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**Chp.12 Cont. – Examples to design Footings**

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Example Design a square footing to support a 18 in. square column tied interior column reinforced with 8 #9 bars. The column carries an unfactored axial dead load of 245 k and an axial live load of 200 k. The base of the footing is 4 ft. below final grade and allowable soil pressure is 5 k/ft2 Use fc = 3 ksi and fy = 60 ksi

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Example 1 Assume a depth of footing. (2 ft or 24 in.) The weight of concrete and the soil are:

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Example 1 The effective soil pressure is given as:

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Example 1 Calculate the size of the footing:

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Example 1 Calculate net upward pressure:

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Example 1 Calculate the depth of the reinforcement use # 8 bars with a crisscrossing layering.

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Example 1 Calculate perimeter for two-way shear or punch out shear. The column is 18 in. square.

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Example 1 Calculate the shear Vu The shape parameter

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Example 1 Calculate d value from the shear capacity according to chose the largest value of d as is 40 for interior, 30 for edge and 20 for corner column

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Example 1 The depth of the footing can be calculated by using two way shear

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Example 1 The second equation bo is dependent on d so use the assumed values and you will find that d is smaller and a = 40 Actual (d = in.) bo= in

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Example 1 The depth of the footing can be calculated by using one-way shear

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Example 1 The depth of the footing can be calculated by using one-way shear The footing is 19.5 in. > 13.9 in. so it will work.

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Example 1 Calculate the bending moment of the footing at the edge of the column

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Example 1 Calculate Ru for the footing to find r of the footing.

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Example 1 From Ru for the footing the r value can be found.

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**Example 1 Compute the area of steel needed**

The minimum amount of steel for shrinkage is The minimum amount of steel for flexure is

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**Example 1 Use a #7 bar (0.60 in2) Compute the number of bars need**

Determine the spacing between bars

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Example 1 Check the bearing stress. The bearing strength N1, at the base of the column, 18 in x 18 in., f = 0.7 The bearing strength, N2, at the top of the footing is

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Example 1 The bearing strength, N2, at the top of the footing is

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Example 1 Pu =683 k < 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.

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Example 1 The development length of the dowels in compression from ACI Code for compression. The minimum ld , which has to be greater than 8 in., is

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Example 1 Therefore, use 4#8 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.

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Example 1 The development length, ld for the #7 bars for the reinforcement of the footing. There is adequate development length provided.

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Example 1 - Final Design

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Example 2 Design a footing to support a 18 in. square column tied interior column reinforced with 8 #9 bars. The column carries an unfactored axial dead load of 245 k and an axial live load of 200 k. The base of the footing is 4 ft. below final grade and allowable soil pressure is 5 k/ft2 Use fc = 3 ksi and fy = 60 ksi. Limit one side of the footing to 8.5 ft.

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Example 2 Assume a depth of footing. (2 ft or 24 in.) The weight of concrete and the soil are:

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Example 2 The effective soil pressure is given as:

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Example 2 Calculate the size of the footing:

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Example 2 Calculate net upward pressure:

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Example 2 Calculate the depth of the reinforcement use # 8 bars with a crisscrossing layering.

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Example 2 The depth of the footing can be calculated by using the one-way shear (long direction) Vu =150.7 k in short direction

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Example 2 The depth of the footing can be calculated by using one-way shear design The footing is 19.5 in. > 18.8 in. so it will work.

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Example 2 Calculate perimeter for two-way shear or punch out shear. The column is 18 in. square.

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Example 2 Calculate the shear Vu The shape parameter

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Example 2 Calculate d from the shear capacity according to chose the largest value of d. as is 40 for interior, 30 for edge and 20 for corner column

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Example 2 The depth of the footing can be calculated for the two way shear

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Example 2 The third equation bo is dependent on d so use the assumed values and you will find that d is smaller and a = 40 Actual (d = in.) bo= in

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Example 2 The depth of the footing can be calculated by using the two way shear

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Example 2 Calculate the bending moment of the footing at the edge of the column (long direction)

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Example 2 Calculate Ru for the footing to find r of the footing.

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Example 2 Use the Ru for the footing to find r.

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**Example 2 Compute the amount of steel needed**

The minimum amount of steel for shrinkage is The minimum amount of steel for flexure is

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Example 2 Use As =8.36 in2 with #8 bars (0.79 in2). Compute the number of bars need Determine the spacing between bars

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Example 2 Calculate the bending moment of the footing at the edge of the column for short length

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Example 2 Calculate Ru for the footing to find r of the footing.

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Example 2 Use Ru for the footing to find r.

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**Example 2 Compute the amount of steel needed**

The minimum amount of steel for shrinkage is The minimum amount of steel for flexure is

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Example 2 Use As =9.36 in2 with #6 bar (0.44 in2) Compute the number of bars need Calculate the reinforcement bandwidth

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**Example 2 The number of bars in the 8.5 ft band is 0.83(22)=19 bars .**

So place 19 bars in 8.5 ft section and 2 bars in each in (12ft -8.5ft)/2 =1.75 ft of the band.

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**Example 2 Determine the spacing between bars for the band of 8.5 ft**

Determine the spacing between bars outside the band

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Example 2 Check the bearing stress. The bearing strength N1, at the base of the column, 18 in x 18 in., f = 0.7 The bearing strength, N2, at the top of the footing is

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Example 2 The bearing strength, N2, at the top of the footing is

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Example 2 Pu =683 k < 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.

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Example 2 The development length of the dowels in compression from ACI Code for compression. The minimum ld , which has to be greater than 8 in., is

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Example 2 Therefore, use 4#8 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.

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**Example 2 The development length, ld for the #8 bars**

There is adequate development length provided.

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**Example 2 The development length, ld for the #6 bars**

There is adequate development length provided.

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Example 2 - Final design 12 #8 23 #6

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