# Chapter 8:Slab Design Two Way Reinforced¶

## Ex8.1:pg-363¶

In [7]:
import math
lx=3.5 #in m
ly=4 #in m
sigma_cbc=5 #in MPa
sigma_st=140 #in MPa
D=lx*10**3.0/35 #in mm
W1=(D/10**3)*25 #self-weight, 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=math.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
print "Summary of design\nSlab thickness=",D," mm\nCover=15 mm\nSteel-\n(i)Short span = 10 mm dia @ ",s1," mm c/c\n(ii)Long span = 10 mm dia @ ",s2," mm c/c\nAlternate bars are bent up at l/7 from support in both directions"

Summary of design
Slab thickness= 100  mm
Cover=15 mm
Steel-
(i)Short span = 10 mm dia @  200  mm c/c
(ii)Long span = 10 mm dia @  210  mm c/c
Alternate bars are bent up at l/7 from support in both directions


## Ex8.2:pg-364¶

In [2]:
import math
sigma_cbc=5 #in MPa
sigma_st=230 #in MPa
lx=3.75 #in m
ly=4 #in m
D=lx*10**3.0/40 #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
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=math.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=3.0/4*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
print "Summary of design\nSlab thickness=",D," mm\nCover=15 mm\nSteel for both panels I and II-\nMain steel= 10 mm dia bars @ ",s1," mm c/c both ways. Alternate bars are bent up at supports.\nTorsion steel=(i) At corners, 6 mm dia bars @ ",s5," mm c/c both ways\n(ii) At continuous support, 6 mm dia bars @ ",s6," mm c/c both ways"

Summary of design
Slab thickness= 100  mm
Cover=15 mm
Steel for both panels I and II-
Main steel= 10 mm dia bars @  765.561904762  mm c/c both ways. Alternate bars are bent up at supports.
Torsion steel=(i) At corners, 6 mm dia bars @  85  mm c/c both ways
(ii) At continuous support, 6 mm dia bars @  170  mm c/c both ways


## Ex8.3:pg-365¶

In [6]:
import math
sigma_cbc=7 #in MPa
sigma_st=275 #in MPa
lx=6 #in m
ly=7 #in m
D=lx*10**3.0/35 #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
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 consdered
Mxs2=Ax*W*lx**2 #in kN-m
#check for depth
M=max(Mxm1,Mym1,Mxs1,Mys1,Mxm2,Mym2,Mxs2) #in kN-m
d=math.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=3/4.0*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
print "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 @ ",s1," mm c/c. Alternate bars are bent up at supports at a distance lx/4 from centre of support\nSupport - 10 mm dia @ ",s2," mm c/c\n2. Long span (ly=7 m)\nMid-span - 10 mm dia bars @ ",s5," mm c/c. Alternate bars are bent up at supports at a distance ly/4 from centre of support\nSupport - 10 mm dia @ ",s7," mm c/c\n(B)Panels III and IV-\n1. Short span (lx=6 m)\nMid-span - 10 mm dia bars @ ",s3," mm c/c. Alternate bars are bent up at supports at a distance lx/4 from centre of support\nSupport - 10 mm dia @ ",s4," mm c/c\n2. Long span (ly=7 m)\nMid-span - 10 mm dia bars @ ",s6," mm c/c. Alternate bars are bent up at supports at a distance ly/4 from centre of support\nSupport - 10 mm dia @ ",s7," mm c/c\nTorsion steel\nOutside corners- 6 mm dia bars @ ",s8,"mm \nContinuous support- 6 mm dia bars @ ",l,"mm"

Summary of design
Slab thickness= 190  mm
Cover=15 mm
Steel:(A)Panels I, II, V and VI-
1. Short span (lx=6 m)
Mid-span - 10 mm dia bars @  195  mm c/c. Alternate bars are bent up at supports at a distance lx/4 from centre of support
Support - 10 mm dia @  565  mm c/c
2. Long span (ly=7 m)
Mid-span - 10 mm dia bars @  240  mm c/c. Alternate bars are bent up at supports at a distance ly/4 from centre of support
Support - 10 mm dia @  550  mm c/c
(B)Panels III and IV-
1. Short span (lx=6 m)
Mid-span - 10 mm dia bars @  235  mm c/c. Alternate bars are bent up at supports at a distance lx/4 from centre of support
Support - 10 mm dia @  775  mm c/c
2. Long span (ly=7 m)
Mid-span - 10 mm dia bars @  300  mm c/c. Alternate bars are bent up at supports at a distance ly/4 from centre of support
Support - 10 mm dia @  550  mm c/c
Torsion steel
Outside corners- 6 mm dia bars @  110 mm
Continuous support- 6 mm dia bars @  1 mm