P1 500kN P2 1000kN
0.3m 5m
qa 20 200 kN/m3 col1 300.0mm X 300.0mm
gc 2.5 25 kN/m3 col2 400.0mm X 400.0mm
gs 1.8 18 kN/m3
fck 15 N/mm2 fy 415 N/mm2
cover 50 mm
dia 20 mm
Footing Design Taking moment about line P2
Eccentricity,e= 0.90m R1= 609.756kN R2= 890.244kN
For footing A
L1= 2.4m Overall thickness of footing, D 600 mm
B1=R1/ (qa-(gc-gs)D)L1 1.298m say 1.30m
For footing B
Assume square footing size L2 Thus, provide
L2^2=R2/(qa-(gc-gs)D)L1 ### L2= 2.132m L2= 2.200m B2=
Analysis of footing
qu1=R1*1.5/L1*1m ### qu2=R2*1.5/L2*1m ###
Thickness of footing
i. Wide beam shear
For footingA
Assume Pt 0.2 so from table IS456, tc= 0.32 32 t/m x=
Assume in direction of B1, width of strap beam (b) is 500 mm
Shear=tcbd=qu(x-d) Therefore d= 0.2817 m
Assume Pt 0.2 so from table IS456, tc= 0.32 32 t/m2 x=
Assume in direction of B1, width of strap beam (b) is 500 mm
Shear=tcbd=qu(x-d) Therefore d= 0.6727 m >600 So increase depth
Thus increase width of the beam to 700.00mm
Assume Pt 0.3 so from table IS456, tc= 0.38 38 t/m2 x=
Assume in direction of B1, width of strap beam (b) is 700.00mm
Shear=tcbd=qu(x-d) Therefore d= 0.5215 m <600mm depth earlier assumed safe
ii. Two way shear
For column A;
From clause 31.6.3.1 of IS456-2000 Bc=width of column/length of column= 1
ks=Bc+0.5= 1.5 put less than or equal to 1 i.e. 1
tc=ks(0.25)sqrt(fck)(N/mm2)= 0.968245837 N/mm2 96.82458366 t/m2
Critical parameter x d x tc = Pu-qux(critical area - dotted area)
Thus eqn becomes
2(0.15+0.3+d/2 +0.3+ d/2+d/2)xd x96.82=75-38.11(0.3+0.15+ d/2)
d^2 d constant d1 d2
290.47375097 164.291753532 -57.8506098 Thus solving 0.245532773 -0.81113208
So, d= 245.53277254 <600mm depth earlier assumed safe
For column A;
From clause 31.6.3.1 of IS456-2000 Bc=width of column/length of column= 1
ks=Bc+0.5= 1.5 put less than or equal to 1 i.e. 1
tc=ks(0.25)sqrt(fck)(N/mm2)= 0.968245837 N/mm2 96.82458366 t/m2
Critical parameter x d x tc = Pu-qux(critical area - dotted area)
Thus eqn becomes
4(0.4+ d)x d x96.82=150-60.7(0.4+ d)
d^2 d constant d1 d2
387.29833462 215.617781742 -125.720621 Thus solving 0.355747696 -0.91247041
So, d= 355.74769565 <600mm depth earlier assumed safe
Among all the required d values (for wide beam shear and two way shear criteria)
d rqrd= 0.5215 m D reqrd= 581.4736 mm
Dprov= 600 Thus dprov= 550 mm
Reinforcement for flexure for footings
i. Design along the length direction
Compairing the moments at the column faces in both footings A & B
distance at side face on B 0.9 m
M max for footing B= 24.5828714 tm
Mu/bd^2 0.812656906 N/mm2
From table 1 of SP 16,Pt 0.242
ii. Design along the width direction
qu1= ### < ### =qu2
So for design along width direction footing B(qu2) is considered
Mu= 17.071 tm < Mu in longer direction 24.58tm
So,pt= 0.242 i.e. same as reinforcement along longer direction
But from wide beam criteria, Pt 0.3 %
Ast reqrd= 2.145
Design of strap beam
i. Reinforcement for flexure
M max 51.3tm d'/d= 0.1 from table 49 sp16
Mu/bd^2 2.4226682409 N/mm2 Thus pt= 0.83 & pc= 0.12
Ast required on tension face 3195.5 mm2 11 20 3455.7519
Asc required on compression face 462 mm2 4 20 1256.6371
ii. Check for shear
Vmax= 83.2t Tact=Vmax/bd 2.161862528 N/mm2 < M15Tcmax 2.5 N/mm2
Pt prov= 0.897597901
2.200m
400.00mm
850.00mm
750.00mm
75.0t 150.0t
300.0mm 400.0mm
0.3m 2.10m 0.4m 1.1m 1.1m
### ###
83.2t
B E 16.5t F
11.4t D
A H
y= 1.67m G
66.8t
C
63.6t
63.6t = 16.5t
y 2.10m -y
51.3tm
0.00 col face
0.00 0.9
###
### ###
cl. 26.2.1 IS 456:200o pg no 42 cl. 26.2.1 IS 456:200o pg no 43
Table 19
100as/bd M15 M20 M25 M30 M35 M40 and above
<= 0.15 0.28 0.28 0.29 0.29 0.29 0.3
0.25 0.35 0.36 0.36 0.37 0.37 0.38
0.5 0.46 0.48 0.49 0.5 0.5 0.51
0.75 0.54 0.56 0.57 0.59 0.59 0.6
1 0.6 0.62 0.64 0.66 0.61 0.68
1.25 0.64 0.61 0.1 0.11 0.73 0.74
1.5 0.68 0.12 0.14 0.76 0.18 0.79
1.75 0.11 0.75 0.78 0.8 0.82 0.84
2 0.11 0.79 0.82 0.84 0.86 0.88
2.25 0.11 0.81 0.85 0.88 0.9 0.92
2.5 0.11 0.82 0.88 0.91 0.93 0.95
2.75 0.71 0.82 0.9 0.94 0.96 0.98
3 0.71 0.82 0.92 0.96 0.99 1.01
and above
Table 20 M15 M20 M25 M30 M35 M40
Tcmax 2.5 2.8 3.1 3.5 3.7 4
Cl40.2
Overall depth 300 275 250 225 200 175 150
of slab,mm or more or less
k 1 1.05 1.1 1.15 1.2 1.25 1.3
column no
fck M20 row no 2
pt 0.15 1 0.28
0.25 2 0.36
0.50 3 0.48 shear 0.43 0.4345949
0.75 4 0.56 pt #NAME? #NAME?
1.00 5 0.62
1.25 6 0.61
1.50 7 0.12
1.75 8 0.75
2.00 9 0.79
2.25 10 0.81
2.50 11 0.82
2.75 12 0.82
3.00 13 0.82
Overall depth k
300 or more 1 1 2
Interpolation 275 1.05 2 3
127 250 1.1
then 225 1.15
1.3 200 1.2
175 1.25
150 or less 1.3
1 1.5
2
3
