diff options
Diffstat (limited to '3683/CH5')
| -rw-r--r-- | 3683/CH5/EX5.1/Ex5_1.sce | 9 | ||||
| -rw-r--r-- | 3683/CH5/EX5.10/Ex5_10.sce | 18 | ||||
| -rw-r--r-- | 3683/CH5/EX5.11/Ex5_11.sce | 26 | ||||
| -rw-r--r-- | 3683/CH5/EX5.12/Ex5_12.sce | 57 | ||||
| -rw-r--r-- | 3683/CH5/EX5.2/Ex5_2.sce | 21 | ||||
| -rw-r--r-- | 3683/CH5/EX5.3/Ex5_3.sce | 20 | ||||
| -rw-r--r-- | 3683/CH5/EX5.4/Ex5_4.sce | 14 | ||||
| -rw-r--r-- | 3683/CH5/EX5.5/Ex5_5.sce | 23 | ||||
| -rw-r--r-- | 3683/CH5/EX5.6/Ex5_6.sce | 15 | ||||
| -rw-r--r-- | 3683/CH5/EX5.7/Ex5_7.sce | 15 | ||||
| -rw-r--r-- | 3683/CH5/EX5.8/Ex5_8.sce | 42 | ||||
| -rw-r--r-- | 3683/CH5/EX5.9/Ex5_9.sce | 24 |
12 files changed, 284 insertions, 0 deletions
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)
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