Chapter 5Footing DesignBy S. Ali Mirza1 and William Brant25.1 IntroductionReinforced concrete foundations, or footings, transmit loads from a structure to the supporting soil.Footings are designed based on the nature of the loading, the properties of the footing and theproperties of the soil.Design of a footing typically consists of the following steps:1. Determine the requirements for the footing, including the loading and the nature of the supportedstructure.2. Select options for the footing and determine the necessary soils parameters. This step is oftencompleted by consulting with a Geotechnical Engineer.3. The geometry of the foundation is selected so that any minimum requirements based on soilsparameters are met. Following are typical requirements: 12The calculated bearing pressures need to be less than the allowable bearing pressures. Bearingpressures are the pressures that the footing exerts on the supporting soil. Bearing pressures aremeasured in units of force per unit area, such as pounds per square foot.The calculated settlement of the footing, due to applied loads, needs to be less than theallowable settlement.The footing needs to have sufficient capacity to resist sliding caused by any horizontal loads.The footing needs to be sufficiently stable to resist overturning loads. Overturning loads arecommonly caused by horizontal loads applied above the base of the footing.Local conditions.Building code requirements.Professor Emeritus of Civil Engineering, Lakehead University, Thunder Bay, ON, Canada.Structural Engineer, Black & Veatch, Kansas City, KS.1

4. Structural design of the footing is completed, including selection and spacing of reinforcing steel inaccordance with ACI 318 and any applicable building code. During this step, the previouslyselected geometry may need to be revised to accommodate the strength requirements of thereinforced concrete sections. Integral to the structural design are the requirements specific tofoundations, as defined in ACI 318-05 Chapter 15.5.2 Types of FoundationsShallow footings bear directly on the supporting soil. This type of foundation is used when the shallowsoils can safely support the foundation loads.A deep foundation may be selected if the shallow soils cannot economically support the foundationloads. Deep foundations consist of a footing that bears on piers or piles. The footing above the piersor piles is typically referred to as a pile cap.The piers or piles are supported by deeper competent soils, or are supported on bedrock. It iscommonly assumed that the soil immediately below the pile caps provides no direct support to the pilecap.5.3 Allowable Stress Design and Strength DesignTraditionally the geometry of a footing or a pile cap is selected using unfactored loads. The structuraldesign of the foundation is then completed using strength design in accordance with ACI 318.ACI Committee 336 is in the process of developing a methodology for completing the entire footingdesign using the strength design method.5.4 Structural DesignThe following steps are typically followed for completing the structural design of the footing or pilecap, based on ACI 318-05:1. Determine footing plan dimensions by comparing the gross soil bearing pressure and the allowablesoil bearing pressure.2. Apply load factors in accordance with Chapter 9 of ACI 318-05.3. Determine whether the footing or pile cap will be considered as spanning one-way or two-ways.4. Confirm the thickness of the footing or pile cap by comparing the shear capacity of the concretesection to the factored shear load. ACI 318-05 Chapter 15 provides guidance on selecting thelocation for the critical cross-section for one-way shear. ACI 318-05 Chapter 11 provides guidanceon selecting the location for the critical cross-section for two-way shear. Chapter 2 of thishandbook on shear design also provides further design information and design aids.2

5. Determine reinforcing bar requirements for the concrete section based on the flexural capacityalong with the following requirements in ACI 318-05. Requirements specific to footingsTemperature and shrinkage reinforcing requirementsBar spacing requirementsDevelopment and splicing requirementsSeismic Design provisionsOther standards of design and construction, as required5.5 Footings Subject to Eccentric LoadingFootings are often subjected to lateral loads or overturning moments, in addition to vertical loads.These types of loads are typically seismic or wind loads.Lateral loads or overturning moments result in a non-uniform soil bearing pressure under the footing,where the soil bearing pressure is larger on one side of the footing than the other. Non-uniform soilbearing can also be caused by a foundation pedestal not being located at the footing center of gravity.If the lateral loads and overturning moments are small in proportion to the vertical loads, then theentire bottom of the footing is in compression and a P/A M/S type of analysis is appropriate forcalculating the soil bearing pressures, where the various parameters are defined as follows:P The total vertical load, including any applied loads along with the weight of all of thecomponents of the foundation, and also including the weight of the soil locateddirectly above the footing.A The area of the bottom of the footing.M The total overturning moment measured at the bottom of the footing, includinghorizontal loads times the vertical distance from the load application location to thebottom of the footing plus any overturning moments.S The section modulus of the bottom of the footing.If M/S exceeds P/A, then P/A - M/S results in tension, which is generally not possible at the footing/soilinterface. This interface is generally only able to transmit compression, not tension. A differentmethod of analysis is required when M/S exceeds P/A.Following are the typical steps for calculating bearing pressures for a footing, when non-uniformbearing pressures are present. These steps are based on a footing that is rectangular in shape whenmeasured in plan, and assumes that the lateral loads or overturning moments are parallel to one of theprincipal footing axes. These steps should be completed for as many load combinations as required toconfirm compliance with applicable design criteria. For instance, the load combination with themaximum downward vertical load often causes the maximum bearing pressure while the loadcombination with the minimum downward vertical load often causes the minimum stability.3L

1. Determine the total vertical load, P.2. Determine the lateral and overturning loads.3. Calculate the total overturning moment M, measured at the bottom of the footing.4. Determine whether P/A exceeds M/S. This can be done by calculating and comparing P/A andM/S or is typically completed by calculating the eccentricity, which equals M divided by P. If eexceeds the footing length divided by 6, then M/S exceed P/A.5. If P/A exceeds M/S, then the maximum bearing pressure equals P/A M/S and the minimumbearing pressure equals P/A-M/S.6. If P/A is less than M/S, then the soil bearing pressure is as shown in Fig. 5-1. Such a soilbearing pressure distribution would normally be considered undesirable because it makes thefooting structurally ineffective. The maximum bearing pressure, shown in the figure, iscalculated as follows:Maximum Bearing pressure 2 P / [(B) (X)]Where X 3(L/2 - e) and e M / PFig. 5-1 Footing under eccentric loading5.6 Footing Design ExamplesThe footing examples in this section illustrate the use of ACI 318-05 for some typical footing designsas well as demonstrate the use of some design aids included in other chapters. However, theseexamples do not necessarily provide a complete procedure for foundation design as they are notintended to substitute for engineering skills or experience.4

FOOTINGS EXAMPLE 1 -Design of a continuous (wall) footingDetermine the size and reinforcement for the continuousfooting under a 12 in. bearing wall of a 10 story buildingfounded on soil.Given:/Νc 4 ksi/y 60 ksiDead Load D 25 k/ftLive Load L 12.5 k/ftWind O.T. W 4 k/ft(axial load due to overturning under wind loading)Seismic O.T. E 5 k/ft(axial load due to overturning under earthquake loading)Allowable soil bearing pressures:D 3 ksf "a"D L 4 ksf "b"D L (W or E) 5 ksf "c"ProcedureSizing the footing.Required strength.ComputationIgnoring the footing self-weight;D/a 25/3 8.3 ft(D L)/b 37.5/4 9.4 ft Ζ controls(D L W)/c 41.5/5 8.3 ft(D L E)/c 42.5/5 8.5 ftUse B 10 ftU 1.4D 1.4(25) 35 k/ft or 3.50 ksfACI318-05SectionDesignAid9.2U 1.2D 1.6L 1.2(25) 1.6(12.5) 50 k/ft or 5.00 ksf (Controls)U 1.2D 1.6W 1.0L 1.2(25) 1.6(4) 12.5 48.9 k/ft or 4.89 ksfU 0.9D 1.6W 0.9(25) 1.6(4) 28.9 k/ft or 2.89 ksfU 1.2D 1.0E 1.0L 1.2(25) (5) 12.55

47.5 k/ft or 4.75 ksfDesign for shear.U 0.9D 1.0E 0.9(25) (5) 27.5 k/ft or 2.75 ksfφshear 0.75Assume Vs 0 (no shear reinforcement)φVn φVcφVc φ ( 2 f 'c bw d )11.3Try d 17 in. and h 21 in.φVc 0.75( 2 4000 )( 12 )( 17 ) / 1000 19.35 k/ftCalculate Vu at d from the face of thewallVu (10/2 - 6/12 - 17/12)(5.00) 15.5 k/ftφVn φVc Vu11.1.3.1OKCalculate moment at the face of the wallMu (5)(4.5)2/2 50.6 ft-k/ftCompute flexural tension reinforcementφKn Mu (12,000)/(bd2)15.4.2φKn 50.6 (12,000)/[(12)(17)2] 176 psiFlexure 1For φKn 176 psi, select ρ 0.34%As ρbd 0.0034 (12) (17) 0.70 in2/ftCheck for As,min 0.0018 bhAs,min 0.0018(12)(21) 0.46 in2/ft 0.7in2/ftOKUse bottom bars #8 @ 13 in c/c hooked atends. If these bars are not hooked, providecalculations to justify the use of straightbars.Note: εt 0.040 0.005 for tensioncontrolled sections and φ 0.97.1210.5.410. 1Use top bars #5 @ 13 in c/c arbitrarilydesigned to take approximately 40% ofbending moment due to possible reversalcaused by earthquake loads.Shrinkage and temperaturereinforcement8# 5 top and bottom longitudinal bars willsatisfy the requirement for shrinkage and7.126

Check shear for earthquake load effects.For structural members resistingearthquake loads, if the nominal shearstrength is less than the shearcorresponding to the development ofnominal flexural resistance, then;φshear 0.6temperature reinforcement in the otherdirection.Mn 61.9 ft-k/ft and the correspondingVfn 18.6 k/ft9.3.4 (a)Vc 2 4000 (12)(17.5) / 1000 26.5 k/ft Vfn 18.6 k/ftTherefore, the use of φshear 0.75 above iscorrect.Final DesignFOOTINGS EXAMPLE 2 -Design of a square spread footingDetermine the size and reinforcing for a square spread footing that supports a 16 in. square column, founded onsoil.Given:ƒ’c 4 ksiƒy 60 ksiDead Load D 200 kLive Load L 100 kAllowable soil bearing pressures:Due to D 4 ksf "a"Due to D L 7 ksf "b"7

ProcedureSizing the footing.Required strength.Design for shear.ComputationDesignAidIgnoring the footing self-weight;D/a 200/4 50 sq. ft. (Controls)(D L)/b 300/7 42.9 sq. ft.Use 7.33 ft x 7.33 ftA 53.7 50 sq. ft. OKU 1.4D 1.4(200) 280 k or (280/53.7) 5.3 ksfU 1.2D 1.6L 1.2(200) 1.6(100) 400k or (400/53.7) 7.5 ksf(Controls)φshear 0.75Assume Vs 0 (no shear reinforcement)φVn φVcTwo-way actionACI 31805Section9. d 16 in. and h 20 4(16 16) 128 in.Vc ( 2 4β) f 'c bo d4) f 'c bo d 6 f 'c bo d16 / 16αdVc ( s 2 ) f 'c bo dbo11. (2 Vc ( 40 )( 16 ) 2 ) f 'c bo d128Vc 7 f 'c bo dVc 4 f 'c bo d (Controls)φVc 0.75( 4 4000 ( 128 )( 16 )) / 1000 388.5 kVu [(7.33)2 – ((16 16)/12)2 ](7.5) 349.6 k8

One-way actionφVn φVc VuOKbw 7.33 (12) 88 in. and d 15.5 in. 2 f 'c bw d11.3.1.1φVc 0.75( 2 4000 )( 88 )( 15.5 ) / 1000 129.4 kVu 7.33 [(7.33/2) – (8 15.5)/12](7.5) 94.0 kφVn φVc Vu OKBearingφbearing 0.659.3.2.410.17.1A2 / A1 2Bearing resistance of footingBr φ ( 0.85 f 'c A1 ) A2 / A1Br 0.65(0.85)(4)(16)2 (2)Br 1131 k 400 kOKCalculate moment at the column faceCompute flexural tension reinforcement(bottom bars) using design aids inChapter 1Mu (7.5)(3)2 (7.33)/2 248 ft-k15.4.2φKn Mu (12,000)/(bd2)Flexure 1φKn 248 (12,000)/[(7.33)(12)(15.5)2] 141 psiFor φKn 141 psi, select ρ 0.27%As ρbd 0.0027 (7.33)(12)(15.5) 3.7in2Check for As,min 0.0018 bhAs,min 0.0018(7.33)(12)(20) 3.2 in2 3.7in2 OKUse 9 #6 straight bars in both directionsNote: εt 0.050 0.005 for tensioncontrolled sections and φ 0.9.Development length:Critical sections for development lengthoccur at the column face.()l d f y Ψt Ψe λ /(25 f 'c ) db7.1210.5.4Flexure ( 60 ,000 )( 1.0 )( 1.0 )( 1.0 ) 0.75l d 254,000 Ρd 29 in. Ρd (provided) (3)(12) – 3 33 in OK9

Final DesignFOOTINGS EXAMPLE 3 -Design of a rectangular spread footing.Determine the size and reinforcing for a rectangular spread footing that supports a 16 in. square column, founded on soil.Given:ƒ’c 4 ksiƒy 60 ksiDead Load D 180 kLive Load L 100 kWind O.T. W 120 k(axial load due to overturning under wind loading)Allowable soil bearing pressures:Due to D 4 ksf “a”Due to D L 6 ksf “b”Due to D L W 8.4 ksf “c”Design a rectangular footing withan aspect ratio 0.6ProcedureSizing the footing.Required StrengthComputationIgnoring the self-weight of the footing;D/a 180/4 45 sq.ft.(D L)/b 280/6 46.7 sq.ft.(D L W)/c 400/8.4 47.6 sq.ft.ControlsUse 5 ft x 10 ftA 50 sq.ft. is OKU 1.4D 1.4(180) 252 k or (252/50) 5.1 ksfACI 31805SectionDesignAid9.2U 1.2D 1.6L10

1.2(180) 1.6(100) 376 k or (376/50) 7.6 ksfU 1.2D 1.6W 1.0L 1.2(180) 1.6(120) 1.0(100) 508 k or 10.2 ksf (Controls)Design for shear.U 0.9D 1.6W 0.9(180) 1.6(120) 354 k or 7.1 ksfφshear 0.75Assume Vs 0 (no shear reinforcement)φVn φVcTwo-way action9.3.