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

2. 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

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

4. Example 1
The effective soil pressure is given as:

5. Example 1
Calculate the size of the footing:

6. Example 1
Calculate net upward pressure:

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

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

9. Example 1
Calculate the shear Vu
The shape parameter

10. 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

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

12. 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

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

14. 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.

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

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

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

18. Example 1 Compute the area of steel needed
The minimum amount of steel for shrinkage is
The minimum amount of steel for flexure is

19. Example 1 Use a #7 bar (0.60 in2) Compute the number of bars need
Determine the spacing between bars

20. 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

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

22. 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.

23. 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

24. 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.

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

26. Example 1 - Final Design

27. 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.

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

29. Example 2
The effective soil pressure is given as:

30. Example 2
Calculate the size of the footing:

31. Example 2
Calculate net upward pressure:

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

33. 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

34. 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.

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

36. Example 2
Calculate the shear Vu
The shape parameter

37. 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

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

39. 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

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

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

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

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

44. Example 2 Compute the amount of steel needed
The minimum amount of steel for shrinkage is
The minimum amount of steel for flexure is

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

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

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

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

49. Example 2 Compute the amount of steel needed
The minimum amount of steel for shrinkage is
The minimum amount of steel for flexure is

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

51. 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.

52. Example 2 Determine the spacing between bars for the band of 8.5 ft
Determine the spacing between bars outside the band

53. 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

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

55. 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.

56. 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

57. 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.

58. Example 2 The development length, ld for the #8 bars
There is adequate development length provided.

59. Example 2 The development length, ld for the #6 bars
There is adequate development length provided.

60. Example 2 - Final design
12 #8
23 #6