Design of Shallow Foundation (Isolated Footings)

AIM: DESIGN A SQUARE FOOTING FOR A COLUMN SIZE 400X400. THE COMPRESSION AXIAL LOAD FOR THE LOAD COMBINATION OF (1.5DL + 1.5 LL) IS 2000KN. THE SAFE SOIL BEARING CAPACITY IS 150 KN/M² AT A DEPTH OF 2 METERS BELOW E.G.L. PARTICIPANTS ARE FREE TO GO FOR EITHER A TAPERED OR STEPPED FOOTING. BESIDES THE total AXIAL LOAD, ALSO ACCOUNT FOR THE SELF – WEIGHT OF THE FOOTING AND SOIL ABOVE IT. ASSUME M25 CONCRETE GRADE. DO THE FOLLWING 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 TIES THE MAXIMUM CONCRETE COMPRESSIVE STRENGTH

PROVIDE A SIMPLE SKETCH SHOWING THE SIZE OF THE FOOTING, MAXIMUM AND MINIMUM DEPTH OF THE SECTION, FLEXURAL REINFORCEMENT IN BOTH DIRECTION AND ANCHORAGE OF COLUMN STEEL.

PLEASE DO GO THROUGH THE SOLVED EXAMPLES IN THE DOCUMENT PROVIDED WITH THE CHALLENGE.

ANS:

1. Steps involved in footing design:
2. Calculation of gross soil pressure for footing area
3. Calculation of net soil pressure for flexure and shear design
4. Initial depth of footing calculation
5. Flexural reinforcement calculation
6. One way shear check
7. Two way shear check

2. Calculating gross soil pressure & footing area:

= unfactored load with surcharge + self-weight of footing / allowable soil pressure

= (2000/1.5x1.1)/150 = 9.78m² …….(assuming we have square footing)

= √9.78 = 3.12-meter side footing

= consider, 3.2 meter sided isolated footing

3. Net soil pressure & initial footing depth:

• Factored load/actual area of footing

= 2000 x 1000/ (3.2 x 3.2)

= p_n =195.3kN/m²

• Assume depth of footing 500mm and checking it for bearing stress as per IS-456-2000 clause 34.4

√(footing base bearing area/loaded area)<2

4. Net soil pressure & initial footing depth:

• Permissible bearing stress 0.45 x fck = 11.25N/mm²
• Permissible bearing stress multiplied with area factor 11.25 x 2 = 22.5N/mm^2
• Actual bearing stress at column base

(2000x1000) / (400x400)=12.5N/mm²

12.5 N/mm^2 actual stress is less than permissible 22.5N/mm². Hence ok we can proceed with 500mm depth footing for further design checks. If we assume 50mm cover for footing. The effective depth (d) shall be taken as 450mm.

5. Flexural reinforcement:

• Conversion of net pressure into uniformly distributed load

= 195.3 x 3.2 = 625 kN/m

• Bending moment due to UDL over a cantilever section

=wL²/2 = 625x1.6x1.6/2

M=800kkNm

• Reinforcement calculation as per IS-456-2000 annex-G

M_U = 0.87f_y A_st d (1-A_stf_y/bdf_ck)

Assume Fy=500N/mm² in result Ast required = 4350mm²

If we provide 16mm dia rebar at 125mm spacing, the actual rebar provided = 3200/125 x 201

Ast provided = 5146mm²

6. One way shear stress check:

• Shear force in the one way shaded area

=0.95 x 3.2 x 195.3 = 593.7kkn

• Design shear stress at one way cut face

T_{v =} 593.7 x 1000/(3200x450) = 0.412N/mm^2

• Shear stress capacity of section as per IS-456-2000 table -19 (included rebar)

=0.425N/mm²

• Design shear stress is less than shear capacity hence ok.

7. Two way shear stress check:

• Shear force in the two way shaded area

=(3.2 x 3.2) – (0.85 x 0.85) x 195.3 = 1859kN

• Design shear stress at two way cut face

T_v= 1859x1000/(3400x450) = 1.215 N/mm^2

• Shear stress capacity if section as per IS-456-2000 clause 31.6.3.1

=0.25 x √Fck = 1.25 N/mm^2

• Design shear stress is less than shear capacity hence ok.