Q. Design a square footing for a column size of 400x400. The compression axial load for the load combination of (1.5 DL + 1.5 LL) is 2000 KN. The safe soil bearing capacity is 150 KN/m2 at a depth of 2 metres 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 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

Provide a simple sketch showing the size of the footing, maximum and minimum depth of the section, flexural reinforcement in both directions and anchorage of column steel.

Ans:

Column Size = 400 x400

The compression axial load for the load combination of (1.5 DL + 1.5 LL) is 2000 KN

The safe soil bearing capacity is 150 KN/m2 at Foundation depth below E.G.L = 2metres

Grade of concrete for footing = M25

 

• Footing Size

column load 2000KN

10% of footing self weight = 2000x10/100 = 200KN

Axial load on footing = 2000+ 200 = 2200KN

 

 Area of footing

Af = Load on footing / safe bearing capacity = (2200/1.5)/150 = 9.78m2

 B = L = Ѵ9.78 = 3.12m Say B = L = 3.20m  = 3200mm

 

• Net Upward pressure

Factored net soil pressure = load on footing /area of the footing

= 2200 / ( 3.20 x 3.20)

 = 214.85KN/m2

 

Assume depth of footing as 500mm and check for bearing stress

=Ѵ(footing base bearing area/Load area) ≤ 2

=Ѵ(2.4²/0.4²) = 6

Permissible bearing stress = 0.45 x F_ck

                                           = 0.45 x 25 = 11.25 N/mm² 

• Permissible  bearing stress multiplied with factor = 11.25 x 2 =22.5 N/mm²                                  

Actual bearing stress at column base 

       = 2200x1000/(400x400) = 13.75 N/mm² 

13.75 N/mm2 actual stress is less than permissible 22.5 N/mm2. Hence Okay.

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 450 mm.

 Reinforcement Calculation

• Converting the net pressure into UDL 

                   = 214.85 x 3.2 = 687.52 KN/m 

• Bending moment due to UDL over a cantilever section 

                   = 687.52 x 1.6 x (1.6/2) = 880.02 KN-m

As per IS 456-2000 Annex G 

M_u= 0.87 f_y A_st d (1 - A_st f_y / bd f_ck)

Assume fy = 500N/mm² , After solving this equation value of A_st = 4818.04 mm²

Provide 16 mm dia bar at 100mm spacing, the actual reinforcement provided = (3200/100) x 201 = 6432 mm²

 Check for one way shear

Shear force in the one way shaded area = 0.95 x 3.2 x 214.85 = 653.15 Kn

Design shear stress at one way cut face (τv">τv) = (653.15 x 1000)/(3200 x 450) = 0.453 N/mm²

Percentage of steel provided = 0.446 %

Shear force capacity of section as per IS-456-2000 Table - 19 (Include Rebar) = 0.4619 N/mm² 

• Hence design stress is less than Shear capacity.

Hence OK.

• Check for Two way shear

The critical section for two-way shear is located at a distance of d/2 from the face of the column.

Shear force in the two way shaded area = [(3.2 x 3.2) - (0.85 x 0.85)] x 214.85 = 2044.85 Kn

Design Shear stress at two way cut face τv = (2044.85x1000)/(3200x450) = 1.42 N/mm²

Shear stress capacity of section as per IS-456-2000 Clause 31.6.3.1

 

 

Here Design shear stress is greater than the shear capacity of the section.

Hence Not Ok.
So revise the total depth of the section from 500 mm to 600 mm.

• So Revise Design Shear stress at two way cut face τv = (2044.85x1000)/(3200x550) = 1.161 N/mm²

Hence OK. 

• The A_st revised but it is in the safer side.

Gross Bearing Capacity:-

Assuming unit weight of Concrete & soil 25 KN/m3 & 18KN/m3

Load on footing = 1333.33 Kn

Wt. of footing = 3.2 x 3.2 x 0.6 x 25 = 154 Kn

wt. of soil = 3.2 x 3.2 x (2-0.6) x 18 = 258 Kn

Total Load = 1333.33 + 154 + 258 = 1745.33 Kn

Hence, gross bearing capacity = 170.44 kN/m2</math>">m2 > 150kN/m2</math>">m2�2

 

Hence,  the size of the footing needs to be revised to 3.6m x 3.6m.

Again,

Load on footing = 1333.33 Kn

Wt. of footing = 3.6 x 3.6 x 0.6 x 25 = 195 Kn

wt. of soil = 3.6 x 3.6 x (2-0.6) x 18 =  327 Kn

Total Load = 1333.33 + 195 + 327 = 1855.33 Kn

Hence, gross bearing capacity = 143.15 kN/m2</math>">m2 > 150kN/m2</math>">m2�2

Hence Safe.

 

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