Proportioning of Footing Area

Proportioning of footing area

By

Vinay Mehta

Introdution

Designing of footing for equal settlement is known as proportioning of area of footing.

Why is it necessary

a) Varying loading from column to column to a great extent.

b) Variation in “Pressure Intensity” due to change in extent of live load acting on column.

c) The above variation cause unequal settlement & thereby subsequently cracking of structure.

Process Of Proportioning

A. Let

W1,W2,W3,………..WN = Load(combination of “Dead Load” & “Live Load”) carried by columns.

Calculation of area required for individual footing:-

A1 = W1 / SBC

A2 = W2 / SBC

A3 = W3 / SBC………… AN = WN/ SBC

Calculation of maximum variation in pressure intensity for 1/3 column load.

Q1= (wd1+wl1/3) / A1

Q2= (wd2+wl2/3) / A2

Q3= (wd3+wl3/3) / A3………….. Qn= (wdn+wln/3) / An

Calculation of variation.

V1 = SBC-Q1

V2 = SBC-Q2

V3 = SBC-Q3……………… Vn0 = SBC-Qn

Calculation maximum pressure variation % :-

Maximum % variation = (Vmax/SBC)*100

Identify the column wit maximum ratio of “Dead Load” to “Live Load” ratio and also calculate area required for that column.

Areq = (Wd+Wl)/SBC [for column with max Wd/Wl ]

Retaning the same area for column idntified, calculate the reduced soil pressure for ½ live load.

Qmod = (Wd+Wl/2)/Areq

By Qmod calculate the area required by other column

Areq1 = (Wd+Wl/2)/ Qmod

Areq2 = (Wd+Wl/2)/ Qmod…….. Areq2n= (Wd+Wl/2)/ Qmod

Calculation of unit pressure under column & their variation:-

Q1 = (W1dead+W1live/3)/Areq1

Q2 = (W2dead+W2live/3)/Areq2…………….

Qn= (Wndead+Wnlive/3)/Areqn

Calculation of variation of pressure intensity:-

V’1 = SBC-Q’1

V’2 = SBC-Q’2

V’3 = SBC-Q’3….......................... V’N = SBC-Q’N


Numerical Problem

• A floor consist of 6column having loads as below.

If the SBC of soil is 150 kN/m2

Explain and carry out the proportioning the area of footing.

Column No

1 2 3 4 5 6

Wd kN 500 600 700 500 600 700

Wl kN 100 300 250 360 400 100

Area required for individual footing

A1 = W1 / SBC = (500+100)/150 = 4.00m2

A2 = W2 / SBC = (600+130)/150 = 6.00m2

A3 = W3 / SBC = (700+250)/150 = 6.33m2

A4 = W4 / SBC = (500+360)/150 = 5.73m2

A5 = W5 / SBC = (600+400)/150 = 6.67m2

A6= W6 / SBC = (700+100)/150 = 5.33m2

Calculation of maximum variation in pressure intensity for 1/3 column load.

Q1= (wd1+wl1/3) / A1

= = (500+100/3)/4 = 133.33 kN/m2

Q2 = (600+300/3)/4 = 116.67 kN/m2

Q3 = 123.75 kN/m2

Q4 = 108.80 kN/m2

Q5 = 109.95 kN/m2

Q6 = 137.58 kN/m2

Calculation of variation.

V1 = SBC-Q1= 150-133.33= 16.67 kN/m2

V1 = 33.33 kN/m2

V1 = 26.26 kN/m2

V1 = 40.06 kN/m2

V1 = 41.80 kN/m2

V1 = 12.42 kN/m2

Calculation maximum pressure variation % :-


= (41.8/ 150) * 100

= 27.86%Identifying the column with maximum DL/ LL ratio.

Column .No

1 2 3 4 5 6

DL/LL Ratio

5 2 2.8 1.38 1.5 7

Calculating the modified soil pressure for full dead & ½ live load by area retained by column No.6

Qmod = (Wd+Wl/2)/Areq

= (700+100/2)/ 5.33

= 140.1 kN/m2

Now by using Qmod calculate the modified area required for other column

Areq1 = (Wd+Wl/2)/ Qmod

= ( 500+100/2)/ 140.71

= 3.90m2

Areq2 = 5.33 m2 Areq6 = 5.33 m2

Areq3 = 5.86 m2

Areq4 = 4.83 m2

Areq5 = 5.58 m2

Unit Pressure under individual column for 1/3 live load

Q1 = (W1dead+W1live/3)/Areq1

= ( 500+100/3)/ 3.90

= 136.40 kN/m2

Q2 = 131.33 kN/m2 Q5 = 129.10 kN/m2

Q3 = 133.67 kN/m2 Q6 = 137.58 kN/m2

Q4 = 128.36 kN/m2

Pressure variation

V’1 = SBC-Q’1

V’1 = 150-136.40

V’1 = 13.6 kN/m2

V’2 = 18.67 kN/m2 V’5 = 20.90 kN/m2

V’3 = 16.33 kN/m2 V’6 = 12.42 kN/m2

V’4 = 21.64 kN/m2

Maximum pressure variation


= (21.64/150)*100

= 14.42%

THANK YOU

Documents

Proportioning of Footing Area