Design of Shallow Foundation (Isolated Footings)

AIM: -

Design a square footing for a column size of 400x400.

Do the following checks:

• If the gross bearing pressure under the footing is within safe bearing capacity
• Provide sufficient depth and longitudinal steel for resisting bending and shear
• Sufficient anchorage for column steel into the footing
• If the bearing pressure at column-footing joint is within 0.45 times the maximum concrete compressive strength

PROCEDURE: -

GIVEN DATA: -

Factored Load = 1.5(D.L+L.L) = 2000KN

Column size = 400mm x 400mm

SBC = 150kN/m2

Grade of Concrete = M25

FOOTING AREA: -

Assume  surcharge and self weight of footing = 10% of unfactored load

unfactored load = 2000/1.5 = 1333.33 kN

Footin Area = (Unfactored load + self weight)/SBC

Area = (1333.33*1.1)/150

  `L^2`   = 9.77 m2

Given as Square Footing

L = `sqrt9.77`

L= 3.12 m

Provide 3.2 m sided isolated Footing.

UPWARD SOIL PRESSURE OR NET SOIL PRESSURE (`P_n`): -

`P_n` = Factored Load/Actual area of footing

 `P_n` = 2000/(3.2*3.2)

 `P_n` = 195.3 kN/m2

BENDING MOMENT: -

Bending moment is critical at face of column from the edge of footing.

`b_f` = (3200-400)/2 = 1400mm

Load on critical section = `P_n` * L

                                  = 195.3 kN/m2 * 3.2 m

                              w  = 624.96 kN/m

                              w  = 625 kN/m

Bending moment = `(w*(b_f)^2)/2`

                         = `(625*1.4^2)/2`

                        = 612.5 kN-m

DEPTH OF FOOTING: -

Assume Fy = 500 N/mm2

`M_u = 0.133*f_(ck)*b*d^2`

`612.50*10^6 = 0.133*25*3200*d^2`

d = 240mm

Provide d = 450mm

Total depth D = 500mm

REINFORCEMENT: - 

`M_u` = 612.5kN-m

`A_(st) = ((0.50*f_(ck)*L*d)/f_y)*(1-sqrt(1-(4.6*M_u)/(f_(ck)*b*d)))`

`A_(st) = ((0.50*25*3200*450)/500)*(1-sqrt(1-(4.6*612.5*10^6)/(25*3200*450)))`

Ast (required)= 3279 mm2

Provide 16mm dia bar at 125mm spacing

Ast(provided) = 5146 mm2

CHECK FOR ONE WAY SHEAR: -

Clause 34.2.4.1

Critical section for One Way Shear is at a distance "d" from face of column.

Critical section  = L/2 - 400/2 -d

                       = 3200/2 - 400/2 - 450

                      = 950mm

Shear force at critical section

Vu = Pn * L * 0.95

Vu = 195.3*3.2*0.95

    = 593.7kN

Design shear stress at  one way cut face

`tau_v = (593.7*1000)/(3200*450)`

          = 0.412 N/mm2

Shear stress capacity of section as per IS 456:2000 Table 19

Pt = 0.35%

Fck = 25

`tau_c` = 0.425mm

Design Shear stress < Shear capacity.

Hence O.K.

CHECK FOR TWO WAY SHEAR 

 

Shear force in two way shaded area

= [(3.2*3.2) - (0.85*0.85)]*195.3 = 1859kN

Design Shear stress (`tau_v`) at two way cut face.

= 1859*1000/(3200*450)

= 1.215 N/mm2

As per IS 456:2000

Clause 31.6.3.1

Shear stress capacity of section

= `0.25*sqrtf_(ck)`= 0.25*5

= 1.25 N/mm2

Shear capacity > Design Shear stress

Hence O.K.

CHECK FOR TRANSFER OF LOAD: -

Clause 34.4

   

Bearing Resistance at Footing - soil Interface

= `0.45 *f_(ck)*sqrt(A_1/A_2`

= 0.45*25*2

= 22.5 N/mm2

Bearing Resistance at Column - Footing Interface

= `0.45 *f_(ck)*sqrt(A_1/A_2`

= 0.45*25*1

= 11.25 N/mm2

Actual Bearing stress at Column Base

= 2000*1000/(400*400)

= 12.5 N/mm2

Bearing Resistance < Actual Bearing stress

`P_(br)`= 11.25*400*400

            = 1800kN

`P_u>P_(br)`

2000kN > 1800kN

Design Development Length of column for force

= `(P_u)-(P_(br))`

= 2000 - 1800

= 200kN

AREA OF STEEL FOR DOWEL: -

= Force in column/0.75*Fy

= 200*1000/(0.75*500)

= 533mm2

= (0.5*400*400)/100

= 800mm2

Provide 800mm2 area of reinforcement as dowel bars

Extend column bars as dowel bars.

CHECK FOR DEVELOPMENT LENGTH: -

Clause 26.2.1

`sigma_s` = 0.87Fy

                 = 0.87 * 500

                 = 435

bar dia = 16mm

Ld = 16*435/(4*1.4*1.6)

     = 777mm

Available Length = (3200-400)/2 - 50

                        = 1350mm

DEVELOPMENT LENGTH FOR COLUMN: -

Assume 16 mm bar dia in column

Ld = 16*435/(4*1.4*1.6*1.25)

     = 621 mm

The above development Length is for fully stressed bars 

i.e. assuming it carries Pu = 2000kN,

However we intend to provide length for a Load = 200kN

Therefore we can safely provide develpment length for columns in the provided depth of footing.

 RESULT: -

Designed a square footing for a column size of 400x400mm.

Calculated Footing Area.

Calculated Net soil pressure for flexure and shear.

Calculated depth of Footing.

Calculated Flexural Reinfofrcement.

Checked for One-way Shear.

Checked for Two-way Shear.

Checked for Bearing stresses.

Checked for Anchorage Length.