mm
+sigma_cbc=5//in MPa
+sigma_st=140//in MPa
+m=18.66//modular ratio
+d=D-bottom_cover//effective depth, in mm
+//to find critical depth of neutral axis
+Xc=d/(1+sigma_st/(m*sigma_cbc))//in mm
+//to find x using b(x^2)/2 + (1.5m-1)Asc(x-d')=mAst(d-x), which becomes of the form px^2+qx+r=0
+p=b/2
+q=(1.5*m-1)*Asc+m*Ast
+r=-(1.5*m-1)*Asc*top_cover-m*Ast*d
+x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm
+//as x<Xc, beam is under-reinforced
+sigma_cbc=(sigma_st/m)*x/(d-x)//in MPa
+sigma_cbc_dash=sigma_cbc*(x-top_cover)/x//in MPa
+sigma_sc=1.5*m*sigma_cbc_dash//in MPa
+//stress in compression steel is found to be less than its permissible limit of 130 N/mm^2
+Mr=b*x*sigma_cbc*(d-x/3)/2+(1.5*m-1)*Asc*sigma_cbc_dash*(d-top_cover)//in N-mm
+mprintf("Moment of resistance of the beam=%f kN-m",Mr/10^6)
diff --git a/3683/CH2/EX2.3/Ex2_3.sce b/3683/CH2/EX2.3/Ex2_3.sce new file mode 100644 index 000000000..45ce17753 --- /dev/null +++ b/3683/CH2/EX2.3/Ex2_3.sce @@ -0,0 +1,25 @@ +b=300//width, in mm
+d=600//effective depth, in mm
+Ast=1256//in sq mm
+Asc=1256//in sq mm
+top_cover=30//in mm
+sigma_cbc=7//in MPa
+sigma_st=190//in MPa
+m=13.33//modular ratio
+//using elastic theory method
+//to find critical depth of neutral axis
+Xc=d/(1+sigma_st/(m*sigma_cbc))//in mm
+//to find x using b(x^2)/2 + (1.5m-1)Asc(x-d')=mAst(d-x), which becomes of the form px^2+qx+r=0
+p=b/2
+q=(1.5*m-1)*Asc+m*Ast
+r=-(1.5*m-1)*Asc*top_cover-m*Ast*d
+x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm
+//as x<Xc, beam is under-reinforced
+sigma_cbc=(sigma_st/m)*x/(d-x)//in MPa
+sigma_cbc_dash=sigma_cbc*(x-top_cover)/x//in MPa
+sigma_sc=1.5*m*sigma_cbc_dash//in MPa
+//stress in compression steel is found to be less than its permissible limit of 130 N/mm^2
+Mr1=b*x*sigma_cbc*(d-x/3)/2+(1.5*m-1)*Asc*sigma_cbc_dash*(d-top_cover)//in N-mm
+//using steel beam theory method
+Mr2=Ast*sigma_st*(d-top_cover)//in N-mm
+mprintf("Moment of resistance of the beam using elastic theory method=%f kN-m\nMoment of resistance of the beam using elastic theory method=%f kN-m",Mr1/10^6,Mr2/10^6)
diff --git a/3683/CH2/EX2.4/Ex2_4.sce b/3683/CH2/EX2.4/Ex2_4.sce new file mode 100644 index 000000000..69d7cee33 --- /dev/null +++ b/3683/CH2/EX2.4/Ex2_4.sce @@ -0,0 +1,24 @@ +b=250//width, in mm
+D=550//overall depth, in mm
+Ast=4*0.785*25^2//four 25 mm dia bars on tension side, in sq mm
+Asc=3*0.785*22^2//three 22 mm dia bars on compression side, in sq mm
+bottom_cover=50//in mm
+top_cover=30//in mm
+d=D-bottom_cover//effective depth, in mm
+sigma_cbc=5//in MPa
+sigma_st=140//in MPa
+sigma_sc=130//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 x using b(x^2)/2 + (1.5m-1)Asc(x-d')=mAst(d-x), which becomes of the form px^2+qx+r=0
+p=b/2
+q=(1.5*m-1)*Asc+m*Ast
+r=-(1.5*m-1)*Asc*top_cover-m*Ast*d
+x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm
+//as x>Xc, beam is over-reinforced
+sigma_cbc_dash=sigma_cbc*(x-top_cover)/x//in MPa
+sigma_sc=1.5*m*sigma_cbc_dash//< 130 MPa, hence OK
+//stress in compression steel is found to be less than its permissible limit of 130 N/mm^2
+Mr=b*x*sigma_cbc*(d-x/3)/2+(1.5*m-1)*Asc*sigma_cbc_dash*(d-top_cover)//in N-mm
+mprintf("Moment of resistance of the beam=%f kN-m",Mr/10^6)
diff --git a/3683/CH2/EX2.5/Ex2_5.sce b/3683/CH2/EX2.5/Ex2_5.sce new file mode 100644 index 000000000..6fc000a60 --- /dev/null +++ b/3683/CH2/EX2.5/Ex2_5.sce @@ -0,0 +1,25 @@ +b=250//width, in mm
+d=450//effective depth, in mm
+Ast=4*0.785*22^2//four 22 mm dia bars on tension side, in sq mm
+Asc=Ast
+top_cover=30//in mm
+sigma_cbc=7//in MPa
+sigma_st=140//in MPa
+sigma_sc=130//in MPa
+m=13.33//modular ratio
+l=5.7//effective span, in m
+//to find critical depth of neutral axis
+Xc=d/(1+sigma_st/(m*sigma_cbc))//in mm
+//to find x using b(x^2)/2 + (1.5m-1)Asc(x-d')=mAst(d-x), which becomes of the form px^2+qx+r=0
+p=b/2
+q=(1.5*m-1)*Asc+m*Ast
+r=-(1.5*m-1)*Asc*top_cover-m*Ast*d
+x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm
+//as x<Xc, beam is under-reinforced
+sigma_cbc=(sigma_st/m)*x/(d-x)//in MPa
+sigma_cbc_dash=sigma_cbc*(x-top_cover)/x//in MPa
+sigma_sc=1.5*m*sigma_cbc_dash//in MPa
+//stress in compression steel is found to be less than its permissible limit of 130 N/mm^2
+Mr=b*x*sigma_cbc*(d-x/3)/2+(1.5*m-1)*Asc*sigma_cbc_dash*(d-top_cover)//in N-mm
+W=(Mr/10^6)*8/l^2//in kN/m
+mprintf("Uniformly distributed load the beam can carry (including self-weight)=%f kN/m",W)
diff --git a/3683/CH2/EX2.6/Ex2_6.sce b/3683/CH2/EX2.6/Ex2_6.sce new file mode 100644 index 000000000..2d03a7e73 --- /dev/null +++ b/3683/CH2/EX2.6/Ex2_6.sce @@ -0,0 +1,21 @@ +b=200//width, in mm
+D=480//overall depth, in mm
+Ast=4*0.785*25^2//four 25 mm dia bars on tension side, in sq mm
+Asc=3*0.785*22^2//three 22 mm dia bars on compression side, in sq mm
+bottom_cover=30//in mm
+top_cover=30//in mm
+d=D-bottom_cover//effective depth, in mm
+m=18.66//modular ratio
+M=100*10^6//in N-mm
+//to find x using b(x^2)/2 + (1.5m-1)Asc(x-d')=mAst(d-x), which becomes of the form px^2+qx+r=0
+p=b/2
+q=(1.5*m-1)*Asc+m*Ast
+r=-(1.5*m-1)*Asc*top_cover-m*Ast*d
+x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm
+//sigma_cbc_dash=sigma_cbc*(x-d')/x=a*sigma_cbc
+a=(x-top_cover)/x
+sigma_cbc=M/(b*x*(d-x/3)/2+(1.5*m-1)*Asc*a*(d-top_cover))//in MPa
+sigma_st=m*sigma_cbc*(d-x)/x//in MPa
+sigma_cbc_dash=a*sigma_cbc//in MPa
+sigma_sc=1.5*m*sigma_cbc_dash//in MPa
+mprintf("Stress in concrete=%f N/mm^2\nStress in tension steel=%f N/mm^2\nStress in compression steel=%f N/mm^2",sigma_cbc,sigma_st,sigma_sc)
diff --git a/3683/CH2/EX2.7/Ex2_7.sce b/3683/CH2/EX2.7/Ex2_7.sce new file mode 100644 index 000000000..e20b7b250 --- /dev/null +++ b/3683/CH2/EX2.7/Ex2_7.sce @@ -0,0 +1,19 @@ +b=300//width, in mm
+d=500//effective depth, in mm
+Ast=4*0.785*20^2//four 20 mm dia bars on tension and compression side, in sq mm
+Asc=Ast
+top_cover=25//in mm
+m=13.33//modular ratio
+M=120*10^6//in N-mm
+//to find x using b(x^2)/2 + (1.5m-1)Asc(x-d')=mAst(d-x), which becomes of the form px^2+qx+r=0
+p=b/2
+q=(1.5*m-1)*Asc+m*Ast
+r=-(1.5*m-1)*Asc*top_cover-m*Ast*d
+x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm
+//sigma_cbc_dash=sigma_cbc*(x-d')/x=a*sigma_cbc
+a=(x-top_cover)/x
+sigma_cbc=M/(b*x*(d-x/3)/2+(1.5*m-1)*Asc*a*(d-top_cover))//in MPa
+sigma_st=m*sigma_cbc*(d-x)/x//in MPa
+sigma_cbc_dash=a*sigma_cbc//in MPa
+sigma_sc=1.5*m*sigma_cbc_dash//in MPa
+mprintf("Stress in concrete=%f N/mm^2\nStress in tension steel=%f N/mm^2\nStress in compression steel=%f N/mm^2",sigma_cbc,sigma_st,sigma_sc)
diff --git a/3683/CH2/EX2.8/Ex2_8.sce b/3683/CH2/EX2.8/Ex2_8.sce new file mode 100644 index 000000000..dcd510ad1 --- /dev/null +++ b/3683/CH2/EX2.8/Ex2_8.sce @@ -0,0 +1,24 @@ +b=250//width, in mm
+D=600//overall depth, in mm
+bottom_cover=50//in mm
+top_cover=50//in mm
+d=D-bottom_cover//effective depth, in mm
+sigma_cbc=5//in MPa
+sigma_st=140//in MPa
+m=18.66//modular ratio
+M=95*10^6//in N-mm
+//to find critical depth of neutral axis
+Xc=d/(1+sigma_st/(m*sigma_cbc))//in mm
+//to find Ast1
+Ast1=b*Xc*sigma_cbc/(2*sigma_st)//in sq mm
+Ast1=982//round-off, in sq mm
+Mr=b*Xc*sigma_cbc/2*(d-Xc/3)//moment of resistance of singly reinforced beam, in N-mm
+M1=M-Mr//remaining bending moment, in N-mm
+//to find Ast2
+Ast2=M1/(sigma_st*(d-top_cover))//in sq mm
+Ast2=421//round-off, in sq mm
+Ast=Ast1+Ast2//in sq mm
+//to find Asc
+Asc=m*Ast2*(d-Xc)/((1.5*m-1)*(Xc-top_cover))//in sq mm
+Asc=565//round-off, in sq mm
+mprintf("Tensile steel required=%d mm^2\nCompression steel required=%d mm^2",Ast,Asc)
diff --git a/3683/CH2/EX2.9/Ex2_9.sce b/3683/CH2/EX2.9/Ex2_9.sce new file mode 100644 index 000000000..0f0833cb3 --- /dev/null +++ b/3683/CH2/EX2.9/Ex2_9.sce @@ -0,0 +1,20 @@ +b=360//width, in mm
+d=750//effective depth, in mm
+top_cover=50//in mm
+sigma_cbc=7//in MPa
+sigma_st=190//in MPa
+m=13.33//modular ratio
+M=300*10^6//in N-mm
+//to find critical depth of neutral axis
+Xc=d/(1+sigma_st/(m*sigma_cbc))//in mm
+//to find Ast1
+Ast1=b*Xc*sigma_cbc/(2*sigma_st)//in sq mm
+Ast1=1638//round-off, in sq mm
+Mr=b*Xc*sigma_cbc/2*(d-Xc/3)//moment of resistance of singly reinforced beam, in N-mm
+M1=M-Mr//remaining bending moment, in N-mm
+//to find Ast2
+Ast2=M1/(sigma_st*(d-top_cover))//in sq mm
+Ast=Ast1+Ast2//in sq mm
+//to find Asc
+Asc=m*Ast2*(d-Xc)/((1.5*m-1)*(Xc-top_cover))//in sq mm
+mprintf("Tensile steel required=%f mm^2\nCompression steel required=%f mm^2",Ast,Asc)
diff --git a/3683/CH3/EX3.1/Ex3_1.sce b/3683/CH3/EX3.1/Ex3_1.sce new file mode 100644 index 000000000..9a079284a --- /dev/null +++ b/3683/CH3/EX3.1/Ex3_1.sce @@ -0,0 +1,12 @@ +Bf=1300//width of flange, in mm
+Df=80//thickness of flange, in mm
+d=600//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
+Xc=240//round-off, in mm
+//to find Ast
+Ast=Bf*Df*(Xc-Df/2)/(m*(d-Xc))//in sq mm
+mprintf("Neutral axis depth=%d mm\nArea of steel=%f mm^2", Xc,Ast)
diff --git a/3683/CH3/EX3.10/Ex3_10.sce b/3683/CH3/EX3.10/Ex3_10.sce new file mode 100644 index 000000000..52802c086 --- /dev/null +++ b/3683/CH3/EX3.10/Ex3_10.sce @@ -0,0 +1,22 @@ +Bf=1300//width of flange, in mm
+Df=100//thickness of flange, in mm
+d=500//effective depth, in mm
+sigma_cbc=5//in MPa
+sigma_st=275//in MPa
+m=18.66//modular ratio
+Ast=1570//in sq mm
+Asc=1256//in sq mm
+top_cover=30//in mm
+//to find critical depth of neutral axis
+Xc=d/(1+sigma_st/(m*sigma_cbc))//in mm
+//assume x>Df; equating moments of area on compression and tension sides about N.A.
+x=(m*Ast*d+Bf*Df^2/2+(1.5*m-1)*Asc*top_cover)/(m*Ast+Bf*Df+(1.5*m-1)*Asc)//in mm
+//as x<Xc, beam is under-reinforced
+sigma_cbc=sigma_st/m*x/(d-x)//in MPa
+sigma_cbc_dash=sigma_cbc*(x-top_cover)/x//stress in concrete at level of compression steel, in MPa
+sigma_cbc_double_dash=sigma_cbc*(x-Df)/x//stress in concrete at the underside of the slab, in MPa
+//to find lever arm
+z=round(d-(sigma_cbc+2*sigma_cbc_double_dash)/(sigma_cbc+sigma_cbc_double_dash)*Df/3)//in mm
+//taking moments about tensile steel
+Mr=Bf*Df*(sigma_cbc+sigma_cbc_double_dash)*z/2+(1.5*m-1)*Asc*sigma_cbc_dash*(d-top_cover)//in N-mm
+mprintf("Moment of resistance of the beam=%f kN-m", Mr/10^6)
diff --git a/3683/CH3/EX3.11/Ex3_11.sce b/3683/CH3/EX3.11/Ex3_11.sce new file mode 100644 index 000000000..34b03a4d7 --- /dev/null +++ b/3683/CH3/EX3.11/Ex3_11.sce @@ -0,0 +1,27 @@ +Bf=1500//width of flange, in mm
+Df=150//thickness of flange, in mm
+d=600//effective depth, in mm
+sigma_cbc=7//in MPa
+sigma_st=230//in MPa
+m=13.33//modular ratio
+Ast=1964//in sq mm
+Asc=1140//in sq mm
+top_cover=50//in mm
+//to find critical depth of neutral axis
+Xc=d/(1+sigma_st/(m*sigma_cbc))//in mm
+//assume x>Df; equating moments of area on compression and tension sides about N.A.
+x=(m*Ast*d+Bf*Df^2/2+(1.5*m-1)*Asc*top_cover)/(m*Ast+Bf*Df+(1.5*m-1)*Asc)// in mm
+//we find that x<Df, hence our assumption that x>Df is wrong
+//to find x using Bf(x^2)/2 + (1.5m-1)Asc(x-d')=mAst(d-x), which becomes of the form px^2+qx+r=0
+p=Bf/2
+q=m*Ast+(1.5*m-1)*Asc
+r=-(m*Ast*d+(1.5*m-1)*Asc*top_cover)
+//solving quadratic equation
+x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm
+//as x<Xc, beam is under-reinforced
+sigma_cbc=sigma_st/m*x/(d-x)//in MPa
+sigma_cbc_dash=sigma_cbc*(x-top_cover)/x//stress in concrete at level of compression steel, in MPa
+//taking moments about tensile steel
+Mr=Bf*x*sigma_cbc*(d-x/3)/2+(1.5*m-1)*Asc*sigma_cbc_dash*(d-top_cover)//in N-mm
+mprintf("Moment of resistance of the beam=%f kN-m", Mr/10^6)
+//answer given in textbook is incorrect
diff --git a/3683/CH3/EX3.12/Ex3_12.sce b/3683/CH3/EX3.12/Ex3_12.sce new file mode 100644 index 000000000..7d4365df5 --- /dev/null +++ b/3683/CH3/EX3.12/Ex3_12.sce @@ -0,0 +1,25 @@ +Bf=1450//width of flange, in mm
+Df=120//thickness of flange, in mm
+d=400//effective depth, in mm
+m=13.33//modular ratio
+Ast=1800//in sq mm
+Asc=450//in sq mm
+top_cover=30//in mm
+M=200*10^6//in N-mm
+//assume x>Df; equating moments of area on compression and tension sides about N.A.
+x=(m*Ast*d+Bf*Df^2/2+(1.5*m-1)*Asc*top_cover)/(m*Ast+Bf*Df+(1.5*m-1)*Asc)//in mm
+//we find that x<Df, hence our assumption that x>Df is wrong
+//to find x using Bf(x^2)/2 + (1.5m-1)Asc(x-d')=mAst(d-x), which becomes of the form px^2+qx+r=0
+p=Bf/2
+q=m*Ast+(1.5*m-1)*Asc
+r=-(m*Ast*d+(1.5*m-1)*Asc*top_cover)
+//solving quadratic equation
+x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm
+//as x<Xc, beam is under-reinforced; let stress in concrete at level of steel be equal to 'a' times the stress in concrete at top
+a=(x-top_cover)/x
+//taking moments about tensile steel
+sigma_cbc=M/(Bf*x*(d-x/3)/2+(1.5*m-1)*Asc*a*(d-top_cover))//in MPa
+sigma_st=m*sigma_cbc*(d-x)/x//in MPa
+sigma_sc=1.5*m*a*sigma_cbc//in MPa
+mprintf("Stress in concrete=%f N/mm^2\nStress in tension steel=%f N/mm^2\nStress in compression steel=%f N/mm^2",sigma_cbc,sigma_st,sigma_sc)
+//answer in textbook is incorrect
diff --git a/3683/CH3/EX3.13/Ex3_13.sce b/3683/CH3/EX3.13/Ex3_13.sce new file mode 100644 index 000000000..cb4a82b0b --- /dev/null +++ b/3683/CH3/EX3.13/Ex3_13.sce @@ -0,0 +1,19 @@ +Bf=500//width of flange, in mm
+Bw=250//breadth of web, in mm
+Df=100//thickness of flange, in mm
+d=500//effective depth, in mm
+sigma_cbc=5//in MPa
+sigma_st=140//in MPa
+m=18.66//modular ratio
+Ast=2000//in sq mm
+//to find critical depth of neutral axis
+Xc=d/(1+sigma_st/(m*sigma_cbc))//in mm
+//assume x>Df
+x=(m*Ast*d+Bf*Df^2/2)/(m*Ast+Bf*Df)//in mm
+//as x>Xc, beam is over-reinforced
+sigma_cbc_dash=sigma_cbc*(x-Df)/x//in MPa
+//to find lever arm
+z=d-(sigma_cbc+2*sigma_cbc_dash)/(sigma_cbc+sigma_cbc_dash)*Df/3//in mm
+//taking moments about tensile steel
+Mr=Bf*Df*(sigma_cbc+sigma_cbc_dash)*z/2//in N-mm
+mprintf("Moment of resistance of the beam=%f kN-m", Mr/10^6)
diff --git a/3683/CH3/EX3.14/Ex3_14.sce b/3683/CH3/EX3.14/Ex3_14.sce new file mode 100644 index 000000000..05c9d6e73 --- /dev/null +++ b/3683/CH3/EX3.14/Ex3_14.sce @@ -0,0 +1,17 @@ +Bf=750//width of flange, in mm
+Bw=250//breadth of web, in mm
+Df=100//thickness of flange, in mm
+d=700//effective depth, in mm
+sigma_cbc=7//in MPa
+sigma_st=190//in MPa
+m=13.33//modular ratio
+M=460*10^6//in N-mm
+//to find critical depth of neutral axis
+Xc=d/(1+sigma_st/(m*sigma_cbc))//in mm
+sigma_cbc_dash=sigma_cbc*(Xc-Df)/Xc//in MPa
+//to find lever arm
+z=d-(sigma_cbc+2*sigma_cbc_dash)/(sigma_cbc+sigma_cbc_dash)*Df/3//in mm
+//taking moments about tensile steel
+Ast=M/(sigma_st*z)//in sq mm
+Ast=3699//round-off, in sq mm
+mprintf("Area of steel required=%d mm^2", Ast)
diff --git a/3683/CH3/EX3.15/Ex3_15.sce b/3683/CH3/EX3.15/Ex3_15.sce new file mode 100644 index 000000000..ead9a0163 --- /dev/null +++ b/3683/CH3/EX3.15/Ex3_15.sce @@ -0,0 +1,20 @@ +Df=120//thickness of flange, in mm
+Bw=200//breadth of web, in mm
+d=550//effective depth, in mm
+l=6//span, in m
+Bf=l*1000/12+Bw+3*Df//in mm
+m=13.33//modular ratio
+Ast=3200//in sq mm
+M=190*10^6//in N-mm
+//assume x>Df; equating moments of area on compression and tension sides about N.A.
+x=(m*Ast*d+Bf*Df^2/2)/(m*Ast+Bf*Df)//in mm
+//we find that x>Df, hence our assumption that x>Df is correct
+//as x<Xc, beam is under-reinforced; let stress in concrete at underside of slab be equal to 'a' times the stress in concrete at top
+a=(x-Df)/x
+//to find lever arm
+z=d-(1+2*a)/(1+a)*Df/3//in mm
+z=500//round-off, in mm
+//taking moments about tensile steel
+sigma_cbc=M/(Bf*Df*(1+a)*z/2)//in MPa
+sigma_st=m*sigma_cbc*(d-x)/x//in MPa
+mprintf("Stress in concrete=%f N/mm^2\nStress in tension steel=%f N/mm^2",sigma_cbc,sigma_st)
diff --git a/3683/CH3/EX3.2/Ex3_2.sce b/3683/CH3/EX3.2/Ex3_2.sce new file mode 100644 index 000000000..186602672 --- /dev/null +++ b/3683/CH3/EX3.2/Ex3_2.sce @@ -0,0 +1,16 @@ +Bf=1500//width of flange, in mm
+Bw=300//breadth of web, in mm
+Df=100//thickness of flange, in mm
+d=700//effective depth, in mm
+m=18.66//modular ratio
+Ast=8*0.785*25^2//eight 25 mm dia bars, in sq mm
+//assume depth of neutral axis is less than or equal to thickness of flange; find x using Bf(x^2)/2=mAst(d-x), which becomes of the form px^2+qx+r=0
+p=Bf/2
+q=m*Ast
+r=-m*Ast*d
+//solving quadratic equation
+x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm
+//x>Df; hence our assumption is incorrect; equating moments of area on compression and tension sides about N.A.
+x=(m*Ast*d+Bf*Df^2/2)/(m*Ast+Bf*Df)//in mm
+x=263//round-off, in mm
+mprintf("Neutral axis depth=%d mm", x)
diff --git a/3683/CH3/EX3.3/Ex3_3.sce b/3683/CH3/EX3.3/Ex3_3.sce new file mode 100644 index 000000000..592c01571 --- /dev/null +++ b/3683/CH3/EX3.3/Ex3_3.sce @@ -0,0 +1,17 @@ +Bf=1200//width of flange, in mm
+Bw=200//breadth of web, in mm
+Df=100//thickness of flange, in mm
+d=400//effective depth, in mm
+m=13.33//modular ratio
+Ast=4*0.785*18^2//four 18mm dia bars, in sq mm
+//assume x > Df; ; equating moments of area on compression and tension sides about N.A.
+x=(m*Ast*d+Bf*Df^2/2)/(m*Ast+Bf*Df)//in mm
+//as x < Df; our assumption was incorrect
+//x < Df; find x using Bf(x^2)/2=mAst(d-x), which becomes of the form px^2+qx+r=0
+p=Bf/2
+q=m*Ast
+r=-m*Ast*d
+//solving quadratic equation
+x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm
+//x<Df; hence our assumption is correct
+mprintf("Neutral axis depth=%f mm", x)
diff --git a/3683/CH3/EX3.4/Ex3_4.sce b/3683/CH3/EX3.4/Ex3_4.sce new file mode 100644 index 000000000..10b56929a --- /dev/null +++ b/3683/CH3/EX3.4/Ex3_4.sce @@ -0,0 +1,25 @@ +Bf=1500//width of flange, in mm
+Bw=300//breadth of web, in mm
+Df=100//thickness of flange, in mm
+d=700//effective depth, in mm
+sigma_cbc=5//in MPa
+sigma_st=140//in MPa
+m=18.66//modular ratio
+Ast=8*0.785*25^2//eight 25 mm dia bars, in sq mm
+//assume x < Df; find x using Bf(x^2)/2=mAst(d-x), which becomes of the form px^2+qx+r=0
+p=Bf/2
+q=m*Ast
+r=-m*Ast*d
+//solving quadratic equation
+x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm
+//x > Df; hence our assumption is incorrect; equating moments of area on compression and tension sides about N.A.
+x=(m*Ast*d+Bf*Df^2/2)/(m*Ast+Bf*Df)//in mm
+//to find critical depth of neutral axis
+Xc=d/(1+sigma_st/(m*sigma_cbc))//in mm
+//as x < Xc, beam is under-reinforced
+sigma_cbc=sigma_st/m*x/(d-x)//in MPa
+sigma_cbc_dash=sigma_cbc*(x-Df)/x//in MPa
+//to find lever arm
+z=d-(sigma_cbc+2*sigma_cbc_dash)/(sigma_cbc+sigma_cbc_dash)*Df/3//in mm
+Mr=Bf*Df*(sigma_cbc+sigma_cbc_dash)*z/2//in N-mm
+mprintf("Moment of resistance of the beam=%f kN-m", Mr/10^6)
diff --git a/3683/CH3/EX3.5/Ex3_5.sce b/3683/CH3/EX3.5/Ex3_5.sce new file mode 100644 index 000000000..fe72aaaf1 --- /dev/null +++ b/3683/CH3/EX3.5/Ex3_5.sce @@ -0,0 +1,22 @@ +Bf=1200//width of flange, in mm
+Bw=200//breadth of web, in mm
+Df=100//thickness of flange, in mm
+d=400//effective depth, in mm
+sigma_cbc=7//in MPa
+sigma_st=190//in MPa
+m=13.33//modular ratio
+Ast=4*0.785*18^2//four 18 mm dia bars, in sq mm
+//assume x < Df; find x using Bf(x^2)/2=mAst(d-x), which becomes of the form px^2+qx+r=0
+p=Bf/2
+q=m*Ast
+r=-m*Ast*d
+//solving quadratic equation
+x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm
+//x < Df; hence our assumption is correct
+//to find critical depth of neutral axis
+Xc=d/(1+sigma_st/(m*sigma_cbc))//in mm
+//as x < Xc, beam is under-reinforced
+sigma_cbc=sigma_st/m*x/(d-x)//in MPa
+//taking moments about tensile steel
+Mr=Bf*x*sigma_cbc*(d-x/3)/2//in N-mm
+mprintf("Moment of resistance of the beam=%f kN-m", Mr/10^6)
diff --git a/3683/CH3/EX3.6/Ex3_6.sce b/3683/CH3/EX3.6/Ex3_6.sce new file mode 100644 index 000000000..2dd196dbd --- /dev/null +++ b/3683/CH3/EX3.6/Ex3_6.sce @@ -0,0 +1,20 @@ +Bf=1500//width of flange, in mm
+Bw=200//breadth of web, in mm
+Df=100//thickness of flange, in mm
+d=400//effective depth, in mm
+sigma_cbc=5//in MPa
+sigma_st=140//in MPa
+m=18.66//modular ratio
+Ast=2190//in sq mm
+//assume x>Df
+x=(m*Ast*d+Bf*Df^2/2)/(m*Ast+Bf*Df)//in mm
+//to find critical depth of neutral axis
+Xc=d/(1+sigma_st/(m*sigma_cbc))//in mm
+//as x<Xc, beam is under-reinforced
+sigma_cbc=sigma_st/m*x/(d-x)//in MPa
+sigma_cbc_dash=sigma_cbc*(x-Df)/x//in MPa
+//to find lever arm
+z=d-(sigma_cbc+2*sigma_cbc_dash)/(sigma_cbc+sigma_cbc_dash)*Df/3//in mm
+//taking moments about tensile steel
+Mr=Bf*Df*(sigma_cbc+sigma_cbc_dash)*z/2//in N-mm
+mprintf("Moment of resistance of the beam=%f kN-m", Mr/10^6)
diff --git a/3683/CH3/EX3.7/Ex3_7.sce b/3683/CH3/EX3.7/Ex3_7.sce new file mode 100644 index 000000000..81006bb90 --- /dev/null +++ b/3683/CH3/EX3.7/Ex3_7.sce @@ -0,0 +1,24 @@ +Bf=1200//width of flange, in mm
+Bw=300//breadth of web, in mm
+Df=120//thickness of flange, in mm
+d=500//effective depth, in mm
+sigma_cbc=7//in MPa
+sigma_st=190//in MPa
+m=13.33//modular ratio
+Ast=5*0.785*20^2//five 20 mm dia bars, in sq mm
+l=6//span, in m
+//assume depth of neutral axis is less than or equal to thickness of flange; find x using Bf(x^2)/2=mAst(d-x), which becomes of the form px^2+qx+r=0
+p=Bf/2
+q=m*Ast
+r=-m*Ast*d
+//solving quadratic equation
+x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm
+//x < Df; hence our assumption is correct
+//to find critical depth of neutral axis
+Xc=d/(1+sigma_st/(m*sigma_cbc))//in mm
+//as x<Xc, beam is under-reinforced
+sigma_cbc=sigma_st/m*x/(d-x)//in MPa
+//taking moments about tensile steel
+Mr=Bf*x*sigma_cbc*(d-x/3)/2//in N-mm
+W=(Mr/10^6)*8/l^2//in kN/m
+mprintf("Moment of resistance of the beam=%f kN-m\nCapacity to take uniformly distributed load(including self-weight)=%f kN/m", Mr/10^6,W)
diff --git a/3683/CH3/EX3.8/Ex3_8.sce b/3683/CH3/EX3.8/Ex3_8.sce new file mode 100644 index 000000000..ebbe7f663 --- /dev/null +++ b/3683/CH3/EX3.8/Ex3_8.sce @@ -0,0 +1,16 @@ +Bf=1400//width of flange, in mm
+Df=120//thickness of flange, in mm
+d=600//effective depth, in mm
+m=18.66//modular ratio
+Ast=4000//in sq mm
+M=160*10^6//in N-mm
+//Assume x>Df; equating moments of area on compression and tension sides about N.A.
+x=(m*Ast*d+Bf*Df^2/2)/(m*Ast+Bf*Df)//in mm
+//let sigma_cbc_dash=a*sigma_cbc
+a=(x-Df)/x
+//to find lever arm
+z=d-(1+2*a)/(1+a)*Df/3//in mm
+sigma_cbc=2*M/(Bf*Df*(1+a)*z)//in MPa
+sigma_st=m*sigma_cbc*(d-x)/x//in MPa
+mprintf("Stress in concrete=%f N/mm^2\nStress in tension steel=%f N/mm^2",sigma_cbc,sigma_st)
+//answer given in textbook is incorrect
diff --git a/3683/CH3/EX3.9/Ex3_9.sce b/3683/CH3/EX3.9/Ex3_9.sce new file mode 100644 index 000000000..aefc35ea1 --- /dev/null +++ b/3683/CH3/EX3.9/Ex3_9.sce @@ -0,0 +1,17 @@ +Bf=1250//width of flange, in mm
+Df=120//thickness of flange, in mm
+d=700//effective depth, in mm
+m=13.33//modular ratio
+Ast=5500//in sq mm
+W=60//UDL including self-weight, in kN/m
+l=8//span, in m
+M=W*l^2/8*10^6//in N-mm
+//Assume x>Df. Equating moments of area on compressiona and tension sides about N.A.
+x=(m*Ast*d+Bf*Df^2/2)/(m*Ast+Bf*Df)//in mm
+//let sigma_cbc_dash=a*sigma_cbc
+a=(x-Df)/x
+//to find lever arm
+z=d-(1+2*a)/(1+a)*Df/3//in mm
+sigma_cbc=2*M/(Bf*Df*(1+a)*z)//in MPa
+sigma_st=m*sigma_cbc*(d-x)/x//in MPa
+mprintf("Stress in concrete=%f N/mm^2\nStress in tension steel=%f N/mm^2",sigma_cbc,sigma_st)
diff --git a/3683/CH4/EX4.1/Ex4_1.sce b/3683/CH4/EX4.1/Ex4_1.sce new file mode 100644 index 000000000..ab9edc58a --- /dev/null +++ b/3683/CH4/EX4.1/Ex4_1.sce @@ -0,0 +1,11 @@ +b=250//width, in mm
+d=500//effective depth, in mm
+W=20//UDL including self-weight, in kN/m
+Pt=1//percentage tensile steel
+l=6//span, in m
+V=W*l/2//in kN
+Tv=(V*10^3)/(b*d)//in MPa
+//for Pt=1% and for M15 grade concrete
+Tc=0.37//in MPa
+//as Tv>Tc, shear reinforcement is required
+mprintf("Nominal shear stress in beam=%f MPa\nShear strength of concrete=%f MPa", Tv,Tc)
diff --git a/3683/CH4/EX4.2/Ex4_2.sce b/3683/CH4/EX4.2/Ex4_2.sce new file mode 100644 index 000000000..10f33cb23 --- /dev/null +++ b/3683/CH4/EX4.2/Ex4_2.sce @@ -0,0 +1,12 @@ +b=230//width, in mm
+d=500//effective depth, in mm
+W=24//UDL including self-weight, in kN/m
+Ast=4*0.785*20^2//four 20 mm dia bars, in sq mm
+Pt=Ast/(b*d)*100//percentage tensile steel
+l=4.5//span, in m
+V=W*l/2//in kN
+Tv=(V*10^3)/(b*d)//in MPa
+//for Pt=1.1% and for M20 grade concrete
+Tc=0.40//in MPa
+//as Tv>Tc, shear reinforcement is required
+mprintf("Nominal shear stress in beam=%f MPa\nShear strength of concrete=%f MPa", Tv,Tc)
diff --git a/3683/CH4/EX4.3/Ex4_3.sce b/3683/CH4/EX4.3/Ex4_3.sce new file mode 100644 index 000000000..28b45f7c4 --- /dev/null +++ b/3683/CH4/EX4.3/Ex4_3.sce @@ -0,0 +1,13 @@ +b=300//width, in mm
+d=600//effective depth, in mm
+W=100//UDL including self-weight, in kN/m
+Pt=2//percentage tensile steel
+l=7.2//span, in m
+sigma_cbc=7//in MPa
+sigma_st=190//in MPa
+m=13.33//modular ratio
+V=W*l/2//in kN
+Tv=(V*10^3)/(b*d)//in MPa
+Tcmax=1.8//in MPa
+//as Tv>Tcmax, section is to be redesigned so that Tv becomes less than Tcmax
+mprintf("Nominal shear stress in beam=%f MPa\nFor given grade of concrete, Tcmax=1.8 MPa and as Tv > Tcmax, section is to be redesigned so that Tv becomes less than Tcmax", Tv)
diff --git a/3683/CH4/EX4.4/Ex4_4.sce b/3683/CH4/EX4.4/Ex4_4.sce new file mode 100644 index 000000000..4d3a2a3f8 --- /dev/null +++ b/3683/CH4/EX4.4/Ex4_4.sce @@ -0,0 +1,17 @@ +b=1000//consider 1 m width of slab
+D=100//depth of slab, in mm
+cover=20//in mm
+d=D-cover//effective depth, in mm
+W=7//uniformly distributed load, in kN/m^2
+dia=10//in mm
+s=100//spacing of 10 mm dia bars, in mm
+l=4//span, in m
+V=W*l/2//in kN
+Pt=1000*.785*dia^2/(s*b*d)*100//in %
+Tv=(V*10^3)/(b*d)//in MPa
+//for given Pt and M15 grade concrete
+Tc=0.37//in MPa
+//and for solid slabs
+k=1.3
+Tc=k*Tc//in MPa
+mprintf("Nominal shear stress in slab, Tv=%f MPa\nShear strength of slab, Tc=%f MPa. As Tc > Tv, no shear reinforcement is required", Tv, Tc)
diff --git a/3683/CH4/EX4.5/Ex4_5.sce b/3683/CH4/EX4.5/Ex4_5.sce new file mode 100644 index 000000000..e9ddc8b3f --- /dev/null +++ b/3683/CH4/EX4.5/Ex4_5.sce @@ -0,0 +1,27 @@ +b=300//width, in mm
+d=1010//effective depth, in mm
+W=45//UDL including self-weight, in kN/m
+Ast=6*0.785*22^2//six 22 mm dia bars, in sq mm
+l=7//span, in m
+sigma_cbc=5//in MPa
+sigma_sv=140//in MPa
+Fy=250//in MPa
+V=W*l/2//in kN
+Tv=(V*10^3)/(b*d)//in MPa
+Tcmax=1.6//in MPa
+//Tv<Tcmax; OK
+Pt=Ast/(b*d)*100//percentage tensile steel
+//for given Pt and for M15 grade concrete
+Tc=0.34//in MPa
+Vs=V-Tc*b*d/10^3//in kN
+//providing 6 mm dia stirrups
+dia=6//in mm
+Asv=2*0.785*dia^2//in sq mm
+Sv1=Asv*sigma_sv*d/(Vs*10^3)//in mm
+Sv1=145//round-off, in mm
+//Sv<0.75d or 450 mm, whichever is less; hence OK
+//calculating minimum spacing of shear reinforcement
+Sv2=Asv*Fy/(b*0.4)//in mm
+Sv2=118//round-off, in mm
+Sv=min(Sv1,Sv2)
+mprintf("Provide 6 mm dia bars at %d mm c/c throughout the length of the beam, as shear reinforcement", Sv)
diff --git a/3683/CH4/EX4.6/Ex4_6.sce b/3683/CH4/EX4.6/Ex4_6.sce new file mode 100644 index 000000000..80481c622 --- /dev/null +++ b/3683/CH4/EX4.6/Ex4_6.sce @@ -0,0 +1,37 @@ +Bf=1600//width, in mm
+Df=100//thickness of slab, in mm
+d=400//effective depth, in mm
+Bw=225//breadth of web, in mm
+b=Bw
+W=30//UDL including self-weight, in kN/m
+Ast=5*0.785*22^2//five 22 mm dia bars, in sq mm
+l=9.2//span, in m
+sigma_cbc=5//in MPa
+sigma_sv=230//in MPa
+Fy=415//in MPa
+V=W*l/2//in kN
+Tv=(V*10^3)/(b*d)//in MPa
+Tcmax=1.6//in MPa
+//Tv<Tcmax; OK
+Pt=Ast/(b*d)*100//percentage tensile steel
+//for given Pt and for M15 grade concrete
+Tc=0.44//in MPa
+Vs=V-Tc*b*d/10^3//in kN
+//providing bent-up bars
+Asv=0.785*22^2//in sq mm
+Vs1=Asv*sigma_sv*sind(45)/10^3//in kN
+//but shear taken up by bent-up bar is limited to Vs/2
+Vs1=Vs/2//in kN
+//providing 6 mm dia stirrups, which will take up remaining shear force
+Vs2=Vs-Vs1//in kN
+dia=6//in mm
+Asv=2*0.785*dia^2//in sq mm
+Sv=Asv*sigma_sv*d/(Vs2*10^3)//in mm
+Sv1=105//round-off, in mm
+//Sv<0.75d or 450 mm, whichever is less; hence OK
+//calculating minimum spacing of shear reinforcement
+Sv2=Asv*Fy/(b*0.4)//in mm
+Sv2=260//round-off, in mm
+//to calculate distance 'x' from support where shear stress in concrete is equal to Tc
+x=Tc/Tv*l/2//in m
+mprintf("Provide 6 mm dia stirrups at %d mm c/c upto %f m from both ends\nFor the remaining portion, provide 6 mm dia stirrups at %d mm", Sv1,(l/2-x),Sv2)
diff --git a/3683/CH4/EX4.7/Ex4_7.sce b/3683/CH4/EX4.7/Ex4_7.sce new file mode 100644 index 000000000..fba2b71a3 --- /dev/null +++ b/3683/CH4/EX4.7/Ex4_7.sce @@ -0,0 +1,23 @@ +D=100//thickness of slab, in mm
+l=3//span of slab, in m
+s=0.23//thickness of support, in m
+Lef=l+s//effective span, in m
+W=5//UDL, in kN/m
+cover=15//in mm
+R=W*Lef/2//in kN
+M=(R*s/2-W*s^2/2)*10^6//bending moment at face of wall, in N-mm
+//10 mm dia bars at 145 mm c/c as main steel
+dia=10//in mm
+c=145//spacing of reinforcement, in mm
+Ast=1000*0.785*dia^2/c//in sq mm
+//as alternate bars are bent up
+Ast=Ast/2//available steel reinforcement at face of wall, in sq mm
+d=D-10/2-cover//in mm
+//assuming balanced section
+z=0.87*d//in mm
+sigma_st=M/(Ast*z)//in MPa
+Tbd=0.6//bond stress, in MPa
+Ld=dia*sigma_st/(4*Tbd)//in mm
+Ld=177//round-off, in mm
+mprintf("Development length required from the face of the support = %d mm",Ld)
+//answer given in textbook is incorrect
diff --git a/3683/CH4/EX4.8/Ex4_8.sce b/3683/CH4/EX4.8/Ex4_8.sce new file mode 100644 index 000000000..d43119ccf --- /dev/null +++ b/3683/CH4/EX4.8/Ex4_8.sce @@ -0,0 +1,28 @@ +b=230//width, in mm
+d=500//effective depth, in mm
+l=6//span, in m
+s=0.3//thickness of support, in m
+Lef=l+s//effective span, in m
+W=60//UDL, in kN/m
+Ast=6*0.785*20^2//six 20 mm dia bars at bottom, in sq mm
+Asc=2*0.785*20^2//two 20 mm dia bars at top, in sq mm
+dia=20//in mm
+sigma_cbc=5//in MPa
+sigma_st=230//in MPa
+m=18.66//modular ratio
+R=W*l/2//in kN
+M=(R*s/2-W*s^2/2)*10^6//bending moment at face of wall, in N-mm
+//assuming balanced section
+z=0.87*d//in mm
+sigma_st1=M/(Ast*z)//in MPa
+Tbd=0.6*1.4//bond stress in MPa for deformed steel and M15
+Ld1=dia*sigma_st1/(4*Tbd)//in mm
+//to find critical depth of neutral axis
+Xc=d/(1+sigma_st/(m*sigma_cbc))//in mm
+Xc=144//round-off, in mm
+//at face of support
+sigma_cbc=sigma_st1/m*Xc/(d-Xc)//in MPa
+sigma_sc=1.5*m*sigma_cbc//in MPa
+Tbd=1.68//bond stress in MPa for M15 and deformed steel in compression
+Ld2=dia*sigma_sc/(4*Tbd)//in mm
+mprintf("Development length required from the face of the support for tension steel = %d mm\nDevelopment length required from the face of the support for compression steel = %d mm",Ld1,Ld2)
diff --git a/3683/CH4/EX4.9/Ex4_9.sce b/3683/CH4/EX4.9/Ex4_9.sce new file mode 100644 index 000000000..8a752d6a2 --- /dev/null +++ b/3683/CH4/EX4.9/Ex4_9.sce @@ -0,0 +1,24 @@ +D=120//thickness of slab, in mm
+l=1.5//span of slab, in m
+s=0.23//thickness of support, in m
+Lef=l+s//effective span, in m
+W1=3//UDL, in kN/m^2
+cover=15//in mm
+sigma_cbc=5//in MPa
+sigma_st=140//in MPa
+m=18.66//modular ratio
+W2=(D/10^3)*1*25//self load, in kN/m
+W=W1+W2//in kN/m
+M=W*l^2/2*10^6//bending moment at face of wall, in N-mm
+//10 mm dia bars at 145 mm c/c as main steel
+dia=10//in mm
+d=D-dia/2-cover
+c=100//spacing of reinforcement, in mm
+Ast=1000*0.785*dia^2/c//in sq mm
+//assuming balanced section
+z=0.87*d//in mm
+sigma_st=M/(Ast*z)//in MPa
+Tbd=0.6//bond stress in MPa
+Ld=dia*sigma_st/(4*Tbd)//in mm
+Ld=412//round-off,in mm
+mprintf("Development length required from the face of the support = %d mm",Ld)
diff --git a/3683/CH5/EX5.1/Ex5_1.sce b/3683/CH5/EX5.1/Ex5_1.sce new file mode 100644 index 000000000..221a76bcb --- /dev/null +++ b/3683/CH5/EX5.1/Ex5_1.sce @@ -0,0 +1,9 @@ +sigma_cc=4//in MPa
+sigma_sc=130//in MPa
+Asc=4*0.785*25^2//four 25 mm dia bars, in sq mm
+b=300//width, in mm
+D=300//depth, in mm
+Ag=b*D//in sq mm
+Ac=Ag-Asc//in sq mm
+P=sigma_cc*Ac+sigma_sc*Asc//in N
+mprintf("Permissible load on the column = %f kN", P/10^3)
diff --git a/3683/CH5/EX5.10/Ex5_10.sce b/3683/CH5/EX5.10/Ex5_10.sce new file mode 100644 index 000000000..07a4c7b6c --- /dev/null +++ b/3683/CH5/EX5.10/Ex5_10.sce @@ -0,0 +1,18 @@ +P=280//in kN
+e=50//eccentricity, in mm
+b=300//width, in mm
+D=300//depth, in mm
+sigma_cc=4//in MPa
+sigma_cbc=5//in MPa
+m=18.66//modular ratio
+cover=50//in mm
+Asc=4*0.785*20^2//four 20 mm dia bars, in sq mm
+Ag=b*D//in sq mm
+Ac=Ag-Asc//in sq mm
+sigma_cc_cal=P*10^3/(Ac+1.5*m*Asc)//in MPa
+I=b*D^3/12 + (m-1)*Asc*(D/2-cover)^2//in mm^4
+z=I/(D/2)//in mm^3
+sigma_cbc_cal=P*10^3*e/z//in MPa
+sigma_max=sigma_cc_cal + sigma_cbc_cal//in MPa
+sigma_min=sigma_cc_cal - sigma_cbc_cal//in MPa
+mprintf("Maximum stress = %f MPa (compressive)\nMinimum stress = %f MPa (tensile)", sigma_max,sigma_min)
diff --git a/3683/CH5/EX5.11/Ex5_11.sce b/3683/CH5/EX5.11/Ex5_11.sce new file mode 100644 index 000000000..f978b3bcf --- /dev/null +++ b/3683/CH5/EX5.11/Ex5_11.sce @@ -0,0 +1,26 @@ +P=200//in kN
+b=200//width, in mm
+D=350//depth, in mm
+sigma_cc=5//in MPa
+sigma_cbc=7//in MPa
+m=13.33//modular ratio
+Mxx=6//in kN-m
+Myy=4//in kN-m
+cover=40//in mm
+eff_cover=cover+25/2//in mm
+Asc=4*0.785*25^2//four 25 mm dia bars, in sq mm
+Ag=b*D//in sq mm
+Ac=Ag-Asc//in sq mm
+sigma_cc_cal=P*10^3/(Ac+1.5*m*Asc)//in MPa
+//to find bending stress on XX axis
+Ixx=b*D^3/12 + (m-1)*Asc*(D/2-eff_cover)^2//in mm^4
+Zxx=Ixx/(D/2)//in mm^3
+sigma_cbc_xx=Mxx*10^6/Zxx//in MPa
+//to find bending stress on YY axis
+Iyy=D*b^3/12 + (m-1)*Asc*(b/2-eff_cover)^2//in mm^4
+Zyy=Iyy/(b/2)//in mm^3
+sigma_cbc_yy=Myy*10^6/Zyy//in MPa
+sigma_cbc_cal=sigma_cbc_xx + sigma_cbc_yy//in MPa
+sigma_max=sigma_cc_cal + sigma_cbc_cal//in MPa
+sigma_min=sigma_cc_cal - sigma_cbc_cal//in MPa
+mprintf("Maximum stress = %f MPa (compressive)\nMinimum stress = %f MPa (tensile)", sigma_max,sigma_min)
diff --git a/3683/CH5/EX5.12/Ex5_12.sce b/3683/CH5/EX5.12/Ex5_12.sce new file mode 100644 index 000000000..2ff93fdfe --- /dev/null +++ b/3683/CH5/EX5.12/Ex5_12.sce @@ -0,0 +1,57 @@ +b=450//width, in mm
+D=900//depth, in mm
+c=80//cover, in mm
+d=D-c//in mm
+Asc=4000//in sq mm
+Ast=Asc//in sq mm
+P=500//in kN
+e=600//in mm
+m=18.66
+//equation for x is: x^2 + (k1 - k2 / sigma_cbc_dash) x - k3 = 0
+k1=2/b*((1.5*m-1)*Asc+m*Ast)
+k2=2*P*10^3/b
+k3=2/b*(c*(1.5*m-1)*Asc+d*m*Ast)
+//equation for sigma_cbc_dash is: sigma_cbc_dash = Q1 x /(Q2 x^2 (d - x/3) + Q3 (x - c))
+Q1=P*10^3*(e+d-D/2)
+Q2=b/2
+Q3=(1.5*m-1)*(d-c)*Asc
+sigma_cbc_dash=7//assume, in MPa
+//solving equation for x
+p=1
+q=(k1-k2/sigma_cbc_dash)
+r=-k3
+x=(-q+sqrt(q^2-4*p*r))/2/p//in mm
+sigma_cbc_dash = Q1*x/(Q2*x^2*(d-x/3)+Q3*(x-c))//in MPa
+//this process is repeated till convergence
+//solving equation for x
+p=1
+q=(k1-k2/sigma_cbc_dash)
+r=-k3
+x=(-q+sqrt(q^2-4*p*r))/2/p//in mm
+sigma_cbc_dash = Q1*x/(Q2*x^2*(d-x/3)+Q3*(x-c))//in MPa
+//solving equation for x
+p=1
+q=(k1-k2/sigma_cbc_dash)
+r=-k3
+x=(-q+sqrt(q^2-4*p*r))/2/p//in mm
+sigma_cbc_dash = Q1*x/(Q2*x^2*(d-x/3)+Q3*(x-c))//in MPa
+//solving equation for x
+p=1
+q=(k1-k2/sigma_cbc_dash)
+r=-k3
+x=(-q+sqrt(q^2-4*p*r))/2/p//in mm
+sigma_cbc_dash = Q1*x/(Q2*x^2*(d-x/3)+Q3*(x-c))//in MPa
+//solving equation for x
+p=1
+q=(k1-k2/sigma_cbc_dash)
+r=-k3
+x=(-q+sqrt(q^2-4*p*r))/2/p//in mm
+sigma_cbc_dash = Q1*x/(Q2*x^2*(d-x/3)+Q3*(x-c))//in MPa
+//solving equation for x
+p=1
+q=(k1-k2/sigma_cbc_dash)
+r=-k3
+x=(-q+sqrt(q^2-4*p*r))/2/p//in mm
+sigma_sc=m*sigma_cbc_dash*(x-c)/x//in MPa
+sigma_st=m*sigma_cbc_dash*x/(d-x)//in MPa
+//answer in textbook is incorrect
diff --git a/3683/CH5/EX5.2/Ex5_2.sce b/3683/CH5/EX5.2/Ex5_2.sce new file mode 100644 index 000000000..79e44233a --- /dev/null +++ b/3683/CH5/EX5.2/Ex5_2.sce @@ -0,0 +1,21 @@ +sigma_cc=5//in MPa
+sigma_sc=190//in MPa
+Asc=6*0.785*20^2//six 20 mm dia bars, in sq mm
+b=250//width, in mm
+D=400//depth, in mm
+Ag=b*D//in sq mm
+Ac=Ag-Asc//in sq mm
+P=sigma_cc*Ac+sigma_sc*Asc//in N
+mprintf("Permissible load on the column = %f kN\n", P/10^3)
+//design of links
+dia=20/4//in mm
+//as this is less than 6
+dia=6//in mm
+//spacing of links
+s1=b//in mm
+s2=16*20//in mm
+s3=48*dia//in mm
+s=min(s1,s2,s3)
+mprintf("Provide %d mm dia links at spacing equal to least of (i)Least lateral dimension = %d mm, (ii) 16 times longitudinal bar dia = %d mm, (iii) 48 times link bar dia = %d mm, i.e., 250 mm\nHence, spacing or pitch = %d mm\n",dia,b,16*20, 48*dia,s)
+Pc=Asc*100/(b*D)//percentage steel
+mprintf("Percentage of steel is in between 0.8 to 4 as prescribed by IS code")
diff --git a/3683/CH5/EX5.3/Ex5_3.sce b/3683/CH5/EX5.3/Ex5_3.sce new file mode 100644 index 000000000..00d6c0600 --- /dev/null +++ b/3683/CH5/EX5.3/Ex5_3.sce @@ -0,0 +1,20 @@ +sigma_cc=5//in MPa
+sigma_sc=130//in MPa
+b=300//width, in mm
+D=400//depth, in mm
+P=1000//axial load, in kN
+Ag=b*D//in sq mm
+Asc=(P*10^3-sigma_cc*Ag)/(sigma_sc-sigma_cc)//in sq mm
+//provide 25 mm dia bars
+n=round(Asc/(0.785*25^2))
+mprintf("Provide %d no. 25 mm dia bars\n", n)
+//design of links
+dia=20/4//in mm
+//provide 8 mm dia links (available as per market size)
+dia=8//in mm
+//spacing of links
+s1=b//in mm
+s2=16*25//in mm
+s3=48*dia//in mm
+s=min(s1,s2,s3)
+mprintf("Provide %d mm dia links at spacing equal to least of (i)Least lateral dimension = %d mm, (ii) 16 times longitudinal bar dia = %d mm, (iii) 48 times link bar dia = %d mm, i.e., 300 mm\nHence, spacing or pitch = %d mm\n",dia,b,16*25,48*dia,s)
diff --git a/3683/CH5/EX5.4/Ex5_4.sce b/3683/CH5/EX5.4/Ex5_4.sce new file mode 100644 index 000000000..7192c51cc --- /dev/null +++ b/3683/CH5/EX5.4/Ex5_4.sce @@ -0,0 +1,14 @@ +sigma_cc=4//in MPa
+sigma_sc=130//in MPa
+Asc=6*0.785*12^2//six 12 mm dia bars, in sq mm
+D=200//dia of column, in mm
+Ag=0.785*D^2//in sq mm
+Ac=Ag-Asc//in sq mm
+P=sigma_cc*Ac+sigma_sc*Asc//in N
+dia=6//dia of links used, in mm
+//spacing of links
+s1=D//in mm
+s2=16*12//in mm
+s3=48*dia//in mm
+s=min(s1,s2,s3)
+mprintf("Permissible load on the column = %f kN\nProvide %d mm dia links at spacing equal to least of (i)Least lateral dimension = %d mm, (ii) 16 times longitudinal bar dia = %d mm, (iii) 48 times link bar dia = %d mm, i.e., %d mm\nHence, spacing or pitch = %d mm", P/10^3, dia,D,16*12, 48*dia,s,s)
diff --git a/3683/CH5/EX5.5/Ex5_5.sce b/3683/CH5/EX5.5/Ex5_5.sce new file mode 100644 index 000000000..eb94682de --- /dev/null +++ b/3683/CH5/EX5.5/Ex5_5.sce @@ -0,0 +1,23 @@ +dia=300//in mm
+Asc=8*0.785*20^2//8-20 mm dia bars, in sq mm
+helical_dia=8//in mm
+pitch=25//in mm
+cover=40//in mm
+sigma_cc=5//in MPa
+sigma_sc=130//in MPa
+fck=25//in MPa
+fy=250//in MPa
+Ag=0.785*dia^2//in sq mm
+Ac=Ag-Asc//in sq mm
+P=sigma_cc*Ac + sigma_sc*Asc//in N
+//to find volume of helical reinforcement
+core_dia=dia-2*cover+2*helical_dia//in mm
+l=%pi*core_dia//length of helical steel for one revolution, in mm
+Ab=l*0.785*helical_dia^2/pitch//volume of helical reinforcement per mm height of column, in mm^3
+Ak=0.785*core_dia^2-Asc//in sq mm
+Ac=0.785*core_dia^2//in sq mm
+m=Ab/Ak
+n=0.36*(Ag/Ac-1)*fck/fy
+//as m > n
+P=1.05*P//in N
+mprintf("Safe load=%f kN",P/10^3)
diff --git a/3683/CH5/EX5.6/Ex5_6.sce b/3683/CH5/EX5.6/Ex5_6.sce new file mode 100644 index 000000000..4e6f245d3 --- /dev/null +++ b/3683/CH5/EX5.6/Ex5_6.sce @@ -0,0 +1,15 @@ +b=250//width, in mm
+D=350//depth, in mm
+Asc=4*0.785*22^2//four 22 mm dia bars, in sq mm
+Lef=5//effective length of column, in m
+sigma_cc=4//in MPa
+sigma_sc=130//in MPa
+a=Lef*10^3/b
+//as Lef/b > 12, it is a long column
+Cr=1.25-Lef*1000/(48*b)//reduction coefficient
+sigma_cc=Cr*sigma_cc//in MPa
+sigma_sc=Cr*sigma_sc//in MPa
+Ag=b*D//in sq mm
+Ac=Ag-Asc//in sq mm
+P=sigma_cc*Ac+sigma_sc*Asc//in N
+mprintf("The safe load on the column=%f kN", P/10^3)
diff --git a/3683/CH5/EX5.7/Ex5_7.sce b/3683/CH5/EX5.7/Ex5_7.sce new file mode 100644 index 000000000..f3ba198f3 --- /dev/null +++ b/3683/CH5/EX5.7/Ex5_7.sce @@ -0,0 +1,15 @@ +dia=500//in mm
+Asc=6*%pi/4*25^2//six 25 mm dia bars, in sq mm
+Lef=8//effective length of column, in m
+sigma_cc=5//in MPa
+sigma_sc=190//in MPa
+a=Lef*10^3/dia
+//as Lef/b >12, it is a long column
+Cr=1.25-Lef*1000/(48*dia)//reduction coefficient
+sigma_cc=Cr*sigma_cc//in MPa
+sigma_sc=Cr*sigma_sc//in MPa
+Ag=%pi/4*dia^2//in sq mm
+Ac=Ag-Asc//in sq mm
+P=sigma_cc*Ac+sigma_sc*Asc//in N
+mprintf("The safe load on the column=%f kN", P/10^3)
+//the answer doesn't match with that given in textbook due to round-off error
diff --git a/3683/CH5/EX5.8/Ex5_8.sce b/3683/CH5/EX5.8/Ex5_8.sce new file mode 100644 index 000000000..36fecaed6 --- /dev/null +++ b/3683/CH5/EX5.8/Ex5_8.sce @@ -0,0 +1,42 @@ +P=850//in kN
+sigma_cc=4//in MPa
+m=18.66//modular ratio
+sigma_sc=130//in MPa
+Lef=5*1.001//effective length, in m
+//assume 1% steel
+Ag=P*10^3/(sigma_cc*0.99+sigma_sc*0.01)//in sq mm
+l=sqrt(Ag)//in mm
+l=400//approximately, in mm
+a=Lef*1000/l
+//as a>12, it is a long column
+//Method I-section to be changed
+b=Lef*1000/12//in mm
+b=420//approximately, in mm
+Ag=b^2//in sq mm
+Asc=(P*1000-sigma_cc*Ag)/(sigma_sc-sigma_cc)//in sq mm
+minimum_steel=0.8/100*b^2//in sq mm
+//as Asc < minimum steel
+Asc=minimum_steel//in sq mm
+//assume 20 mm dia bars
+n=Asc/(%pi/4*20^2)//no. of bars
+n=5//round-off
+//design of links
+dia=1/4*20//in mm
+//as dia < 6 mm, provide 6 mm diameter links
+dia=6//in mm
+spacing=min(b,16*20,48*dia,300)//in mm
+mprintf("Method I\nColumn size %d x %d mm\nMain steel =%d-20 mm dia bars\nLinks=6 mm dia links @ %d mm c/c\n", b,b,n,spacing)
+//Method II-same section
+b=400//in mm
+Ag=b^2//in sq mm
+Cr=1.25-Lef*1000/(48*b)//reduction coefficient
+sigma_cc=Cr*sigma_cc//in MPa
+sigma_sc=Cr*sigma_sc//in MPa
+Asc=(P*1000-sigma_cc*Ag)/(sigma_sc-sigma_cc)//in MPa
+n=round(Asc/(%pi/4*20^2))//no. of bars
+//design of links
+dia=1/4*20//in mm
+//as dia < 6 mm, provide 6 mm diameter links
+dia=6//in mm
+spacing=min(b,16*20,48*dia,300)//in mm
+mprintf("Method II\nColumn size %d x %d mm\nMain steel =%d-20 mm dia bars\nLinks=6 mm dia links @ %d mm c/c", b,b,n,spacing)
diff --git a/3683/CH5/EX5.9/Ex5_9.sce b/3683/CH5/EX5.9/Ex5_9.sce new file mode 100644 index 000000000..593709962 --- /dev/null +++ b/3683/CH5/EX5.9/Ex5_9.sce @@ -0,0 +1,24 @@ +P=400//in kN
+b=200//width, in mm
+sigma_cc=4//in MPa
+sigma_sc=190//in MPa
+Lef=3.5//effective length, in m
+//assume 1% steel
+Ag=P*10^3/(sigma_cc*0.99+sigma_sc*0.01)//in sq mm
+D=Ag/b//in mm
+D=340//round-off, in mm
+a=Lef*1000/b
+//as a > 12, it is a long column
+Cr=1.25-Lef*1000/(48*b)//reduction coefficient
+sigma_cc=Cr*sigma_cc//in MPa
+sigma_sc=Cr*sigma_sc//in MPa
+Asc=(P*1000-sigma_cc*Ag)/(sigma_sc-sigma_cc)//in sq mm
+//assume 18 mm dia bars
+n=Asc/(%pi/4*18^2)//no. of bars
+n=4//round-off
+//design of links
+dia=1/4*20//in mm
+//as dia < 6 mm, provide 6 mm diameter links
+dia=6//in mm
+spacing=min(b,16*20,48*dia,300)//in mm
+mprintf("Column size %d x %d mm\nMain steel =%d-18 mm dia bars\nLinks=6 mm dia links @ %d mm c/c\n", b,D,n,spacing)
diff --git a/3683/CH7/EX7.1/Ex7_1.sce b/3683/CH7/EX7.1/Ex7_1.sce new file mode 100644 index 000000000..8bc8f67c4 --- /dev/null +++ b/3683/CH7/EX7.1/Ex7_1.sce @@ -0,0 +1,52 @@ +sigma_cbc=5//in MPa
+sigma_st=140//in MPa
+MF=1.6//modification factor
+//let a be span to depth ratio
+l=4//span, in m
+a=MF*20
+D=l*1000/a//in mm
+//to calculate loading
+self_weight=25*(D/10^3)//in kN/m
+finish=1//in kN/m
+live_load=2//in kN/m
+W=self_weight+finish+live_load//total load, in kN/m
+lef=l+D/1000//in m
+M=W*lef^2/8//in kN-m
+//check for depth
+d=round((M*10^6/(0.87*1000))^0.5)//in mm
+//assume 12 mm dia bars
+D=d+12/2+15//in mm
+//the calculated value of D is more than its assumed value
+D=150//revised value of depth, in mm
+self_weight=25*(D/10^3)//in kN/m
+finish=1//in kN/m
+live_load=2//in kN/m
+W=self_weight+finish+live_load//total load, in kN/m
+lef=l+D/1000//in m
+M=W*lef^2/8//in kN-m
+//check for depth
+d=round((M*10^6/(0.87*1000))^0.5)//in mm
+D=d+12/2+15//in mm
+Ast=round(M*10^6/(sigma_st*0.87*d))//in sq mm
+s1=1000*0.785*12^2/Ast//which is less than 3d= 387 mm
+s1=120//approximately, in mm
+Ads=0.15/100*1000*D//distribution steel, in sq mm
+//assume 8 mm dia bars
+s2=1000*0.785*8^2/Ads//which is less than 5d= 645 mm
+s2=220//approximately, in mm
+//to calculate development length
+w=0.345//support width, in m
+lef=l+w//in m
+R=W*lef/2//reaction at support, in kN
+M1=R*w/2-W*w^2/2//bending moment at the face of wall, in kN-m
+sigma_st=M1*10^6/(Ast/2*0.87*d)//in MPa
+Tbd=0.6//in MPa
+Ld=12*sigma_st/(4*Tbd)//in mm
+La=w*1000-25//available length for bar over wall, which is greater than development length
+//check for shear
+V=W*4.15/2//in kN
+Tv=V*10^3/(1000*d)//in MPa
+Tc=0.33//permissible shear in concrete for p=0.71 and M15, in MPa
+Tc=1.3*Tc//permissible shear for slabs, in MPa
+//Tc>Tv; hence no shear reinforcement is required
+mprintf("Summary of design\nSlab thickness=%d mm\nCover=15 mm\nMain steel = 12 mm dia @ %d mm c/c\nAlternate bars are bent up @ 45-degree at support at a distance l/7 from support face\nDistribution steel=8 mm dia @ %d mm c/c",D,s1,s2)
diff --git a/3683/CH7/EX7.2/Ex7_2.sce b/3683/CH7/EX7.2/Ex7_2.sce new file mode 100644 index 000000000..570bb956a --- /dev/null +++ b/3683/CH7/EX7.2/Ex7_2.sce @@ -0,0 +1,58 @@ +sigma_cbc=5//in MPa
+sigma_st=230//in MPa
+MF=1.4//modification factor
+//let a be span to depth ratio
+l=4.5//span, in m
+a=MF*20
+D=l*1000/a//in mm
+D=160//approximately, in mm
+//to calculate loading
+self_weight=25*(D/10^3)//in kN/m
+finish=1//in kN/m
+partitions=1//in kN/m
+live_load=4//in kN/m
+W=self_weight+finish+partitions+live_load//total load, in kN/m
+lef=l+D/1000//in m
+M=W*lef^2/8//in kN-m
+//check for depth
+d=(M*10^6/(0.9*sigma_cbc/2*0.29*1000))^0.5//in mm
+//assume 12 mm dia bars
+D=d+12/2+15//in mm
+//the calculated value of D is more than its assumed value
+D=1.1*D//revised value of depth, in mm
+D=250//assume, in mm
+self_weight=25*(D/10^3)//in kN/m
+finish=1//in kN/m
+partitions=1//in kN/m
+live_load=4//in kN/m
+W=self_weight+finish+partitions+live_load//total load, in kN/m
+lef=l+D/1000//in m
+M=W*lef^2/8//in kN-m
+//check for depth
+d=round((M*10^6/(0.9*sigma_cbc/2*0.29*1000))^0.5)//in mm
+D=d+12/2+15//in mm
+D=250//approximately, in mm
+Ast=round(M*10^6/(sigma_st*0.9*d))//in sq mm
+s1=1000*0.785*12^2/Ast//which is less than 3d= 690 mm
+s1=155//approximately, in mm
+pt=Ast/1000/d*100//in %
+Ads=0.12/100*1000*D//distribution steel, in sq mm
+//assume 8 mm dia bars
+s2=1000*0.785*8^2/Ads//which is less than 5d= 1150 mm
+s2=165//approximately, in mm
+//to calculate development length
+w=0.23//support width, in m
+l=l+w//in m
+R=W*l/2//reaction at support, in kN
+M1=R*w/2-W*w^2/2//bending moment at the face of wall, in kN-m
+sigma_st=M1*10^6/(Ast/2*0.9*d)//in MPa
+Tbd=0.6//in MPa
+Ld=12*sigma_st/(4*Tbd)//in mm
+La=w*1000-25//available length for bar over wall, which is greater than development length
+//check for shear
+V=W*lef/2//in kN
+Tv=V*10^3/(1000*d)//in MPa
+Tc=0.2212//permissible shear in concrete for p=0.315 and M15, in MPa
+Tc=1.15*Tc//permissible shear for slabs, in MPa
+//Tc>Tv; hence no shear reinforcement is required
+mprintf("Summary of design\nSlab thickness=%d mm\nCover=15 mm\nMain steel = 12 dia @ %d mm c/c\nAlternate bars are bent up at 45-degree at support at a distance of l/7 from support face\nDistribution steel=8 dia @ %d mm c/c",D,s1,s2)
diff --git a/3683/CH7/EX7.3/Ex7_3.sce b/3683/CH7/EX7.3/Ex7_3.sce new file mode 100644 index 000000000..40114f8dd --- /dev/null +++ b/3683/CH7/EX7.3/Ex7_3.sce @@ -0,0 +1,47 @@ +sigma_cbc=7//in MPa
+sigma_st=230//in MPa
+MF=1.22//modification factor
+//let a be span to depth ratio
+l=5//span, in m
+a=MF*26
+D=l*1000/a//in mm
+D=160//assume, in mm
+//to calculate loading
+self_weight=25*(D/10^3)//in kN/m
+finish=0.75//in kN/m
+partitions=1//in kN/m
+live_load=3//in kN/m
+Wd=self_weight//dead load, in kN/m
+Wl=finish+partitions+live_load//live load, in kN/m
+lef=5.15//effective span, in m
+M1=Wd*lef^2/12+Wl*lef^2/10//bending moment at mid-span, in kN-m
+M2=Wd*lef^2/10+Wl*lef^2/9//bending moment at support next to end support, in kN-m
+//check for depth
+d=(M2*10^6/(0.89*1000))^0.5//in mm
+dia=12//assume 12 mm dia bars
+D=d+12/2+15//>160, hence depth not suitable
+D=1.1*D//in mm
+D=210//assume, in mm
+self_weight=25*(D/10^3)//in kN/m
+Wd=self_weight//in kN/m
+M1=Wd*lef^2/12+Wl*lef^2/10//bending moment at mid-span, in kN-m
+M2=Wd*lef^2/10+Wl*lef^2/9//bending moment at support next to end support, in kN-m
+//check for depth
+d=round((M2*10^6/(0.9*sigma_cbc/2*0.29*1000))^0.5)//in mm
+D=d+12/2+15//<210, hence OK
+D=200//assume, in mm
+d=D-dia/2-15//in mm
+//main steel at mid-span
+Ast1=round(M1*10^6/(sigma_st*0.91*d))//in sq mm
+s1=1000*0.785*12^2/Ast1//in mm
+s1=175//approximately, in mm
+//main steel at support
+Ast2=round(M2*10^6/(sigma_st*0.91*d))//in sq mm
+//alternate bars from mid-span are available at the central support as bent up bars; assuming same amount of steel is available from another adjoining mid-span steel
+Ast2=Ast2-Ast1//which is nominal, hence no separate steel is required
+Ads=0.12/100*1000*D//distribution steel, in sq mm
+//assume 8 mm dia bars
+s2=1000*0.785*8^2/Ads//in mm
+s2=200//approximately, in mm
+mprintf("Summary of design\nSlab thickness=%d mm\nMain steel = 12 mm dia @ %d mm c/c\nAlternate bars are bent up at support\nDistribution steel=8 mm dia @ %d mm c/c",D,s1,s2)
+//answer given in textbook is incorrect
diff --git a/3683/CH7/EX7.4/Ex7_4.sce b/3683/CH7/EX7.4/Ex7_4.sce new file mode 100644 index 000000000..f3ba0720d --- /dev/null +++ b/3683/CH7/EX7.4/Ex7_4.sce @@ -0,0 +1,38 @@ +sigma_cbc=5//in MPa
+sigma_st=230//in MPa
+MF=1.4//modification factor
+//let a be span to depth ratio
+l=1//span, in m
+a=MF*7
+D=l*1000/a//in mm
+D=105//assume, in mm
+//to calculate loading
+self_weight=25*(D/10^3)*1.5//in kN/m
+finish=0.5*1.5//in kN/m
+live_load=0.75*1.5//in kN/m
+W=self_weight+finish+live_load//in kN/m
+lef=l+0.23/2//effective span, in m
+M=W*lef/2//in kN-m
+//check for depth
+d=(M*10^6/(0.65*1500))^0.5//in mm
+dia=12//assume 12 mm dia bars
+D=d+12/2+15//<105, hence OK
+D=100//assume, in mm
+d=D-dia/2-15//in mm
+//main steel at mid-span
+Ast=M*10^6/(sigma_st*0.9*d)//in sq mm
+s1=1500*0.785*12^2/Ast//>3d = 237 mm
+s1=235//assume, in mm
+Ads=0.12/100*1000*D//distribution steel, in sq mm
+//assume 6 mm dia bars
+s2=1000*0.785*6^2/Ads//in mm
+s2=235//assume, in mm
+Tbd=0.84//in MPa
+Ld=dia*sigma_st/4/Tbd// in mm
+Ld=821//round-off, in mm
+Tv=W*10^3/1500/d//in MPa
+As=1500*0.785*12^2/235//in sq mm
+pt=As/1500/d*100//in %
+Tc=0.316//in MPa
+//as Tc>Tv, no shear reinforcement required
+mprintf("Summary of design\nThickness of slab = %d mm\nCover = 15mm\nMain steel = 12 mm dia @ %d mm c/c\nProvide development length of %d mm in the beam from face of beam\nDistribution steel = 6 mm dia @ %d mm c/c",D,s1,Ld,s2)
diff --git a/3683/CH8/EX8.1/Ex8_1.sce b/3683/CH8/EX8.1/Ex8_1.sce new file mode 100644 index 000000000..48a4703ba --- /dev/null +++ b/3683/CH8/EX8.1/Ex8_1.sce @@ -0,0 +1,31 @@ +lx=3.5//in m
+ly=4//in m
+sigma_cbc=5//in MPa
+sigma_st=140//in MPa
+D=lx*10^3/35//in mm
+W1=(D/10^3)*25//self-weight, in kN/m
+W2=1.5//live load, in kN/m
+W=W1+W2//in kN/m
+a=ly/lx
+Ax=0.078
+Ay=0.0602
+Mx=Ax*W*lx^2//in kN-m
+My=Ay*W*lx^2//in kN-m
+d=sqrt(Mx*10^6/0.87/10^3)//in mm
+d=70//assume, in mm
+//assume 10 mm dia bars
+dia=10//in mm
+D=d+dia/2+15//<100 mm assumed value
+D=100//in mm
+d=D-dia/2-15//in mm
+//steel - short span
+z=0.87*d//in mm
+Ast=Mx*10^6/sigma_st/z//in sq mm
+s1=1000*0.785*dia^2/Ast//in mm
+s1=200//assume, in mm
+//long span
+d=d-dia/2-dia/2//in mm
+Ast=My*10^6/sigma_st/0.87/d//in sq mm
+s2=1000*0.785*dia^2/Ast//>3d = 210 mm
+s2=210//assume, in mm
+mprintf("Summary of design\nSlab thickness=%d mm\nCover=15 mm\nSteel-\n(i)Short span = 10 mm dia @ %d mm c/c\n(ii)Long span = 10 mm dia @ %d mm c/c\nAlternate bars are bent up at l/7 from support in both directions",D,s1,s2)
diff --git a/3683/CH8/EX8.2/Ex8_2.sce b/3683/CH8/EX8.2/Ex8_2.sce new file mode 100644 index 000000000..2b1460086 --- /dev/null +++ b/3683/CH8/EX8.2/Ex8_2.sce @@ -0,0 +1,67 @@ +sigma_cbc=5//in MPa
+sigma_st=230//in MPa
+lx=3.75//in m
+ly=4//in m
+D=lx*10^3/40//in mm
+D=100//assume, in mm
+W1=(D/10^3)*25//self-weight, in kN/m
+W2=0.5//floor finish, in kN/m
+W3=2//live load, in kN/m
+W=W1+W2+W3//in kN/m
+a=ly/lx
+//panels I and III belong to case 8 and panel II belong to case 6
+//for panels I and III
+//at mid-span
+Ax=0.0483
+Ay=0.043
+Mx1=Ax*W*lx^2//in kN-m
+My1=Ay*W*lx^2//in kN-m
+//at support
+Ay=0.057
+Ms=Ay*W*lx^2//in kN-m
+//for panel II
+//at mid-span
+Ax=0.0403
+Ay=0.035
+Mx2=Ax*W*lx^2//in kN-m
+My2=Ay*W*lx^2//in kN-m
+//at support
+Ay=0.045//<0.057, hence not considered
+d=sqrt(Ms*10^6/0.65/10^3)//in mm
+d=80//assume, in mm
+//assume 10 mm dia bars
+dia=10//in mm
+D=d+dia/2+15
+//steel at centre
+//for panels I and III
+//short span
+z=0.9*d//in mm
+Ast=Mx1*10^6/sigma_st/z//in sq mm
+s1=1000*0.785*dia^2/Ast//>3d
+//long span
+Ast=My1*10^6/sigma_st/z//in sq mm
+s2=1000*0.785*dia^2/Ast//>3d
+//for panel II
+//short span
+Ast=Mx2*10^6/sigma_st/z//in sq mm
+s3=1000*0.785*dia^2/Ast//>3d
+//long span
+Ast=My2*10^6/sigma_st/z//in sq mm
+s3=1000*0.785*dia^2/Ast//>3d
+//steel at support
+Ast=Ms*10^6/sigma_st/z//in sq mm
+s4=1000*0.785*dia^2/Ast//>3d
+s=3*d//maximum spacing of bars in both directions as per IS 456, in mm
+Ast=1000*0.785*dia^2/s//in sq mm
+pt=Ast/10^3/d*100//in %
+//steel for torsion, provide 6 mm dia bars
+//(i)at outer corner of slab
+At1=3/4*Ast//in sq mm
+l=lx/5//in m
+s5=750*0.785*6^2/At1//in mm
+s5=85//assume, in mm
+//(ii)at continuous support
+At2=At1/2//in sq mm
+s6=750*0.785*6^2/At2//in mm
+s6=170//assume, in mm
+mprintf("Summary of design\nSlab thickness=%d mm\nCover=15 mm\nSteel for both panels I and II-\nMain steel= 10 mm dia bars @ %d mm c/c both ways. Alternate bars are bent up at supports.\nTorsion steel=(i) At corners, 6 mm dia bars @ %d mm c/c both ways\n(ii) At continuous support, 6 mm dia bars @ %d mm c/c both ways",D,s,s5,s6)
diff --git a/3683/CH8/EX8.3/Ex8_3.sce b/3683/CH8/EX8.3/Ex8_3.sce new file mode 100644 index 000000000..724b8fb88 --- /dev/null +++ b/3683/CH8/EX8.3/Ex8_3.sce @@ -0,0 +1,92 @@ +sigma_cbc=7//in MPa
+sigma_st=275//in MPa
+lx=6//in m
+ly=7//in m
+D=lx*10^3/35//in mm
+D=180//assume, in mm
+W1=(D/10^3)*25//self-weight, in kN/m
+W2=0.5//floor finish, in kN/m
+W3=1//partitions, in kN/m
+W4=5//live load, in kN/m
+W=W1+W2+W3+W4//in kN/m
+a=ly/lx
+//panels I, II, V and VI belong to case 4 and panels III and IV belong to case 3
+//for panels I, II, V and VI
+//at mid-span
+Ax=0.043
+Ay=0.035
+Mxm1=Ax*W*lx^2//in kN-m
+Mym1=Ay*W*lx^2//in kN-m
+//at support
+Ax=0.058
+Ay=0.047
+Mxs1=Ax*W*lx^2//in kN-m
+Mys1=Ay*W*lx^2//in kN-m
+//for panels III and IV
+//at mid-span
+Ax=0.036
+Ay=0.028
+Mxm2=Ax*W*lx^2//in kN-m
+Mym2=Ay*W*lx^2//in kN-m
+//at support
+Ax=0.047
+Ay=0.037//<0.047, hence will not be considered
+Mxs2=Ax*W*lx^2//in kN-m
+//check for depth
+M=max(Mxm1,Mym1,Mxs1,Mys1,Mxm2,Mym2,Mxs2)//in kN-m
+d=sqrt(M*10^6/0.81/10^3)//in mm
+d=170//assume, in mm
+//assume 10 mm dia bars
+dia=10//in mm
+D=d+dia/2+15//>180 mm assumed value
+D=190//in mm
+d=D-dia/2-15//in mm
+//main steel-short span
+//for panels I, II, V and VI-at mid-span
+z=0.92*d//in mm
+Astm=Mxm1*10^6/sigma_st/z//in sq mm
+s1=1000*0.785*dia^2/Astm//in mm
+s1=195//assume, in mm
+//at support
+Ast=Mxs1*10^6/sigma_st/z//in sq mm
+Astr=Ast-Astm//balance steel required at support, in sq mm
+s2=1000*0.785*dia^2/Astr//in mm
+s2=565//assume, in mm
+//for panels III and IV-at mid-span
+Astm=Mxm2*10^6/sigma_st/z//in sq mm
+s3=1000*0.785*dia^2/Astm//in mm
+s3=235//assume, in mm
+//at support
+Ast=Mxs2*10^6/sigma_st/z//in sq mm
+Astr=Ast-Astm//balance steel required at support, in sq mm
+s4=1000*0.785*dia^2/Astr//in mm
+s4=775//assume, in mm
+//long span
+//at mid-span
+//for panels I, II, V and VI
+Astm1=Mym1*10^6/sigma_st/z//in sq mm
+s5=1000*0.785*dia^2/Astm1//in mm
+s5=240//assume, in mm
+//for panels III and IV
+Astm2=Mym2*10^6/sigma_st/z//in sq mm
+s6=1000*0.785*dia^2/Astm2//in mm
+s6=300//assume, in mm
+//at support
+//for panels I, II, V and VI
+Ast=Mys1*10^6/sigma_st/z//in sq mm
+Astr=Ast-Astm1/2-Astm2/2//balance steel required at support, in sq mm
+s7=1000*0.785*dia^2/Astr//in mm
+s7=550//assume, in mm
+//steel for torsion, provide 6 mm dia bars
+//(i)at outside corners of slab
+Ast=Mxm1*10^6/sigma_st/z//in sq mm
+At1=3/4*Ast//in sq mm
+l=lx/5//in m
+s8=l*10^3*0.785*6^2/At1//in mm
+s8=110//assume, in mm
+//(ii)at continuous support
+At2=At1/2//in sq mm
+s9=l*10^3*0.785*6^2/At2//in mm
+s9=225//assume, in mm
+mprintf("Summary of design\nSlab thickness=%d mm\nCover=15 mm\nSteel:(A)Panels I, II, V and VI-\n1. Short span (lx=6 m)\nMid-span - 10 mm dia bars @ %d mm c/c. Alternate bars are bent up at supports at a distance lx/4 from centre of support\nSupport - 10 mm dia @ %d mm c/c\n2. Long span (ly=7 m)\nMid-span - 10 mm dia bars @ %d mm c/c. Alternate bars are bent up at supports at a distance ly/4 from centre of support\nSupport - 10 mm dia @ %d mm c/c\n(B)Panels III and IV-\n1. Short span (lx=6 m)\nMid-span - 10 mm dia bars @ %d mm c/c. Alternate bars are bent up at supports at a distance lx/4 from centre of support\nSupport - 10 mm dia @ %d mm c/c\n2. Long span (ly=7 m)\nMid-span - 10 mm dia bars @ %d mm c/c. Alternate bars are bent up at supports at a distance ly/4 from centre of support\nSupport - 10 mm dia @ %d mm c/c\nTorsion steel\nOutside corners- 6 mm dia bars @ %d mm c/c both ways at top and bottom for a length of %f m\nContinuous support- 6 mm dia bars @ %d mm c/c both ways at top and bottom for a length of %f m",D,s1,s2,s5,s7,s3,s4,s6,s7,s8,l,s9,l)
+//answer in textbook is incorrect
diff --git a/3683/CH9/EX9.1/Ex9_1.sce b/3683/CH9/EX9.1/Ex9_1.sce new file mode 100644 index 000000000..d57844387 --- /dev/null +++ b/3683/CH9/EX9.1/Ex9_1.sce @@ -0,0 +1,41 @@ +l=3//span, in m
+b=225//wall thickness, in mm
+Dm=19.2//weight of masonry, in kN/cu m
+sigma_cbc=5//in MPa
+sigma_st=230//in MPa
+fy=415//in MPa
+//area of triangle of brick masonry
+A=sqrt(3)/4*l^2//in sq m
+V=A*(b/10^3)//volume of triangle of masonry, in cu m
+W=V*Dm//weight of masonry, in kN
+M1=W*l/6//in kN-m
+D=l*10^3/12//in mm
+D=300//approximately, in mm
+self_weight=25*(D/10^3)*(b/10^3)//in kN/m
+M2=self_weight*l^2/8//in kN-m
+M=M1+M2//in kN-m
+//check for depth
+d=sqrt(M*10^6/0.65/b)//in mm
+d=265//approximately, in mm
+dia=10//in mm
+D=d+dia/2+25//<300 mm, hence OK
+D=300//in mm
+Ast=M*10^6/sigma_st/0.9/d//in sq mm
+n=Ast/0.785/10^2//no. of 10 mm dia bars required
+//provide 2-10 mm dia + 1-8 mm dia bars
+Ast=2*0.785*10^2+0.785*8^2//in sq mm
+pt=Ast/b/d*100//pt=0.35, approximately
+W=W+self_weight*l//in kN
+V=W/2//in kN
+Tv=V*10^3/b/d//in MPa
+//for M15 grade concrete and pt=0.35
+Tc=0.248//in MPa
+//as Tc>Tv, no shear reinforcement required; provide nominal stirrups
+//provide 6 mm dia bars
+Asv=2*0.785*6^2//in sq mm
+Sv=Asv*fy/0.4/b//in mm
+Sv=260//approximately, in mm
+Svmax=0.75*d//in mm
+Svmax=200//approximately, in mm
+Sv=min(Sv,Svmax)//in mm
+mprintf("Summary of design\nSize of lintel beam=%d x %d mm\ncover = 35 mm\nsteel = 2-10 mm dia bars + 1-8 mm dia bar\nstirrups = 6 mm dia @ %d mm c/c throughout",b,D,Sv)
diff --git a/3683/CH9/EX9.2/Ex9_2.sce b/3683/CH9/EX9.2/Ex9_2.sce new file mode 100644 index 000000000..81b87a314 --- /dev/null +++ b/3683/CH9/EX9.2/Ex9_2.sce @@ -0,0 +1,39 @@ +l=4.2//span, in m
+b=225//width, in mm
+D=300//depth, in mm
+sigma_cbc=5//in MPa
+sigma_st=230//in MPa
+fy=415//in MPa
+m=18.66//modular ratio
+W1=25*(D/10^3)*(b/10^3)//self-weight, in kN/m
+W2=6//load on beam, in kN/m
+W=W1+W2//in kN/m
+M=W*l^2/8//in kN-m
+dia=12//in mm
+d=D-dia/2-25//in mm
+Xc=0.29*d//in mm
+Mr=0.65*b*d^2/10^6//M>Mr, hence doubly reinforced beam
+Ast1=round(Mr*10^6/sigma_st/0.9/d)//steel required for singly reinforced beam, in sq mm
+M1=M-Mr//balance of moment, in kN-m
+d1=25//top cover, in mm
+Ast2=round(M1*10^6/sigma_st/(d-d1))//in sq mm
+Ast=Ast1+Ast2//in sq mm
+n1=Ast/0.785/12^2//no. of 12 mm dia bars on tension side
+n1=3//assume
+Asc=m*Ast2*(d-Xc)/(1.5*m-1)/(Xc-d1)//in sq mm
+n2=Asc/0.785/12^2//no. of 12 mm dia bars on compression side
+n2=3//assume
+V=W*l/2//in kN
+Tv=V*10^3/b/d//in MPa
+pt=n1*0.785*12^2/b/d*100//pt=0.56, approximately
+//for M15 grade concrete and pt=0.56
+Tc=0.302//in MPa
+//as Tc>Tv, no shear reinforcement required; provide nominal stirrups
+//provide 6 mm dia bars
+Asv=2*0.785*6^2//in sq mm
+Sv=Asv*fy/0.4/b//in mm
+Sv=260//approximately, in mm
+Svmax=0.75*d//in mm
+Svmax=200//approximately, in mm
+Sv=min(Sv,Svmax)//in mm
+mprintf("Summary of design\nSize of beam = %d x %d mm\nCover, bottom = 25 mm\nTop = 25 mm\nSteel, bottom = %d-12 mm dia bars\nTop = %d-12 mm dia bars\nStirrups = 6 mm dia @ %d mm c/c throughout",b,D,n1,n2,Sv)
diff --git a/3683/CH9/EX9.3/Ex9_3.sce b/3683/CH9/EX9.3/Ex9_3.sce new file mode 100644 index 000000000..5a50268e7 --- /dev/null +++ b/3683/CH9/EX9.3/Ex9_3.sce @@ -0,0 +1,44 @@ +l=7//span, in m
+sigma_cbc=5//in MPa
+sigma_st=140//in MPa
+fy=250//in MPa
+m=18.66//modular ratio
+b=300//assume, in mm
+W1=35//imposed load on beam, in kN/m
+M=W1*l^2/8//in kN-m
+d=(M*10^6/0.87/b)^0.5//in mm
+d=910//approximately, in mm
+D=1.1*d+50//increase d by 10% for self-weight and cover is 50 mm
+D=1050//approximately, in mm
+W2=25*(b/10^3)*(D/10^3)//self-weight, in kN/m
+W=W1+W2//in kN/m
+M=W*l^2/8//in kN-m
+d=(M*10^6/0.87/b)^0.5//in mm
+d=1000//approximately, in mm
+dia=20//in mm
+D=d+dia/2+35//in mm
+Ast=round(M*10^6/sigma_st/0.87/d)//in sq mm
+n=Ast/0.785/20^2//no. of 20 mm dia bars
+n=7//assume
+Ast=n*0.785*20^2//in sq mm
+pt=Ast/b/D*100//pt=0.7, approximately
+As=round(0.85/fy*b*d)//minimum steel, As<Ast, hence OK
+Asf=0.1/100*b*d/2//side faced steel on each face, in sq mm
+//provide 6 mm dia bars
+s=1000*0.785*6^2/Asf//in mm
+s=188//assume, in mm
+V=W*l/2//in kN
+Tv=V*10^3/b/d//<Tcmax=1.6 MPa, hence OK
+//for M15 grade concrete and pt=0.7
+Tc=0.33//in MPa
+//as Tv>Tc, shear reinforcement required
+Vs=V-Tc*b*d/10^3//in kN
+//provide 6 mm dia bars
+Asv=2*0.785*6^2//in sq mm
+sigma_sv=140//in MPa
+Sv=Asv*sigma_sv*d/Vs/10^3//in mm
+Sv=155//approximately, in mm
+Svmin=Asv*fy/0.4/b//in mm
+Svmin=117//approximately, in mm
+Sv=min(Sv,Svmin)//in mm
+mprintf("Summary of design\nSize of beam = %d x %d mm\nCover = 35 mm\nSteel= %d-20 mm dia bars\nStirrups = 6 mm dia @ %d mm c/c throughout\nSide faced steel-6 mm dia @ %d mm c/c on both vertical faces of beam",b,D,n,Sv,s)
diff --git a/3683/CH9/EX9.4/Ex9_4.sce b/3683/CH9/EX9.4/Ex9_4.sce new file mode 100644 index 000000000..4c5703818 --- /dev/null +++ b/3683/CH9/EX9.4/Ex9_4.sce @@ -0,0 +1,45 @@ +l=10//span, in m
+sigma_cbc=5//in MPa
+sigma_st=140//in MPa
+fy=250//in MPa
+m=18.66//modular ratio
+Df=100//slab thickness, in mm
+D=l*10^3/12//in mm
+D=850//approximately, in mm
+d=D-100//cover=100 mm
+bw=300//in mm
+bf=l*10^3/6+bw+6*Df//>2500 mm c/c distance of beams
+bf=2500//in mm
+W1=(bw/10^3)*(d-Df)/10^3*25//in kN/m
+W2=(Df/10^3)*(bf/10^3)*25//in kN/m
+W3=(bf/10^3)*5//imposed load, in kN/m
+W=W1+W2+W3//in kN/m
+W=24//approximately, in kN/m
+M=W*l^2/8//in kN-m
+V=W*l/2//in kN
+Ast=round(M*10^6/sigma_st/0.87/d)//in sq mm
+//provide 4-25 mm dia bars + 4-20 mm dia bars
+Ast=4*0.785*25^2+4*0.785*20^2//in sq mm
+//verification of trial section
+//assume x>Df
+x=(m*Ast*d+bf*Df^2/2)/(bf*Df+m*Ast)//in mm
+//sigma_cbc'=sigma_cbc (x-Df)/x
+a=(x-Df)/x
+z=d-(1+2*a)/(1+a)*Df/3//in mm
+sigma_st=M*10^6/Ast/z//<140 MPa, hence OK
+sigma_cbc=sigma_st/m*x/(d-x)//<5 MPa, hence OK
+Tv=V*10^3/bw/d//in MPa
+pt=Ast*100/(bw*d+(2500-300)*100)//pt=0.72, approximately
+//for M15 grade concrete and pt=0.72
+Tc=0.33//in MPa
+//as Tv>Tc, shear reinforcement required
+Vs=V-Tc*bw*d/10^3//in kN
+//provide 6 mm dia bars
+Asv=2*0.785*6^2//in sq mm
+sigma_sv=140//in MPa
+Sv=Asv*sigma_sv*d/Vs/10^3//in mm
+Sv=130//approximately, in mm
+Svmin=Asv*fy/0.4/bw//in mm
+Svmin=117//approximately, in mm
+Sv=min(Sv,Svmin)//in mm
+mprintf("T beam:bf=%d mm\nDf=%d mm\nd=%d mm\nbw=%d mm\nCover = 50 mm\nSteel= 4-25 mm dia + 4-20 mm dia bars\nStirrups = 6 mm dia @ %d mm c/c throughout",bf,Df,d,bw,Sv)
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