Design of Shallow Foundation (Isolated Footings)

Aim

• To design a square footing for a column size of 400x400.

Introduction

• The footing is a structural member that safely transmits the load of the upper building to the ground, and is the first construction member of the building.
• The basic method of footing design is to distribute the load so that the size per area the load transmitted from the upper part of the building is less than the strength that the ground can support, that is, of the bearing capacity.
• with this function, the footing is a structure installed between the ground and the column or wall immediately above it,
• basic design is to reduce the total amount of settlement and prevent the occurrence of immobile settlement.
• In a general building, the footing design is to determine the area of the footing, the thickness of the footing and the amount of required rebar.

Procedure 

Step 1)

Given Data

• Column size 400mmx400mm
• Compression axial load for the load combination of (1.5 DL+ 1.5 LL) is 2000 KN Safe soil bearing capacity at a depth of 2 meters below E.G.L is 150 kN/m²
• Assuming the self-weight of the footing and soil above it as 10% load
• Grade of concrete = 25 kN/m²    

• Assuming fy  = 415 N/mm²
• Here a sloped footing is designed.

Step 2)

Size of the footing

• Unfactored load              2000/1.5  = 1333.33KN
• Safe Bearing Capacity of Soil           = 150
• Area of footing           1333.55 X 1.1/ 150  = 9.78 m2

• Since its a square footing, B     = √9.78
• B-L                                        = 3.5m
• Area of footing                        = 12.25 m²
• Therefore area of footing provided is greater than area of footing required 12.25 > 9.78..................Okay

Step 3)

Net soil upwared pressure.

• Notupward Pressure ='(Factored Load)/(Area of footing provided

                                      =  (2000)/12.25")

                                      = 163.26 kn/m2

Step 4)

Depth of footing

• Maximum bending moment at the face of column
• Length of the critical section             = 3.5-0.2 = 1.55m
• Load on critical section                     = Net upward pressure X Length

                                                             = 163.26 X 3.5

                                                             = 571.76 kN/m

• Moment                                          = 672 X (155) -= 683.4kN/m
• Ultimate moment, Mu                      = 1.5 X 686.4-1030kN/m
• Depth of the footing                        = D-Mu -0.138 X fek XBXd

                                                             = 1030 X 10 = 0.138 X .25 X 3500X d

                                                             = d=√85300 = 292mm

• By thumb rule taking 2.5 times higher value for shear check
•                                                 d   = 292 X 2.5=730mm
• providing 50mm cover,               d   = 730+50 780mm-800mm

Step 5)

Gross bearing Capacity

• Assuming unit weight of the soil to be                   18kN/m³
• Load on the footing                                           = 1333.3kN
• Weight of the footing.                                   g   = 3.5 X 3.5 X 25 X 0.8 = 245KN
• weight of the soil                                               = 3.5 X 3.5 X (2-0.8) X 18 = 261.6kN
• Total load                                                           =1852kN
• Gross bearing capacity                                        = 1852)/(3.5x3.5) = 257kN / m²
• As 257 kN/m²>150kN/m², hence we need to increase the size of footing to 3.8m X 3.8m
• New total load                                                     = 1934KN
• gross bearing capacity                                           133.9 kN/m²<150kN/m², hence safe
• Corrected net soil pressure

Stop 6)

Reinforcement

• Percentage of Reinforcement                                Ast/Bd x 100
•                                                                      P = 3640x100/3800x800 = .119%
• Number of bars required for reinforcement         =    Ast/ Area of one bar (16mm)
• Number of bars                                                =   3640/(3.14x16x16/4)
• Spacing between the bars                                 =   B / No of Bars
• Let's provide 18 number of 16mm dia bars at 160 mm c/c

Step 7)

Check for One way Shear

• The critical section for shear is at distance d from the face of column.
• Shear force (Vu                              = Net Soil pressure X B (1/2(B-b)-d)

                                                            = 138.5 x 3.8 X (1/2 X (3.8 - 0.4)

                                                            =  473.67KN

Step 8)

Check for two way shear

• The critical section for shear is at distance d/2 from face of column
• Shear force, Shear force (1)                = Net Soil pressure X(B² – b₀²)

                                                                = 138.5x(3.8²-(0.8+0.4)²)

                                                               = 1800.5 kN

• periphery of section                          B₀       = 2(1.2+1.2)=4.8m

                                                               V_u/ B₀d = (1800.5x10³)/(4800x800)  =  0.46 N/mm²

• Permissible shear stress                                       = ks,XTc, (from IS 456 2000)

                                                                   Ks            = 1 (max)

                                                                   Tv             = 0.25 X √fck

                                                                                = 0.25 X √25

                                                                                = 1.25 N/mm²

Tv< Tc. Hence Ok

                                             

Step 9) 

Development Length

                                    L_d  = 0.87xf_s x φ / 4x τbd

                                         =  0.87x25x16/4x1.6x1.4

                                         =  677

Length available

                                            = 1600-50

                                            = 1550mm>677mm

 

Results

• The sloped isolated footing is designed for square Column of size 400mmx400mm
• The footing is safe against the bearing pressure
• Footing is safe against the one way and two way shear (Less than1)
• Permissible stress is less than the 0.45fck.