DESIGN OF COLUMN & BOX FOOTING FOR CRITICAL LOADS

1.0 DEFAULT VALUES

1.1 Material Properties :

1.1.1 Grade of Conc:( M 15/20/25/30/35/40 ) fck = 30 N/mm²
1.1.2 Grade of steel:( Fe 250/415/500 ) fy = 500 N/mm²
1.2 Unit weight of concrete = 24000 N/m³
1.3 Cover to reinforcement in Z- Direction = 40.00 mm
1.4 Cover to reinforcement in X- Direction = 40.00 mm

2.0 INPUT DATA

2.1 GENERAL DATA

2.1.1 Unit : KN AND METERS

2.1.2 Joint no : -------
A'3,A'4,H'3,
2.1.3 Column no. :
H'4
2.1.4 Reference drawing no. :
2.1.6 Remarks : Col Size750 x 750

2.2 DIMENSIONS OF COLUMN

2.2.1 Longer dimension of column along X axis. D = 500 mm

2.2.2 Shorter dimension of column along Z axis. b = 750 mm
2.2.3 Unsupported length for bending parallel to larger dimension Lx = 5.35 m
2.2.4 Unsupported length for bending parallel to shorter dimension. Lz = 5.35 m

(Unsupported length as per clause 25.1.3 of IS:456-2000 )

2.2.5 Multi. Factor for calculating eff. Length for bending about Z axis. rx = 1.0
2.2.6 Multi. Factor for calculating eff. Length for bending about X axis. rz = 1.0
Unsupported length multiplication factor as per annex E Table 28, pg 94 of IS:456
-2000 for calculation of effective length depending on end restraint conditions.
Effective length of bending parallel to larger dimension. { Lx * rx } Lex = 5.35 m
Effective length of bending parallel to shorter dimension. { Lz * rz } Lez = 5.35 m

2.3 LOADS ON COLUMN

2.3.1 LOAD CASES CONSIDERED :
1. ( STATIC LOADS) = (DL+LL) AT COLUMN H'3
2. ( STATIC LOAD + SESMIC LOAD) =(DL+LL+EQ Z) AT COLUMN H'3
3. ( STATIC LOAD + WIND LOAD) =(DL+LL+WL) AT COLUMN H'3

2.3.2 Load case 1.STATIC LOAD (STAAD OUT PUT COLUMN H'3) Self wt = 48.15 KN
Axial load on compression member Excluding selfweight. P = 36.96 KN
Moment in the direction of larger dimension (i.e. about Z axis ) Mz = 0.00 KN-M
Moment in the direction of shorter dimension ( ie. about X axis ) Mx = 0.00 KN-M
 Load case 2. STATIC LOAD + SESMIC LOAD (STAAD OUT PUT COLUMN H'3)
Axial load on compression member Excluding selfweight. P = 36.96 KN
Moment in the direction of larger dimension (ie. about Z axis ) Mz = 0.00 KN-M
Moment in the direction of shorter dimension ( i.e. about X axis ) Mx = 8.83 KN-M

Load case 3. STATIC LOAD + WIND (STAAD OUT PUT COLUMN H'3)
Axial load on compression member Excluding selfweight. P = 36.96 KN
Moment in the direction of larger dimension (i.e. about Z axis ) Mz = 0.00 KN-M
Moment in the direction of shorter dimension ( i.e. about X axis ) Mx = 18.64 KN-M

3 DESIGN OF COLUMN
Longer dimension of column along X axis. D = 500
Shorter dimension of column along Z axis. b = 750
Cover to reinforcement in Z- Direction = 40.00 mm
Cover to reinforcement in X- Direction = 40.00 mm

3.1 CALCULATIONS ( For Load Case 1 )

3.1.1 MOMENTS DUE TO SLENDERNESS.

Lex/D = 10.70
<12.HENCE NOT SLENDER
Lez/b = 7.13
<12.HENCE NOT SLENDER

3.1.2 MOMENTS DUE TO MINIMUM ECCENTRICITY

Minimum eccentricity in X-Dir. { Max [ (Lx/500 + D/30) , 20mm ] } ex = 27.37 mm
Moment due to minimum eccentricity in X-dir. {P* ex } Mzmin = 1.01 KN-m
Minimum eccentricity in Z-Dir. { Max [ (Lz/500 + b/30) , 20mm ] } ez = 35.70 mm
Moment due to minimum eccentricity in Z-dir. {P* ez } Mxmin = 1.32 KN-m

3.2 DESIGN MOMENTS AND DESIGN AXIAL LOAD THE COLUMN :

Load case 1.STATIC LOAD
{Mz*1.5} Muz = 1.21 KN-m
{Mx*1.5} Mux = 1.58 KN-m
{ P * 1.5 } Pu = 127.66 KN

Load case 2. STATIC LOAD +SESMIC LOAD

{Mz*1.2} Muz = 1.21 KN-m
{Mx*1.2} Mux = 12.18 KN-m
{ P * 1.2 } Pu = 102.13 KN

Load case 3. STATIC LOAD + WIND LOAD

{Mz*1.2} Muz = 1.21 KN-m
{Mx*1.2} Mux = 23.95 KN-m
{ P * 1.5 } Pu = 102.13 KN

3.2.1 Properties of reinforcement :

Diameter of lateral ties = 8 mm
Diameter of bar provided d = 20 mm.
No. of bars provided. N = 12 No.
% of reinforcement provided. Pt pro = 1.0 %
' VALUE OF Pt IS WITHIN LIMITS OF MAX. & MIN. Pt..'
 SUMMARY OF COLUMN DESIGN.
Longer dimension of column (D) = 500 mm
Shorter dimension of column (b) = 750 mm
Diameter of vertical main bars = 20 mm
No.of bars = 12 nos.
Diameter of lateral ties = 8 mm
Spacing of lateral ties = 190 mm

PART B :- DESIGN OF RECTANGULAR BOX FOOTING

3.0 DEFAULT DATA FOR FOOTING :
Clear cover at bottom for footing = 75 mm
Clear cover at sides and top for footing = 50 mm
Density of soil ds = 20.00 KN/m³

4.0 INPUT DATA FOR FOOTING :

Depth of bottom of footing below FFL h' = 5000 mm
Net SBC of soil at bottom of footing = 400.00 KN/m²
Considering the 25% higher SBC for EQ & WL Combinations = 500.00 KN/m²
Length of the footing along X-axis (Longer Dimension) Fx = 1500 mm
Length of the footing along Z-axis Fz = 1500 mm
Thickness of footing near column Tf1 = 450.00 mm
Effective depth of footing = 367.00 mm
Bar dia. Used = 16.00 mm

5.0 CALCULATIONS FOR FOOTING

Plan area of footing = { Fx * Fz } Af = 2.25 m²
Section modulus of footing for bending about X-Axis = {(Fx * Fz²)/6} Zx = 0.56 m³
Section modulus of footing for bending about Z-Axis = {(Fz * Fx²)/6} Zz = 0.56 m³
Selfweight of the footing = {volume of footing* density } = 24.30 KN
DL. of soil { (Fx*Fz*h'-volume of footing-vol. of col portion)* ds } = 170.63 KN

6.0 DESIGN OF R.C.C. BOX FOOTING

(Subjected to axial load and bending)
Net Pressure intensities for individual load
cases are calculated as follows :

Load case 1.STATIC LOAD

Max. gross pressure = ( P+Wt. of footing+Wt. of soil) /Af + Mx/Zx + Mz/Zz = 103.06 KN/m2
Min. gross pressure = ( P+Wt. of footing+Wt. of soil) /Af - Mx/Zx - Mz/Zz = 103.06 KN/m2
Max. gross pressure = ( P+Wt. of footing+Wt. of sioil) /Af - Mx/Zx + Mz/Zz = 103.06 KN/m2
Min. gross pressure = ( P+Wt. of footing+Wt. of sioil) /Af + Mx/Zx - Mz/Zz = 103.06 KN/m2
Max. net pressure = ( P+Wt. of footing) /Af + Mx/Zx + Mz/Zz = 27.22 KN/m2
Min. net pressure = ( P+Wt. of footing) /Af - Mx/Zx - Mz/Zz = 27.22 KN/m2
Max. net pressure = ( P+Wt. of footing) /Af - Mx/Zx + Mz/Zz = 27.22 KN/m2
Min. net pressure = ( P+Wt. of footing) /Af + Mx/Zx - Mz/Zz = 27.22 KN/m2

Load case 2.STATIC LOAD +SESMIC LOAD

Max. gross pressure = ( P+Wt. of footing+Wt. of sioil) /Af + Mx/Zx + Mz/Zz = 118.75 KN/m2
Min. gross pressure = ( P+Wt. of footing+Wt. of sioil) /Af - Mx/Zx - Mz/Zz = 87.36 KN/m2
Max. gross pressure = ( P+Wt. of footing+Wt. of sioil) /Af - Mx/Zx + Mz/Zz = 87.36 KN/m2
Min. gross pressure = ( P+Wt. of footing+Wt. of sioil) /Af + Mx/Zx - Mz/Zz = 118.75 KN/m2
 Max. net pressure = ( P+Wt. of footing) /Af + Mx/Zx + Mz/Zz = 42.92 KN/m2
Min. net pressure = ( P+Wt. of footing) /Af - Mx/Zx - Mz/Zz = 11.53 KN/m2
Max. net pressure = ( P+Wt. of footing) /Af - Mx/Zx + Mz/Zz = 11.53 KN/m2
Min. net pressure = ( P+Wt. of footing) /Af + Mx/Zx - Mz/Zz = 42.92 KN/m2

Load case 3.STATIC LOAD + WIND LOAD

Max. gross pressure = ( P+Wt. of footing+Wt. of sioil) /Af + Mx/Zx + Mz/Zz = 136.20 KN/m2
Min. gross pressure = ( P+Wt. of footing+Wt. of sioil) /Af - Mx/Zx - Mz/Zz = 69.92 KN/m2
Max. gross pressure = ( P+Wt. of footing+Wt. of sioil) /Af - Mx/Zx + Mz/Zz = 69.92 KN/m2
Min. gross pressure = ( P+Wt. of footing+Wt. of sioil) /Af + Mx/Zx - Mz/Zz = 136.20 KN/m2
Max. net pressure = ( P+Wt. of footing) /Af + Mx/Zx + Mz/Zz = 60.36 KN/m2
Min. net pressure = ( P+Wt. of footing) /Af - Mx/Zx - Mz/Zz = 5.91 KN/m2
Max. net pressure = ( P+Wt. of footing) /Af - Mx/Zx + Mz/Zz = 5.91 KN/m2
Min. net pressure = ( P+Wt. of footing) /Af + Mx/Zx - Mz/Zz = 60.36 KN/m2

FOOTING SAFE IN COMPRESSION!!! FOOTING SAFE IN TENTION!!!

6.1.1 BENDING MOMENTS FOR DESIGN OF FOOTING

Load case 1.STATIC LOAD

6.1.1. Bending Moment about X-direction at bottom of footing
Dist. of edge of footing from face of column along Z-dir. { (Fz-b)/2 } dz = 375.00 mm
Pressure ordinate at face of column X1 = 103.058 KN/m²
Pressure ordinate at face of column X2 = 27.225 KN/m²
Pressure ordinate at edge of footing X1 = 103.058 KN/m²
Pressure ordinate for maximum bending moment = 103.058 KN/m²
Max. Bending moment at the face of column, Mx1 = 10.869 KN-m
Ultimate Bending moment at the face of column, Mux1 = 16.304 KN-m

6.1.1. Bending Moment about Z-direction at bottom of footing

Dist. of edge of footing from face of column along X-dir. { (Fz-b)/2 } dz = 500.00 mm
Pressure ordinate at face of column X1 = 103.058 KN/m²
Pressure ordinate at face of column X2 = 27.225 KN/m²
Pressure ordinate at edge of footing X1 = 103.058 KN/m²
Pressure ordinate for maximum bending moment = 103.058 KN/m²
Max. Bending moment at the face of column, Mx1 = 19.323 KN-m
Ultimate Bending moment at the face of column, Mux1 = 28.985 KN-m

Load case 2.STATIC LOAD +SESMIC LOAD

6.1.1. Bending Moment about X-direction at bottom of footing
Dist. of edge of footing from face of column along Z-dir. { (Fz-b)/2 } dz = 375.00 mm
Pressure ordinate at face of column X1 = 110.906 KN/m²
Pressure ordinate at face of column X2 = 42.921 KN/m²
Pressure ordinate at edge of footing X1 = 118.754 KN/m²
Pressure ordinate for maximum bending moment = 118.754 KN/m²
Max. Bending moment at the face of column, Mx1 = 12.111 KN-m
Ultimate Bending moment at the face of column, Mux1 = 14.533 KN-m

6.1.1. Bending Moment about Z-direction at bottom of footing

Dist. of edge of footing from face of column along X-dir. { (Fz-b)/2 } dz = 500.00 mm
Pressure ordinate at face of column X1 = 108.290 KN/m²
Pressure ordinate at face of column X2 = 32.457 KN/m²
Pressure ordinate at edge of footing X1 = 118.754 KN/m²
Pressure ordinate for maximum bending moment = 118.754 KN/m²
Max. Bending moment at the face of column, Mx1 = 21.285 KN-m
Ultimate Bending moment at the face of column, Mux1 = 25.543 KN-m
 Load case 3.STATIC LOAD + WIND LOAD
6.1.1. Bending Moment about X-direction at bottom of footing
Dist. of edge of footing from face of column along Z-dir. { (Fz-b)/2 } dz = 375.00 mm
Pressure ordinate at face of column X1 = 119.627 KN/m²
Pressure ordinate at face of column X2 = 46.750 KN/m²
Pressure ordinate at edge of footing X1 = 60.363 KN/m²
Pressure ordinate for maximum bending moment = 119.627 KN/m²
Max. Bending moment at the face of column, Mx1 = 12.617 KN-m
Ultimate Bending moment at the face of column, Mux1 = 15.140 KN-m

6.1.1. Bending Moment about Z-direction at bottom of footing

Dist. of edge of footing from face of column along X-dir. { (Fz-b)/2 } dz = 500.00 mm
Pressure ordinate at face of column X1 = 114.104 KN/m²
Pressure ordinate at face of column X2 = 42.213 KN/m²
Pressure ordinate at edge of footing X1 = 136.196 KN/m²
Pressure ordinate for maximum bending moment = 136.196 KN/m²
Max. Bending moment at the face of column, Mx1 = 29.494 KN-m
Ultimate Bending moment at the face of column, Mux1 = 35.393 KN-m

6.1.2 Check for effective depth

Required effective depth = 130.760 mm
Hence overall depth required = 190.760 mm
SAFE IN BENDING!!!

6.1.3 Area of steel required = 182.13 sq.mm

Required spacing = 1103.959 mm
Hence provided spacing in both directions = 200.000 mm

No. of bars reqd. 8 Nos.

Actual Ast Provided 1005 mm²
pt provided = 0.274 %
Shear stress = 0.38 N/mm2

6.1.4 One way Shear

Load case 1.STATIC LOAD

Parallel to Z-direction :
Dist. of critical section from edge of footing along Z-dir. {dz-d} d1 = 8 mm
Depth of footing at critical section dzc = 367 mm
Width of footing at critical section bzc = 1500 mm
Area of footing at critical section azc = 0.55 m2
Shear stress = 0.38 N/mm2
Shear resisted by concrete = 207.9 KN
Pressure ordinate corr. to critical section X9 = 27.22 KN/m²
Pressure ordinate corr. to critical section X10 = 27.22 KN/m²
Pressure ordinate for maximum shear = 27.22 KN/m²
Shear at critical section = 0.22 KN
Ultimate shear at critical section 0.33 KN
SAFE IN ONE WAY SHEAR
Parallel to X-direction :
Dist. of critical section from edge of footing along X-dir. {dz-d} d1 = 133 mm
Depth of footing at critical section dzc = 367 mm
Width of footing at critical section bzc = 1500 mm
Area of footing at critical section azc = 0.55 m2
Shear stress = 0.38 N/mm2
Shear resisted by concrete = 207.9 KN
Pressure ordinate corr. to critical section X9 = 27.22 KN/m²
Pressure ordinate corr. to critical section X9 = 27.22 KN/m²
Pressure ordinate for maximum shear = 27.22 KN/m²
Shear at critical section = 3.62 KN
Ultimate shear at critical section 5.43 KN
SAFE IN ONE WAY SHEAR

Load case 2.STATIC LOAD +SESMIC LOAD

Parallel to Z-direction :
Dist. of critical section from edge of footing along Z-dir. {dz-d} d1 = 8 mm
Depth of footing at critical section dzc = 367 mm
Width of footing at critical section bzc = 1500 mm
Area of footing at critical section azc = 0.55 m2
Shear stress = 0.38 N/mm2
Shear resisted by concrete = 207.9 KN
Pressure ordinate corr. to critical section X9 = 42.75 KN/m²
Pressure ordinate corr. to critical section X10 = 42.92 KN/m²
Pressure ordinate for maximum shear = 42.92 KN/m²
Shear at critical section = 0.34 KN
Ultimate shear at critical section 0.52 KN
SAFE IN ONE WAY SHEAR
Parallel to X-direction :
Dist. of critical section from edge of footing along X-dir. {dz-d} d1 = 133 mm
Depth of footing at critical section dzc = 367 mm
Width of footing at critical section bzc = 1500 mm
Area of footing at critical section azc = 0.55 m2
Shear stress = 0.38 N/mm2
Shear resisted by concrete = 207.9 KN
Pressure ordinate corr. to critical section X9 = 40.14 KN/m²
Pressure ordinate corr. to critical section X10 = 42.92 KN/m²
Pressure ordinate for maximum shear = 42.92 KN/m²
Shear at critical section = 5.71 KN
Ultimate shear at critical section = 8.56 KN
SAFE IN ONE WAY SHEAR

Load case 3.STATIC LOAD + WIND LOAD

Parallel to Z-direction :
Dist. of critical section from edge of footing along Z-dir. {dz-d} d1 = 8 mm
Depth of footing at critical section dzc = 367 mm
Width of footing at critical section bzc = 1500 mm
Area of footing at critical section azc = 0.55 m2
Shear stress = 0.38 N/mm2
Shear resisted by concrete = 207.9 KN
Pressure ordinate corr. to critical section X9 = 60.07 KN/m²
Pressure ordinate corr. to critical section X10 = 60.36 KN/m²
Pressure ordinate for maximum shear = 60.36 KN/m²
Shear at critical section = 0.48 KN
Ultimate shear at critical section 0.72 KN
SAFE IN ONE WAY SHEAR
Parallel to X-direction :
Dist. of critical section from edge of footing along X-dir. {dz-d} d1 = 133 mm
Depth of footing at critical section dzc = 367 mm
Width of footing at critical section bzc = 1500 mm
Area of footing at critical section azc = 0.55 m2
Shear stress = 0.38 N/mm2
Shear resisted by concrete = 207.9 KN
Pressure ordinate corr. to critical section X9 = 55.53 KN/m²
 Pressure ordinate corr. to critical section X10 = 60.36 KN/m²
Pressure ordinate for maximum shear = 60.36 KN/m²
Shear at critical section = 8.03 KN
Ultimate shear at critical section = 12.04 KN
SAFE IN ONE WAY SHEAR

6.1.5 Two way (Punching) Shear

Load case 1.STATIC LOAD

(Critical section is at a distance 'd/2'allround from the face of column )
Perimeter at critical section = 3.968 m
Effective area {Af - (D+d)*(b+d)} = 0.79 m²
Punching force={(qP'+qS'+qQ'+qR')*Effec. area/4-dc*Effec. area*Density*LF} = 81.80 KN
Ultimate shear = 122.703 KN
ßc = Ratio of short side to long side of column = { b / D } ßc = 0.667
Ks={0.5 + ßc} [Max. 1.0] (Cl.34.2.4 b of IS:456-2000 ) Ks = 1.000
tc={0.25 * Sqrt(fck)} tc = 1.369 N/mm²
Permissible shear stress {Ks * tc} = 1.369 N/mm²
Shear area = 1.456 m²
Permissible shear force = 1994.06 KN
SAFE IN TWO WAY SHEAR

Load case 2.STATIC LOAD +SESMIC LOAD

(Critical section is at a distance 'd/2'allround from the face of column )
Perimeter at critical section = 3.968 m
Effective area {Af - (D+d)*(b+d)} = 0.79 m²
Punching force={(qP'+qS'+qQ'+qR')*Effec. area/4-dc*Effec. area*Density*LF} = 81.80 KN
Ultimate shear = 122.703 KN
ßc = Ratio of short side to long side of column = { b / D } ßc = 0.667
Ks={0.5 + ßc} [Max. 1.0] (Cl.34.2.4 b of IS:456-2000 ) Ks = 1.000
tc={0.25 * Sqrt(fck)} tc = 1.369 N/mm²
Permissible shear stress {Ks * tc} = 1.369 N/mm²
Shear area = 1.456 m²
Permissible shear force = 1994.06 KN
SAFE IN TWO WAY SHEAR

Load case 3.STATIC LOAD + WIND LOAD

(Critical section is at a distance 'd/2'allround from the face of column )
Perimeter at critical section = 3.968 m
Effective area {Af - (D+d)*(b+d)} = 0.79 m²
Punching force={(qP'+qS'+qQ'+qR')*Effec. area/4-dc*Effec. area*Density*LF} = 81.80 KN
Ultimate shear = 122.703 KN
ßc = Ratio of short side to long side of column = { b / D } ßc = 0.667
Ks={0.5 + ßc} [Max. 1.0] (Cl.34.2.4 b of IS:456-2000 ) Ks = 1.000
tc={0.25 * Sqrt(fck)} tc = 1.369 N/mm²
Permissible shear stress {Ks * tc} = 1.369 N/mm²
Shear area = 1.456 m²
Permissible shear force = 1994.06 KN
SAFE IN TWO WAY SHEAR

SUMMARY OF FOOTING DESIGN

Length of the footing along X-axis = 1500 mm
Length of the footing along Z-axis = 1500 mm
Thickness of footing = 450 mm
BOTTOM REINFORCEMENT
ALONG FZ === 16 @ 200 mm C/C
ALONG FX === 16 @ 200 mm C/C
TOP REINFORCEMENT
ALONG FZ === 0 @ 0 mm C/C
ALONG FX === 0 @ 0 mm C/C
Lateral reinforcement in footing not required
 DESIGN OF RECTANGULAR COLUMN
WITH BIAXIAL BENDING (USING SP 16)
LOAD CASE 1 : STATICS LOAD
1 MATERIAL PARAMETERS 500
Z
Grade of concrete fck M 30

###
Grade of steel fy Fe 500

2 SECTION PROPERTIES
X
Side dimension along X direction 500 mm
Side dimension along Z direction 750 mm

3 LOADS
Factored axial load Pu 128 KN
Factored moment about X-X Mux 1.58 KNm
Factored moment about Z-Z Muz 1.21 KNm

4 ASSUMPTION
Let percentage of steel p 1.00531 %
Cover to reinforcement d' 40 mm

5 DESIGN

p = 1.0053 = 0.03
fck 30

5 Uniaxial moment capacity of the section about X-X axis :

d' = 40 = 0.053
D 750

Hence chart for d'/D = 0.05 will be used

Pu = 128 x 1000 = 0.01

fck bD 30 x 500 x 750

Mu = 0.06
fck bD2

MuX1 = 0.06 x 30 x 500 x 750 x 750

 = 506.25 KNm

5 Uniaxial moment capacity of the section about Z-Z axis :

d' = 40 = 0.08
D 500

Hence chart for d'/D = 0.10 will be used

Pu = 128 x 1000 = 0.011

fck bD 30 x 750 x 500

Mu = 0.055
fck bD2

Muz1 = 0.055 x 30 x 750 x 500 x 500

= 309.375 KNm

5 Calculation of Puz
Referring to chart 63, corresponding to
p = 1.0053 fy = 500 fck = 30

Puz = 16
Ag

Puz = 16 x 500 x 750

= 6000 KN

5 Calculation of interaction ratio :

Muy an + Muz an < 1

Muy1 Muz1

Pu = 128 = 0.021
Puz 6000

an = 1

Interaction ratio = 1.583 1 + 1.2136 1 = 0.00705 Hence OK

506 309.38
 DESIGN OF RECTANGULAR COLUMN
WITH BIAXIAL BENDING (USING SP 16)
LOAD CASE 2:-STATIC LOAD + SESMIC LOAD
1 MATERIAL PARAMETERS 500
Z
Grade of concrete fck M 30

750
Grade of steel fy Fe 500

2 SECTION PROPERTIES
X
Side dimension along X direction 500 mm
Side dimension along Z direction 750 mm

3 LOADS
Factored axial load Pu 103 KN
Factored moment about X-X Mux 12.18 KNm
Factored moment about Z-Z Muz 1.21 KNm

4 ASSUMPTION
Let percentage of steel p 1.01 %
Cover to reinforcement d' 40 mm

5 DESIGN

p = 1.005 = 0.0335
fck 30

5 Uniaxial moment capacity of the section about X-X axis :

d' = 40 = 0.0533
D 750

Hence chart for d'/D = 0.05 will be used

Pu = 103 x 1000 = 0.01

fck bD 30 x 500 x 750

Mu = 0.06
fck bD2

MuX1 = 0.06 x 30 x 500 x 750 x 750

 = 506.25 KNm

5 Uniaxial moment capacity of the section about Z-Z axis :

d' = 40 = 0.08
D 500

Hence chart for d'/D = 0.10 will be used

Pu = 103 x 1000 = 0.009

fck bD 30 x 750 x 500

Mu = 0.055
fck bD2

Muz1 = 0.055 x 30 x 750 x 500 x 500

= 309.375 KNm

5 Calculation of Puz
Referring to chart 63, corresponding to
p = 1.005 fy = 500 fck = 30

Puz = 16
Ag

Puz = 16 x 500 x 750

= 6000 KN

5 Calculation of interaction ratio :

Muy an + Muz an < 1

Muy1 Muz1

Pu = 103 = 0.0172
Puz 6000

an = 1

Interaction ratio = 12.178 1 + 1.2136 1 = 0.028 Hence OK

506.25 309.38
 DESIGN OF RECTANGULAR COLUMN
WITH BIAXIAL BENDING (USING SP 16)
LOAD CASE 3 :-STATIC LOAD + WIND LOAD
1 MATERIAL PARAMETERS 500
Z
Grade of concrete fck M 30

750
Grade of steel fy Fe 500

2 SECTION PROPERTIES
X
Side dimension along Y direction 500 mm
Side dimension along Z direction 750 mm

3 LOADS
Factored axial load Pu 103 KN
Factored moment about X-X Mux 23.95 KNm
Factored moment about Z-Z Muz 1.21 KNm

4 ASSUMPTION
Let percentage of steel p 1.00531 %
Cover to reinforcement d' 40 mm

5 DESIGN

p = 1.0053 = 0.0335
fck 30

5 Uniaxial moment capacity of the section about X-X axis :

d' = 40 = 0.0533
D 750

Hence chart for d'/D = 0.05 will be used

Pu = 103 x 1000 = 0.01

fck bD 30 x 500 x 750

Mu = 0.06
fck bD2

MuX1 = 0.06 x 30 x 500 x 750 x 750

 = 506.25 KNm

5 Uniaxial moment capacity of the section about Z-Z axis :

d' = 40 = 0.08
D 500

Hence chart for d'/D = 0.10 will be used

Pu = 103 x 1000 = 0.009

fck bD 30 x 750 x 500

Mu = 0.055
fck bD2

Muz1 = 0.055 x 30 x 750 x 500 x 500

= 309.375 KNm

5 Calculation of Puz
Referring to chart 63, corresponding to
p = 1.0053 fy = 500 fck = 30

Puz = 16
Ag

Puz = 16 x 500 x 750

= 6000 KN

5 Calculation of interaction ratio :

Muy an + Muz an < 1

Muy1 Muz1

Pu = 103 = 0.0172
Puz 6000

an = 1

Interaction ratio = 23.951 1 + 1.2136 1 = 0.0512 Hence OK

506.25 309.38
 PART B :- DESIGN OF COMBINED FOOTING

4.0 DEFAULT DATA FOR FOOTING :

Clear cover at bottom for footing =
Clear cover at sides and top for footing =
Coefficient of friction against sliding m =
Factor of safety against sliding ( As per Cl. 20.2 of IS:456-2000 ) FOSs =
Factor of safety against overturning (As per Cl. 20.1 of IS:456-2000) FOSo =
Density of soil ds =
Unit weight of concrete =

5.0 INPUT DATA FOR FOOTING :

Centre to centre spacing of columns =
Depth of bottom of footing below FFL h' =
Net SBC of soil at bottom of footing =
Length of the footing along X-axis (Longer Dimension) Fx =
Length of the footing along Z-axis Fz =
Width of beam =
Depth of beam =
Depth of slab =

6.0 CALCULATIONS FOR FOOTING

Plan area of footing = { Fx * Fz } Af =
Section modulus of footing for bending about X-Axis = {(Fx * Fz²)/6} Zx =
Section modulus of footing for bending about Z-Axis = {(Fz * Fx²)/6} Zz =
Selfweight of the footing = {volume of footing* density } =
DL. of soil { (Fx*Fz*h'-volume of footing-vol. of col portion)* ds } =
Selfweight of the footing per meter = =
Catelever distance of footing from centre of column(longer direction) =

6.1 DESIGN OF COMBINED R.C.C. FOOTING

(Subjected to axial load and bending)
6.1.1 Net Pressure intensities for individual load
cases are calculated as follows :

Load case 1. DL. + LL.

Momet at centre of footing about X-Axis =
Momet at centre of footing about Z-Axis =
Max. gross pressure = ( P+Wt. of footing+Wt. of sioil) /Af + Mx/Zx + Mz/Zz =
Min. gross pressure = ( P+Wt. of footing+Wt. of sioil) /Af - Mx/Zx - Mz/Zz =
Max. net pressure = ( P+Wt. of footing) /Af + Mx/Zx + Mz/Zz =
Min. net pressure = ( P+Wt. of footing) /Af - Mx/Zx - Mz/Zz =

Load case 2. DL. + LL. + WL (across conveyor) +ve

Momet at centre of footing about X-Axis =
Momet at centre of footing about Z-Axis =
Max. gross pressure = ( P+Wt. of footing+Wt. of sioil) /Af + Mx/Zx + Mz/Zz =
Min. gross pressure = ( P+Wt. of footing+Wt. of sioil) /Af - Mx/Zx - Mz/Zz =
Max. net pressure = ( P+Wt. of footing) /Af + Mx/Zx + Mz/Zz =
Min. net pressure = ( P+Wt. of footing) /Af - Mx/Zx - Mz/Zz =
 Load case 2. DL. + LL. + WL (across conveyor) +ve
Momet at centre of footing about X-Axis =
Momet at centre of footing about Z-Axis =
Max. gross pressure = ( P+Wt. of footing+Wt. of sioil) /Af + Mx/Zx + Mz/Zz =
Min. gross pressure = ( P+Wt. of footing+Wt. of sioil) /Af - Mx/Zx - Mz/Zz =
Max. net pressure = ( P+Wt. of footing) /Af + Mx/Zx + Mz/Zz =
Min. net pressure = ( P+Wt. of footing) /Af - Mx/Zx - Mz/Zz =

FOOTING SAFE IN COMPRESSION REVISE FOOTING AREA

6.1.2 Shear force & Bending moment (for beam design)

Load case 1. DL. + LL.

Pressure ordinate at column C1 =
Pressure ordinate at column C1 =
Shear at column C1 =
=
Shear at column C2 =
=
Point of zero shear (Q) =
Bending moment at column C1 =
=
Bending moment at column C2 =
=
Bending moment at point of zero shear (Q) =

Load case 2. DL. + LL. + WL (across conveyor) +ve

Pressure ordinate at column C1 =
Pressure ordinate at column C2 =
Shear at column C1 =
=
Shear at column C2 =
=
Point of zero shear (Q) =
Pressure ordinate at zero shear =
Bending moment at column C1 =
=
Bending moment at column C2 =
=
Bending moment at point of zero shear (Q) =

6.2 Beam design

Load case 1. DL. + LL.
Maximum saging bending moment in the beam =
Maximum hogging bending moment in the beam =
Maximum shear force in the beam =

Load case 2. DL. + LL. + WL (across conveyor) +ve

 Maximum saging bending moment in the beam =
Maximum hogging bending moment in the beam =
Maximum shear force in the beam =

Ultimate saging bending moment in the beam =

Ultimate hogging bending moment in the beam =
Ultimate shear in beam =

Max moment resisting capacity of beam =

Max shear capacity of beam =
Area of steel required for sagging bending moment TOP STEEL =
Area of steel required for sagging bending moment BOTTOM STEEL =

SAFE IN SHEAR SAFE IN BENDING

Provide 25 # bars
Hence no. of bars required = 2.00
Number of bars provided = 4

6.3 Slab design

Clear Cantilever of slab =

Load case 1. DL. + LL.
Upward pressure on slab =
Maximum bending moment =
Maximum shear force =
Shear at distance "d", from face of beam =

Load case 2. DL. + LL. + WL (across conveyor) +ve

Upward pressure on slab =
Maximum bending moment =
Maximum shear force =
Shear at distance "d", from face of beam =

Maximum ultimate bending momet for slab design =

Maximum ultimate shear force in slab =

Depth of slab =
Effetive depth of slab =
Required effective depth of slab =
Area of steel required =
Provide bar diameter =
Required spacing of bars =
Hence provide 16 # @ 150 mm spacing

Distributation steel required =

Provide distributation steel bar diameter =
Required spacing of bars =
Hence provide 8 # @ 150 mm spacing
 Check for shear
Area of steel provided =
Percentage steel provided =
Permissible shear stress =
Shear resisted by concrete =
HENCE SAFE!!!

6.4 Check for two-way shear

The critical section is taken at db/2 from face of column & half the effective depth
of slab ds/2 on other side

Area of critical section =

Shear stress resisted by concrete =
Hence shear resisted by concrete =
Design shear =
HENCE SAFE!!!

SUMMARY OF DESIGN.
Length of footing = 6000 mm
Breadth of footing = 2000 mm
Width of beam = 700 mm
Depth of beam = 450 mm
Diameter of longitudinal main bars = 25 mm
No.of top bars = 4 nos.
No.of bottom bars
Diameter of stirrups = 0 mm
Spacing of stirrups = 0 mm
Depth of slab = 150 mm
Main steel in slab = 16 mm
Spacing of main steel = 150 mm
Distributation steel in slab = 8 mm
Spacing of distibutation steel = 150 mm
 75 mm
50 mm
0.4
1.4
1.4
8.00 KN/m³ Z
24 KN/m³ 2000

2500 mm
2000 mm
90.00 KN/m²
2000 mm
6000 mm
700.00 mm X X
450.00 mm
150.00 mm
6000

12.00 m²
12.00 m³
4.00 m³
73.44 KN Z
177.60 KN
12.24 KN/m
1.75 m

0 KNm
0 KNm
27.08 KN/m²
27.08 KN/m²
12.28 KN/m²
12.28 KN/m²

274.25 KNm
0 KNm
49.93 KN/m²
4.23 KN/m²
35.13 KN/m²
-10.57 KN/m²
 274.25 KNm
0 KNm
49.93 KN/m²
4.23 KN/m²
35.13 KN/m²
-10.57 KN/m²

21.56 KN
-15.40 KN
15.40 KN
-21.56 KN
3 m
18.86 KNm
18.86 KNm
18.86 KNm
18.86 KNm
9.24 KNm

5.51 KN/m²
43.60 KN/m²
-35.10 KN
-72.06 KN
-41.26 KN
-78.22 KN
7.60 m
94.64 KN/m
-37.52 KNm
-18.88 KNm
-190.18 KNm Check
-171.54 KNm 75.2445
-47.21 KNm
MOMENTS DO NOT MATCH

18.86 KNm
0.00 KNm
21.56 KN
 0.00 KNm
-190.18 KNm
78.22 KN

28.29 KNm
285.26 KNm
117.33

231.84 KNm
252.00 KN
645.18 sq.mm
2692.62 sq.mm

SAFE IN BENDING

0.75 m

12.28 KN/m
3.45 KNm
9.21 KN
6.22 KN

35.13 KN/m
9.88 KNm
26.35 KN
17.79 KN

26.68 KNm
39.53 KN

150.00 mm
75.00 mm
113.53 mm
1074.96 sqmm
16 #
187.042 mm

225 sqmm
8 #
223.402 mm
 1340.41 sqmm
1.79 %
0.6
45 KN
ENCE SAFE!!!

736250 sqmm
1.37 N/sqmm
1008.15 KN
36.96 KN
ENCE SAFE!!!
 DESIGN OF COLUMN & COMBINED FOOTING

1.0 DEFAULT VALUES

1.1 Material Properties :

1.1.1 Grade of Conc:( M 15/20/25/30/35/40 ) fck = 35 N/mm²
1.1.2 Grade of steel:( Fe 250/415/500 ) fy = 415 N/mm²
1.2 Unit weight of concrete = 24000 N/m³
1.3 Cover to reinforcement in Z- Direction = 40.00 mm
1.4 Cover to reinforcement in X- Direction = 40.00 mm

2.0 INPUT DATA

2.1 GENERAL DATA

2.1.1 Unit : KN AND METER

2.1.2 Joint no : -------
2.1.3 Column no. : H1,H2 G1,G2
2.1.4 Reference drawing no. : A1,A2 B1,B2
2.1.6 Remarks :

2.2 DIMENSIONS OF COLUMN

H1,H2 G1,G2 UNITS
2.2.1 Longer dimension of column along X axis. D = 900 1800 mm
2.2.2 Shorter dimension of column along Z axis. b = 762 762 mm
2.2.3 Unsupported length for bending parallel to larger dimension Lx = 3.12 3.12 m
2.2.4 Unsupported length for bending parallel to shorter dimension. Lz = 3.12 3.12 m

(Unsupported length as per clause 25.1.3 of IS:456-2000 )

2.2.5 Multi. Factor for calculating eff. Length for bending about Z axis. rx = 1.0 1.0
2.2.6 Multi. Factor for calculating eff. Length for bending about X axis. rz = 1.0 1.0
Unsupported length multiplication factor as per annex E Table 28, pg 94 of IS:456
-2000 for calculation of effective length depending on end restraint conditions.
Effective length of bending parallel to larger dimension. { Lx * rx } Lex = 3.12 3.12 m
Effective length of bending parallel to shorter dimension. { Lz * rz } Lez = 3.12 3.12 m

2.3 LOADS ON COLUMN

2.3.1 LOAD CASES CONSIDERED :

1.( STATIC LOAD + SESMIC LOAD ) = ((DL+LL+EQZ) FOR MAX. Mx AT NODE 43 (COL. G1)

2.( STATIC LOAD + SESMIC LOAD) =((DL+LL+EQX) FOR MAX. FY AT NODE 22 (COL. H2)
AND MAX MZ AT NODE 19 (COL. G2)

3.( STATIC LOAD + SESMIC LOAD) =((DL+LL+EQX) FOR MIN. FY AT NODE 19(COL. G2)
AND MAX MX AT NODE 22 (COL. H2)
H1 G1 UNITS
2.3.2 Load case 1.STATIC LOAD + SESMIC LOAD X Self wt = 51.35 102.71 KN
Axial load on compression member inclusive of selfweight. P = 6479.00 9702.00 KN
Moment in the direction of larger dimension (i.e. about Z axis ) Mz = 426.48 73.65 KN-M
Moment in the direction of shorter dimension ( ie. about X axis ) Mx = 159.00 523.00 KN-M

Load case 2. STATIC LOAD + SESMIC LOAD Z H2 G2 UNITS

Axial load on compression member inclusive of selfweight. P = 6479.00 9702.00 KN
Moment in the direction of larger dimension (ie. about Z axis ) Mz = 426.48 73.65 KN-M
Moment in the direction of shorter dimension ( i.e. about X axis ) Mx = 159.00 523.00 KN-M

Load case 3. STATIC LOAD + SESMIC LOAD X H2 G2 UNITS

Axial load on compression member inclusive of selfweight. P = 6479.00 9702.00 KN
Moment in the direction of larger dimension (i.e. about Z axis ) Mz = 426.48 73.65 KN-M
Moment in the direction of shorter dimension ( i.e. about X axis ) Mx = 159.00 523.00 KN-M
3 PART A :- DESIGN OF COLUMN H1,H2 G1,G2 UNITS
Longer dimension of column along X axis. D = 900 1800 mm
Shorter dimension of column along Z axis. b = 762 762 mm
Cover to reinforcement in Z- Direction = 40.00 mm mm
Cover to reinforcement in X- Direction = 40.00 mm mm

3.1 CALCULATIONS

3.1.1 MOMENTS DUE TO SLENDERNESS. H1,H2 G1,G2 UNITS

Lex/D = 3.47 1.73
<12.HENCE NOT SLENDER
Lez/b = 4.09 4.09
<12.HENCE NOT SLENDER

3.1.2 MOMENTS DUE TO MINIMUM ECCENTRICITY H1,H2 G1,G2 UNITS

Minimum eccentricity in X-Dir. { Max [ (Lx/500 + D/30) , 20mm ] } ex = 36.24 66.24 mm
Moment due to minimum eccentricity in X-dir. {P* ex } Mzmin = 234.80 642.66 KN-m
Minimum eccentricity in Z-Dir. { Max [ (Lz/500 + b/30) , 20mm ] } ez = 31.64 31.64 mm
Moment due to minimum eccentricity in Z-dir. {P* ez } Mxmin = 205.00 306.97 KN-m

3.2 DESIGN MOMENTS AND DESIGN AXIAL LOAD ON COLUMN :

Load case 1.STATIC LOAD +SESMIC LOAD X H1 G1 UNITS
{Mz*1.2} Muz = 793.53 859.58 KN-m
{Mx*1.2} Mux = 436.79 995.97 KN-m
{ P * 1.2 } Pu = 7774.80 11642.40 KN

Load case 2. STATIC LOAD +SESMIC LOADZ H2 G2 UNITS

{Mz*1.2} Muz = 793.53 859.58 KN-m
{Mx*1.2} Mux = 436.79 995.97 KN-m
{ P * 1.2 } Pu = 7774.80 11642.40 KN

Load case 3. STATIC LOAD + SESMIC LOAD X H2 G2 UNITS

{Mz*1.2} Muz = 793.53 859.58 KN-m
{Mx*1.2} Mux = 436.79 995.97 KN-m
{ P * 1.2 } Pu = 7774.80 11642.40 KN

3.2.1 Properties of reinforcement : H1,H2 G1,G2 UNITS

Diameter of lateral ties = 8 8 mm
Diameter of bar provided d = 25 25 mm.
No. of bars provided. N = 18 30 No.
% of reinforcement provided. Pt pro = 1.3 1.1 %
' VALUE OF Pt IS WITHIN LIMITS OF MAX. & MIN. Pt..'

3.4 LATERAL TIES

3.4.1 Spacing of the lateral ties = {Min ( 300mm, 16*dia. of main rein., ' b')} = 190 190 mm
Cl. 26.5.3.2 c of IS:456-2000

SUMMARY OF COLUMN DESIGN.

H1,H2 G1,G2 UNITS

Longer dimension of column (D) = 900 1800 mm
Shorter dimension of column (b) = 762 762 mm
Diameter of vertical main bars = 25 25 mm
No.of bars = 18 30 nos.
Diameter of lateral ties = 8 8 mm
Spacing of lateral ties = 190 190 mm
 PART B :- DESIGN OF SLAB AND BEAM TYPE COMBINED FOOTING

4.0 DEFAULT DATA FOR FOOTING :

Clear cover at bottom for footing = 75 mm
Clear cover at sides and top for footing = 50 mm
Density of soil ds = 20.00 KN/m³
Unit weight of concrete = 24 KN/m³

5.0 INPUT DATA FOR FOOTING :

Centre to centre spacing of columns = 3150 mm
Depth of bottom of footing below FFL h' = 1500 mm
Net SBC of soil at bottom of footing = 450.00 KN/m²
Considering the 25% higher SBC for EQ & WL Combinations = 563.00 KN/m²
Length of the footing along X-axis (Longer Dimension) L = 6600 mm
Length of the footing along Z-axis (Shorter Dimension) B = 6600 mm
Width of beam = 2100.00 mm
Depth of beam = 1650.00 mm
Depth of slab = 1450.00 mm

DECIDING THE SIZE OF FOOTING

b1
H1,H2 G1,G2

X LONGITUDINAL BEAM B X

L
a1 X1 X2 a2

Z
 LOAD CASE 1 LOAD CASE2 LOAD CASE 3

Total working load on =P = H1 + G1 =P = H2 + G2 =P = H2 + G2

footing due to both
columns = 6479 + 9702 = 6479 + 9702 = 6479 + 9702
= 16181KN = 16181KN = 16181KN
Self weight of footing = 3236.2KN = 3236.2KN = 3236.2KN
20% of axial loading
Total working load on
footing due to both
columns +self Wt of = 19417.2KN = 19417.2KN = 19417.2KN
footing
Area of footing required = 19417.2 / 450 = 19417.2 / 450 = 19417.2 / 450
Af = 43.1Sqt m = 43.145Sqt m = 43.145Sqt m

C.G of col. load (X1) 1.889 m 1.889 1.889 m

C.G of col. load (X2) 1.261 m 1.261 1.261 m

Length of footing 6.600 m 6.600 6.600 m
required
Width of footing required
6.538 m 6.538 6.538 m
=Af / L

a1 = = 3.3 - 1.85 = 3.3 - 1.85 = 3.3 - 1.885

1.411 m 1.411 1.411 m
Available a1 = 1.414 m 1.414 1.414 m

a2 = = 3.3 - 1.26 m = 3.3 - 1.25 = 3.3 - 1.25

2.039 m 2.039 2.039
Available a2 = 2.036 m 2.036 2.036 m

Eccentricity of Resultant
load due to shifting of 0.000 m 0.000 0.000 m
C.G "ex"=

Moment in footing due to

0 KN-m 0 0 KN-m
shifting of Resultant load

6.0 CALCULATIONS FOR FOOTING

Plan area of footing = { Fx * Fz } Af = 43.56 m²
Section modulus of footing for bending about X-Axis = {(Fx * Fz²)/6} Zx = 47.92 m³
Section modulus of footing for bending about Z-Axis = {(Fz * Fx²)/6} Zz = 47.92 m³
Selfweight of the footing = {volume of footing* density } = 1582.42 KN
DL. of soil { (Fx*Fz*h'-volume of footing-vol. of col portion)* ds } = 43.56 KN
Selfweight of the footing per meter = = 239.76 KN/m

6.1 DESIGN OF COMBINED R.C.C. FOOTING

(Subjected to axial load and bending)
6.1.1 Net Pressure intensities for individual load
cases are calculated as follows :

LOAD CASE 1

Max. gross pressure

=( P+Wt. of footing+Wt. of soil) /Af = (6479+9702+1582.416+43.5600000000001 )/43.56
+ (MxG1 +MxH1)/Zx = (159 + 523 ) / 47.9 = 433.46 KN/m²
+ (MzG1 +MzH1)/Zz = (426.48 + 73.653 ) / 47.9
+ (Mx)/Zx = 0 / 47.9
Min. gross pressure
=( P+Wt. of footing+Wt. of soil) /Af = (6479+9702+1582.416+43.5600000000001 )/43.56
- (MxG1 +MxH1)/Zx = (159 + 523 ) / 47.9 = 384.12 KN/m²
- (MzG1 +MzH1)/Zz = (426.48 + 73.653 ) / 47.9
- (Mx)/Zx = 0 / 47.9
Max. net pressure
=( P+Wt. of footing) /Af = (6479+9702+1582.416)/43.56
+ (MxG1 +MxH1)/Zx = (159 + 523 ) / 47.9 = 432.46 KN/m²
+ (MzG1 +MzH1)/Zz = (426.48 + 73.653 ) / 47.9
+ (Mx)/Zx = 0 / 47.9
Min. net pressure
=( P+Wt. of footing) /Af = (6479+9702+1582.416)/43.56
- (MxG1 +MxH1)/Zx = (159 + 523 ) / 47.9 = 346.79 KN/m²
- (MzG1 +MzH1)/Zz = (426.48 + 73.653 ) / 47.9
- (Mx)/Zx = 0 / 47.9

LOAD CASE 2

Max. gross pressure =

=( P+Wt. of footing+Wt. of soil) /Af = (6479+9702+1582.416+43.5600000000001 )/43.56
+ (MxG1 +MxH1)/Zx = (159 + 523 ) / 47.9 = 433.46 KN/m²
+ (MzG1 +MzH1)/Zz = (426.48 + 73.653 ) / 47.9
+ (Mx)/Zx = 0 / 47.9
Min. gross pressure =
=( P+Wt. of footing+Wt. of soil) /Af = (6479+9702+1582.416+43.5600000000001 )/43.56
- (MxG1 +MxH1)/Zx = (159 + 523 ) / 47.9 = 384.12
- (MzG1 +MzH1)/Zz = (426.48 + 73.653 ) / 47.9
- (Mx)/Zx = 0 / 47.9
Max. net pressure
=( P+Wt. of footing) /Af = (6479+9702+1582.416 )/43.56
+ (MxG1 +MxH1)/Zx = (159 + 523 ) / 47.9 = 432.46 KN/m²
+ (MzG1 +MzH1)/Zz = (426.48 + 73.653 ) / 47.9
+ (Mx)/Zx = 0 / 47.9
Min. net pressure
=( P+Wt. of footing) /Af = (6479+9702+1582.416 )/43.56
- (MxG1 +MxH1)/Zx = (159 + 523 ) / 47.9 = 383.12 KN/m²
- (MzG1 +MzH1)/Zz = (426.48 + 73.653 ) / 47.9
- (Mx)/Zx = 0 / 47.9

LOAD CASE 3

Max. gross pressure

=( P+Wt. of footing+Wt. of soil) /Af = (6479+9702+1582.416+43.5600000000001 )/43.56
+ (MxG1 +MxH1)/Zx = (159 + 523 ) / 47.9 = 433.46 KN/m²
+ (MzG1 +MzH1)/Zz = (426.48 + 73.653 ) / 47.9
+ (Mx)/Zx = 0 / 47.9
Min. gross pressure
=( P+Wt. of footing+Wt. of soil) /Af = (6479+9702+1582.416+43.5600000000001 )/43.56
- (MxG1 +MxH1)/Zx = (159 + 523 ) / 47.9
- (MzG1 +MzH1)/Zz = (426.48 + 73.653 ) / 47.9 = 384.12 KN/m²
- (Mx)/Zx = 0 / 47.9
Max. net pressure
=( P+Wt. of footing) /Af = (6479+9702+1582.416 )/43.56
+ (MxG1 +MxH1)/Zx = (159 + 523 ) / 47.9 = 432.46 KN/m²
+ (MzG1 +MzH1)/Zz = (426.48 + 73.653 ) / 47.9
+ (Mx)/Zx = 0 / 47.9
Min. net pressure
=( P+Wt. of footing) /Af = (6479+9702+1582.416 )/43.56
- (MxG1 +MxH1)/Zx = (159 + 523 ) / 47.9
- (MzG1 +MzH1)/Zz = (426.48 + 73.653 ) / 47.9 = 383.12 KN/m²
- (Mx)/Zx = 0 / 47.9

FOOTING SAFE IN COMPRESSION FOOTING SAFE IN TENTION

6.1.2 SHEAR FORCE AND BENDING MOMENTS FOR BEAM DESIGN

Load case 1: Axial load on column H1 = 6479 KN G1 = 9702 KN

Load case 2: Axial load on column H2 = 6479 KN G2 = 9702 KN

Load case 3: Axial load on column H2 = 6479 KN G2 = 9702 KN

H1, G1
H1,
A BH2 C D E F

a1 X1 X2 a2

PRESSURE DISTRIBUTION DIAGRAM

Load case 1.

Pmin = 346.75KN/M2
Pmax = 433.45KN/M2

Load case 2.

Pmin = 383.1KN/M2
Pmax = 433.45KN/M2

Load case 3.

Pmin = 383.1KN/M2
Pmax = 433.45KN/M2

ASSUMED PRESSURE DISTRIBUTION DIAGRAM

Load Case 1 Pmax = 433.45KN/M2

Load Case 2 Pmax = 433.45KN/M2
Load Case 3 Pmax = 433.45KN/M2

A B C D E F S.F DIAGRAM

O
 SHEAR FORCE
LOAD CASE 1 LOAD CASE 2 LOAD CASE 3
Vu,AB in KN 4045.2488 0 0
Vu,BC in KN -2433.751 0 0
Vu,CB in KN 2757.86 2750.096 2750.096
Vu,CD in KN -1146.37 -1154.13 -1154.13
Vu,DC in KN 6577.94 6570.17 6570.174
Vu,EDin KN -8399.47 -8407.24 -8407.24
Vu,EF in KN 0 0 0
Point of zero shear = at O-O 2.30 2.30 2.30 m

BENDING MOMENTS
B.M at C in KN-M 2859.91 2859.906 2859.906
B.M at D in KN-M 9386.2069 9386.207 9386.207 HOGGING TOP
B.M at O in KN-M 1826.2721 1826.014 1826.014 SAGGING BOTTOM
B.M at E in KN-M 5929.3692 5929.369 5929.369

6.2 BEAM DESIGN

LOAD CASE 1
Maximum saging bending moment in the beam = 9386.21 KNm
Maximum hogging bending moment in the beam = 1826.27 KNm
Maximum shear force in the beam = 8399.47 KN

LOAD CASE 2
Maximum saging bending moment in the beam = 9386.21 KNm
Maximum hogging bending moment in the beam = 1826.01 KNm
Maximum shear force in the beam = 8407.24 KN

LOAD CASE 3
Maximum saging bending moment in the beam = 9386.21 KNm
Maximum hogging bending moment in the beam = 1826.01 KNm
Maximum shear force in the beam = 8407.24 KN

Ultimate saging bending moment in the beam = 14079.31 KNm

Ultimate hogging bending moment in the beam = 2739.41 KNm
Ultimate shear in beam = 12610.86 KN

Depth of beam = 1650.00 mm

Effetive depth of BEAM = 1594.00 mm
Required effective depth of BEAM = 1178.17 mm

PROVIDED DEPTH OF BEAM IS SAFE

Max moment resisting capacity of beam = 0.138fck x b x de^2 = 25966.00 KNm

Refer page no. 87, Table 51, of SP-16 for Doubly Reinforced Beams
Refer page no. 49, Table 3 of SP-16 for Singly Reinforced Beams

Area of steel required for Hogging bending moment TOP STEEL = 26946.79546 sq.mm
Area of steel required for sagging bending moment BOTTOM STEEL = 6881.927711 sq.mm

Provide bar diameter at TOP =

Provide bar diameter at BOTTOM = 32 #
Nos of bar required at TOP = 33.51
SAY = 28 Nos

Nos of bar required at BOTTOM = 8.56

SAY = 8 Nos

Hence provide Main steel AT TOP of 32# - 28 Nos

Hence provide Main steel AT BOTTOM of 32# - 8 Nos

CHECK FOR SHEAR

Percentage steel provided pt % = 0.672 %
Permissible shear stress (From SP-16-1980) = 0.4 Mpa
 Maximum Allowable shear stress = 3.1 Mpa
Shear resisted by concrete = (0.4 x 2100x 1594)/ 1000 = 1338.5 KN
Design Shear Force = (12610.8565125217 - 1338.5) = 11272.35651 KN
Stirrup dia = 12 #
Asv = 1357.1 mm2
Nominal Stirrupe Spacing = 575 mm
OR 0.75 x d = 1195.5 mm
Design Stirrups Spacing = 65 mm
Provide Spacing = 65 mm
Hence provide 4legged stirrups of 12# @ 65 c/c

6.3 SLAB DESIGN

Clear Cantilever of slab b1 = 2.25 m

Working Upward pressure on slab Max from Load Case 1,2 and 3 = 433.46 KN/m2
Maximum bending moment = 1097.20 KNm
Maximum shear force = 975.29 KN
Shear at distance "d", from face of beam = 384.70 KN

Maximum ultimate bending moment for slab design = 1645.80 KNm

Maximum ultimate shear force in slab = 577.05 KN

Depth of slab Provided = 1450.00 mm

Effetive depth of slab = 1362.50 mm
Required effective depth of slab = 583.73 mm

PROVIDED DEPTH OF SLAB IS SAFE

Area of steel required = [(0.5xfck/fy)x(1-Sqrt((1-((4.6 x B.Mmax)/(fck x 1000 x de^2))] = 3450.91 sqmm

Provide bar diameter = 25 #
Required spacing of bars = (1000 x Abar/ Ast) = 142.245 mm
Say = 125 mm
Hence provide Main steel of 25# @ 125 mm c/c

Distributation steel required = (0.12 x 1000 x D)/100 = 1740 sqmm

Provide distributation steel bar diameter = 25 #
Required spacing of bars = (1000 x Abar/ Ast) = 282.111 mm
Say = 125 mm
Hence provide Distribution steel of 25# @ 125 mm c/c

Check for shear

Area of steel provided Ast = (1000 x Abar/ Spacing) = 3926.99 sqmm

Percentage steel provided pt % = (3926.99081698724 x 100/ (1000x 1362.5)) = 0.32 %
Permissible shear stress (From SP-16-1980) = 0.6
Shear resisted by concrete = (0.6 x 1000x 1362.5)/ 1000 = 817.5 KN
HENCE SAFE!!!

SUMMARY OF DESIGN.
Length of footing = 6600 mm
Breadth of footing = 6600 mm
Width of beam = 2100 mm
Depth of beam = 1650 mm
Diameter of longitudinal main bars = 32 #
No.of top bars = 28 nos.
No.of bottom bars = 8 nos.
Diameter of stirrups = 12 #
Spacing of stirrups = 65 mm
Depth of slab = 1450 mm
Main steel in slab = 25 #
Spacing of main steel = 125 mm
Distributation steel in slab = 25 #
Spacing of distibutation steel = 125 mm
 DESIGN OF RECTANGULAR COLUMN
WITH BIAXIAL BENDING (USING SP 16)
1.( STATIC LOAD + SESMIC LOAD ) = ((DL+LL+EQZ) COLUMN H1
1 MATERIAL PARAMETERS 900
Z
Grade of concrete fck M 35

###
Grade of steel fy Fe 415

2 SECTION PROPERTIES
X
Side dimension along X direction 900 mm
Side dimension along Z direction 762 mm

3 LOADS
Factored axial load Pu 7775 KN
Factored moment about X-X Mux 436.79 KNm
Factored moment about Z-Z Muz 793.53 KNm

4 ASSUMPTION
Let percentage of steel p 1.288 %
Cover to reinforcement d' 40 mm

5 DESIGN

p = 1.2884 = 0.04
fck 35

5 Uniaxial moment capacity of the section about X-X axis :

d' = 40 = 0.052
D 762

Hence chart for d'/D = 0.05 will be used

Pu = 7774.8 x 1000 = 0.32

fck bD 35 x 900 x 762

Mu = 0.07
fck bD 2

MuX1 = 0.07 x 35 x 900 x 762 x 762

 = 1280.32 KNm

5 Uniaxial moment capacity of the section about Z-Z axis :

d' = 40 = 0.044
D 900

Hence chart for d'/D = 0.05 will be used

Pu = 7774.8 x 1000 = 0.324

fck bD 35 x 762 x 900

Mu = 0.075
fck bD2

Muz1 = 0.075 x 35 x 762 x 900 x 900

= 1620.2 KNm

5 Calculation of Puz
Referring to chart 63, corresponding to
p = 1.2884 fy = 415 fck = 35

Puz = 16.5
Ag

Puz = 16.5 x 900 x 762

= 11315.7 KN

5 Calculation of interaction ratio :

Muy an + Muz an < 1

Muy1 Muz1

Pu = 7774.8 = 0.687
Puz 11316

an = 1.8118

Interaction ratio = 437 2 + 793.53 2 = 0.41687 Hence OK

1280 1620
 DESIGN OF RECTANGULAR COLUMN
WITH BIAXIAL BENDING (USING SP 16)
1.( STATIC LOAD + SESMIC LOAD ) = ((DL+LL+EQZ) COLUMN G1
1 MATERIAL PARAMETERS 1800
Z
Grade of concrete fck M 35

762
Grade of steel fy Fe 415

2 SECTION PROPERTIES
X
Side dimension along X direction 1800 mm
Side dimension along Z direction 762 mm

3 LOADS
Factored axial load Pu 11642 KN
Factored moment about X-X Mux 995.97 KNm
Factored moment about Z-Z Muz 859.58 KNm

4 ASSUMPTION
Let percentage of steel p 1.07 %
Cover to reinforcement d' 40 mm

5 DESIGN

p = 1.074 = 0.0307
fck 35

5 Uniaxial moment capacity of the section about X-X axis :

d' = 40 = 0.0525
D 762

Hence chart for d'/D = 0.05 will be used

Pu = 11642.4 x 1000 = 0.24

fck bD 35 x 1800 x 762

Mu = 0.07
fck bD 2

MuX1 = 0.07 x 35 x 1800 x 762 x 762

 = 2560.64 KNm

5 Uniaxial moment capacity of the section about Z-Z axis :

d' = 40 = 0.0222
D 1800

Hence chart for d'/D = 0.05 will be used

Pu = 11642.4 x 1000 = 0.243

fck bD 35 x 762 x 1800

Mu = 0.07
fck bD2

Muz1 = 0.07 x 35 x 762 x 1800 x 1800

= 6048.756 KNm

5 Calculation of Puz
Referring to chart 63, corresponding to
p = 1.074 fy = 415 fck = 35

Puz = 16
Ag

Puz = 16 x 1800 x 762

= 21945.6 KN

5 Calculation of interaction ratio :

Muy an + Muz an < 1

Muy1 Muz1

Pu = 11642 = 0.5305
Puz 21946

an = 1.551

Interaction ratio = 996 2 + 859.58 2 = 0.2797 Hence OK

2561 6049
 DESIGN OF RECTANGULAR COLUMN
WITH BIAXIAL BENDING (USING SP 16)
2.( STATIC LOAD + SESMIC LOAD ) = ((DL+LL+EQZ) COLUMN H1
1 MATERIAL PARAMETERS 900
Z
Grade of concrete fck M 30

762
Grade of steel fy Fe 500

2 SECTION PROPERTIES
X
Side dimension along Y direction 900 mm
Side dimension along Z direction 762 mm

3 LOADS
Factored axial load Pu 7775 KN
Factored moment about X-X Mux 436.79 KNm
Factored moment about Z-Z Muz 793.53 KNm

4 ASSUMPTION
Let percentage of steel p 1.288383 %
Cover to reinforcement d' 40 mm

5 DESIGN

p = 1.2884 = 0.0429
fck 30

5 Uniaxial moment capacity of the section about X-X axis :

d' = 40 = 0.0525
D 762

Hence chart for d'/D = 0.05 will be used

Pu = 7774.8 x 1000 = 0.38

fck bD 30 x 900 x 762

Mu = 0.075
fck bD 2

MuX1 = 0.075 x 30 x 900 x 762 x 762

 = 1175.8041 KNm

5 Uniaxial moment capacity of the section about Z-Z axis :

d' = 40 = 0.0444
D 900

Hence chart for d'/D = 0.05 will be used

Pu = 7774.8 x 1000 = 0.378

fck bD 30 x 762 x 900

Mu = 0.07
fck bD2

Muz1 = 0.07 x 30 x 762 x 900 x 900

= 1296.162 KNm

5 Calculation of Puz
Referring to chart 63, corresponding to
p = 1.2884 fy = 500 fck = 30

Puz = 16.5
Ag

Puz = 16.5 x 900 x 762

= 11315.7 KN

5 Calculation of interaction ratio :

Muy an + Muz an < 1

Muy1 Muz1

Pu = 7774.8 = 0.6871
Puz 11316

an = 1.8118

Interaction ratio = 436.79 2 + 793.53 2 = 0.5773 Hence OK

1176 1296
 BEAM DESIGN
ultimate shear = 117.33 KN WIDTH OF BEAM (B) =
ultimate sagging B.M. = 28.29444 KNm DEPTH OF BEAM (D) =
ultimate hogging B.M. = 285.2647 KNm fck. =
max moment resisting capacity of beam = 231.84 KNm fy =

Ru =
FOR SAGGING MOMENT cover =
area of steel required = 199.9667 sqmm eff. Depth =
min steel required = 645.1807 sqmm Ku =
Xu =
hence required Ast = 645.1807 sqmm fsc =

FOR HOGGING MOMENT

area of steel required = 2692.622 sqmm
min steel required = 645.1807 sqmm

hence required Ast = 2692.622 sqmm Area of steel provided =

SHEAR REINFORCEMENT
pt% = 0.701 shear stress =
Vuc = 140 KN
Vusvmin = 112 KN
Vurmin = 252 KN

FOR DOUDLY REINFORCED

Mu2 = 53.42474
Ast1 = 2010.669
Ast2 = 422.7728
hence total tension steel required = 2433.441
compersion steel required = 433.6424 hence providede steel =
SHEAR REINFORCEMENT
pt% = 0.7 shear stress =
Vuc = 179.2
Vusvmin = 112
Vurmin = 291.2
Vud =
Vus =
F BEAM (B) = 700.00
F BEAM (D) = 450.00
15
415

2.07
50
400
0.48
192
352

eel provided = 1963.50

0.5

1960

0.64