1. Footings

2. Acknowledgement
This Powerpoint presentation was prepared by Dr. Terry Weigel, University of Louisville. This work and other contributions to the text by Dr. Weigel are gratefully acknowledged.

3. Footings Support structural members and transfer loads to the soil
Structural members are usually columns or walls
Design for load transfer to soil uses unfactored loads
Structural design of footing is done with factored loads

4. Footings
Footings must be designed to prevent bearing failure, sliding and overturning
Footings must be designed to prevent excessive settlement or tilting
Typically, bottom of footing must be located below frost line
Excavation may be required to reach a depth where satisfactory bearing material is located

5. Wall Footing
Wall footings – enlargement of the bottom of the wall

6. Isolated Square Footing
Isolated or single column square footing – loads relatively light and columns not closely spaced

7. Combined Footing
Combined footings – support two or more columns – heavily loaded columns; closely spaced columns; columns near property line

8. Mat Footing
Mat or raft foundation – continuous concrete slab supporting many columns; soil strength relatively low; large column loads; isolated spread footings would cover more than 50 percent of area; reduce differential settlement

9. Pile Cap
Pile caps – distribute column loads to groups of piles

10. Soil Pressure
Soil pressure is assumed to be uniformly distributed beneath footing if column load is applied at the center of gravity of the footing
Footings supported by sandy soils
Footings supported by clayey soils
Footings supported eccentric loads

11. Assumed Soil Pressure

12. Soil Pressure - Sandy Soil

13. Soil Pressure - Clayey Soil

14. Allowable Soil Pressure
Actual soil pressure is based on unfactored loads
Allowable soil pressure may be determined by a geotechnical engineer
When soil exploration is not feasible, values provided by building codes may be used
Factor of safety is typically 3

15. Allowable Soil Pressure (Table 12.1)
Maximum Allowable Soil Pressure
Material
Allowable Pressure, ksf
Rock
20% of ultimate strength
Compact coarse or fine sand, hard clay or sand clay 8
Medium stiff clay or sandy clay 6
Compact inorganic sand and silt mixtures 4
Loose sand 3
Soft sand clay or clay 2
Loose inorganic sand-silt mixtures 1
Loose organic sand-silt mixtures, muck or bay mud

16. Design of Wall Footings
Generally, beam design theory is used
Shear strength almost always controls footing depth
Compute moment at the face of the wall (concrete wall) or halfway between wall face and its centerline (masonry walls)

17. Design of Wall Footings

18. Design of Wall Footings

19. Design of Wall Footings

20. Design of Wall Footings

21. Design of Wall Footings
Shear may be calculated at distance d from face of the wall
Use of stirrups is not economical – set d so that concrete carries all the shear

22. Design of Wall Footings
Design a 12-in wide strip
Section 15.7 of ACI Code:
Depth of footing above bottom reinforcement not less than 6 in for footings on soil and not less than 12 in for footings on piles
Minimum practical depth of footing is 10 in and 16 in for pile caps

23. Wall Footing Design Examples

24. Example 12.1
Design a wall footing to support a 12-in. wide reinforced concrete wall with a dead load of 20 k/ft and a live load of 15 k/ft. The bottom of the footing is to be 4 foot below final grade, the soil weighs 100 lb/ft3 the allowable soil pressure is 4 ksf. The concrete strength is 3,000 psi and the steel is Grade 60.

25. Example 12.1

26. Example 12.1
Assume a footing thickness of 12 in. With a minimum cover of 3 in., this gives a d value of about 8.5 in. Compute the footing weight and
soil weight:

27. Example 12.1
Effective soil pressure and required width of footing:

28. Example 12.1
Factored bearing pressure for design of concrete:

29. Example 12.1
Compute design shear (at distance d from face of wall):

30. Example 12.1

31. Example 12.1

32. Example 12.1

33. Example 12.1
Appendix Table 4.12, r = < , section is tension controlled; f = 0.9
Use No 7 at 10 in (As = 0.72 in2 / ft from Table A.6)

34. Example 12.1
Development length:

35. Example 12.1

36. Example 12.1
Available length for development

37. Example 12.1 Temperature and shrinkage steel
Use No 5 at 8 in (As = in2 / ft)

38. Design of Isolated Square Footings
Most isolated square footings have a constant thickness
For very thick footings, it may be economical to step or taper footing
Two types of shear must be considered – one-way shear and two-way shear

39. Design of Isolated Square Footings
Constant thickness

40. Design of Isolated Square Footings
Stepped

41. Design of Isolated Square Footings
Tapered

42. One-way Shear
Same as for wall footings

43. One-way Shear

44. Two-way Shear
ACI Code Section states that critical section is at a distance d/2 from face of support

45. Two-way Shear

46. Two-way Shear

47. Two-way Shear <- ACI Code Equation 11-33

48. Two-way Shear as = 40 for interior columns
as = 30 for exterior columns
as = 20 for corner columns

49. Flexural Design – Isolated Square Footings
Flexural reinforcement is required in two directions
The values of d for the layers of steel in the two directions will be different
For square footings, design using the value of d for the upper layer is typical
For square footings supporting non-square columns, moments are larger in the shorter direction of the column

50. Flexural Design – Isolated Square Footings
Reinforcing steel areas required to resist moment are often less than minimum required steel:
Code Section states that minimum area and maximum spacing need only be equal to values required for temperature and shrinkage steel

51. Flexural Design – Isolated Square Footings
Maximum steel spacing may not exceed three times the footing thickness or 18 in.

52. Load Transfer from Column to Footing
All forces at the base of the column must be transferred to the footing
Compressive forces must be transferred by bearing
Tensile forces may be transferred by reinforcement or mechanical connectors

53. Load Transfer from Column to Footing
Columns transfer loads directly over the area of the column
Load transfer into the footing may by assumed to occur over an effective area which may be larger than the column area
For the same strength of concrete, the footing can support more bearing load than can the column

54. Load Transfer from Column to Footing
Bearing strength permitted at the base of the column ->
Bearing strength permitted on the footing is the same value multiplied by ->
See ACI Code Section

55. Definition of A1 and A2 A1 is the area of the column
A2 is the area of footing geometrically similar to and concentric with the column

56. Column Dowels

57. Excess Bearing Load
Excess bearing load can be carried by dowels or column bars extended into footing
ACI Code Section requires that the dowel area not be less than times the gross cross-sectional area of the column

58. Development Length for Dowels
Development length of dowels must be sufficient to transfer column force to footing
Development length of dowels may not be less than the length required if bearing stress was not exceeded

59. Splice Length for Dowels
ACI Code does not permit splicing of No 14 or No 18 bars
ACI Code Section does permit No 14 or No 18 bars to be spliced to No 11 (or larger) dowels in footings
These dowels must extend into the column not less than the development length for the No 14 or No 18 bar, or the compression lap splice length for the dowels, whichever is larger

60. Splice Length for Dowels
These dowels must extend into the footing for a distance not less than the development length for dowels

61. Insufficient Development or Splice Length
Use a larger number of smaller dowels
Use a deeper footing
Add a cap or pedestal to the footing

62. Column Uplift Development length must be those for tension
Splice requirements are those found in ACI Code Section 12.17

63. Isolated Rectangular Footings
Square footings are more econonical than rectangular footings
Long direction steel is uniformly distributed along short direction
Short direction steel is non uniformly distributed along long direction

64. Isolated Rectangular Footings
ACI Code Section
b is the ratio of the length of the footing in the long direction to the length in the short direction
Remaining steel is distributed uniformly throughout the two portions of the footing outside the band

65. Isolated Rectangular Footings

66. Footing Design Examples

67. Example 12.2
Design a square column footing for a 16-in. square tied interior column that supports loads of D = 200 k and L = 160 k. The column is reinforced with eight No 8 bars, the bottom of the footing is 5 foot below final grade, the soil weighs 100 lb/ft3 the allowable soil pressure is 5 ksf. The concrete strength is 3,000 psi and the steel is Grade 60.

68. Example 12.2
Assume a footing thickness of 24 in. with a minimum cover of 3 in., this gives a d value of about 19.5 in. Compute the footing weight and
soil weight:

69. Example 12.2
Effective soil pressure and required area of footing:

70. Example 12.2
Factored bearing pressure for design of concrete:

71. Example 12.2
Depth required to resist punching shear:

72. Example 12.2

73. Example 12.2
Depth required to resist one-way shear:

74. Example 12.2
Flexural design

75. Example 12.2 Appendix Table 4.12, r = 0.00225 < rmin
Use nine No 8 (As = 7.07 in2)

76. Example 12.2
Development length:

77. Example 12.2

78. Example 12.2
Available length for development

79. Example 12.3
Design for load transfer for the column and footing in Example The strength of the sand-lightweight concrete (different from Example 12.2) in the column is 4 ksi.

80. Example 12.3 Bearing force at the column base:
Design bearing force at the column base:

81. Example 12.3 Design bearing force in the footing concrete:
Minimum dowel area:

82. Example 12.3 Dowel development length into the column
Dowel development length into the footing

83. Example 12.3
Development length must not be less than:

84. Example 12.4
Design for load transfer for a 14-in. square column to a 13 ft square footing if Pu = 800 k. Normal weight concrete is used in both the column and the footing. The concrete in the column is 5 ksi and in the footing is 3 ksi. The column is reinforced with eight No 8 bars.

85. Example 12.4 Bearing force at the column base = 800 k
Design bearing force at the column base:

86. Example 12.4
Design bearing force in the footing concrete:

87. Example 12.4 Design dowels to resist excess bearing force:
Use eight No 7 bars (As = 4.80 in2)

88. Example 12.4
Dowel development length into the column

89. Example 12.4
Dowel development length into the footing

90. Example 12.5
Design a rectangular footing for an 18-in. interior square column for D = 185 k and L = 150 k. The long side of the footing should be twice the length of the short side. The normal weight concrete strength for both the column and the footing is 4 ksi. The allowable soil pressure is 4000 psf and the bottom of the footing is 5 ft below grade.

91. Example 12.5
Assume a footing thickness of 24 in. with a minimum cover of 3 in., this gives a d value of about 19.5 in. Compute the footing weight and
soil weight:

92. Example 12.5
Effective soil pressure and required area of footing:

93. Example 12.5
Depth required to resist one-way shear. Take b = 7 ft.

94. Example 12.5

95. Example 12.5
Depth required to resist punching shear:

96. Example 12.5

97. Example 12.5
Flexural design (steel in long direction)

98. Example 12.5 Appendix Table 4.13, r = 0.00467
Use ten No 8 (As = 7.85 in2)

99. Example 12.5 Flexural design (steel in short direction)
Too low for Table A.13

100. Example 12.5
Use 18 No 7 (As = in2)

101. Example 12.5
Use 2/3 x 18 = 12 bars in band width

102. Example 12.5