1. FOR 5TH SEMESTER DIPLOMA IN CIVIL ENGINEERING
CONCEPTs AND PROBLEMS
DESIGN OF RCC COLUMN FOOTING
2. Learning Outcomes:
1. Concept of column footings.
2. Design criteria.
3. Design steps for column footing.
4. Reinforcement detailing.
3. Column footing:
RCC columns are supported by the foundation structures which are
located below the ground level are called footings.
Purpose of Footings:
1) To support the upper structure.
2) To transfer the Loads and moments safely to subsoil.
3) Footings are designed to resist the bending moment and shear
forces developed due to soil reaction.
S.J.(Govt.) POLYTECHNIC BENGALURU
5. Isolated footing.
The footings which are provided below the column
independently are called as isolated footings.
This type of footing may be square ,
rectangular or circular in section
Isolated footing consists of thick slab which
may be flat or sloped or stepped.
S.J.(Govt.) POLYTECHNIC BENGALURU
P
6. The structural design of the footing includes the design of
1) Depth of footing
2) Reinforcement requirement
3) Check on serviceability
S.J.(Govt.) POLYTECHNIC BENGALURU
9. Design Considerations:
Minimum reinforcement : (As per IS456:2000, clause 26.5.2.1&2
The mild steel reinforcement in either direction in slabs shall not be
less than 0.15 percent of the total cross sectional area. However,
this value can be reduced to 0.12 percent when high strength
deformed bars or welded wire fabric are used
The diameter of reinforcing bars shall not exceed one eight of the
total thickness of the slab.
S.J.(Govt.) POLYTECHNIC BENGALURU
12. ..IS456:2000.pdf
When the depth required for the above development length or the
other causes is very large, it is more economical to adopt a stepped or
sloped footing so as to reduce the amount of concrete that should go
into the footing.
SHEAR:
1. One way shear(Wide beam Shear):
One way shear is similar to Bending shear in slabs considering the
footing as a wide beam. Shear is taken along the vertical plane
extending the full width of the base
Lowest value of allowable shear in Table 13 of IS 456:2000
Is 0.35N/mm2 is recommended.
16. 3. Bending Moment for Design:
Consider the entire footing as
cantilever beam from the face of
The column and calculate the
BM.
Calculate span for the
cantilever portion (Hashed portion)
= plx
𝑙
2
=
𝑝𝑙2
2
Substitute l=[(B-D)/2]
Mxx= p (
𝐵−𝐷
2
)2 x
1
2
This is BM for 1m width of the beam
17. DESIGN STEPS:
1. Assume self weight of footing =0.1p
Total load w= P+0.1P
2. Area of footing required, A =
𝑤
𝑆𝐵𝐶
For square footing, Size of footing = 𝐴
For Rectangular footing, assume L
LxB=A
Provide L x B square footing,
Total Area = _ _ _ _ _ m2
19. 5. Effective depth :
d required =
Mu
0.138 x fckx b
increase depth for 1.75 to 2 times more than calculated value for shear
considerations.
6. Area of tension reinforcement :
Mu = 0.87fy Astd(1-
Ast fy
bdfck
)
This is a quadratic equation, calculate the value for Ast and consider the
minimum of values
Area of steel per m = Ast /span = _ _ _mm2
20. Assume diameter bars
Area of one bar ast=
π x 𝑑𝑖𝑎2
4
= _ _ _ mm2
Spacing of reinforcement , S =
1000 ast
Ast
7) Check for one way shear :
The critical section is taken at a distance “d” away from the face of the
column y-y axis.
Shear force per m,
Vu = p x B x [(
L−D
2
)-d]
21. Nominal Shear stress,𝜏 𝑣 =
𝑉 𝑢
𝑏𝑑
=_ _ _N/mm2
Percentage steel =
100Ast
𝐵𝑑
= pt?
Refer table No. 19 of IS 456:2000 for 𝜏 𝑐
𝜏 𝑐 = _ _ _N/mm2
𝜏v should be less than 𝜏 𝑐,
design is safe against one way shear.
𝜏v < 𝜏 𝑐
22. 8) Check for two way shear :
The critical section is taken at a distance
“d/2” away from the faces of the column
Shear force per m,
Vu = p x [A-(0.4+0.5)2]
Nominal Shear stress, 𝜏 𝑣=
Vu
b0
d
b0 = perimeter = 4( D + d)
Maximum shear stress permitted
𝜏 𝑐=0.25 𝑓 𝑐𝑘
𝜏 𝑐 should be greater than 𝜏v , Then design is safe against Punching shear /
two way shear.
23. 9) Development Length
Ld =
fsx dia of bar
4𝜏 𝑏𝑑
=
0.87x415x dia of bar
4𝑥2.4
= 37.6∅
For Fe 415 steel and M20 concrete the values substituted to the above
equation and Ld = 37.6∅
Taken to be , Ld= 40∅
available Ld=( L-D)/2 = _ _ _mm
This is alright
26. PROBLEM 1:
Design a square footing to carry a column load of 1100kN
from a 400mm square column. The bearing capacity of soil is
100kN/mm2. Use M20 concrete and Fe 415 steel.
27. 1. Assume self weight of footing =0.1p= 0.1x 1100 =110kN
Total load w= P+0.1P = 1100+110= 1210kN
2. Area of footing required, A =
𝑤
𝑆𝐵𝐶
=
1210
100
= 12.1m2
Size of footing = 𝐴 = 12.1= 3.478
Provide 3.5m x 3.5m square footing,
Total Area = 12.25m2
29. BM about axis x-x passing through face of the
Column as shown in fig.
Mu= p x B x [
L−D
2
]2 X
1
2
= 148.16x3.5 x[
3.5−0.4
2
]2 X
1
2
= 622.92kN − m
L = B for square footing
D = Size of column = 400mm = 0.4m
Mu =622.92kN − m
30. 5. Effective depth :
d required =
Mu
0.138 x fck
x b
=
622.92x106
0.138 x 20x 3500
= 253.93mm
Adopt 500mm effective depth and overall depth 550mm. (increase
depth for 1.75 to 2 times more than calculated value for shear
considerations)
6. Area of tension reinforcement :
Mu = 0.87fy Astd(1-
Ast fy
bdfck
)
622.92 x 106 = 0.87 x 415 x Astx 500(1-
Ast
x 415
3500x500x20
)
622.92 x 106 = 180525Ast- 2.14 Ast
2
31. 622.92 x 106 = 180525Ast- 2.14 Ast
2
2.14 Ast
2 - 180525Ast+ 622.92 x 106 = 0
This is a quadratic equation, calculate the value for Ast and consider the
minimum of values
There fore, Ast = 3604.62mm2
Area of steel per m = 3604.5/3.5 = 1029.85mm2
Provide 12mm diameter bars
Area of one bar ast=
π x 122
4
= 113.09mm2
32. Spacing of reinforcement , S =
1000 ast
Ast
=
1000x113.09
1029.85
= 109.81mm
Providing 12mm dia bars @ 100mm c/c.
7) Check for one way shear :
The critical section is taken at a distance “d” away from the face of the
column y-y axis.
Shear force per m,
Vu = p x B x [(
L−D
2
)-d] = 148.16x 1 x [(
3.5−0.40
2
)- 0.50] = 155.57kN
Nominal Shear stress,𝜏 𝑣 =
𝑉 𝑢
𝑏𝑑
=
155.57x103
1000x500
= 0.31N/mm2
33.
34. Percentage steel =
100Ast
𝐵𝑑
=
100x3604.62
3500x 500
= 0.20
Refer table No. 19 of IS 456:2000 for 𝜏 𝑐
Since ,
% steel 𝜏 𝑐
0.15 0.28
0.20 x
0.25 0.36
For 𝜏 𝑐 at 0.2 = 0.28 +
(0.36−0.28)
(0.25−0.15)
x(0.2-0.15)
𝜏 𝑐 = 0.32N/mm2
35. 𝜏v is less than 𝜏 𝑐, design is safe against one way shear.
8) Check for two way shear :
The critical section is taken at a distance
“d/2” away from the faces of the column
Shear force per m,
Vu = p x [A-(0.4+0.5)2]
= 148.16 x [12.25-(0.4+0.5)2] = 148.16x 11.44
=1695kN
36. b0 = perimeter = 4( D + d)
= 4(400+500)
=3600mm
Nominal Shear stress, 𝜏 𝑣=
Vu
b0d
=
1695 x103
3600x 500
𝜏 𝑣 = 0.941N/mm2
Maximum shear stress permitted
𝜏 𝑐=0.25 𝑓 𝑐𝑘 =0.25 20= 1.11N/mm2
since , 𝜏 𝑐 >𝜏v, design is safe against Punching / two way shear.
37. 9) Development Length
Ld =
fsx dia of bar
4𝜏 𝑏𝑑
=
0.87x415x dia of bar
4𝑥2.4
= 37.6∅
For Fe 415 steel and M20 concrete the values substituted to the above
equation and Ld = 37.6∅
Taken to be , Ld= 40∅ = 40 x 12 = 480mm
available Ld=( 3500-400)/2 = 1550mm
This is alright
Having sloped footing is much economical and also safer in overturning too, Hence many design engineers adopt stepped/slopped footing rather square or rectangular
