Design of Shallow Foundation (Isolated Footings)
Aim:
To manually calculate the spread footing dimensions and reinforcement details with respect to limit state design of soil and structure.
Calculation of Gross soil pressure:
Unfactored load = 2000/1.5 = 1333 kN
Assume thickness of footing (t) = 0.5 m
Depth of footing as given in data (h) = 2 m, So soil surcharge depth = 2 - 0.5 = 1.5 m
Assume soil density = 20 kN/cu.m
Assume RCC density = 25 kN/cu.m
Consider square shape footing, area of the Footing = b x b = `b^2`
Condition: The safe bearing capacity of soil should be greater than gross soil pressure.
150 > `(1333/b^2) + (1.5*20) + (0.5*25)`
150 > `(1333/b^2) + 42.5`
`b^2 > 1333/107.5`
b > 3.52 m
So we can provide 3.6 m size of square spread footing
Gross soil pressure = `(1333/3.6^2)+(1.5*20)+(0.5*25)`
= 0.145 N/sq.mm
Calculation of Net soil pressure:
Net soil pressure = Factored load / Area of footing
= `2000/3.6^2`= 0.154 N/sq.mm
Calculation of Bearing Pressure:
= Net load / column area = `2000000/400^2`
= 12.5 N/sq.mm
Allowable bearing pressure as per clause 34.4 from IS456-2000,
= `root()(A_1/A_2)`x 0.45 `f_(ck)`
Where `A_1`= Base area of Footing
`A_2`= Base area of column
`root()(A_1/A_2)`but not greater than 2 in calculation
`root()(A_1/A_2)`= 3
So Allowable bearing pressure = 2 x 0.45 x 25 = 22.5 N/sq.mm Hence OK
Calculation of Oneway Shear check:
Considering concrete cover 50mm, the effective depth of footing shall be 500 - 50 = 450 mm
Taking critical section at one side of footing as shown below,
Net Load on the shaded area = 1150 x 3600 x 0.154 = 637.56 kN
Design Footing area at critical section = 3.6 x 0.45 = 1.62 sq.m
Oneway shear stress = 637560 / 1620000 = 0.393 N/sq.mm
As per Table-20 from IS456-2000, the maximum concrete shear stress for M25 = 3.1 N/sq.mm. Hence OK.
Calculation of Twoway Shear check:
Considering first critical perimeter of twoway shear at "d/2" distance either side from column face. As shown below,
Net Load from the shaded area = (0.154x3.6x3.6) - (0.154x0.85x0.85) = 1884.5 kN
Design Footing area at critical perimeter = 4 x 0.85 x 0.45 = 1.53 sq.m
Twoway shear stress = 1884500 / 1530000 = 1.23 N/sq.mm
As per Cluase 31.6.3.1 from IS456-2000, the permissible twoway shear stress for M25 concrete with 0.4 m square column,
= `k_s tau_c`
`k_s`= 0.4/0.4 = 1
`k_s tau_c`= 1 x 0.25`root()(f_(ck))`
= 1.25 N/sq.mm Hence OK.
Calculation of Flexural reinforcement:
Ultimate Footing Bending moment at face of column: `(wl^2)/2`
w = 0.154x1000 = 154 N/mm
l = (3600-400)/2 = 1600mm
BMD = 197.12 kNm / meter width of footing
As per Table-2 of SP16 guidelines, percentage of reinforement for `M_u/(bd^2)`with Fe500 and M25,
`p_t`= 0.2372%
So the flexure rebar per meter width = `(0.2372/100)*1000*450`= 1067 sq.mm / meter width
Calculation of Oneway shear reinforcement:
Oneway shear stress = 0.393 N/sq.mm
As per table-19 of IS456-2000, For concrete M25 with design shear stress 0.393 N/sq.mm, the required reinforcement is,
`100(A_s/(bd))`= 0.3077
= 1385 sq.mm / meter width
We will provide greater of the two reinforement with 20mm dia with 225 mm spacing.
So, 1000/225 x 314 = 1395 sq.mm which is greater than the design reinforement. Hence OK.
Calculation of Development length:
As per cluase 26.2.1 from IS456-2000, the development length of rebar should be minimum,
`L_d = (phi sigma_s)/(4tau_(bd)`
`phi`= diameter of bar = 20mm
`sigma_s`= allowable stress of rebar = 0.55 Fy (As per Note-1 from Table 22 of IS456-2000) = 0.55x500 = 275 N/sq.mm
`tau_(bd)`= 1.4 (for M25 from clause 26.2.1.1 of IS456-2000)
`L_d =`982 mm Minimum, rounding it off to Ld = 1000 mm
Calculation of Stepped footing:
Critical distance of Oneway shear from column face = 450mm
Critical distance of Twoway shear from column face = 225mm
We have to provide 500mm footing thickness at least 450mm from column face, rounding it off to 500mm uniform around the column, as shown below.
Schematic Representation of Footing step and reinforcement:
Conclusion:
Thus the required spread footing is designed and detailed as per given inputs. All the reuired limite state criteria are verified and found to OK.