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FOUNDATION DESIGNProportioning elements for:Transfer of seismic forcesStrength and stiffnessShallow and deep foundationsElastic and plastic analysisInstructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-1

Load Path and Transfer to SoilSoil PressurePile supporting structureForce on a piledeflectedshapesoilpressureUnmoving soilInertial forceEQ on unloaded essureEQ MotionInstructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-2

Load Path and Transfer to SoilSoil-to-foundation Force TransferPassive earthpressureShallowFrictionEQ motionInstructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-3

Load Path and Transfer to SoilSoil-to-foundation Force TransferDeepMotionSoilpressureBendingmomentEQ MotionInstructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-4

Load Path and Transfer to SoilVertical Pressures - ShallowOverturning momentEQ motionInstructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-5

Load Path and Transfer to SoilVertical Pressures - DeepOverturningmomentEQ MotionInstructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-6

Reinforced ConcreteFootings: Basic DesignCriteria (concentricallyloaded)Outside face of concretecolumn or line midwaybetween face of steelcolumn and edge ofsteel base plate (typical)(a)Critical sectionfor flexureextent of footing(typical)d(b)Critical sectionfor one-way shear(c)Critical sectionfor two-way sheard/2(all sides)Instructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-7

PM(a)LoadingFooting Subject toCompression andMoment: UpliftNonlinear(b)Elastic, no uplift(c)Elastic, at uplift(d)Elastic, after uplift(e)Some plastification(f)Plastic limitInstructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-8

7 Bays @ 25'-0" 175'-0"1'-2"5 Bays @ 25'-0" undationsdesigned forperimeterframe andcore bracing.Instructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-9

Shallow Footing ExamplesSoil parameters: Medium dense sand (SPT) N 20 Density 120 pcf Friction angle 33oGravity load allowables 4000 psf, B 20 ft 2000 psf, B 40 ftBearing capacity (EQ) 2000B concentric sq. 3000B eccentricφ 0.6Instructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-10

Footingsproportionedfor gravityloads aloneCorner:6'x6'x1'-2" thickInterior:11'x11'x2'-2" thickPerimeter:8'x8'x1'-6" thickInstructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-11

Design ofFootingsforPerimeterMomentFrame5 at 25'-0"7 at 25'-0"NInstructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-12

7-Story Frame, DeformedInstructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-13

Combining Loads Maximum downward load: 1.2D 0.5L EMinimum downward load:0.9D EDefinition of seismic load effect E:E ρ1QE1 0.3 ρ2QE2 /- 0.2 SDSDρx 1.08 ρy 1.11 and SDS 1.0Instructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-14

ReactionsGridDeadLiveExEyA-5P203.8 kMxxMyy43.8 k-3.8 k53.6 k-ft-243.1 k-ft21.3 k-1011.5 k-ft8.1 k-ftA-6P103.5 kMxxMyy22.3 k-51.8 k47.7 k-ft-246.9 k-ft-281.0 k-891.0 k-ft13.4 k-ftInstructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-15

Reduction of Overturning Moment NEHRP Recommended Provisions allow base overturning moment to be reduced by25% at the soil-foundation interface.For a moment frame, the column verticalloads are the resultants of base overturningmoment, whereas column moments areresultants of story shear.Thus, use 75% of seismic vertical reactions.Instructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-16

Additive Load w/ Largest Eccentricity At A5: P 1.4(203.8) 0.5(43.8) 0.75(0.32(-3.8) 1.11(21.3)) 324 kMxx 0.32(53.6) 1.11(-1011.5) -1106 k-ftAt A6: P 1.4(103.5) 0.5(22.3) 0.75(0.32(-51.8) 1.11(-281)) -90.3 kMxx 0.32(47.7) 1.11(-891) -974 k-ftSum Mxx 12.5(-90.3-324) -1106 -974 -7258Instructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-17

Counteracting Load with Largest e At A-5: P 0.7(203.8) 0.75(0.32(-3.8) 1.11(21.3)) 159.5 kMxx 0.32(53.6) 1.11 (-1011.5) -1106 k-ftAt A-6: P 0.7(103.5) 0.75(0.32(-51.8) 1.11(-281)) -173.9 kMxx 0.32(47.7) 1.11(-891) -974 k-ftSum Mxx 6240 k-ftInstructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-18

Elastic Response Objective is to set L and W to satisfyequilibrium and avoidoverloading soil.Successive trialsusually necessary.LPMWReInstructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-19

Additive CombinationGiven P 234 k, M 7258 k-ftTry 5 foot around, thus L 35 ft, B 10 ft Minimum W M/(L/2) – P 181 k 517 psfTry 2 foot soil cover & 3 foot thick footing W 245 k; for additive combo use 1.2W Qmax (P 1.2W)/(3(L/2 – e)B/2) 9.4 ksf φQn 0.6(3)Bmin 10.1 ksf, OK by ElasticInstructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-20

Plastic Response Same objective as for elastic response.Smaller footings canbe shown OK thus:LPMWReInstructional Materials Complementing FEMA 451, Design ExamplesRFoundation Design 14-21

Counteracting CaseGiven P -14.4 k; M 6240Check prior trial; W 245 k (use 0.9W) e 6240/(220.5 – 14.4) 30.3 35/2 NGNew trial: L 40 ft, 5 ft thick W 400 k; e 18.0 ft; plastic Qmax 8.6 ksf φQn 0.6(3)4 7.2 ksf, close Solution is to add 5 k, then e 17.8 ft andQmax φQn 7.9 ksfInstructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-22

Additional Checks Moments and shears for reinforcement should be checked for the overturning case.Plastic soil stress gives upper bound onmoments and shears in concrete.Horizontal equilibrium: Hmax φμ(P W)in this case friction exceeds demand; passivecould also be used.Instructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-23

Results forall ner: 10'x40'x5'-0" w/top of footing 2'-0" below gradeInstructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-24

Design of Footingsfor Core-braced 7story Building25 foot square bays atcenter of buildingInstructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-25

Solution for Central MatVery high upliftsat individualcolumns; mat isonly practicalshallowfoundation.Mat: 45'x95'x7'-0"with top of mat3'-6" below gradeInstructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-26

Bearing Pressure Solution12.2 ksf 124(a)Plasticsolution16 (b)8 Elastic solution0 pressures (ksf)Instructional Materials Complementing FEMA 451, Design ExamplesPlasticsolution issatisfactory;elastic is not;see linked filefor moredetail.Foundation Design 14-27

Pile/Pier FoundationsPilecapPassive resistance(see Figure 4.2-5)Pilep-y springs(see Figure 4.2-4)View of cap withcolumn above andpiles below.Instructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-28

Pile/Pier FoundationsPile Stiffness: Short (rigid) Intermediate LongCap influenceGroup actionSoil Stiffness Linear springs –nomographs e.g.NAVFAC DM7.2 Nonlinear springs –LPILE or similaranalysisInstructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-29

Sample p-y Curves100,000Soil resistance, p (lb/in.)10,0001,000100Site Class C, depth 30 ftSite Class C, depth 10 ft10Site Class E, depth 30 ftSite Class E, depth 10 ft10.00.10.20.30.4 0.5 0.6 0.7Pile deflection, y (in.)Instructional Materials Complementing FEMA 451, Design Examples0.80.91.0Foundation Design 14-30

P/PultPassive 0.030.04δ/HInstructional Materials Complementing FEMA 451, Design Examples0.050.06Foundation Design 14-31

Group Effect1.0Group effect factors 4D0.8s 3D0.6s 2D0.4s 1.5 D0.20.01234Group size (piles per side)Instructional Materials Complementing FEMA 451, Design Examples5Foundation Design 14-32

Pile Shear: Two SoilStiffnesses05Depth (ft)10152025Site Class CSite Class E30-50510Shear, V (kip)15Instructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-33

0PileMomentvs Depth5Depth (ft)10152025Site Class CSite Class E30-1000-5000Moment, M (in.-kips)500Instructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-34

PileReinforcement4" pileembedment6'-4"(6) #521'-0"23'-0"A#4 spiral at3.75 inch pitchSection A(6) #5B#4 spiral at7.5 inch pitchSection B(4) #5C#4 spiral at11 inch pitch Site Class C Larger amounts wheremoments and shears arehigh Minimum amounts mustextend beyond theoreticalcutoff points “Half” spiral for 3DSection CInstructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-35

Pile Design12'-4"4" pileembedment(8) #7A#5 spiral at3.5 inch pitch20'-0"Section A(6) #7B#5 spiral at3.5 inch pitch32'-0"Section B Site Class E Substantially morereinforcement “Full” spiral for 7D Confinement atboundary of soft andfirm soils (7D up and3D down)(4) #7C#4 spiral at11 inch pitchSection CInstructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-36

Other Topics for Pile Foundations Foundation Ties: F PG(SDS/10) Pile Caps: high shears, rules of thumb; look for 3D strut and tie methods in futureLiquefaction: another topicKinematic interaction of soil layersInstructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-37

Tie Between Pile Caps2" clearat sides(2) #6 top bars#4 ties at 7" o.c.3" clear attop and bottom(3) #6 bottom bars Designed for axial force ( /-) Pile cap axial load times SDS/10 Often times use grade beams orthickened slabs one gradeInstructional Materials Complementing FEMA 451, Design ExamplesFoundation Design 14-38