Foundation BS 8110

Foundation Type :

MATERIAL DATA:

Grade of Concrete Fc = 40 N/mm2

Yield Strength of reinforcement = 460 N/mm2

Reinf. dia in direction of L & spacing = 12 mm @ 200mm

Reinf. dia in direction of B & spacing = 12 mm @ 200mm

Clear Cover to Reinforcement = 75 mm

Unit Weight of Concrete 25 KN/m3

Unit Weight of Soil = 18 KN/m3

Unit Weight of Backfill = 18 KN/m3

Net allowable bearing pressure = 100 KN/m2

Internal angle of friction f of soil = 30O _{(Refer soil report )}

Coeff. of friction bet. conc and soil, tan(2/3*d) = 0.36

Load factor for S/w and Soil wt =

1.4

Factor of safety against overturning = 1.75

Factor of safety against sliding = 1.75

Depth of Water table from Ground = 100 m (no water table encountered)

Number of Unfactored Load Combinations 9 nos

Number of Factored Load Combinations 26 nos

GEOMETRICAL DATA :

(Water Table)

Width of Footing, B = 2.10 m Width of Pedestal, CB = 0.50 m

Length of Footing, L = 2.10 m Length of Pedestal, CL = 0.50 m

Embedment depth, H = 1.20 m

Height of Pedestal, lo = 1.00 m Depth of Footing, D = 0.40 m

Projection of pedestal above ground = 0.2 m

Ecc. about Z axis,ezp = 0.00 m Ecc. about X axis, exp = 0.00 m

X Y Z FY FX FZ H D L lo

1.75 without wind or seismic case 1.50 with wind or seismic case

CL CB _B L Z X ezp exp

LOAD DATA (+ve value of FY implies compression in Pedestal) (a) Load for Stability

JOINT L/C FY FX FZ MX MZ

14 109 47.7 0.046 27.082 5.139 17.223

(b) Ultimate load combination for concrete design.

JOINT L/C FY FX FZ MX MZ

14 225 80.64 0.055 42.99 7.85 30.028

(c) Load combination for bearing pressure check:.

JOINT _{L/C FY FX FZ MX MZ}

14 109 47.7 0.046 27.082 5.139 17.223

1. CHECK FOR STABILITY AGAINST SLIDING AND OVERTURNING

(a) Sliding :

Sliding force in X direction = FX = 0.046 kN

Sliding force in Z direction = FZ = 27.082 kN

Resultant force = F = (Fx2+Fz2)0.5 27.08 kN

Resisting frictional force = P*m = 57.49 kN

P= FY+Footing weight + Pedestal weight +Soil weight- Buoyant force = 157.95 kN

F.O.S. against sliding = 2.12

O.K. as value greater than permissible value (b) Overturning about Z

Forces acting at bottom of footing about Z

FY = 47.70 kN

MZtot = (MZ +FX*(lo+D)+(Fy+Pwt)*ezp) = 17.29 kN-m

Self Weight of Foundation = 44.1 kN

Weight of Pedestal, Pwt = 6.25 kN

Weight of Backfill = 59.90 kN

Buoyancy force = 0.00 kN

0.2 Taking moment about P

Overturning moment due to Tension =

0.80 0.00 kN-m

Overturning moment = MZtot =

17.29 kN-m

1.05

Total overturning moment 17.29 kN-m

Restoring Moment 165.85 kN-m

Factor of safety against overturning = restoring mom/overturning mom = 9.59

O.K. as value greater than permissible value (c) Overturning about X

Forces acting at bottom of footing about X

FY = 47.70 kN

MXtot = (MX +FZ*(lo+D)+(Fy+Pwt)*exp) = 43.05 kN-m

Self Weight of Foundation = 44.10 kN

Weight of Pedestal,Pwt = 6.25 kN

Weight of Backfill = 59.90 kN

Buoyancy force = 0.00 kN

0.2

0.80 Taking moment about P

Overturning moment due to Tension = 0 kN-m

Overturning Moment = MXtot

1.05 43.05 kN-m

Total overturning moment = 43.05 kN-m

Restoring Moment = 165.85 kN-m

Factor of safety against Overturning = restoring Moment / over turning Moment =

3.85 O.K. as value greater than permissible value

2. CHECK FOR NET BEARING PRESSURE

Gross vertical load PY = FY+ Weight of Footing including pedestal+ Weight of back fill = 157.95 kN

Total Moment about X = MXtot = MX+ FZ(lo+D)+(Fy+Pwt)*exp = 43.05 kN-m

Total Moment about Z = MZtot = MZ+ FX(lo+D)+(Fy+Pwt)*ezp = 17.29 kN-m

ex = MZtot/PY = 0.11 M e<L/6, No Tension in footing.

ez = MXtot/PY = 0.27 M e<B/6, No Tension in Footing.

Gross pressure distribution under footing is given by: q =

= 74.91 52.51 19.12 0.00 Kn/m2 _p3

p1 p2 p3 p4 +Mx

Mx (If there is negative gross pressure then it will be corrected

using Teng's Chart) p2 Mz p1

ex/L = 0.05 ez/B = 0.13

Sign Convention

From Teng's chart value of k = 2.100

Maximum Gross Pressure = K*P/BL = 75.20 KN/m2

Net pressure intensities under the footing is given by:

p1net = 53.60 KN/m 2 p3net = 0.00 KN/m2 p2net = 31.11 KN/m 2 p4net = 0.00 KN/m2

Maximum net pressure intensity = 53.60 KN/m2 O.K. Less than allowable bearing pressure

)

B

e

6

L

e

6

1

(

LB

P

±

±

å

3. CHECK FOR MOMENT AND SHEAR

Net pressure generated below footing due to ultimate load.

Gross vertical load PY = FY+ Weight of Footing including pedestal+ Weight of back fill = 235.00 kN

Total Moment about X = MXtot = MX+ FZ(lo+D)+(Fy+Pwt)*exp = 68.04 kN-m

Total Moment about Z = MZtot = MZ+ FX(lo+D)+(Fy+Pwt)*ezp = 30.11 kN-m

ex = MZtot/PY = 0.13 M e<L/6, No Tension in footing.

ez = MXtot/PY = 0.29 M e<B/6, No Tension in Footing.

Gross pressure distribution under footing is given by: q =

= 116.87 77.86 28.71 0.00 Kn/m2 p3

p1 p2 p3 p4 +Mx

Mx (If there is negative gross pressure then it will be corrected

using Teng's Chart) p2 Mz p1

ex/L = 0.06 ez/B = 0.14

Sign Convention

From Teng's chart value of k = 2.210

Maximum Gross Pressure = K*P/BL = 117.75 KN/m2

Net pressure intensities under the footing is given by:

p1net = 96.15 KN/m 2 p3net = 7.22 KN/m2 p2net = 56.56 KN/m 2 p4net = 0.00 KN/m2

Max. net pressure intensity (fac)= 96.15 KN/m2

)

B

e

6

L

e

6

1

(

LB

P

±

±

å

(a) Check for Moment and One way Shear in X direction

p2 =

56.56 93.1 p1 =

81.07 87.08 96.15 ( d= D-75-6 = 319 mm )

Moment at the Critical section 1: 29.16 kN-m/m Width of Footing.

Shear at critical section 1: 148.86 kN

Shear at critical section 2: 92.54 kN

Shear at critical section 3: 32.19 kN

Tensile Reinforcement: K= M/fcubd 2 = 0.0072 < 0.156 z= d[0.5+(0.25-k/0.9)] = 316.44 mm 0.95*d = 303.05 mm Hence z = 303.05 mm Ast = M/0.95fyz = 220.18 mm2/m Minimum Reinforcement 0.13% = 520.00 mm2 /m

Reqd. Spacing of 12 mm dia bar = 218 mm

Provided Spacing = 200 mm Ast,provided 565 mm2/m

Design Concrete shear stress uc = 0.439 N/mm2 (Ref. Table 3.8 of BS 8110)

Section 1 Ultimate shear stress v1 = 0.222 N/mm2

Maximum allowed 0.8fcu = 5.060 N/mm2 O.K. (Clause 3.7.7.2)

Section 2 Ultimate shear stress v2 = 0.138 N/mm2

Maximum allowed 1.5uc = 0.659 N/mm2 O.K. (Clause 3.7.7.4)

Section 3 Ultimate shear stress v3 = 0.048 N/mm2

Maximum allowed uc = 0.439 N/mm2 O.K.

d d

1 2 3

1 2 3

CRITICAL SECTIONS FOR MOMENT AND SHEAR.

(b) Check for Moment and One way Shear in Z direction

p3 = 89.29

7.22 p1 = ( d= D-75-12-6 = 307 mm )

62.27 75.27 96.15

Moment at the Critical section 1: 27.15 kN-m/m Width of Footing.

Shear at critical section 1: 133.07 kN

Shear at critical section 2: 88.74 kN

Shear at critical section 3: 36.22 kN

Tensile Reinforcement: K= M/fcubd 2 = 0.00720268 <0.156 z= d[0.5+(0.25-k/0.9)] = 304.52 mm 0.95*d = 291.65 mm Hence z = 291.65 mm Ast = M/0.95fyz = 213.05 mm2/m Minimum Reinforcement 0.13% = 520.00 mm2 /m

Reqd. Spacing of 12 mm dia bar = 218 mm

Provided Spacing = 200 mm Ast,provided 565 mm2/m

Design Concrete shear stress uc = 0.449 N/mm2 ( Refer Table 3.8 of BS 8110 )

Section 1 Ultimate shear stress v1 = 0.206 N/mm2

Maximum allowed 0.8fcu = 5.060 N/mm2 O.K. (Clause 3.7.7.2)

Section 2 Ultimate shear stress v2 = 0.138 N/mm2

Maximum allowed 1.5uc = 0.674 N/mm2 O.K. (Clause 3.7.7.4)

Section 3 Ultimate shear stress v3 = 0.056 N/mm2

Maximum allowed uc = 0.449 N/mm2 Hence O.K.

d d 1 2 3 1 2 3

FACTORED PRESSURE DISTRIBUTION AT SALIENT POINTS CRITICAL SECTIONS FOR MOMENT AND SHEAR. d d 1 2 3

(c) Check for Punching Shear

d = average of effective depth in two directions = 313 mm

U0 = 2(CB+CL) = 2000 mm

U1 = 5756.000 mm

Area A0 = 2.071 m2

Maximum ultimate Vertical load on column 1.15FY = 92.74 kN

Ultimate shear stress for U0 = 0.148 N/mm2 O.K.

Maximum allowed 0.8fcu = 5.060 N/mm2

Ultimate shear stress for U1 = 0.093 N/mm2 O.K.

Maximum allowed uc = 0.449 N/mm2 UO U1 1.5d 1.5d A₀