Chapter 15:Doubly Reinforced Sections

Ex15.1:pg-792

In [1]:
import math
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
print "Moment of resistance of the beam = ",Mu," kN-m"

Moment of resistance of the beam =  556.299941443  kN-m

Ex15.2:pg-793

In [2]:
import math
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
print "Moment of resistance of the beam = ",Mu," kN-m"

Moment of resistance of the beam =  281.483345273  kN-m

Ex15.3:pg-794

In [4]:
import math
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
print "As factored moment is less than limiting moment, no steel is required on compression side (as per LSM)"

As factored moment is less than limiting moment, no steel is required on compression side (as per LSM)

Ex15.4:pg-794

In [8]:
import math
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
print "Moment of resistance of the beam = ",Mu," kN-m"

Moment of resistance of the beam =  135.03389454  kN-m

Ex15.5:pg-795

In [7]:
import math
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
print "Compression steel = ",Asc," sq mm\nTension steel = ",Ast," sq mm"

Compression steel =  267.0  sq mm
Tension steel =  1907.0  sq mm

Ex15.6:pg-796

In [6]:
import math
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
print "Compression steel = ",Asc," sq mm\nTension steel = ",Ast," sq mm"

Compression steel =  262.0  sq mm
Tension steel =  823.0  sq mm

Ex15.7:pg-797

In [5]:
import math
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
print "Compression steel = ",Asc," sq mm\nTension steel = ",Ast," sq mm"

Compression steel =  163.0  sq mm
Tension steel =  447.0  sq mm