Schuyler d.
dela Torre rcstruc 2 TTH 1:30-3:00 9/23/19
Spread Footing design for columns
BACKGROUND
Spread footing is the part of a foundation which is widened and is responsible for
spreading the weight transmitted from a column load over larger and broader soil area.
APPLICATIONS
Spread footing is classified as shallow foundation is can be either be designed as an
isolated footing or as a continuous footing.
DESIGN THEORY
There are two determining factors in the design and sizing of spread footing, these factors
are as follows:
1. Soil bearing capacity
2. Column Load
1. Soil Bearing capacity
Soil bearing pressure is equivalent to:
q= P/A
Where: q = Soil Bearing Pressure/allowable soil bearing in lb/sqft
P = Load applied
A = Area of footing
Soil bearing pressure or allowable soil bearing in lb/sqft is attained through this table:
Soil Bearing Capacities
Soil Bearing
Soil type Pressure/allowable soil Drainage
bearing in lb/sqft
Bedrock 4000 to 12000 Poor
Gravel 3000 Good
Gravel w/ Fines 3000 Good
Sand 2000 Good
Sand w/ Fines 2000 Good
Silt 1500 Medium
Clays 1500 Medium
Organics 0 to 400 Poor
2. Column loads
Column loads, denoted as P column, is the sum of the following:
1. Roof loads
2. Supported floor loads
3. Weight of the column
4. Weight of the foundation
Notable, if the ground floor is situated on grade, its loads are not included.
FORMULAS FOR SIZING
1. Sizing of spread footing
The sizing of spread footing is determined by two factors:
1. Total load applied to the soil (P column)
2. The allowable soil bearing capacity (q net)
2. Required Footing Area
q allowable > q
q allowable > P/A
A > P/q allowable
Where: q allowable = allowable soil bearing pressure found in table of soil bearing
capacities
q = soil bearing pressure
P = Load applied
A = area of footing
3. P footing
P footing = t footing (150 lb/cu.ft)
Where: t footing = thickness of footing
150 lb/cu.ft = density of concrete
4. Net Allowable soil bearing capacity
q net = q allowable – p footing
Where: q allowable = allowable soil bearing pressure found in table of soil bearing
capacities
p footing = t footing (150 lb/cu.ft)
5. Column loads
Column load is denoted as P column and is the summation of all loads acting on the
column.
6. Required footing area
A > P column / q net
Where: P column = summation of all loads acting on the column
q net = q allowable – p footing
7. Footing shape
1. Area of square = x^2
2. Area of rectangle = bh
3. Area of circle = ^2
FORMULAS FOR RE-BAR ESTIMATION
1. Needed variables
Variable Denoted as
Length of footing X
Breadth of footing Y
Height of the footing (thickness) h
Diameter of main reinforcement dm
Diameter of distribution reinforcement
dd
bars
Spacing of main re-bars sm
Spacing of distribution of re-bars sd
Cover for re-bars/concreter cover c
2. Calculated Number of main rebars (x-bars)
Nm = (Y / Spacing of Main Reinforcement) + 1
3. Calculation of Number of Distribution Reinforcement (Y-Bars)
Nd = (X/Spacing of Distribution
Reinforcement) +1
4. Cutting Length of Main Reinforcement (X-Bars)
Cm1 = [X-2C] +2[h-2C]-2[2dm]
5. Total Cutting Length of Main Reinforcement (X-Bars)
Cm= Nm {[X-2C] +2[h-2C]-2[2dm]}
6. Cutting Length of Distribution Reinforcement (Y-Bars)
Cd1= [Y-2C] +2[h-2C]-2[2dm]
7. Total Cutting Length of Main Reinforcement (Y-Bars)
Cd = Nd x Cd1
8. Estimation of Steel Quantity
Wm = D2Cm/162
Wd = D2Cd/162
Where: Wm = steel quantity for main reinforcement
Wd = steel quantity for distribution reinforcement
Notably, W = D2L/162 gives the weight of one bar.
SAMPLE PROBLEM
Size a spread footing for Column B-3 in the building shown below. The footing thickness
is 1ft 9in. Assume that the footings bear on silty sand with an allowable soil bearing
pressure of 3000 psf.
Reactions:
Roof beam reaction = 5,000 lb
Roof girder reaction = 10,000 lb
2nd floor beam reaction = 13,500 lb
2nd floor girder reaction = 27,000 lb
Column loads:
1) Roof beam
2(Roof beam reaction)
= 2(5000)
= 10,000 lb
2) Roof girder
2(Roof girder reaction)
= 2(10,000)
= 20,000 lb
3) Second floor beam
2(Floor beam reaction)
= 2(13,500)
= 27,000 lb
4) Second floor girder
2(girder reaction)
= 2(27,000)
= 54,200 lb
5) Column weight
Column weight = 1,500 lb
6) Total weight acting on column
10,000+20,000+27,000+54,200+1,500 = 112,500 lb
7) P footing
P footing = t footing (150 lb/cu.ft)
P footing = (1.75)(150 lb/cu.ft)
P footing = 262.5 lb/sqft
8) Net allowable soil bearing pressure
q net = q allowable – p footing
q net = 3000 lb/sqft – 262.5 lb/sqft
q net = 2737.5 lb/sqft
9) Required footing area
A > P column/q net
A > 112,500/2737.5
A > 41.1 ft^2
10) Shape of footing and sizing
Area of square = x^2
41.1 ft^2 = x^2
X = 6.4 ft
Use 6’ – 6” x 6’ – 6” x 1’ – 9” thk
Re-bar estimation
1) Needed variables
Variable Denoted as Value
Length of footing X 6.4” or 1.95 m
Breadth of footing Y 6.4” or 1.95 m
Height of the footing
h 1.9” or .58 m
(thickness)
Diameter of main
dm 12 mm
reinforcement
Diameter of distribution
dd 12 mm
reinforcement bars
Spacing of main re-bars sm 150 mm
Spacing of distribution of
sd 150 mm
re-bars
Cover for re-
c 50 mm
bars/concreter cover
2) Calculated Number of main rebars (x-bars)
Nm = (Y / Spacing of Main Reinforcement) + 1
Nm = (1.95 / .150) + 1
Nm = 14 bars
3) Calculation of Number of Distribution Reinforcement (Y-Bars)
Nd = (X/Spacing of Distribution Reinforcement) +1
Nd = (1.95/.150) + 1
Nd = 14 bars
4) Cutting Length of Main Reinforcement (X-Bars)
Cm1 = [X-2C] +2[h-2C]-2[2dm]
Cm1 = [1.95-2(.05)] +2[.58-2(.05)]-2[2(.012)]
Cm1 = 2.762m
5) Total Cutting Length of Main Reinforcement (X-Bars)
Cm= Nm {[X-2C] +2[h-2C]-2[2dm]}
Cm = 14(2.762)
Cm = 38.668 m
6) Cutting Length of Distribution Reinforcement (Y-Bars)
Cd1= [Y-2C] +2[h-2C]-2[2dm]
Cd1 = [1.95-2(.05)] +2[.58-2(.05)]-2[2(.012)]
Cd1 = 2.762 m
7) Total Cutting Length of Main Reinforcement (Y-Bars)
Cd = Nd x Cd1
Cd = 14(2.762)
Cd = 38.668 m
8) Estimation of Steel Quantity
Wm = D2Cm/162
Wm = (12 x 12 x 38.668)/162
Wm = 34.37 kg
Wd = D2Cd/162
Wd = (12 x 12 x 38.668)/162
d = 34.37 kg
