# 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