Short Notes: Footing | Short Notes for Civil Engineering - Civil Engineering (CE) PDF Download

 Page 1


 
 
FOOTING 
1. Bearing capacity of soil  
Bearing capacity of soil governs the dimensions and depth of foundation. Under no case the loading 
on foundation can be greater than bearing capacity of foundation 
(A) Gross Bearing capacity:  Total bearing capacity at based on foundation which includes weight 
of foundation, super structure load, earth lying over footing. 
(B) Net Bearing capacity: It can be defined as follows 
Net bearing capacity= Gross Bearing capacity - W 
W= weight of soil at level of footing before trench was made for footing 
2. Depth of foundation 
 
H= 
?? ?? [
1-sin?? 1+sin?? ]
2
 
p=  Bearing capacity of foundation 
?=Density of soil 
?=angle of repose 
H= Depth of foundation 
3. SOME IMPORTANT SPECIFICATION 
A. Thickness of edge 
? As per IS 456 the minimum thickness for edge of footing on basis of serviceability critical will 
be 150 mm. 
 
B. Minimum percentage of steel 
? For Fe 250, 0.15%of gross area  
? For Fe 415/ Fe 500, 0.12% of gross area must be provided. 
  
Page 2


 
 
FOOTING 
1. Bearing capacity of soil  
Bearing capacity of soil governs the dimensions and depth of foundation. Under no case the loading 
on foundation can be greater than bearing capacity of foundation 
(A) Gross Bearing capacity:  Total bearing capacity at based on foundation which includes weight 
of foundation, super structure load, earth lying over footing. 
(B) Net Bearing capacity: It can be defined as follows 
Net bearing capacity= Gross Bearing capacity - W 
W= weight of soil at level of footing before trench was made for footing 
2. Depth of foundation 
 
H= 
?? ?? [
1-sin?? 1+sin?? ]
2
 
p=  Bearing capacity of foundation 
?=Density of soil 
?=angle of repose 
H= Depth of foundation 
3. SOME IMPORTANT SPECIFICATION 
A. Thickness of edge 
? As per IS 456 the minimum thickness for edge of footing on basis of serviceability critical will 
be 150 mm. 
 
B. Minimum percentage of steel 
? For Fe 250, 0.15%of gross area  
? For Fe 415/ Fe 500, 0.12% of gross area must be provided. 
  
 
 
C. Nominal cover as per IS 456:200 
 
Minimum Nominal cover as per exposure condition 
Member Mild (mm) Moderate (mm) Severe (mm) Very severe (mm) 
Extreme 
(mm) 
Foundation 40 50 50 50 75 
 
LIMIT STATE OF SHEAR 
 
1. NOMINAL SHEAR STRESS 
 
? The average shear stress can be calculated using the following formula: 
?? ?? =
?? ?? ????
 
Where, 
Vu = ultimate shear stress at the section 
b = width of the section 
d = effective depth of the section 
? For beams with varying depth 
( )
2u
v
V M d tan
bd
?? ??
?=??
??
??
 
Where, 
ß = inclination of flexural tensile force to the horizontal. 
Mu = factored bending moment at the section.  
  
Page 3


 
 
FOOTING 
1. Bearing capacity of soil  
Bearing capacity of soil governs the dimensions and depth of foundation. Under no case the loading 
on foundation can be greater than bearing capacity of foundation 
(A) Gross Bearing capacity:  Total bearing capacity at based on foundation which includes weight 
of foundation, super structure load, earth lying over footing. 
(B) Net Bearing capacity: It can be defined as follows 
Net bearing capacity= Gross Bearing capacity - W 
W= weight of soil at level of footing before trench was made for footing 
2. Depth of foundation 
 
H= 
?? ?? [
1-sin?? 1+sin?? ]
2
 
p=  Bearing capacity of foundation 
?=Density of soil 
?=angle of repose 
H= Depth of foundation 
3. SOME IMPORTANT SPECIFICATION 
A. Thickness of edge 
? As per IS 456 the minimum thickness for edge of footing on basis of serviceability critical will 
be 150 mm. 
 
B. Minimum percentage of steel 
? For Fe 250, 0.15%of gross area  
? For Fe 415/ Fe 500, 0.12% of gross area must be provided. 
  
 
 
C. Nominal cover as per IS 456:200 
 
Minimum Nominal cover as per exposure condition 
Member Mild (mm) Moderate (mm) Severe (mm) Very severe (mm) 
Extreme 
(mm) 
Foundation 40 50 50 50 75 
 
LIMIT STATE OF SHEAR 
 
1. NOMINAL SHEAR STRESS 
 
? The average shear stress can be calculated using the following formula: 
?? ?? =
?? ?? ????
 
Where, 
Vu = ultimate shear stress at the section 
b = width of the section 
d = effective depth of the section 
? For beams with varying depth 
( )
2u
v
V M d tan
bd
?? ??
?=??
??
??
 
Where, 
ß = inclination of flexural tensile force to the horizontal. 
Mu = factored bending moment at the section.  
  
 
 
2. DESIGN SHEAR STRENGTH 
The design shear strength of concrete depends upon two factors: 
(i) Grade of concrete 
(ii) Percentage tensile reinforcement 
The value of tc is given in table 19 of IS: 456. 
s
100 A
bd
 Concrete grade 
(1) 
M20 
(2) 
M25 
(3) 
M30 
(4) 
= 0.15 0.28 0.29 0.29 
0.25 0.36 0.36 0.37 
0.50 0.48 0.49 0.50 
0.75 0.56 0.57 0.59 
1.00 0.62 0.64 0.66 
1.25 0.67 0.70 0.71 
1.50 0.72 0.74 0.76 
 
The nominal shear stress should not exceed the maximum shear strength of concrete as given 
in table 20 of IS: 456 to avoid compression failure. Maximum shear strength is given in the 
following table: 
Concrete Grade M-15 M-20 M-25 M-30 M-35 M-40 and above 
tc max (N/mm
2
) 2.5 2.8 3.1 3.5 3.7 4.0 
 
3. MINIMUM SHEAR REINFORCEMENT 
Minimum amount of shear reinforcement should always be provided in RCC section to 
? Avoid sudden shear failure.  
? To hold the reinforcing bars together 
? To prevent cracks in concrete due to shrinkage, thermal stresses etc. 
? IS 456 specifies the following formula for calculation of minimum shear reinforcement. 
sv
vy
A 0.4
bS 0.87 f
??
??
? ? ?
??
??
??
??
??
 
Where Asv = total cross-sectional area of stirrup legs effective in shear. 
Sv = spacing of stirrups. 
b = breadth of the beam or breadth of web of flanged beams. 
fy = characteristic strength of stirrup reinforcement in N/mm
2
 which shall not be taken greater 
than 415 N/mm
2
. 
 
4. DESIGN OF SHEAR REINFORCEMENT 
Page 4


 
 
FOOTING 
1. Bearing capacity of soil  
Bearing capacity of soil governs the dimensions and depth of foundation. Under no case the loading 
on foundation can be greater than bearing capacity of foundation 
(A) Gross Bearing capacity:  Total bearing capacity at based on foundation which includes weight 
of foundation, super structure load, earth lying over footing. 
(B) Net Bearing capacity: It can be defined as follows 
Net bearing capacity= Gross Bearing capacity - W 
W= weight of soil at level of footing before trench was made for footing 
2. Depth of foundation 
 
H= 
?? ?? [
1-sin?? 1+sin?? ]
2
 
p=  Bearing capacity of foundation 
?=Density of soil 
?=angle of repose 
H= Depth of foundation 
3. SOME IMPORTANT SPECIFICATION 
A. Thickness of edge 
? As per IS 456 the minimum thickness for edge of footing on basis of serviceability critical will 
be 150 mm. 
 
B. Minimum percentage of steel 
? For Fe 250, 0.15%of gross area  
? For Fe 415/ Fe 500, 0.12% of gross area must be provided. 
  
 
 
C. Nominal cover as per IS 456:200 
 
Minimum Nominal cover as per exposure condition 
Member Mild (mm) Moderate (mm) Severe (mm) Very severe (mm) 
Extreme 
(mm) 
Foundation 40 50 50 50 75 
 
LIMIT STATE OF SHEAR 
 
1. NOMINAL SHEAR STRESS 
 
? The average shear stress can be calculated using the following formula: 
?? ?? =
?? ?? ????
 
Where, 
Vu = ultimate shear stress at the section 
b = width of the section 
d = effective depth of the section 
? For beams with varying depth 
( )
2u
v
V M d tan
bd
?? ??
?=??
??
??
 
Where, 
ß = inclination of flexural tensile force to the horizontal. 
Mu = factored bending moment at the section.  
  
 
 
2. DESIGN SHEAR STRENGTH 
The design shear strength of concrete depends upon two factors: 
(i) Grade of concrete 
(ii) Percentage tensile reinforcement 
The value of tc is given in table 19 of IS: 456. 
s
100 A
bd
 Concrete grade 
(1) 
M20 
(2) 
M25 
(3) 
M30 
(4) 
= 0.15 0.28 0.29 0.29 
0.25 0.36 0.36 0.37 
0.50 0.48 0.49 0.50 
0.75 0.56 0.57 0.59 
1.00 0.62 0.64 0.66 
1.25 0.67 0.70 0.71 
1.50 0.72 0.74 0.76 
 
The nominal shear stress should not exceed the maximum shear strength of concrete as given 
in table 20 of IS: 456 to avoid compression failure. Maximum shear strength is given in the 
following table: 
Concrete Grade M-15 M-20 M-25 M-30 M-35 M-40 and above 
tc max (N/mm
2
) 2.5 2.8 3.1 3.5 3.7 4.0 
 
3. MINIMUM SHEAR REINFORCEMENT 
Minimum amount of shear reinforcement should always be provided in RCC section to 
? Avoid sudden shear failure.  
? To hold the reinforcing bars together 
? To prevent cracks in concrete due to shrinkage, thermal stresses etc. 
? IS 456 specifies the following formula for calculation of minimum shear reinforcement. 
sv
vy
A 0.4
bS 0.87 f
??
??
? ? ?
??
??
??
??
??
 
Where Asv = total cross-sectional area of stirrup legs effective in shear. 
Sv = spacing of stirrups. 
b = breadth of the beam or breadth of web of flanged beams. 
fy = characteristic strength of stirrup reinforcement in N/mm
2
 which shall not be taken greater 
than 415 N/mm
2
. 
 
4. DESIGN OF SHEAR REINFORCEMENT 
 
 
? When the nominal shear stress exceeds the design shear strength, extra shear reinforcement 
is provided in the form of 
• Vertical/Inclined stirrup 
 
• Bent up bars 
 
 
 
? The design shear stress is given by the following formula: 
Vus = (Vu – Vc) = (tv – tc) bd 
Where, 
Vu = total Shear Force. 
Vc = shear resisted by concrete 
Vus = shear resisted by reinforcements (Links or bent up bars) 
tv = nominal shear stress. 
tc = design shear stress of concrete  
5. Vertical/Inclined Stirrup 
? The spacing of vertical stirrup can be calculated by using the following formula: 
y sv
v
us
0.87 f .A .d
S
V
??
=
??
??
??
 
Where, 
Asv = total area of the legs of shear reinforcement. 
Sv = spacing of the links. 
d = effective depth of section. 
Page 5


 
 
FOOTING 
1. Bearing capacity of soil  
Bearing capacity of soil governs the dimensions and depth of foundation. Under no case the loading 
on foundation can be greater than bearing capacity of foundation 
(A) Gross Bearing capacity:  Total bearing capacity at based on foundation which includes weight 
of foundation, super structure load, earth lying over footing. 
(B) Net Bearing capacity: It can be defined as follows 
Net bearing capacity= Gross Bearing capacity - W 
W= weight of soil at level of footing before trench was made for footing 
2. Depth of foundation 
 
H= 
?? ?? [
1-sin?? 1+sin?? ]
2
 
p=  Bearing capacity of foundation 
?=Density of soil 
?=angle of repose 
H= Depth of foundation 
3. SOME IMPORTANT SPECIFICATION 
A. Thickness of edge 
? As per IS 456 the minimum thickness for edge of footing on basis of serviceability critical will 
be 150 mm. 
 
B. Minimum percentage of steel 
? For Fe 250, 0.15%of gross area  
? For Fe 415/ Fe 500, 0.12% of gross area must be provided. 
  
 
 
C. Nominal cover as per IS 456:200 
 
Minimum Nominal cover as per exposure condition 
Member Mild (mm) Moderate (mm) Severe (mm) Very severe (mm) 
Extreme 
(mm) 
Foundation 40 50 50 50 75 
 
LIMIT STATE OF SHEAR 
 
1. NOMINAL SHEAR STRESS 
 
? The average shear stress can be calculated using the following formula: 
?? ?? =
?? ?? ????
 
Where, 
Vu = ultimate shear stress at the section 
b = width of the section 
d = effective depth of the section 
? For beams with varying depth 
( )
2u
v
V M d tan
bd
?? ??
?=??
??
??
 
Where, 
ß = inclination of flexural tensile force to the horizontal. 
Mu = factored bending moment at the section.  
  
 
 
2. DESIGN SHEAR STRENGTH 
The design shear strength of concrete depends upon two factors: 
(i) Grade of concrete 
(ii) Percentage tensile reinforcement 
The value of tc is given in table 19 of IS: 456. 
s
100 A
bd
 Concrete grade 
(1) 
M20 
(2) 
M25 
(3) 
M30 
(4) 
= 0.15 0.28 0.29 0.29 
0.25 0.36 0.36 0.37 
0.50 0.48 0.49 0.50 
0.75 0.56 0.57 0.59 
1.00 0.62 0.64 0.66 
1.25 0.67 0.70 0.71 
1.50 0.72 0.74 0.76 
 
The nominal shear stress should not exceed the maximum shear strength of concrete as given 
in table 20 of IS: 456 to avoid compression failure. Maximum shear strength is given in the 
following table: 
Concrete Grade M-15 M-20 M-25 M-30 M-35 M-40 and above 
tc max (N/mm
2
) 2.5 2.8 3.1 3.5 3.7 4.0 
 
3. MINIMUM SHEAR REINFORCEMENT 
Minimum amount of shear reinforcement should always be provided in RCC section to 
? Avoid sudden shear failure.  
? To hold the reinforcing bars together 
? To prevent cracks in concrete due to shrinkage, thermal stresses etc. 
? IS 456 specifies the following formula for calculation of minimum shear reinforcement. 
sv
vy
A 0.4
bS 0.87 f
??
??
? ? ?
??
??
??
??
??
 
Where Asv = total cross-sectional area of stirrup legs effective in shear. 
Sv = spacing of stirrups. 
b = breadth of the beam or breadth of web of flanged beams. 
fy = characteristic strength of stirrup reinforcement in N/mm
2
 which shall not be taken greater 
than 415 N/mm
2
. 
 
4. DESIGN OF SHEAR REINFORCEMENT 
 
 
? When the nominal shear stress exceeds the design shear strength, extra shear reinforcement 
is provided in the form of 
• Vertical/Inclined stirrup 
 
• Bent up bars 
 
 
 
? The design shear stress is given by the following formula: 
Vus = (Vu – Vc) = (tv – tc) bd 
Where, 
Vu = total Shear Force. 
Vc = shear resisted by concrete 
Vus = shear resisted by reinforcements (Links or bent up bars) 
tv = nominal shear stress. 
tc = design shear stress of concrete  
5. Vertical/Inclined Stirrup 
? The spacing of vertical stirrup can be calculated by using the following formula: 
y sv
v
us
0.87 f .A .d
S
V
??
=
??
??
??
 
Where, 
Asv = total area of the legs of shear reinforcement. 
Sv = spacing of the links. 
d = effective depth of section. 
 
 
7. For inclined stirrup: 
( )
y st
us
v
0.87 f A d
V sin cos
S
= ? + ? 
Where, 
a = Angle of inclination of stirrup 
8. The spacing between two stirrup shall be minimum of following values: 
(?? ) ?? ??  >
?  (?? ?? )
??????  ?? h??????  ?????? (???? ) ?? ??  >
?  0.75??  (??????  ?? -???????????????? )
              >
?  ??  (??????  ????????????????  ???????????????? ) 
(?????? ) ?? ??  >
?  300 ????
}
 
 
 
 
 ??????  ?????????????? ???? ?? h?????? 
9. Bent Up Bars 
Vus = 0.87 fy Asb sin a  
Where, 
a = Angle of inclination of bar with horizontal 
Asb = Area of bent up bar