Lecture 40 Footings

1
Lecture 40 - Footings

• April 26, 2002
• CVEN 444

2
Lecture Goals

• Footing Examples

3
Example 1
Design a rectangular footing to support two
square columns. The exterior column (I) has a
section 16 x 16 in., which carries DL of 180 k
and a LL of 120 k. The interior column (II) has a
section of 20 x 20 in.,
which carries a DL of 250 k and a LL of 140 k.
The base of the footing is 5 ft. below final
grade and allowable soil pressure is 5 k/ft2 Use
fc 4 ksi and fy 60 ksi The external column
is located 2 ft from the property line.
4
Example 1
Determine the location of an equivalent point and
its location select the datum at column I
Extend the footing up to the property line, so
the length is l 9 ft 2 ft. 11 ft. So the
length of the footing is 2(11 ft.) 22 ft.
5
Example 1
Assume a depth of footing. (36 in.) The weight
of concrete and the soil are
6
Example 1
The effective soil pressure is given as
7
Example 1
Calculate the size of the footing
8
Example 1
Calculate net upward pressure
9
Example 1
Calculate the depth of the reinforcement use 8
bars with a crisscrossing layering.
10
Example 1
Compute the shear and bending moment diagrams.
The columns are considered point loads but shear
values are taken at each side of the column.
11
Example 1
The location of the maximum moment is
12
Example 1
Compute the shear and bending moment diagrams.
The columns are considered point loads but
moments are taken at each side of the column. It
will not balance because center is at 9.04 ft
13
Example 1
The maximum shear force occurs at the edge of the
20 in. column. So maximum shear is measured at
distance d from the column.
14
Example 1
The depth of the footing can be calculated by
using one-way shear
The footing is 31.5 in. gt 24.2 in. so it will
work.
15
Example 1
Calculate perimeter for two-way shear or punch
out shear. The column is 20 in. square.
16
Example 1
Calculate the shear Vu
The other column will not be critical, Pu 456 k
for the 16 in. column
17
Example 1
The depth of the footing can be calculated by
using two way shear
18
Example 1
Calculate Ru for the footing to find r of the
footing.
19
Example 1
From Ru for the footing the r value can be found.
20
Example 1
Compute the area of steel needed
The minimum amount of steel for shrinkage is
The minimum amount of steel for flexure is
21
Example 1
Use a 9 bar (1.00 in2) Compute the number of
bars need
Determine the spacing between bars
22
Example 1
The minimum amount is steel is going to be due to
the flexural restrictions. So below the columns
with positive moment, the reinforcement will be
10 9 bars running longitudinally. The
development length will have to be calculated.
23
Example 1
The development length, ld for the 7 bars for
the reinforcement of the footing.
The bars have more than 12-in. of concrete below
them, therefore ld 1.3 ld.
24
Example 1
To determine the reinforcement in the short
direction. The bandwidth of the two columns must
be determined for the 16 in. column.
Compute the moment at the edge
25
Example 1
The bending moment will be
Compute the Ru
26
Example 1
From Ru for the footing the r value can be found.
27
Example 1
Compute the area of steel needed
The minimum amount of steel for shrinkage is
The minimum amount of steel for flexure is
28
Example 1
Use a 9 bar (1.00 in2) Compute the number of
bars need
Determine the spacing between bars
29
Example 1
To determine the reinforcement in the short
direction. The 20-in. interior column extends
beyond 4 ft from the center therefore the band is
7.5 ft x 7.5 ft. Compute the moment at the edge
30
Example 1
The bending moment will be
Compute the Ru
31
Example 1
From Ru for the footing the r value can be found.
32
Example 1
Compute the area of steel needed
The minimum amount of steel for shrinkage is
The minimum amount of steel for flexure is
33
Example 1
Check the bearing stress. The bearing strength
N1, at the base of the column, 16 in x 16 in., f
0.7
The bearing strength, N2, at the top of the
footing is
34
Example 1
The bearing strength, N2, at the top of the
footing is
35
Example 1
Pu 456 k lt N1, bearing stress is adequate. The
minimum area of dowels is required.
Use minimum number of bars is 4, so use 4 7
bars placed at the four corners of the column.
Note if the Pu gt N1 the area of steel will be
As long as the area of steel is greater than the
minimum amount.
36
Example 1
The development length of the dowels in
compression from ACI Code 12.3.2 for compression.
The minimum ld , which has to be greater than 8
in., is
37
Example 1
Therefore, use 47 dowels in the corners of the
column extending 17 in. into the column and the
footing. Note that ld is less than the given d
31.5 in., which is sufficient development length.
38
Example 1
Use a 9 bar (1.00 in2) Compute the number of
bars need
Determine the spacing between bars
39
Example 1
Check the bearing stress. The bearing strength
N1, at the base of the column, 20 in x 20 in., f
0.7
The bearing strength, N2, at the top of the
footing is
40
Example 1
The bearing strength, N2, at the top of the
footing is
41
Example 1
Pu 588 k lt N1, bearing stress is adequate. The
minimum area of dowels is required.
Use minimum number of bars is 4, so use 4 8
bars placed at the four corners of the column.
42
Example 1
The development length of the dowels in
compression from ACI Code 12.3.2 for compression.
The minimum ld , which has to be greater than 8
in., is
43
Example 1
Therefore, use 48 dowels in the corners of the
column extending 19 in. into the column and the
footing. Note that ld is less than the given d
31.5 in., which is sufficient development length.
44
Example 2
Determine the footing areas required for equal
settlement (balanced footing design) if the usual
live load is 25 for all footings. The footings
are subjected to dead loads and live loads as
indicated by the table. The net soil pressure is
6 ksf.
45
Example 2
Find the ratio of the live load to dead load, the
largest ratio will control the settlement.
Column 3 has the largest ratio.
46
Example 2
Compute the usual loading for the footing, DL
0.25LL
Column 3 has the largest ratio.
47
Example 2
Determine the need area for the footing with the
largest LL/DL ratio.
The usual net soil pressure acting on the footing
is
48
Example 2
Use the qnet (3.353 k/ft2) to determine need area
for each of the other footings to have the same
settlement.
Compute the qnet for each of the footings
49
Example 2
Use the qnet (3.353 k/ft2) to determine need area
for each of the other footings to have the same
settlement.
50
Example 3
51
Example 3
Find the combined actual loads, P0 and M0
Determine the eccentricity of the footing
52
Example 3
Assume a depth of footing, 24 in. The weight
of concrete and the soil are
53
Example 3
The effective soil pressure is given as
54
Example 3
Calculate the size of the footing
Compute the sizes of the footing if width is 9 ft.
55
Example 3
Use the long section and place the column 10 in.
off-center for the 10 ft segment
56
Example 3
Calculate net upward pressure
57
Example 3
Calculate the depth of the reinforcement use 8
bars with a crisscrossing layering.
58
Example 3
The depth of the footing can be calculated by
using the one-way shear (long direction)
59
Example 3
The depth of the footing can be calculated by
using one-way shear design
The footing is 19.5 in. gt 16.3 in. so it will
work.
60
Example 3
Calculate perimeter for two-way shear or punch
out shear. The column is 12 in. x 24 in.
61
Example 3
Calculate the shear Vu
The shape parameter
62
Example 3
Calculate d from the shear capacity according to
11.12.2.1 chose the largest value of d.
63
Example 3
The depth of the footing can be calculated for
the two way shear
64
Example 3
The third equation bo is dependent on d so use
the assumed values and you will find that d is
smaller and a 40
65
Example 3
The depth of the footing can be calculated by
using the two way shear
66
Example 3
Calculate the bending moment of the footing at
the edge of the column (long direction)
67
Example 3
Calculate Ru for the footing to find r of the
footing.
68
Example 3
Use the Ru for the footing to find r.
69
Example 3
Compute the amount of steel needed
The minimum amount of steel for shrinkage is
The minimum amount of steel for flexure is
70
Example 3
Use As 8.36 in2 with 8 bars (0.79 in2).
Compute the number of bars need
Determine the spacing between bars
71
Example 3
Calculate the bending moment of the footing at
the edge of the column for short length
72
Example 3
Calculate Ru for the footing to find r of the
footing.
73
Example 3
Use Ru for the footing to find r.
74
Example 3
Compute the amount of steel needed
The minimum amount of steel for shrinkage is
The minimum amount of steel for flexure is
75
Example 3
Use As 9.36 in2 with 6 bar (0.44 in2) Compute
the number of bars need
Calculate the reinforcement bandwidth
76
Example 3
The number of bars in the 9 ft band is
0.947(18)17 bars . So place 17 bars in 9 ft
section and 1 bars in each in (10ft -
9ft)/2 0.5 ft of the band.
77
Example 3
Determine the spacing between bars for the band
of 9 ft
Determine the spacing between bars outside the
band
78
Example 3
Check the bearing stress. The bearing strength
N1, at the base of the column, 12 in x 24 in., f
0.7
The bearing strength, N2, at the top of the
footing is
79
Example 3
The bearing strength, N2, at the top of the
footing is
80
Example 3
Pu 683 k lt N1, bearing stress is adequate. The
minimum area of dowels is required.
Use minimum number of bars is 4, so use 4 8
bars placed at the four corners of the column.
81
Example 3
The development length of the dowels in
compression from ACI Code 12.3.2 for compression.
The minimum ld , which has to be greater than 8
in., is
82
Example 3
Therefore, use 48 dowels in the corners of the
column extending 19 in. into the column and the
footing. Note that ld is less than the given d
19.5 in., which is sufficient development length.
83
Example 3
The development length, ld for the 8 bars
There is adequate development length provided.
84
Example 3
The development length, ld for the 6 bars
There is adequate development length provided.