Analysis and Design Reinforced Concrete Foundations

Note:The source of the technical material in this volume is the ProfessionalEngineering Development Program (PEDP) of Engineering Services.War ning:The material contained in this document was developed for SaudiAramco and is intended for the exclusive use of Saudi Aramcosemployees.Any material contained in this document which is notalready in the public domain may not be copied, reproduced, sold, given,or disclosed to third parties, or otherwise used in whole, or in part,without the written permission of the Vice President, EngineeringServices, Saudi Aramco.Chapter : Structural, On-shore For additional information on this subject, contactFile Reference:CSE10804 C.C. Baldwin on 873-1567Engineering EncyclopediaSaudi Aramco DeskTop StandardsAnalysisand Design OfReinforced Concrete FoundationsEngineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop StandardsCont ent s PagesPREPARING A STRUCTURAL DESIGN FOR A FOUNDATION ............................................... 1IDENTIFYING TYPICAL REFINERY EQUIPMENT FOUNDATIONS ....................................... 2DETERMINING STABILITY RATIO, LATERAL RESTRAINT, AND SOIL-BEARING PRESSURE.................................................................................................................. 10Stability Ratio and Lateral Restraint Check ...................................................................... 10Soil-bearing Pressure Calculation ..................................................................................... 11DESIGNING FOOTINGS .............................................................................................................. 19Approximate Required Thickness..................................................................................... 19Shear Considerations ........................................................................................................ 19Development Length for Dowels ...................................................................................... 23Reinforcing Steel Area...................................................................................................... 26Reinforcing Steel Size/Distribution .................................................................................. 26DESIGNING PEDESTALS............................................................................................................ 32DETERMINING ANCHOR BOLT REQUIREMENTS................................................................. 34INTRODUCTION TO PILED FOUNDATIONS ........................................................................... 36Introduction to Piled Foundations..................................................................................... 36Laterally Loaded Piles ...................................................................................................... 37Single Piles vs. Pile Groups .............................................................................................. 38Pile-Group Considerations................................................................................................ 38STRUCTURAL DESIGN OF PILE CAPS..................................................................................... 42Checking the Structural Design of Pile Caps .................................................................... 44Shear Considerations ........................................................................................................ 45Development Length for Dowels ...................................................................................... 48Reinforcing Steel Area...................................................................................................... 48Reinforcing Steel Size/Distribution .................................................................................. 48Design Aids Available ...................................................................................................... 48WORK AID 1: STEPS IN PREPARING A STRUCTURAL DESIGN FOR AFOUNDATION ............................................................................................... 52Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop StandardsWORK AID 2: DETERMINING STABILITY RATIO, LATERAL RESTRAINTAND SOIL-BEARING PRESSURE................................................................ 53WORK AID 3: DESIGNING FOOTINGS ............................................................................... 56WORK AID 4: DESIGNING PEDESTALS............................................................................. 57WORK AID 5: DETERMINING ANCHOR BOLT REQUIREMENTS.................................. 58WORK AID 6: DESIGNING PILE CAPS................................................................................ 60GLOSSARY................................................................................................................................... 61DESIGN AIDS ............................................................................................................................... 62Procedure For Using Design Aids: ................................................................................... 62Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 1Preparing a Structural Design for a FoundationIn this module, the participant will learn to design reinforced concrete footings, pile caps, and pedestals, as wellas determine the associated anchor bolt requirements.The steps in preparing a structural design for a foundation are:1) Select a size and shape of footing, or arrangement of piles and pile caps, appropriate for the purpose.2) Determine the weight of the equipment, structure, foundation elements, and the soil backfill acting at thebottom of the foundation.3) Determine the lateral forces and overturning moments at the level of the anchor bolts and at the top andbottom of the foundation.4) Calculate average and maximum soil-bearing pressures and stability ratios for erection, operation, watertesting, and other significant load cases.5) Adjust footing size or piling arrangements to meet minimum design criteria or to eliminate unnecessaryconservatism.6) Design the reinforcement of slab, pedestals, and other foundation members to resist moments and shearscorresponding to the critical loading conditions.If the detailed structural design requires substantialchange in foundation slab thickness or other dimensions, recheck the soil bearing or pile loading andstability calculations.Unfactored service loads must be used when bearing pressures and stability ratios are compared to allowablevalues, as in Steps 4 and 5 above.For structural design of the foundation, factored loads are used inconjunction with the strength design method to determine the thickness and reinforcement.Consequently,unfactored and factored loads must be determined separately, and both must be used.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 2Identifying Typical Refinery Equipment FoundationsShallow footings or pile caps used in a refinery can be grouped into broad categories, depending on the type ofequipment to be supported: Furnace foundations. Overhead structure foundations. Vertical vessel foundations. Horizontal drum foundations. Grade-level heat exchanger foundations. Pipe support structure foundations. Grade-level machinery foundations. Elevated machinery foundations.Some of these foundation types are shown in Figures 1-6.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 3VERTICAL CYLINDRICAL HEATER FOUNDATIONFIGURE 1Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 4ELEVATED REACTOR FOUNDATIONFIGURE 2Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 5ELEVATED VERTICAL VESSEL SUPPORT STRUCTUREVERTICAL VESSEL FOUNDATIONAnchor Bolt (Typ.)FIGURE 3Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 6HORIZONTAL DRUM FOUNDATIONAnchor BoltPedestalGrade LevelFootingFIGURE 4Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 7GRADE-LEVEL HEAT EXCHANGER FOUNDATION FIGURE 5Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 8ELEVATED MACHINERY FOUNDATIONFIGURE 6Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 9The shape and configuration can vary significantly within the foundation categories.For example, a grade-level exchanger can be supported on pedestals with separate footings, footings connected together with a gradebeam, or pedestals with one large slab.The choice depends on equipment size and loading, soil conditions,layout of adjacent foundations, construction costs, and designer's preference.For pedestals supporting verticalprocess vessels, the choice between a solid concrete block and an annular wall with a sand-filled interiordepends largely on material availability and cost.Placing two vertical vessels or two exchangers on a single (combined) foundation may be necessary ordesirable for particular equipment layouts.In some cases, a required spacing of two vertical vessels may notgive sufficient room for separate foundations.In other cases, efficiencies in construction effort and materialsmay be gained by using combined foundations.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 10Determining Stability Ratio, Lateral Restraint, and Soil-Bearing PressureStability Ratio and Lateral Restraint CheckFoundations supporting tall equipment or structures subjected to significant horizontal loading (H) must bedesigned for adequate stability against overturning and checked to ensure lateral restraint through slidingfriction.Foundation design includes checking the stability r atio, which is the ratio of r estor ing moment toover tur ning moment, taken about a point at the periphery of the footing base (see Figure 7).Vertical forcesused to calculate the restoring moment include the weight of the vessel with internals, fittings, ladders, andplatforms; the weight of contained fluid; and the weight of foundationconcrete and soil backfill.Buoyant unitweights for the foundation concrete and soil backfill should be used if the groundwater level for any designcondition is above the base of the foundation.The vertical forces can be assumed to act through the centroid of the base area for foundations of most verticalvessels and other symmetrical equipment.If equipment is significantly nonsymmetrical, the effect must beincluded in the stability and soil-bearing pressure calculations as an increase in the eccentricity.Unfactoreddesign loads and weights are used to calculate stability ratio.STABILITY RATIOD 2D 2hPHRestoring Moment, MR = P D2Overturning Moment, MOT = H hStability Ratio = MRMOTEccentricity, e = MOTPFIGURE 7Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 11The stability r atio shall exceed 2.0 for all service conditions other than during construction or erection, per theSaudi Aramco Standard SAES-Q-005, Concrete Foundations.During erection, the ratio shall be greater than1.5.The erection loading condition results in a "lighter" structure that is more vulnerable to overturning.The stability ratio applies directly to soil-supported footings and slabs.For pile-supported foundations, thestability ratio is indirectly satisfied as long as the individual pile loads do not exceed either the allowabletension or compression pile capacity.Foundations for structures or vessels subjected to horizontal loading must be laterally restrained through slidingfriction at the base of the foundation.Per Saudi Aramco Standard SAES-Q-005, passive earth pressure shall notbe considered when computing lateral restraint for foundations.A suitable value of the friction coefficient forthe ultimate resistance between the foundation base and the soil is 0.40.Therefore, theultimate fr ictionallater al r estr aint, Vf, is:Vf = 0.40 x Wwhere W is the total load.SAES-Q-005 states that foundations shall be designed so that the safety factor against sliding exceeds 1.5.Thesafety factor is equal to the ratio of the computed frictional restraint capacity, Vf, divided by the totalunfactored horizontal load.Soil-bearing Pressure CalculationThe stability ratio is calculated from overturning about a centroidal axis parallel to a side of the base.Forcalculating soil-bear ing pr essur e beneath the foundation, it is important to note that greater soil-bearingpressure exists beneath a corner because of the overturning moment around an axis that is perpendicular to thediagonal between corners.Although wind and seismic forces are considered as coming from any direction, it isnormal practice to check soil-bearing pressure at corners only.Using the method of calculation outlined in thissection, the calculated soil-bearing pressure is a gr oss pr essur e; it corresponds to the total pressure exerted bythe footing upon the bearing soil at a given depth, including the effect of the foundation weight and the weightof the backfill above the footing.When comparing the calculated soil-bearing pressure for a trial footing size with the specified allowable soil-bearing pressure, it is necessary to note whether allowable soil-bearing pressure is stated as gross pressure for agiven depth, or as net pr essur e.When working toward an allowable net soil-bearing pressure, the calculatedgross pressure must be converted to an equivalent net pressure by subtracting the effective weight ofoverburden soil acting at the level of the base of the foundation before foundation construction.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 12Allowable soil-bearing pressure values are usually stated in terms of net soil-bearing pressure, because thispressure increase at the bottom of footing contributes to shearing failure and differential settlement in the soil.The calculation of pressure on the soil beneath a foundation subjected tover tical load and over tur ningmoment is directly comparable to calculation of stress in a structural member caused by axial force combinedwith bending, only when the entire area of the footing base exerts compressive load on the soil. When therelative magnitude of the overturning moment becomes large enough that calculation by the combined flexureformula (P/A + Mc/I) begins to show tensile stresses on one side, the combined flexure formula is no longerapplicable for calculating the soil-bearing pressure.Tensile stresses cannot be developed between the base ofthe footing and the supporting soil.When overturning is great enough that compression acts on only a part of the base,statics must be consideredin calculating the stress distribution over the foundation/soil interface.This calculation may be simplified byutilizing the nomographs shown in Figures 8 and 9.Figures 8 and 9 illustrate the relationship between bearingpressure and load eccentricity for square and octagonal foundations, respectively.Geometric properties ofoctagonal shapes used in foundation design are shown in Figure 10.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 13RECTANGULAR SPREAD FOOTING DESIGN CURVES6.05.04.03.02.01.00.0 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40-0.5 -0.4 -0.3 -0.2 -0.1 0.0+0.5 +1.0 +1.5 +2.0e/D RatioMaximum and Minimum Soil-Bearing Pressures at Face of Rectangle:DDPePminPmax+KDxxx xPe-KDPmaxPmax=L .PAPmin = Pmax

K1 + KPmin, For K > 0=0, For K 0L LA = Area of FoundationFIGURE 8Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 14RECTANGULAR SPREAD FOOTING DESIGN CURVES (CONT' D)8.07.06.05.04.03.02.01.00.0 0.040.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40PSoil-Bearing Pressure at Corner of Square= L PmaxPASquare Footinge/D RatioOePmaxFIGURE 8 (CONT' D)Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 15OCTAGONAL FOOTING DESIGN CURVESL L0.00 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40+3.010.09.08.07.06.05.04.03.02.01.0-0.6-0.5-0.4-0.3-0.2-0.10.0+0.5+1.0+1.5+2.0+2.5K-Value for Moment AboutAxis x - xL - Values for Moment About Axis x - xL - Values for Moment About Axis y - ye/D RatioMinimum Soil-Bearing Pressure at Face of Octagon:Maximum Soil-Bearing Pressure at Face or Corner of Octagon: P maxePD DxyxyPmaxeP+KDyxyxminPPmin = Pmax K1 + KPmax=LPA, For K > 0A = Area = 0.828-KDPmin= 0, For K< 2D0FIGURE 9Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 16PROPERTIES OF OCTAGONAL SHAPED FOOTINGSB= 0.293 DC= 0.414 DZ= 1.08 DA= 0.828 D2I= 0.0547 D4S= 0.109 D3DftZftAft2Ift4Sft3DftZftAft2Ift4Sft34.0 4 13.3 14. 7 23.5 25.44 457.5 16694. 14214.5 4.67 16.8 22. 10 24.0 25.98 477.2 18161. 15125.0 5.41 20.7 34. 14 24.5 26.52 497.3 19722. 16105.5 5.95 25.1 50. 18 25.0 27.06 517.8 21382. 17116.0 6.49 29.8 71. 24 26.0 28.14 560.0 25014. 19246.5 7.04 35.0 98. 30 27.0 29.22 603.9 29090. 21557.0 7.58 40.6 131. 37 28.0 30.31 649.5 33645. 24037.5 8.12 46.6 173. 46 29.0 31.39 696.7 38715. 26708.0 8.66 53.0 224. 56 30.0 32.47 745.6 44338. 29568.5 9.20 59.9 286. 67 31.0 33.55 796.1 50552. 32619.0 9.74 67.1 359. 80 32.0 34.64 848.3 57397. 35879.5 10.28 74.8 468. 94 33.0 35.72 902.2 64915. 393410.0 10.82 82.8 547. 109 34.0 36.80 957.7 73148. 430310.5 11.37 91.3 685. 127 35.0 37.88 1014.8 82141. 469411.0 11.91 100.2 801. 146 36.0 38.97 1073.6 91938. 510811.5 12.45 109.6 957. 166 37.0 40.05 1134.1 102587. 554512.0 12.99 119.3 1135. 189 38.0 41.13 1196.2 114136. 600712.5 13.53 129.4 1336. 214 39.0 42.21 1260.0 126633. 649413.0 14.07 140.0 1563. 240 40.0 43.30 1325.5 140129. 700613.5 14.61 151.0 1818. 269 41.0 44.38 1392.6 154646. 754514.0 15.15 162.4 2103. 300 42.0 45.46 1461.3 170327. 811114.5 15.69 174.2 2420. 334 43.0 46.54 1531.8 187138. 870415.0 16.24 186.4 2771. 369 44.0 47.63 1603.8 205163. 932615.5 16.78 199.0 3159. 408 45.0 48.71 1677.6 224459. 997616.0 17.32 212.1 3587. 448 46.0 49.79 1753.0 245086. 1065616.5 17.86 225.5 4057. 492 47.0 50.87 1830.0 267103. 1136617.0 18.40 239.4 4572. 538 48.0 51.95 1908.7 290571. 1210717.5 18.94 253.7 5134. 587 49.0 53.04 1989.1 315553. 1288018.0 19.48 268.4 5746. 638 50.0 54.12 2071.1 342111. 1368418.5 20.02 283.5 6412. 693 51.0 55.20 2154.7 370312. 1452219.0 20.57 299.1 7133. 751 52.0 56.28 2240.1 400222. 1539319.5 21.11 315.0 7915. 812 53.0 57.37 2327.1 431908. 1629820.0 21.65 331.4 8758. 876 54.0 58.45 2415.7 465439. 1723820.5 22.19 348.1 9667. 943 55.0 59.53 2506.0 500885. 1821421.0 22.73 365.3 10645. 1014 56.0 60.61 2597.9 538319. 1922621.5 23.27 382.9 11696. 1088 57.0 61.70 2691.6 577812. 2027422.0 23.81 401.0 12823. 1166 58.0 62.78 2786.8 619440. 2136022.5 24.35 419.4 14029. 1247 59.0 63.86 2883.8 663278. 2248423.0 24.90 438.2 15318. 1332 60.0 64.94 2982.3 709402. 23647FIGURE 10Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 17Example Problem 1 - Bearing PressureGiven:10-ft diameter x 40-ft high process tower.Normal operating weight = 340 kips (excluding the foundation).Overturning moment at foundation base = 1250 kip-ft.Foundation/soil buoyant weight = 85 kips.Depth below grade = 5 ft.Octagon foundation, D = 16.5 ft.Soil Density = 120 lbs/ft3Determine:Stability ratio.Maximum soil pressure (gross and net).Solution:1)Stability ratio = MRMOT 340 + 85 16. 5/21250= 2.8 OK2)From Figure 10, AFDN = 225.5 ft2, SFDN = 492 ft33)Check using flexure formula.Q PAtMS425225.5t1250492 4.42, 0.66 kips / ft2Not OK (tension indicated)4) e 1250425 2.94 e/D 2.94 / 16.5 0.1785)From nomograph on Figure 9, L = 2.656)Maximum gross pressure = (2.65) (1.88) = 4.98 kips/ft2Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 187)Net pressure = 4.98 - (5) (0.12) = 4.4 kips/ft2Note: Maximum gross pressure of 4.98 kips/ft2 calculated in Step 6 exceeds that calculated in Step 3.This isexpected since in Step 3 the whole foundation area is used (erroneously) to calculate A and S, whereasin Step 5, the nomograph correctly considers only that part of the area that remains in compression.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 19Designing FootingsWhen the plan dimensions of the footing have been established, the depth and reinforcement are determined.For this purpose, the contact pressures and all loads are increased by the appropriate load factors covered inCSE 108.01.The factored loads and related internal shears and moments are used to design the footing.Design steps are:1) Determine thickness based on shear and development considerations. One-way beam shear . Two-way punching shear . Development length of column or pedestal rebars (dowels).2) Determine reinforcing steel area. Flexure considerations. ACI minimum/maximum requirements.3) Determine reinforcing steel bar size and distribution. Development length of bars. ACI paragraph 15.4 for footings.Approximate Required ThicknessA simple approach for determining preliminary footing thickness, hf, in inches, is given by:hf> 12 + L/10where L is the larger footing dimension in inches.Shear ConsiderationsShear strength of a footing near the face of the column pedestal or wall must be checked for two conditions.Both beam action (ACI section 11.12.1.1) and two-way action (ACI section 11.12.1.2) for the footing must bechecked to determine the footing depth.Beam action assumes that the footing acts as a wide beam with acr itical section across the entire width.If this condition governs, the design for shear follows ACI shearequations 11-1 and 11-3.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 20Beam ActionVu < VnACI 318 Eqn. 11-1Vu< 2 f cbwd ACI 318 Eqn. 11-3where footing width, bw, and factored shear force, Vu, are computed for the critical section.The critical section is located a distance d from the face of the column, pedestal, or wall (see Figure 11);d is thedepth from the top of the footing to the steel reinforcement.Two-way action for the footing checks punching shear.The critical section (dimension bo) completely enclosesthe column or pedestal and is located a distance d/2 from the outside face (see Figure 11).The shear strength fortwo-way action is a function of support size, c, which is the ratio of the long side to the short side of the columnor support area.Figure 12 illustrates the shear strength reduction as a function of c.Two-way ActionVu < Vn ACI 318 Eqn. 11-1Vu< 2 +4c _ , f cbodACI 318 Eqn. 11-36but not greater than 4 f cbod( )or sdbo+ 2 _ , f cbod wheres is 40 for interior columns, 30 for edge columns, or 20 for corner columns.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 21SHEAR CRITICAL SECTIONSbfor Two-Way Actionob for Beam Actionw13 ft-0 in.13 ft-0 in.30 in. + d30 in.12 in.12 in. + ddd 2b = 2[(30 + d) + (12 + d)] od 2Source:Notes on ACI 318-89.Reprinted with permission from Portland Cement Association, 5420 OldOrchard Rd., Skokie, Illinois 60077.FIGURE 11Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 22SHEAR STRENGTH OF FOOTINGSEngineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 23If the factored shear force, Vu, at the critical section exceeds the shear strength of the concrete, Vc, determinedfor either beam or two-way action, the thickness of the footing must be increased or shear reinforcement added.It is generally preferred to increase the thickness rather than to add shear reinforcement, to simplify theconstruction effort.Development Length for DowelsAfter the shear considerations are included in the calculations, the preliminary footing thickness must bechecked to ensure that sufficient anchorage or development length exists for the column or pedestalreinforcement. If the thickness is inadequate, then either the thickness of thefooting must be increased, or thecolumn or pedestal design revised.Procedures for determining the development length of dowels or reinforcing steel for various conditions arecovered in Section 12.Section 12 requirements are also summarized in Figures 13a and 13b for tension andcompression reinforcement, respectively.For pedestal or column tension reinforcement, the rebars are usually terminated in the footing with a standardhook below the bottom steel in the footing.For example, using Figure 13a, the development length requiredfor a #9 Grade 60 bar in 3 ksi concrete with a hook, sufficient cover and no stirrups is given by 24.7 inchesmultiplied by an - factor of 0.7, or 17.3 inches.For pedestals or columns where reinforcing steel is necessary to achieve the required strength for compressiveloads, the development length in compression can be greater than for a standard hook in tension.Per Figure 13bfor a #9 bar, the standard development length is 24.7 inches for Grade 60 rebar in 3 ksi concrete.Note that thedevelopment length significantly increases with increasing bar diameters.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 24DEVELOPMENT OF STANDARD HOOKS IN TENSIONAuthorized reprint from ACI, SP-17, Vol. 1, Reinforcement 18-1, Page 233, with permission from theAmerican Concrete Institute.FIGURE 13aEngineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 25DEVELOPMENT OF BARS IN COMPRESSIONAuthorized reprint from ACI SP-17, Vol. 1, Reinforcement 17.4, Page 232, with permission fromAmerican Concrete Institute.FIGURE 13bEngineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 26Reinforcing Steel AreaThe designer uses the factored soil pressures and calculates the moment, Mu, at the critical section, per ACI 318,Section 15.4.For most cases, the critical section is located at the faces of the column, pedestal, or wall.Themoment is calculated for both directions.Negative moments, if present, must also be calculated in order todetermine the need for top steel.The procedure for determining the amount of steel reinforcement (in both directions, top and bottom) in thefooting follows that outlined in CSE 108.02.Based on Mu and F determined from footing dimensions, calculateKn.Given Kn, fc' , and fy, use Work Aids 2 through 5 of CSE 108.02 to determine reinforcing steel percentage,.The value ofmust be greater than 0.0018 (for shrinkage) but less than 0.75 b.ACI 318, Section 10.5requires that the amount of reinforcement be increased by 33% if < 200/fy.Reinforcing Steel Size/DistributionNote that the distance from the critical section to the footing edge, af, must be great enough to provide thenecessary development length for the footing reinforcement.Work Aids 6,7 and 8 of CSE 108.02 can be used todetermine maximum permitted bar size (straight bar in tension) that can be developed for a development lengthequal to af.The amount of reinforcing steel must be distributed across the footing width, per ACI 318, Paragraph 15.4.Thisprovision states that reinforcement shall be uniformly spaced across the entire width, except for reinforcement inthe short direction of two-way rectangular footings.For this special case, ACI states that a portion of the totalreinforcement must be distributed within a bandwidth centered on the column or pedestal, with a dimension equalto the length of the short side (see Figure 14).The remainder of the reinforcement is to be equally spaced in thearea outside the bandwidth.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 27FOOTING STEEL DISTRIBUTIONaaBLBA=sbAstotA A = (1-)so stotAsbAsoAso22 + 1= L/B2 2 + 1Astot= Total r equir ed steel ar eaAsb = Steel ar ea within bandwidthAso= Steel ar ea outside bandwith (one-half toeach side) = Shape r atioFIGURE 14Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 28Example Problem 2 - FootingsGiven:qs (factored)fc'fyaf1af2Column sizeFooting size#11 dowel bars=======6.67 kips/ft23000 psi50,000 psi72 in50 in42 x 20 in15.5 x 10 ftAuthorized reprint from ACI SP(17), ACI Design Handbook - Volume 1, 1991, Page137.FIGURE 15Step 1Determine minimum depth.Use rule-of-thumb sizing.hf = 12 in. + 15.5 x 12/10= 30.6 in., say 30 in hf = footing thickness.Assume 3 in. cover and #9 bars.d= 30 - 3 - 1.128 - 0.564 = 25.31 in., say 25 ind = footing effective depth.Step 2Check beam shear.af = (15.5x12-[42+2(25)])/2 = 47.0 inaf= footing stem length.Vu = (6.67)(10)(47.0/12) = 261 kipsVu = shear ultimate capacity.Vn= (0.85)(2)( 3000)(120)(25)/1000 = 279 kips Vn = shear design capacity.279> 261 OKStep 3Check perimeter shear.AFV = Loaded area for perimeter shear.AFV (15.5)(10) 42 + 2512 _ , 20 + 2512 _ , 1 ] 1 134 ft2Vu=(6.67)(134) = 894 kipsEngineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 29Example Problem 2 (Cont'd)c=42/20 = 2.1bo = Critical section dimension.bo = (42+25)2+(20+25)2 = 224 inVN =(0.85)[2+4/2.1]( 3000)(224)(25.0)/1000VN =1018 kips > Vu = 894 kips OKStep 4Check dowel development length per Figure 13a, Development Length Standard Hook in Tension.For d 25.0, up to #11 BarOK (25.7" required)Step 5Check conservatism/understrength.One-way shear 279/261 7% extra capacityTwo-way shear1018/89414% extra capacityDowel development25.0/1838% extra capacity(Including = 0.7 factor for good coverrequirements.) Seems Reasonably DesignedStep 6Determine reinforcement in long direction.Mu = (6.67)(10)(72/12)(3) = 1200 kip-ftF = (120)(25.0)2/12,000 = 6.25KN = 1200/6.25 = 192Per Work Aid 2 of CSE 108.02, = 0.0045 As = (0.0045)(120)(25) = 13.5 in2Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 30Example Problem 2 (Cont'd)Step 7Determine reinforcement in short direction.Mu =(6.67)(15.5)(50/12)(25/12) = 897 kip-ftF =(15.5)(12)(25.0)2/12000 = 9.7KN =897/9.7 = 93Per Work Aid 2 of CSE 108.02, = 0.0021Since < min = 200/fy = 0.004, increase by 33%.Therefore, = 0.0028. As = (0.0028)(15.5)(12)(25.0) = 13.0 in2For L = 15.5 ft and b = 10 ft2/(+1) = 0.78Bandwidth As = (0.78)(13.0) = 10.1 in2 B = 10.1/(25.0)(120) = 0.0034 OKOutside As = (0.22)(13.0) = 2.9 in2 o= 2.9/(25.0)(66) = 0.0018 OK (Exceeds Min.Shrinkage Reinforcement)Step 8Select bar size and spacing.Long direction:AF = 72 inDB #11 bar (Work Aid 6 of CSE 108.02.)Short direction:AF = 50 inDB #10 bar (Work Aid 6 of CSE 108.02.)Long direction: For 12 in spacing, As / bar = 13.5/11 = 1.22 in2/BarUse #10 bars @ 12 in spaces.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 31Example Problem 2 (Cont'd)Short direction:Within BandwidthFor 8 in spacing (15 bars total), As/bar = 10.1/15 = 0.67 in2/barUse #8 @ 8 in spacing (15 bars in bandwidth)Outside of BandwidthFor 16 in spacing As/bar (4 bars total) = 2.9/4 = 0.73 in2/barUse #8 bars @ 16 in spacing, two in each region outside bandwidthsNote: From a construction practicality point of view, it would be easier to also use #8 barsin the longdirection.No. of bars required = 13.5/0.79 = 17 total, evenly spaced.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 32Designing PedestalsThe structural design of the pedestal principally involves determining the amount of vertical reinforcementnecessary to transfer tensile stresses into the footing.Although compression and shear stresses are usually lowfor pedestals supporting process equipment, they should be checked using the procedures given in CSE 108.02and 108.03.The foundation designer should also ensure that the base ring or base plates are adequate totransfer the vessel loads to the top of the pedestal without exceeding the bearing stress permitted by the ACIcode.Usually, octagonal pedestals are used for vertical process vessels.When the strength design method is used, the bearing stresses cannot exceed 0.6 fc'unless the supportingsurface is wider on all sides of the loaded area.In such cases, the permitted bearing stress may be increased bythe square root of the ratio of the supporting concrete surface area, Ac, to the loaded area, ABP, however thisfunction cannot exceed 2.0.Bearing stress0. 6 f cAc/ ABP( ) where:Ac/ ABP( ) 2. 0The vertical reinforcement may be designed on the basis of treating the pedestal as a column member subjectedto axial load and bending.It is sufficient, however, to use the following simplified equation to determine therequired area of pedestal steel.As = 1ft 4MDp - Wwhere:As = Total area of vertical reinforcement, in2.Dp= Bar octagon diameter, ft.ft = Allowable stress in pedestal reinforcement, psi.= 0.9 fy.M = Factored moment at top of footing, lb-ft.W = Vertical load at top of footing, lb.The minimum number of vertical bars in octagonal pedestals is eight, with one bar placed at each of the eightcorners of the octagon.For pedestals larger than 6 ft in diameter, additional bars are placed in each side.Toreduce cracking at the upper surface and exposed sides, horizontal reinforcement should be added per ACIshrinkage and temperature requirements.All vertical rebars should be embedded into the footing with astandard 90_ hook.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 33ACI Section 15.8 states that the designer is required to check for sufficient reinforcement to transfer loads fromthe pedestal to the footing.The minimum vertical reinforcement extending across the interface shall be 0.005times the pedestal gross area.As discussed earlier, the footing or pile cap thickness must be sufficient todevelop anchorage of the bars.ACI Section 11.7 lists shear-friction provisions to ensure that the verticalreinforcement can also transfer the shear forces across the interface.ACI 11.7 assumes that the interface iscracked and that all shear is transferred through dowel action of the vertical reinforcement.The followingequation is used for this shear-friction check:Vu As Fy where is the coefficient of friction across the interface and can be conservatively taken as 0.6 for normalweight concrete.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 34Determining Anchor Bolt RequirementsAnchor bolts are required to resist the uplift from the overturning moment and maintain the vessel in a verticalposition.The number, size, length, and bolt circle diameter are usually established during vessel design, but arerechecked and detailed as part of the foundation design.Plastic sleeves may be provided at the top of the concrete pedestal to permit adjustment for centering and fittinginto the bolt holes on the baseplate.After the vessel is placed and the grout under the baseplate has hardened,the nuts on the anchor bolts are tightened until the bolts are pretensioned.This initial tension does not increasethe maximum bolt tension caused by earthquake or wind.Note that the level of tension is much lower than istypical for high-strength structural bolted connections.Anchor bolts should be sized using the allowable capacities given in Figure 16. No increase in allowable stressshould be taken when wind or earthquake is considered.Anchor bolts sized by this method include a 25%corrosion allowance.Note that at least 1/8 inch is added to the diameter as a corrosion allowance.This level ofconservatism is not costly and provides additional protection against excessive stretching of the bolts duringearthquakes or high winds.There should be at least 8 bolts, preferably 12 or more, equally spaced around a circle.If N is the number ofanchor bolts and Db the bolt-circle diameter, the maximum bolt tension, T, may be calculated from thissimplified formula:T = 4MDbN - PNwhere:M is the overturning moment (unfactored).P is the corresponding vertical load at the top of the pedestal (unfactored).The anchor bolts most commonly used in vessel foundations are made of steel rods, hooked or with amechanical anchorage at one end and threaded at the other.Development length of anchor bolts should bechecked using Figure 16.For ease of construction,it is generally preferred that the anchor bolts do not extendinto the footing.Where they do extend into the footing, they should not be considered in the calculations ofload transfer across the pedestal or footing interface.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 35ANCHOR BOLT DATADIMENSIONS (INCHES) LOAD CAPACITY (KIPS)A B C D E F G SHEAR TENSIONAnchorBolt Dia.Min.DepthType2OnlyLengthThr eadLengthThr ead3.5 Dia.LengthHook15 Dia.LengthSleeveNut onType 4Type1, 2,3, 4Type1Type2Type3, 41/2 10 4 1-5/8 - 7-1/2 - - 1.0 1.5 1.8 2.15/8 10 4 1-5/8 - 9-3/8 - - 1.5 1.7 2.3 3.43/4 12 6 2 2-5/8 11-1/4 1-7/8 11 2.2 2.3 3.2 5.17/8 14 6 2 3-1/8 13-1/8 2-1/4 12-3/4 3.2 2.9 4.1 7.01 16 8 2-1/2 3-1/2 15 2-1/2 14-3/4 4.2 3.6 5.1 9.11-1/8 18 8 3 4 16-7/8 2-7/8 16-1/2 5.3 3.8 5.5 11.51-1/4 20 8 3 4-3/8 18-3/4 3-1/8 18-1/4 6.7 4.1 6.5 14.71-3/8 22 8 3-5/8 4-7/8 20-5/8 3-1/2 20-1/4 7.9 7.6 17.61-1/2 24 8 3-5/8 5-1/4 22-1/2 3-3/4 22 9.7 8.7 21.41-5/8 26 8 4-1/8 5-3/4 24-3/8 4-1/8 23-3/4 11.5 9.9 24.41-3/4 28 10 4-3/8 6-1/8 26-1/4 4-3/8 25-1/2 13.2 10.5 28.92 32 10 5 7 30 5 29-1/2 17.4 13.2 38.02-1/4 36 10 5-5/8 7-7/8 33-3/4 5-5/8 33 22.9 15.9 47.72-1/2 40 10 6-1/4 8-3/4 37-1/2 6-1/4 37-1/2 28.3 18.9 58.2FIGURE 16Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 36Introduction to Piled FoundationsIntroduction to Piled FoundationsPiles are structural members of timber, concrete, and/or steel, used to transmit surface loads to lower levels inthe soil mass.This may be by vertical distribution of the load along the pile shaft, or by a direct application ofload to a lower stratum through the pile point.A vertical distribution of the load is made using a friction, or"floating," pile and a direct load application is made by a point, or "end-bearing," pile.This distinction of pilesis purely one of convenience because all piles function as a combination of side resistance and point bearing,except when the pile penetrates an extremely soft soil to a solid base.Refer to Figure 17.PILE USESaaFIGURE 17Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 37Piles are commonly used to:1. Carry the superstructure loads into or through a soil stratum.Both vertical and lateral loadsmay be involved.2. Resist uplift or overturning forces (as for basement mats below the water table) or to supporttower legs subjected to overturning.3. Compact loose, cohesionless deposits through a combination of pile volume displacement anddriving vibrations.These piles may later be pulled.4. Control settlements when spread footings or a mat are on a marginal soil or are underlain by ahighly compressible stratum.5. Stiffen the soil beneath machine foundations to control both amplitudes of vibration and thenatural frequency of the system.6. As an additional safety factor beneath bridge abutments and/or piers, particularly if scour is apotential problem.7. In offshore construction to transmit loads above the water surface through the water and into theunderlying soil.This is a case of partially embedded piling subjected to vertical (and buckling)as well as lateral loads.Laterally Loaded PilesStructures supported on piles are often subjected to horizontal design loads caused by wind or earthquake.These horizontal loads can be resisted by the piles in two different modes:Axially, by use of battered or angled piles.Bending, for vertical piles.Battered piles are more effective for axially resisting lateral forces."Battered" means that the pile(s) is installedat a vertical inclination angle flatter than 90.The batter angle is usually defined as the ratio of the length of thevertical side to the horizontal side (seeFigure 18).Typical batter angles range from 2V:1H to 4V:1H.Whenbattered piles are used, the lateral resistance of any vertical piles is neglected (because the battered piles aremuch stiffer).The resulting axial load in the battered piles and vertical piles is determined on the basis of staticequilibrium.Battered piles are common for precast piles, because they can be easily driven within the range ofbatter angles given above.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 38Cast-in-place piles cannot be easily installed on a batter angle because of the difficulty of drilling a hole on anangle and the increased possibility of soil collapsing into the hole.Consequently, cast-in-place piles are almostalways installed vertically; they resist lateral forces by lateral deflection to mobilize the reaction of thesurrounding soil.The magnitude and distribution of the resisting pressures are a function of the relativestiffness of the pile and soil.Design criteria for laterally loaded vertical piles are based on the maximum combined stress in the pile, theallowable deflection at the top of the pile, and soil-bearing considerations.These criteria are used in conjunction with a laterally loaded pile analysis computer program by thegeotechnical engineer to define the pile deformation, shears, and moments.Single Piles vs. Pile GroupsFoundations rarely consist of a single pile.Generally, there will be a minimum of two or three piles under afoundation element or footing to allow for misalignments and other inadvertent eccentricities.Building codesmay stipulate the minimum number of piles under a building element.The load capacity, settlement, andindividual pile loads associated with pile groups is the concern of this discussion.Figure 19 presents sometypical pile clusters, for illustrative purposes only, since the designer must make up the group geometry tosatisfy any given problem.Pile-Group ConsiderationsWhen several piles are clustered, it is reasonable to expect that the soil pressures produced from side friction orpoint bearing will overlap, as idealized in Figure 20.The superimposed pressure intensity will depend on boththe pile load and spacing and, if it is sufficiently large, the soil will fail in shear or the settlement will beexcessive.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 39BATTER PILES41Batter Angle 4V= 1HFIGURE 18Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 40TYPICAL PILE-GROUP PATTERNSFIGURE 19Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 41The stress intensity from overlapping stressed zones will obviously decrease with increased pile spacings.However, large spacings are often impractical because a pile cap is cast over the pile group for the column baseand/or to spread the load to the several piles in the group.STRESSES SURROUNDING A FRICTION PILEAND THE SUMMATION EFFECTS OF A PILE-GROUPFIGURE 20Minimum pile spacings suggested by several building codes are as shown in Figure 21:Pile type BOCA, 1984 NBC, 1976 Chicago, 1987Friction 2D or 1.75H 30 in. 2D or 1.75H 30 in. 1D or 1.75 H 30 in.Point bearing 2D or 1.75H 24 in. 2D or 1.75H 24 in.FIGURE 21In Figure 21, D = pile diameter and H = diagonal of a rectangular shape or H pile.The BOCA code alsostipulates that spacing for friction piles in loose sand or loose sand gravels shall be increased 10% for eachinterior pile to a maximum of 40%.Optimal spacing seems to be on the order of 2.5-3.5D or 2-3H for verticalloads; for groups carrying lateral and/or dynamic loads, larger pile spacings are usually more efficient.Maximum pile spacings are not given in building codes, but spacings as high as 8 or 10D have been used onoccasion.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 42Structural Design of Pile CapsUnless a single pile is used, a cap is necessary to spread the vertical and horizontal loads and any overturningmoments to all the piles in the group.The cap is usually of reinforced concrete, poured on the ground, unlessthe soil is expansive.Caps for offshore structures may be fabricated from steel shapes.The pile cap has areaction that is a series of concentrated loads (from the piles), and the design considers the column loads andmoments, any soil overlying the cap (if it is below the ground surface), and the weight of the cap.It is usualpractice to assume that:1. Each pile carries an equal amount of the load for a concentric axial load on the cap, or, for npiles carrying a total Q, the load, Pp, per pile is:Pp = Qn2. The combined stress equation (assuming a planar stress distribution) is valid for a pile capnoncentrally loaded, or loaded with a load, Q, and a pair of bending moments, asPPQn+Myxx2+Mxyy2where:Mx, My= Moments about x and y axes, respectively.x, y = Distances from y and x axes to any pile.x2, y2 = Moment of inertia of the group, computed asI = Io + Ad2 (see Figure 22)but Io is negligible, and the A term cancels, because it is the pile load that is being computed,and A appears in both the numerator and denominator.The assumption that each pile in a group carries equal load may be nearly correct when all the following criteriaare met:1. The pile cap is in contact with the ground.2. The piles are all vertical.3. Load is applied at the center of the pile group.4. The pile group is symmetrical and the cap is very thick, i.e., very stiff.In a practical case of a four-pile symmetrical group centrally loaded, each pile will carry one-fourth of thevertical load regardless of cap rigidity (or thickness).With a fifth pile directly under the load, cap rigidity willbe a significant factor.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 4320-FT X 20-FT PILE CAPy2 = 232.52 + 37.52 = 375 pile-ft2x2 = 247.52 = 450 pile-ft2FIGURE 22Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 44Checking the Structural Design of Pile CapsWhen the layout of the pile cap has been established, the depth and reinforcement are determined in a waysimilar to that for footings.The factored loads and related internal shears and moments are used to design thepile cap.Given below are important guidelines for structural design of pile caps:1. Bending moments are taken at the same sections as for reinforced concrete footings and aredefined in Section 15.4 of the ACI Code.2. Pile caps must be reinforced for both positive and negative bending moments.Reinforcementshould be placed so that there is a minimum cover of 3 inches for concrete adjacent to the soil.Where piles extend into the cap only about 3 inches, the bottom reinforcement should be 3inches above the pile top in case of concrete cracking around the pile head.3. Pile caps should extend at least 6 inches beyond the outside face of exterior piles andpreferably 10 inches.When piles extend into the cap more than 3 inches, the bottom rebarsshould loop around the pile to avoid splitting a part of the cap due to the pile head momentsand shears.4. When pile heads are assumed to be fixed, they should extend into the pile cap at least 12inches.The minimum thickness of pile caps above pile heads is 12 inches (required by ACI318, Section 15.7).5. Tension connectors should be used on the pile heads if the piles are subjected to tensionforces.6. Pile cap shear is computed at critical sections as shown in Figure 23.The design steps are:Determine thickness (based on shear and development length considerations).-Beam shear near column.- Perimeter shear near column.-Beam shear near corner pile.-Perimeter shear near corner pile.-Development length of rebars from column or pedestals.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 45Determine reinforcing steel area.-Flexure considerations.-ACI minimum/maximum requirements.Determinereinforcing steel bar size and distribution.-Development length of bars.-ACI Section 15.4.Shear ConsiderationsPile caps must be checked for beam shear and perimeter shear near the column or pedestal, in a way similar tothe method used for footings:1.Beam shear at a distance, d, from the column.Vu< 2 f cbwd( )2.Perimeter shear at a distance, d/2, from the column.Vu< 2 +4c _ , f cbodbut not greater than 4 f cbod ( )or sdbo+ 2 _ , f cbod These are the same equations as for footings. The critical sections for these two cases are shown on Figure 23.In addition, two additional shear conditions must be considered;3. Beam shear for a corner pile (diameter dp) at a distance, d, from the pile, with edgedistance, de.d >Factored pile capacity(lbs)2 f cdp+ 2d + 2 2de [ ]inches4. Perimeter shear around corner pile at a distance, d/2, from the pile, with edgedistance, de.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 46d >Factored pile capacity(lbs)4 f cdp+ d( )/4 + 2de [ ]inchesThe critical sections for Items 3 and 4 are shown in Figures 24 and 25.If any of the above considerations are not satisfied, the thickness of the footing must be increased or shearreinforcement added.Because most pile caps only have one layer of reinforcement, at the bottom, it isgenerally preferred to increase the thickness rather than add shear reinforcement.PILE CAP SHEAR CRITICAL SECTIONSd1'-3"3'-0"8'-6"1'-3"3'-0"d/21'-3" 3'-0" 3'-0"1'-3"Critical Section for Two-Way ActionCritical Section for Beam ActionSource:Notes on ACI 318-89, Page 24-21.Reprinted with permission from Portland Cement Association,5420 Old Orchard Rd., Skokie, Illinois 60077.FIGURE 23Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 47CORNER PILE BEAM SHEAREdge Distance ddPile dPseudocritical Section for Beam Shearep45Authorized reprint from ACI 340.1R - 91, ACI Design Handbook - Volume 1, 1991, Page 354.FIGURE 24CORNER PILE PERIMETER SHEAREdge DistancePilededpPseudocritical Secti on for Perimeter Sheard/2Authorized reprint from ACI 340.1R - 91, ACI Design Handbook - Volume 1, 1991, Page 354.FIGURE 25Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 48Development Length for DowelsIf the shear capacity is inadequate, the pile cap thickness is increased.Shear reinforcement is generally notused in pile caps. After the shear considerations are checked, the preliminary footing thickness also must bechecked to ensure sufficient anchorage or development lengthfor the column or pedestal reinforcement.Shearconsiderations will usually govern the thickness.Dowel development length was provided in Figures 13a and13b.Reinforcing Steel AreaThe designer, using the factored loads and pile reactions, calculates the moment, Mu, at the critical section, perACI 318, Section 15.4, in each direction, top and bottom, as necessary. Reinforcement based on flexure isthen determined using Work Aids 2 through 5 of CSE 108.02.For most cases, the amount of steel is governedby minimum requirements in ACI 318, Section 7.12 for shrinkage and temperature ( = 0.0018 - 0.002).Reinforcing Steel Size/DistributionNote that the maximum bar diameter is again governed by the development length.The available length isequal to the distance from the column face to the edge of the pile cap.The reinforcing steel is uniformly distributed across the width of the pile cap except for reinforcement in theshort direction of a rectangular pile cap.For footings, ACI 15.4 dictates that a certain percentage of the totalsteel be distributed within the bandwidth.Note that this distribution provision applies only wherereinforcement is governed by flexure and exceeds the minimum requirements.Design Aids AvailableMost of the structural design requirements have been previously determined for standard pile cap layouts.Theminimum thickness, based on shear considerations, reinforcing steel percentage, and maximum bar size, isprovided in the Appendix, which includes design aids for pile caps containing from two to nine piles.Note thatdevelopment length for column dowels and steel distribution in rectangular pile caps must be checkedseparately.Several notes on the use of these design aids follow.Shear Checks: The design aids check Shear Considerations 1 and 2 discussed previously. Forthin caps, the designer must manually check for Shear Considerations 3 and 4.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 49Pile Capacities: The pile capacities of 20-100 tons per pile are the maximum allowable serviceloads (not factored) that must be carried by each pile.It is assumed that all pilesare equally loaded to their full allowable capacity.Load Factor: Pile caps are designed by the strength design method, using an average loadfactor of 1.55 (for dead plus live load) to be conservative for most designconditions.Should the effective load factor be higher, a higher pile capacityshould be used with the table.Footing Thickness: The design aids provide the effective depth, d, of the pile caps and leave thedetermination of total thickness, hf, to the designer.Pile Diameter and Spacing:The design aids are based on relatively small pile size (8-in. diameter for 20-60 ton piles and 10 in. for 80-100 ton piles).Pile spacings of 2.5-3 ft areassumed.Column Dimension, hc: For symmetrical pile caps with the same reinforcement in both directions,hc is the smaller column dimension.Column Width, bc:Values given under "min bc" are minimum column dimensions, in inches,required to satisfy shear provisions for fc' = 3000 psi.Values of bc may bereduced for higher-strength concrete.Values must be modified by the designerwhen the column aspect ratio is greater than 2.Reinforcement Area: Values are based on fy = 60,000 psi; adjust for different yield strengths bymultiplying values by 60,000/fy.Values shown above solid stepped lines satisfythe minimum shrinkage and temperature requirements.Note that for one-waypile caps supporting structures such as walls, the minimum steel area ratio, r,should be increased to 200/fy.Maximum Bar Size: The design aids indicate the maximum bar size that can be developed for pile capreinforcing steel.Bar development lengths are based on a minimum edgedistance of 1 ft-3 in.Minimum Depth:It should be noted that the values of effective depth given in the tables areminimum values.These values are sensitive to pile position and may beunconservative if piles are misaligned during installation.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 50Example Problem 3SYMMETRICAL PILE-SUPPORTED FOOTING; MINIMUM DEPTH AND REINFORCEMENTREQUIREDAuthorized reprint from ACI 340.1R - 91, ACI Design Handbook - Volume 1, 1991, Page 139.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 51Example Problem 3(Cont'd)Authorized reprint from ACI 340.1R - 91, ACI Design Handbook - Volume 1, 1991, Page 140.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 52Work Aid 1: Steps in Preparing a Structural Design For a FoundationThe steps in preparing a structural design for a foundation are:1) Select a size and shape of footing, or arrangement of piles and pile cap, appropriate for the purpose.2) Determine the weight of the equipment, structure, the foundation elements, and the soil backfill acting atthe bottom of the foundation.3) Determine the lateral forces and overturning moments at the level of the anchor bolts and at the top andbottom of the foundation.4) Calculate average and maximum soil-bearing pressures and stability ratios for erection, operation, watertesting, and other significant load cases.5) Adjust footing size or piling arrangements to meet minimum design criteria or to eliminate unnecessaryconservatism.6) Design the reinforcement of slab, pedestals, and other foundation members to resist moments and shearscorresponding to the critical loading conditions.If this detailed structural design requires substantialchange in foundation slab thickness or other dimensions, recheck the soil-bearing or pile loading andstability calculations.Unfactored service loads must be used when bearing pressures and stability ratios are compared to allowablevalues as in Steps 4 and 5 above.For structural design of the foundation, factored loads are used in conjunctionwith the strength design method to determine the thickness and reinforcement.Consequently, unfactored andfactored loads must be determined separately, and both must be used.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 53(Sheet 1 of 3)Work Aid 2: Determining Stability Ratio, Lateral Restraint and Soil-BearingPressure1.Stability ratio.STABILITY RATIOD 2D 2hPHRestoring Moment MR = P D2Overturning Moment MOT = H hStability Ratio = MRMOTEccentricity e = MOTPFIGURE 292.Lateral restraint.Vf = 0.40 x W3. Soil-bearing pressure.a) From "Properties Table" (Figure 31), select values for AFDN and SFDN.b) Check using flexure formula Q = PA t MS.If both values of Q are positive (i.e., no tension), go to Step (f).c) Calculate e = MOTP,then calculate e/D.d)From the nomograph (Figure 30), determine L.e)Calculate maximum gross pressure, Pmax = LPAf)Calculate maximum net pressure.Q = Pmax - d (overburden pressure).Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 54(Sheet 2 of 3)OCTAGONAL FOOTING DESIGN CURVESL L0.00 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40+3.010.09.08.07.06.05.04.03.02.01.0-0.6-0.5-0.4-0.3-0.2-0.10.0+0.5+1.0+1.5+2.0+2.5K-Value for Moment AboutAxis x - xL - Val ues for Moment About Axis x - xL - Val ues for Moment About Axis y - ye/D RatioMinimum Soil-Bearing Pressure at Face of Octagon:Maximum Soil-Bearing Pressure at Face or Corner of Octagon: P maxePD Dx yxyPmaxeP+KDyxyxmi nPPmin= Pmax K1 + KPmax =LPA, For K > 0A = Area = 0.828-KDPmin= 0, For K< 2D0FIGURE 30Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 55(Sheet 3 of 3)PROPERTIES OF OCTAGONAL SHAPED FOOTINGSB= 0.293 DC= 0.414 DZ= 1.08 DA= 0.828 D2I= 0.0547 D4S= 0.109 D3DftZftAft2Ift4Sft3DftZftAft2Ift4Sft34.0 4 13.3 14. 7 23.5 25.44 457.5 16694. 14214.5 4.67 16.8 22. 10 24.0 25.98 477.2 18161. 15125.0 5.41 20.7 34. 14 24.5 26.52 497.3 19722. 16105.5 5.95 25.1 50. 18 25.0 27.06 517.8 21382. 17116.0 6.49 29.8 71. 24 26.0 28.14 560.0 25014. 19246.5 7.04 35.0 98. 30 27.0 29.22 603.9 29090. 21557.0 7.58 40.6 131. 37 28.0 30.31 649.5 33645. 24037.5 8.12 46.6 173. 46 29.0 31.39 696.7 38715. 26708.0 8.66 53.0 224. 56 30.0 32.47 745.6 44338. 29568.5 9.20 59.9 286. 67 31.0 33.55 796.1 50552. 32619.0 9.74 67.1 359. 80 32.0 34.64 848.3 57397. 35879.5 10.28 74.8 468. 94 33.0 35.72 902.2 64915. 393410.0 10.82 82.8 547. 109 34.0 36.80 957.7 73148. 430310.5 11.37 91.3 685. 127 35.0 37.88 1014.8 82141. 469411.0 11.91 100.2 801. 146 36.0 38.97 1073.6 91938. 510811.5 12.45 109.6 957. 166 37.0 40.05 1134.1 102587. 554512.0 12.99 119.3 1135. 189 38.0 41.13 1196.2 114136. 600712.5 13.53 129.4 1336. 214 39.0 42.21 1260.0 126633. 649413.0 14.07 140.0 1563. 240 40.0 43.30 1325.5 140129. 700613.5 14.61 151.0 1818. 269 41.0 44.38 1392.6 154646. 754514.0 15.15 162.4 2103. 300 42.0 45.46 1461.3 170327. 811114.5 15.69 174.2 2420. 334 43.0 46.54 1531.8 187138. 870415.0 16.24 186.4 2771. 369 44.0 47.63 1603.8 205163. 932615.5 16.78 199.0 3159. 408 45.0 48.71 1677.6 224459. 997616.0 17.32 212.1 3587. 448 46.0 49.79 1753.0 245086. 1065616.5 17.86 225.5 4057. 492 47.0 50.87 1830.0 267103. 1136617.0 18.40 239.4 4572. 538 48.0 51.95 1908.7 290571. 1210717.5 18.94 253.7 5134. 587 49.0 53.04 1989.1 315553. 1288018.0 19.48 268.4 5746. 638 50.0 54.12 2071.1 342111. 1368418.5 20.02 283.5 6412. 693 51.0 55.20 2154.7 370312. 1452219.0 20.57 299.1 7133. 751 52.0 56.28 2240.1 400222. 1539319.5 21.11 315.0 7915. 812 53.0 57.37 2327.1 431908. 1629820.0 21.65 331.4 8758. 876 54.0 58.45 2415.7 465439. 1723820.5 22.19 348.1 9667. 943 55.0 59.53 2506.0 500885. 1821421.0 22.73 365.3 10645. 1014 56.0 60.61 2597.9 538319. 1922621.5 23.27 382.9 11696. 1088 57.0 61.70 2691.6 577812. 2027422.0 23.81 401.0 12823. 1166 58.0 62.78 2786.8 619440. 2136022.5 24.35 419.4 14029. 1247 59.0 63.86 2883.8 663278. 2248423.0 24.90 438.2 15318. 1332 60.0 64.94 2982.3 709402. 23647FIGURE 31Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 56Work Aid 3:Designing FootingsStep 1. Determine minimum depth.Use rule-of-thumb sizing.Step 2. Check one-way beam shear.Step 3. Check two-way perimeter shear.Step 4. Check dowel development length according to Figures 13a and 13b for tension andcompression reinforcement, respectively.Step 5. Check conservatism/understrength.Step 6. Determine reinforcement in long direction.Step 7. Determine reinforcement in short direction.Step 8. Select bar size and spacing.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 57Work Aid 4: Designing PedestalsStep 1. Check base plate stress.Step 2. Select pedestal reinforcing bar size and layout, and calculate minimum horizontalreinforcement according to the codes.Step 3. Size vertical reinforcement.AS = 1ft 4MDp - Wwhere: As = Total area of vertical reinforcement, in2.Dp= Bar octagon diameter, ft.ft = Allowable stress in pedestal reinforcement, psi.= 0.9 fy.M = Moment at top of footing, lb-ft.W = Vertical load at top of footing, lb.Step 4. Consider pedestal/footing interface and load transfer (ACI Section 15.8).Calculate dowelrequirements to code minimum and standards (ACI Section 11.7).(As > 0.005 Ap)where Ap = Gross pedestal areaVu AsFyEngineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 58Work Aid 5: Determining Anchor Bolt RequirementsStep 1.Calculate bolt tension.T = 4MDbN - PNwhere: N = Number of anchor bolts.Db= Bolt-circle diameter.M = Overturning moment (unfactored).P = Corresponding vertical load at top of pedestal (unfactored).T = Maximum bolt tension.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 59Step 2. Size to allowable capacities.ANCHOR BOLT DATADIMENSIONS (INCHES) LOAD CAPACITY (KIPS)A B C D E F G SHEAR TENSIONAnchorBolt Dia.Min.DepthType2OnlyLengthThr eadLengthThr ead3.5 Dia.LengthHook15 Dia.LengthSleeveNut onType 4Type1, 2,3, 4Type1Type2Type3, 41/2 10 4 1-5/8 - 7-1/2 - - 1.0 1.5 1.8 2.15/8 10 4 1-5/8 - 9-3/8 - - 1.5 1.7 2.3 3.43/4 12 6 2 2-5/8 11-1/4 1-7/8 11 2.2 2.3 3.2 5.17/8 14 6 2 3-1/8 13-1/8 2-1/4 12-3/4 3.2 2.9 4.1 7.01 16 8 2-1/2 3-1/2 15 2-1/2 14-3/4 4.2 3.6 5.1 9.11-1/8 18 8 3 4 16-7/8 2-7/8 16-1/2 5.3 3.8 5.5 11.51-1/4 20 8 3 4-3/8 18-3/4 3-1/8 18-1/4 6.7 4.1 6.5 14.71-3/8 22 8 3-5/8 4-7/8 20-5/8 3-1/2 20-1/4 7.9 7.6 17.61-1/2 24 8 3-5/8 5-1/4 22-1/2 3-3/4 22 9.7 8.7 21.41-5/8 26 8 4-1/8 5-3/4 24-3/8 4-1/8 23-3/4 11.5 9.9 24.41-3/4 28 10 4-3/8 6-1/8 26-1/4 4-3/8 25-1/2 13.2 10.5 28.92 32 10 5 7 30 5 29-1/2 17.4 13.2 38.02-1/4 36 10 5-5/8 7-7/8 33-3/4 5-5/8 33 22.9 15.9 47.72-1/2 40 10 6-1/4 8-3/4 37-1/2 6-1/4 37-1/2 28.3 18.9 58.2FIGURE 32Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 60Work Aid 6: Designing Pile CapsStep 1. Determine thickness (based on shear and development length considerations).- Beam shear near column.- Perimeter shear near column.- Beam shear near corner pile.- Perimeter shear near corner pile.- Development length of rebars from column or pedestals.Step 2. Determine reinforcing steel area.- Flexure considerations.- ACI minimum/maximum requirements.Step 3. Determine reinforcing steel bar size and distribution.- Development length of bars.- ACI Section 15.4.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 61GLOSSARYbeam shear Behavior where shear failure is across entire width of a member.continuous str ip footing Foundation supporting multiple columns in a row or supporting a wall.cr itical sectionCritical location where shear and/or moment capacity is computed.development length Distance required to transfer force in reinforcing steel into surroundingconcrete by bond/friction stresses.footing Soil-supported foundation.gr oss pr essur e Maximum soil bearing pressure exerted by foundation and overburden.mat foundation Large foundation supporting multiple columns.net pr essur e Bearing pressure exceeding existing overburden stress.over tur ning moment Moment applied to foundation due to lateral loading.punching shear Behavior where shear failure encircles a column, pedestal, or pile.r estor ing moment Total weight of foundation/vessel times one half of foundation diameter orwidth.soil-bear ing pr essur e Pressure applied to soil under foundation.stability r atio Measure of foundation stability, restoring moment/overturning moment(dimensionless).ultimate fr ictionallater al r estr aintMaximum resistance against sliding of foundation afforded by soil friction.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 62Design AidsProcedure For Using Design Aids:ACI 318-89SectionStep Description Design AidUse serviceloadsGivenStr ength Design of Pile Caps Using Special Tables forPile Cap DesignN (kips) total column load (D+L) (service).N (kips) estimated weight of pile cap and surchargeover area of cap.Pa (tons) allowable pile capacity (service).b x h, pier size, h in investigated direction.1A. Numberof pilesrequirednn = N + N2Pa = round up to next full number.11.11.22A.Thickness ofpile cap hf2A.1. Select table with required number of piles.Enterwith allowable pile capacity Pa (tons) and pier size h (in.)in the direction to be investigated.2A.1a. Ifc, ratio of long side to short side of thesupported column, is greater than 2, enter table withadjusted allowable pile capacity Pa

x Kv6.Kv6 = 4 /2 + 4/cFOOTINGS 4Commentary15.52A.2. Select effective depth, d, of pile cap for conditionwhere actual pier size, b (perpendicular to investigateddirection), is larger than bmin given in table.Note: Investigate shear around individual piles other thanbeam shear and perimeter shear around corner piles(which have been considered in FOOTINGS 4 tables).2A.3.Determine hf = d + (~7 in.).Note: ACI 318-89 Commentary Section 15.5.3 says:"When piles are located inside the critical sections d ord/2 from face of column, analysis for shear in deepflexure members in accordance with Section 11.8 must beconsidered."Authorized reprint from ACI 340.1R - 91, ACI Design Handbook - Volume 1, 1991, Pages 50-51.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 63ACI 318-89SectionStep Description Design Aid3A.ReinforcementAs = (Table value is total As in investigated direction).Note: Reinforcement selection is made using actual Paeven though an adjusted value may have been used inStep 2A.1a to find hf.4A. Barselection4A.1. Read maximum bar size that can be used, at top oftable.4A.2. Determine bar size and number of bars to be used ininvestigated direction.Note: Unless pile arrangement and pier are square, repeatinvestigation for other direction.Recompute thickness, selecting the larger of:(a) Using d required for beam shearhf = d +db / 2+ 7 in.(b) Using d required for perimeter shearhf = d + db + 7 in.15.4.4 5A. Bardistribution5A.1. For square pile caps, piers, and pile arrangement,use uniform spacing of bars in both directions.5A.2. For rectangular pile caps, piers, and pilearrangement, place bars as required by code.For uniform spacing in either direction, increasereinforcement in short direction to Asa2As +1, /b As= Area of steel in short direction as calculated forflexure.ACI Section 15.4ACI Section 15.4Authorized reprint from ACI 340.1R - 91, ACI Design Handbook - Volume 1, 1991, Pages 50-51.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 64Authorized reprint from ACI 340.1R - 91, ACI Design Handbook - Volume 1, 1991, Page 265.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 65Authorized reprint from ACI 340.1R - 91, ACI Design Handbook - Volume 1, 1991, Page 266.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 66Authorized reprint from ACI 340.1R - 91, ACI Design Handbook - Volume 1, 1991, Page 267.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 67Authorized reprint from ACI 340.1R - 91, ACI Design Handbook - Volume 1, 1991, Page 268.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 68Authorized reprint from ACI 340.1R - 91, ACI Design Handbook - Volume 1, 1991, Page 269.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 69Authorized reprint from ACI 340.1R - 91, ACI Design Handbook - Volume 1, 1991, Page 270.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 70Authorized reprint from ACI 340.1R - 91, ACI Design Handbook - Volume 1, 1991, Page 271.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 71Authorized reprint from ACI 340.1R - 91, ACI Design Handbook - Volume 1, 1991, Page 272.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 72Authorized reprint from ACI 340.1R - 91, ACI Design Handbook - Volume 1, 1991, Page 273.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 73Authorized reprint from ACI 340.1R - 91, ACI Design Handbook - Volume 1, 1991, Page 274.Engineering Encyclopedia Structural, On-shoreAnalysis and Design ofReinforced Concrete FoundationsSaudi Aramco DeskTop Standards 74Authorized reprint from ACI 340.1R - 91, ACI Design Handbook - Volume 1, 1991, Page 275.