DESIGN OF FOUNDATIONS - Universiti Teknologi Malaysia

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DESIGN OF FOUNDATIONSDr. Izni Syahrizal bin IbrahimFaculty of Civil EngineeringUniversiti Teknologi MalaysiaEmail: iznisyahrizal@utm.my

Introduction Foundation – Part of structure whichtransmits load from the structure to theunderlying soil or rock All soils compress noticeably when loadedcausing structure to settle

Introduction Requirements in the design of foundations:(i) Total settlement of the structure to belimited to a tolerably small amount(ii) Differential settlement of various partsof structure shall be eliminated

Introduction To limit settlement, it is necessary to transmit thestructure load to a soil stratum of sufficientstrength Spread the structure load over a sufficiently largearea of stratum to minimize bearing pressure Satisfactory soil: Use footings Adequate soil: Use deep foundations i.e. piles

Introduction Pressure distribution under a footingUniformdistributedCohesive soilCohesionless soil

Types of FoundationPad Footings Transmit load from piers andcolumns Simplest and cheapest type Use when soil is relatively strong orwhen column loads are relativelylight Normally square or rectangularshape in plan Has uniform thickness

Types of FoundationCombine Footings Use when two columns are closedtogether Combine the footing to form acontinuous base Base to be arranged so that itscentreline coincides with the centreof gravity of the load – provideuniform pressure on the soil

Types of FoundationStrap Footings Use where the base for an exteriorcolumn must not project beyondthe property line Strap beam is constructed betweenexterior footing & adjacent interiorfooting Purpose of strap – to restrainoverturning forces due to loadeccentricity on the exterior footing

Types of FoundationStrap Footings (continued) Base area of the footings areproportioned to the bearingpressure Resultant of the loads on the twofootings should pass through thecentroid of the area of the twobases Strap beam between the twofootings should NOT bear againstthe soil

Types of FoundationStrip Footings Use for foundations to load-bearingwall Also use when pad footings fornumber of columns are closelyspaced Also use on weak ground toincrease foundation bearing area

Types of FoundationRaft Foundations Combine footing which covers thewhole building Support all walls & columns Useful where column loads areheavy or bearing capacity is low –need large base Also used where soil mass containscompressible layers or soil isvariable – differential settlementdifficult to control

Types of FoundationPile Foundations More economic to be used whensolid bearing stratum i.e. rock isdeeper than about 3 m Pile loads can either be transmittedto a stiff bearing layer (somedistance below surface) or byfriction along the length of pile Pile types – precast (driven into thesoil) or cast in-situ (bored) Soil survey is important to provideguide on the length of pile and safeload capacity of the pile

Types of FoundationPile FoundationsLoad fromStructurePile CapLower DensityMedium DensityHigh DensityPILEPILEPILEPILE

Design of Pad FootingThickness and Size of FootingArea of pad:𝑮𝒌 𝑸𝒌 𝑾𝑨 𝑺𝒐𝒊𝒍 𝒃𝒆𝒂𝒓𝒊𝒏𝒈 𝒄𝒂𝒑𝒄𝒊𝒕𝒚Minimum effective depth of pad:𝒅 𝑵𝑬𝒅𝒗𝒓𝒅,𝒎𝒂𝒙 𝒖𝒐NEd Ultimate vertical load 1.35Gk 1.5Qk𝑓vrd,max 0.5vfcd 0.5 0.6 1 𝑐𝑘250uo Column perimeter𝑓𝑐𝑘1.5

Design of Pad FootingDesign for Flexure Critical section for bending – At the face of the column Moment is taken on a section passing completely across thefooting and due to ultimate load on one side of the section Moment & shear is assessed using STR (Structure) combinationxyyxSTR Combination 1:𝑵 𝟏. 𝟑𝟓𝑮𝒌 𝟏. 𝟓𝑸𝒌

Design of Pad FootingCheck for Shear May fail in shear as vertical shear or punching shearVertical shearsectionsPunching shearperimeters2ddhBends may berequiredd

Design of Pad FootingCheck for Shear(i)Vertical Shear Critical section at distance d from the face of column Vertical shear force Load acting outside the section If VEd VRd,c No shear reinforcement is required

Design of Pad FootingCheck for Shear(ii) Punching ShearAxial Force Only Critical section at a perimeter 2d from the face of the columnPunching shear force Load outside the critical perimeter𝑽𝑬𝒅Shear stress, 𝒗𝑬𝒅 where u Critical perimeter𝒖 𝒅If vEd vRd,c No shear reinforcement is requiredAlso ensure that VEd VRd,max

Design of Pad FootingCheck for Shear(ii) Punching Shear (continued)Axial Force & Bending Moment Punching shear resistance can be significantly reduced of a coexisting bending, MEd However, adverse effect of the moment will give rise to a nonuniform shear distribution around the control perimeter Refer to Cl. 6.4.3(3) of EC2

Design of Pad FootingCheck for Shear(ii) Punching Shear (continued)Shear stress, 𝒗𝑬𝒅 𝜷𝑽𝑬𝒅𝒖𝟏 𝒅where; factor used to include effect of eccentric load & bending moment 1 𝑘𝑀𝐸𝑑𝑉𝐸𝑑𝑢1𝑊1k coefficient depending on the ratio between column dimension c1 & c2c1/c2 0.51.02.0 3.0k0.450.600.700.80u1 length of basic control perimeterW1 function of basic control perimeter corresponds to the distribution ofshear 0.5𝑐1 2 𝑐1 𝑐2 4𝑐2 𝑑 16𝑑 2 2𝜋𝑑𝑐1

Design of Pad FootingCheck for Shear(ii) Punching Shear (continued)

Design of Pad FootingCracking & Detailing Requirements All reinforcements should extend the full length of the footing If 𝐿𝑥 1.5 𝑐𝑥 3𝑑 , at least two-thirds of the reinforcement parallelto Ly should be concentrated in a band width 𝑐𝑥 3𝑑 centred atcolumn where Lx & Ly and cx & cy are the footing and column dimensionin x and y directions Reinforcements should be anchored each side of all critical sections forbending. Usually possible to achieve using straight bar Spacing between centre of reinforcements 20 mm for fyk 500N/mm2 Reinforcements normally not provided in the side face nor in the topface (except for balanced & combined foundation) Starter bar should terminate in a 90 bend tied to the bottomreinforcement, or in the case of unreinforced footing spaced 75 mmoff the building

Example 1PAD FOOTING(AXIAL LOAD ONLY)

Example 1: Pad Footing (Axial Load)Axial Force, N:Gk 600 kNQk 400 kNColumn size:300 300 mmhBH fck 25 N/mm2fyk 500 N/mm2 soil 150 N/mm2Unit weight of concrete 25 kN/m3Design life 50 yearsExposure Class XC2Assumed bar 12 mm

Example 1: Pad Footing (Axial Load)Durability & Bond RequirementsMin cover regards to bond, cmin,b 12 mmMin cover regards to durability, cmin,dur 25 mmAllowance in design for deviation, cdev 10 mmNominal cover, cnom cmin cdev 25 10 35 mm cnom 35 mmcmin 25 mm

Example 1: Pad Footing (Axial Load)SizeService load, NAssumed selfweight 10% of service load , WArea of footing required 𝑁 𝑊𝛾𝑠𝑜𝑖𝑙 1000 kN 100 kN1000 100150 7.33 𝑚2 Try footing size, B H h 3 m 3 m 0.45 mArea, A 9 m2Selfweight, W 9 0.45 25 101 kNCheck Service Soil Bearing Capacity 122 kN/m2 150 kN/m2 OK𝑵 𝑾𝑨 𝟏𝟎𝟎𝟎 𝟏𝟎𝟏𝟗

Example 1: Pad Footing (Axial Load)AnalysisUltimate axial force, NEd 1.35Gk 1.5Qk 1.35 (600) 1.5 (400) 1410 kN𝑁1410Soil pressure at ultimate load, P 𝐸𝑑 157 kN/m2𝐴9Soil pressure per m length, w 157 3 m 470 kN/m0.3 m1.35 mw 470 kN/m1.35 m

Example 1: Pad Footing (Axial Load)AnalysisUltimate axial force, NEd 1.35Gk 1.5Qk 1.35 (600) 1.5 (400) 1410 kN𝑁1410Soil pressure at ultimate load, P 𝐸𝑑 157 kN/m2𝐴9Soil pressure per m length, w 157 3 m 470 kN/mMEd0.3 m1.35 mw 470 kN/m1.35 m𝟏. 𝟑𝟓𝑴𝑬𝒅 𝟒𝟕𝟎 𝟏. 𝟑𝟓 𝟐 428 kNm

Example 1: Pad Footing (Axial Load)Main ReinforcementEffective depth, d h – c – 1.5 bar 450 – 35 – (1.5 12) 397 mm𝐾 𝑀𝐸𝑑𝑓𝑐𝑘 𝑏𝑑 2 428 10625 3000 3972 0.036 Kbal 0.167 Compression reinforcement is NOT required𝑧 𝑑 0.25 𝐴𝑠,𝑟𝑒𝑞 𝐾1.134𝑀𝐸𝑑0.87𝑓𝑦𝑘 𝑧 0.97𝑑 0.95d428 1060.87 500 0.95 397 𝟐𝟔𝟏𝟏 mm2

Example 1: Pad Footing (Axial Load)Minimum & Maximum Area of Reinforcement𝑓𝑐𝑡𝑚2.56𝑏𝑑 0.260.0013𝑏𝑑 0.0013𝑏𝑑𝑓𝑦𝑘500 0.0013bd 0.0013 3000 397 1589 mm2𝐴𝑠,𝑚𝑖𝑛 0.26 As,minAs,max 0.04Ac 0.04bh 0.04 3000 397 54000 mm2Provide 24H12 (As,prov 2715 mm2)

Example 1: Pad Footing (Axial Load)(i) Vertical Shear3m1.35 md 397 mmVEd953 mm3mw 470 kN/m0.953 mCritical shear at 1.0d from face of column: Design shear force, VEd 470 0.953 448 kN

Example 1: Pad Footing (Axial Load)(i) Vertical Shear𝑘 1 200𝑑 1 200397 1.71 2.0Note:Bar extend beyond critical section at 953 – 35 918 mm 𝑙𝑏𝑑 𝑑 40 𝑑 40 12 397 877 mm𝐴𝑠𝑙2715𝜌𝑙 0.0023 0.02𝑏𝑑 3000 397 Asl 2715 mm2

Example 1: Pad Footing (Axial Load)(i) Vertical Shear𝑉𝑅𝑑,𝑐 0.12𝑘 100𝜌𝑙 𝑓𝑐𝑘 1/3 𝑏𝑑 0.12 1.71 100 0.0023 251/33000 397 436463 N 436 kN𝑉𝑚𝑖𝑛 0.035𝑘 3/2 𝑓𝑐𝑘 𝑏𝑑 0.035 1.713/2 25 3000 397 465970 𝑁 466 kNVEd (448 kN) Vmin (466 kN) OK

Example 1: Pad Footing (Axial Load)(ii) Punching ShearCritical shear at 2.0d from face of column:Average d 450 – 35 – 12 403 mm 2d 806 mm13502d 806Control perimeter, u (4 300) (2 806) 6265 mm3002d 806300Area within perimeter, A (0.30 0.30) (4 0.30 0.806) ( 0.8062) 3.10 m2544 𝑙𝑏𝑑 𝑑 40 𝑑 40 12 397 877mm Reinforcement NOT contributed to punchingresistance

Example 1: Pad Footing (Axial Load)(ii) Punching ShearPunching shear force:VEd 157 (32 – 3.10) 925 kNAall 9 m2Aperimeter 3.10 m2Punching shear resistance:𝑉𝑅𝑑,𝑐 𝑉𝑚𝑖𝑛 0.035𝑘 3/2 𝑓𝑐𝑘 1/2 𝑢𝑑 0.035 1.71 3/2 25 1/2 6265 403 983199 N 983 kN VEd (925 kN) OKSoil pressure 157 kN/m2

Example 1: Pad Footing (Axial Load)(iii) Maximum Punching Shear at Column PerimeterMaximum punching shear force:VEd,max 157 (32 – 0.09) 1400 kNAall 9 m2Acolumn 0.09 m2Maximum shear resistance:𝑓𝑐𝑘 0.5𝑢𝑑 0.6 1 250𝑓𝑐𝑘𝑉𝑅𝑑,𝑚𝑎𝑥1.525 0.5 4 300 403 0.6 1 250 2176 kN VEd,max OK251.5Soil pressure 157 kN/m2

Example 1: Pad Footing (Axial Load)Crackingh 450 mm 200 mmMax bar spacing𝐴𝑠.𝑟𝑒𝑞𝐺𝑘 0.3𝑄𝑘Steel stress, 𝑓𝑠 1.35𝐺𝑘 1.5𝑄𝑘𝐴𝑠,𝑝𝑟𝑜𝑣600 0.3 4002611500 2131.35 600 1.5 40027151.15𝑓𝑦𝑘1.15N/mm2For design crack width 0.3 mm:Maximum allowable bar spacing 200 mmActual bar spacing 3000 2 35 1223 127 mm 200 mmCracking OK

Example 1: Pad Footing (Axial Load)Detailing24H12300024H123000450300024H12Plan ViewSection View

Example 2PAD FOOTING(AXIAL LOAD & MOMENT)

Example 2: Pad Footing (Axial Load &Moment)Axial Force, N 1500 kNMoment 50 kNmColumn size:250 350 mmhBH Design Life 50 years (Table 2.1: EN1990) Exposure Class XC3 fck 30 N/mm2 fyk 500 N/mm2 soil 150 N/mm2 Unit weight of concrete 25 kN/m3 Assumed bar 12 mm

Example 2: Pad Footing (Axial Load &Moment)Durability & Bond RequirementsMin cover regards to bond, cmin,b 12 mmMin cover regards to durability, cmin,dur 25 mmAllowance in design for deviation, cdev 10 mmNominal cover, cnom cmin cdev 25 10 35 mm cnom 35 mmcmin 25 mm

Example 2: Pad Footing (Axial Load &Moment)SizeService axial, NService moment, MAssumed selfweight 10% of service load , WArea of footing required 𝑁 𝑊𝛾𝑠𝑜𝑖𝑙 1071 107.1150 1500 kN / 1.40 1071 kN 50 kNm / 1.40 36.1 kNm 100 kN 7.85 𝑚2 Try footing size, B H h 2.80 m 3.50 m 0.65 mArea, A 9.80 m2Selfweight, W 9.80 0.65 25 159 kN

Example 2: Pad Footing (Axial Load &Moment)Size (Continued)𝐵𝐻 32.8 3.53𝐼𝑥𝑥 1212𝐻3.5𝑦 1.75 m2210.0 m4Maximum soil pressure, 𝑃 132 kN/m2 150 kN/m2𝑁 𝑊𝐴𝑀𝑦 𝐼 OK1071 1599.80 50 1.7510.0BxHx

Example 2: Pad Footing (Axial Load &Moment)AnalysisUltimate soil pressure, 𝑃 50 1.7510.0𝑁𝐴 𝑀𝑦𝐼 15009.80x 153 8.7 kN/m21.275 Pmin 144 kN/m2 and Pmax 162 kN/m2yyx0.35 m1.575 m1.575 m144162144154162

Example 2: Pad Footing (Axial Load &Moment)Analysis (Continued)𝑀𝑥𝑥x1.5752 154 21.2751.5752 1.575 23 197 kNm/m 2.80 m 553 kNm 162 154𝑀𝑦𝑦 𝟏𝟓𝟑1.2752 2yyx 124 kNm/m 3.50 m 0.35 m1.575 m435 kNm 144 16221441.575 m154162

Example 2: Pad Footing (Axial Load &Moment)Effective Depthdx h – c – 0.5 bar 650 – 35 – (0.5 12) 609 mmdy h – c – 1.5 bar 650 – 35 – (1.5 12) 597 mmMain Reinforcement – Longitudinal Bar𝐾 𝑀𝑥𝑥𝑓𝑐𝑘 𝑏𝑑 2 553 10630 2800 6092 0.018 Kbal 0.167 Compression reinforcement is NOT required𝑧 𝑑 0.25 𝐴𝑠,𝑟𝑒𝑞 𝐾1.134𝑀𝑥𝑥0.87𝑓𝑦𝑘 𝑧 0.98𝑑 0.95d553 1060.87 500 0.95 609 𝟐𝟏𝟗𝟕 mm2

Example 2: Pad Footing (Axial Load &Moment)Minimum & Maximum Area of Reinforcement𝑓𝑐𝑡𝑚2.90𝑏𝑑 0.260.0013𝑏𝑑 0.0013𝑏𝑑𝑓𝑦𝑘500 0.0013bd 0.0013 2800 609 2217 mm2𝐴𝑠,𝑚𝑖𝑛 0.26 As,minAs,max 0.04Ac 0.04bh 0.04 2800 609 72800 mm2Since As As,min, Use As,min 2217 mm2Provide 21H12 (As 2375 mm2)

Example 2: Pad Footing (Axial Load &Moment)Main Reinforcement – Transverse Bar𝐾 𝑀𝑦𝑦𝑓𝑐𝑘 𝑏𝑑 2 435 10630 3500 5972 0.018 Kbal 0.167 Compression reinforcement is NOT required𝑧 𝑑 0.25 𝐴𝑠,𝑟𝑒𝑞 𝐾1.134𝑀𝑦𝑦0.87𝑓𝑦𝑘 𝑧 0.99𝑑 0.95d435 1060.87 500 0.95 597 𝟏𝟕𝟔𝟓mm2

Example 2: Pad Footing (Axial Load &Moment)Minimum & Maximum Area of Reinforcement𝑓𝑐𝑡𝑚2.90𝑏𝑑 0.260.0013𝑏𝑑 0.0013𝑏𝑑𝑓𝑦𝑘500 0.0013bd 0.0013 3500 597 3147 mm2𝐴𝑠,𝑚𝑖𝑛 0.26 As,minAs,max 0.04Ac 0.04bh 0.04 3500 597 91000 mm2Since As As,min, Use As,min 3147 mm2Provide 28H12 (As 3167 mm2)

Example 2: Pad Footing (Axial Load &Moment)(i) Vertical Shear2.891Critical shear at 1.0d from face of column:2.8Average pressure at critical section:2.8913.50 18 159 kN/m2d 0.609 144 Design shear force, VEd 159 0.966 2.80 431 kN0.966144159Note:Bar extend beyond critical section at 966 – 35 931 mm 𝑙𝑏𝑑 𝑑 36 𝑑 36 12 609 1041 mm162 Asl 0 mm2

Example 2: Pad Footing (Axial Load &Moment)(i) Vertical Shear𝑘 1 𝜌𝑙 200𝑑 1 200609 1.57 2.0𝐴𝑠𝑙 0𝑏𝑑 𝑉𝑅𝑑,𝑐 0.12𝑘 100𝜌𝑙 𝑓𝑐𝑘 1/3 𝑏𝑑 0.12 1.57 100 0 30 1/3 2800 609 0 N 0 kN 𝑉𝑚𝑖𝑛 0.035𝑘 3/2 𝑓𝑐𝑘 𝑏𝑑 0.035 1.573/2 30 2800 609 644949 𝑁 645 kNVEd (430 kN) Vmin (645 kN) OK

Example 2: Pad Footing (Axial Load &Moment)(ii) Punching ShearCritical shear at 2.0d from face of column:609 597 603 mm3500Control perimeter;u 2(350 250) (2 1206) 8779 mm2d 12063502d 1206250Area within perimeter;A (0.35 0.25) (2 0.35 1.206) (2 0.25 1.206) ( 1.2062) 6.10 m22800Average 𝑑 2 2d 1206 mm69369 𝑙𝑏𝑑 𝑑 36 𝑑 36 12 609 1041 mm Reinforcement NOT contributed to punching resistance

Example 2: Pad Footing (Axial Load &Moment)(ii) Punching ShearAverage punching shear force at control perimeter:VEd 153 [(2.80 3.50) – 6.10] 566 kNPunching shear stress:𝛽𝑉𝐸𝑑𝑣𝐸𝑑 𝑢𝑑𝑀Where 𝛽 1 𝑘 𝑉 𝐸𝑑k 0.65 𝐸𝑑𝑐1𝑐2Aall 2.8 3.5 mAperimeter 6.10 m2𝑢1𝑊1350 250 1.4W1 0.5𝑐1 2 𝑐1 𝑐2 4𝑐2 𝑑 16𝑑 2 2𝜋𝑑𝑐1 0.5(3502 ) 350 250 4 250 603 16 6032 2𝜋 603 350 7.9 106 mm2 𝛽 1 0.6550 106566 103Therefore, 𝒗𝑬𝒅 𝟏.𝟎𝟔 𝟓𝟔𝟔 𝟏𝟎𝟑𝟖𝟕𝟕𝟗 𝟔𝟎𝟗87797.9 106 1.06 𝟎. 𝟏𝟏 N/mm2Soil pressure 153 kN/m2

Example 2: Pad Footing (Axial Load &Moment)(ii) Punching ShearPunching shear resistance:Aall 2.8 3.5 m𝑘 1 200𝑑 1 200609 1.57 2.0𝑣𝑅𝑑,𝑐 𝑣𝑚𝑖𝑛 0.035𝑘 3/2 𝑓𝑐𝑘 1/2 0.035 1.57 3/2 30 1/2 0.38 N/mm2 vEd (0.11 N/mm2)Aperimeter 6.10 m2 OKSoil pressure 153 kN/m2

Example 2: Pad Footing (Axial Load &Moment)(iii) Maximum Punching Shear at Column PerimeterMaximum punching shear force:VEd,max 1500 kNColumn perimeter, uo 2(350 250) 1200 mmPunching shear stress:𝛽𝑉𝐸𝑑𝑣𝐸𝑑 𝑢𝑜 𝑑𝑀Where 𝛽 1 𝑘 𝐸𝑑k 0.65 𝑉𝐸𝑑𝑐1 𝑐2𝑢𝑜𝑊1350250Aall 2.8 3.5 m 9.8 m2Acolumn 0.09 m2Soil pressure 153 kN/m2 1.4W1 0.5𝑐1 2 𝑐1 𝑐2 0.5(3502 ) 350 250 0.15 106 mm2

Example 2: Pad Footing (Axial Load &Moment)(iii) Maximum Punching Shear at Column Perimeter 𝛽 1 0.6550 1061500 103Therefore, 𝒗𝑬𝒅 𝟏.𝟏𝟕 𝟏𝟓𝟎𝟎 𝟏𝟎𝟑𝟏𝟐𝟎𝟎 𝟔𝟎𝟑12000.15 106Maximum shear resistance:𝑓𝑐𝑘𝑣𝑅𝑑,𝑚𝑎𝑥 0.5 0.6 1 2503030 0.5 0.6 1 2501.5 5.28 N/mm2 vEd 1.17 𝟐. 𝟒𝟒N/mm2Aall 2.8 3.5 m 9.8 m2Acolumn 0.09 m2𝑓𝑐𝑘1.5Soil pressure 153 kN/m2 OK

Example 2: Pad Footing (Axial Load &Moment)Crackingh 650 mm 200 mmMax bar spacingAssume steel stress is under quasi-permanent loading: 𝑟𝑜𝑣 0.65001.1521972375 241 N/mm2For design crack width 0.3 mm:Maximum allowable bar spacing 150 mm2800 2 35 12 136 mm 150 mm203500 2 35 12 126 mm 150 mm27Actual bar spacing at x-x ctual bar spacing at y-y Cracking OK

Example 2: Pad Footing (Axial Load 12Plan ViewSection View

Example 3DESIGN OF COMBINEDFOOTING

Example 3: Design of Combined FootingNA 1610 kN(Ultimate)NB 1950 kN(Ultimate)3.4 mColumn size:300 300 mmColumn size:400 400 mmhBH fck 35 N/mm2fyk 500 N/mm2 soil 200 N/mm2Unit weight of concrete 25 kN/m3Cover 40 mmAssumed bar 12 mm

Example 3: Design of Combined FootingSizeService axial:NANBTotal service axial, Ntotal 1610 kN / 1.40 1150 kN 1950 kN / 1.40 1393 kN 1150 1393 2543 kNAssumed selfweight 10% of service load , W 254.3 kNArea of footing required 𝑁 𝑊𝛾𝑠𝑜𝑖𝑙 2543 254.3200 14.0 𝑚2 Try footing size, B H h 2.70 m 6.00 m 0.65 mArea, A 16.2 m2Selfweight, W 16.2 0.65 25 252.7 kN

Example 3: Design of Combined FootingSize (Continued)𝑁 𝑊𝐴Check Service Soil Bearing Capacity 173 kN/m2 200 kN/m2 OK 2543 252.716.2Arrange position of footing so that the distribution of soil pressure is uniform:Ntotal 2543 kNNA 1150 kNNB 1393 kNx3.4 m MA 01393(3.4 ) 2543x 0x 1.86 m

Example 3: Design of Combined FootingAnalysis𝑁(1610 1950)Soil pressure at ultimate load, P 𝐸𝑑 219.8 kN/m2𝐴16.2Soil pressure per m width, w 219.8 2.7 m 593.5 kN/m

Example 3: Design of Combined FootingShear Force & Bending Moment Diagram3m3m1610 kN0.30.991950 kN1.341.711.260.40.65x 1.86593.5 kN/m10829645876761.621.43SFD (kN)868934749846353289250384BMD (kNm)473430634

Example 3: Design of Combined FootingMain ReinforcementLongitudinal Reinforcement: BottomEffective depth: dx h – c – 0.5 bar 650 – 40 – (0.5 12) 604 mm𝐾 𝑀𝐸𝑑𝑓𝑐𝑘 𝑏𝑑 2 473 10635 2700 6042 0.014 Kbal 0.167 Compression reinforcement is NOT required𝑧 𝑑 0.25 𝐴𝑠,𝑟𝑒𝑞 𝐾1.134𝑀𝐸𝑑0.87𝑓𝑦𝑘 𝑧 0.99𝑑 0.95d473 1060.87 500 0.95 604 𝟏𝟖𝟗𝟒 mm2 As,min 2722 mm2

Example 3: Design of Combined FootingMain ReinforcementLongitudinal Reinforcement: Top𝐾 𝑀𝐸𝑑𝑓𝑐𝑘 𝑏𝑑 2 353 10635 2700 6042 0.010 Kbal 0.167 Compression reinforcement is NOT required𝑧 𝑑 0.25 𝐴𝑠,𝑟𝑒𝑞 𝐾1.134𝑀𝐸𝑑0.87𝑓𝑦𝑘 𝑧 0.99𝑑 0.95d353 1060.87 500 0.95 604 𝟏𝟒𝟏𝟑 mm2 As,min 2722 mm2

Example 3: Design of Combined FootingMinimum & Maximum Area of 0.26𝑏𝑑 0.260.0017𝑏𝑑 0.0013𝑏𝑑𝑓𝑦𝑘500 As,min 0.0017bd 0.0017 2700 604 2722 mm2As,max 0.04Ac 0.04bh 0.04 2700 650 70200 mm2Provide 25H12 at both top and bottom (As,prov 2828 mm2)

Example 3: Design of Combined FootingMain ReinforcementTransverse Reinforcement: BottomConsider b 1000 mm: Soil pressure per 1 m width, w 219.8 1.0 m 219.8 kN/mMEd0.3 m1.2 mw 219.8 kN/m1.2 m𝟏. 𝟐𝑴𝑬𝒅 𝟐𝟏𝟗. 𝟖 𝟏. 𝟐 𝟐 158 kNm/m

Example 3: Design of Combined FootingMain ReinforcementTransverse Reinforcement: BottomEffective depth: dy h – c – 1.5 bar 650 – 40 – (1.5 12) 592 mm𝐾 𝑀𝐸𝑑𝑓𝑐𝑘 𝑏𝑑 2 158 10635 𝟏𝟎𝟎𝟎 5922 0.013 Kbal 0.167 Compression reinforcement is NOT required𝑧 𝑑 0.25 𝐴𝑠,𝑟𝑒𝑞 𝐾1.134𝑀𝐸𝑑0.87𝑓𝑦𝑘 𝑧 0.99𝑑 0.95d158 1060.87 500 0.95 592 𝟔𝟒𝟕 mm2/m As,min 988 mm2/m

Example 3: Design of Combined FootingMinimum & Maximum Area of 0.26𝑏𝑑 0.260.0017𝑏𝑑 0.0013𝑏𝑑𝑓𝑦𝑘500 As,min 0.0017bd 0.0017 1000 592 988 mm2/mAs,max 0.04Ac 0.04bh 0.04 1000 650 26000 mm2/mSince As As,min, then use As,min 988 mm2/mProvide H12-100 (As,prov 1131 mm2/m)For secondary bar reinforcement:Provide H12-100 (As,prov 1131 mm2/m)

Example 3: Design of Combined Footing(i) Vertical ShearCritical shear at 1.0d from face of column:VEd964𝑉𝐸𝑑 1.021.62 964 𝟔𝟎𝟓 kN58710826761.431.02𝑘 1 𝜌𝑙 200𝑑 1 200604 1.6 2.0934846d 0.6048687491.62𝐴𝑠𝑙2828 0.0017 0.02𝑏𝑑 2700 604 𝑉𝑅𝑑,𝑐 0.12𝑘 100𝜌𝑙 𝑓𝑐𝑘 1/3 𝑏𝑑 0.12 1.6 100 0.0017 35 1/3 2700 604 562369 N 562.4 kN 𝑉𝑚𝑖𝑛 0.035𝑘 3/2 𝑓𝑐𝑘 𝑏𝑑 0.035 1.63/2 35 2700 604 6667734 𝑁 667 kNVEd (605 kN) Vmin (667 kN) OK

Example 3: Design of Combined Footing(ii) Punching ShearCritical shear at 2.0d from face of column:604 592 598 mm2d 11964002d 1196400Control perimeter;u 2(400 400) (2 1196) 9116 mmArea within perimeter;A (0.40 0.40) (2 0.40 1.196) (2 0.40 1.196) ( 1.1962) 6.57 m21042700Average 𝑑 2 2d 1196 mm

Example 3: Design of Combined Footing(ii) Punching ShearAverage punching shear force at control perimeter:VEd 1950 – (219.8 6.57) 506 kNPunching shear stress:𝑣𝐸𝑑 𝑉𝐸𝑑𝑢𝑑 506 1039116 598 0.09 N/mm2Aperimeter 6.57 m2Punching shear resistance:𝑘 1 200𝑑 1 2006093/2 1.57 2.01/2𝑣𝑅𝑑,𝑐 𝑣𝑚𝑖𝑛 0.035𝑘 𝑓𝑐𝑘 0.035 1.6 3/2 35 1/2 0.41 N/mm2 vEd (0.09 N/mm2) OKSoil pressure 219.8 kN/m2

Example 3: Design of Combined Footing(iii) Maximum Punching Shear at Column PerimeterMaximum punching shear force:VEd,max 1950 kNColumn perimeter, uo 4 400 1600 mmAcolumn 0.16 m2Maximum shear resistance:𝑉𝑅𝑑,𝑚𝑎𝑥𝑓𝑐𝑘 0.5𝑢𝑑 0.6 1 25035250 OK 0.5 1600 598 0.6 1 2880 kN VEd,max𝑓𝑐𝑘1.5351.5Soil pressure 219.8 kN/m2

Example 3: Design of Combined FootingCrackingh 650 mm 200 mmMax bar spacingAssume steel stress is under quasi-permanent loading: 𝑟𝑜𝑣 0.65001.1518942828 175 N/mm2For design crack width 0.3 mm:Maximum allowable bar spacing 250 mmActual bar spacing 1 2700 2 40 12242700 2 40 1224 109 mm 250 mmActual bar spacing 2 109 mm 250 mmActual bar spacing 3 100 mm 250 mmCracking OK

Example 4DESIGN OF STRAP FOOTING

Example 4: Design of Strap FootingNBGk 1000 kN, Qk 525 kNNAGk 800 kN, Qk 275 kN6000 Beam size:300 900 mmColumn size:300 300 mmColumn size:300 300 mm700RARBHS2000Sfck 30 N/mm2fyk 500 N/mm2 soil 200 N/mm2Unit weight of concrete 25kN/m3Cover 40 mmAssumed bar 12 mm

Example 4: Design of Strap FootingLoadingColumnSize (mm mm)Load (kN)GkQkTotal (1.0Gk 1.0Qk)Column A300 3008002751075Column B300 30010005251525

Example 4: Design of Strap FootingSizeAssumed self weight of footing is 10% of service load: WA 108 kN and WB 153 kNBeam self weight, WR 25 (0.3 0.9 5.7) 38 kN

Example 4: Design of Strap Footing𝑀@𝐵 0Size𝑅𝐴 𝑊𝐴 6.15 1.0 𝑁𝐴 6.0 𝑊𝑅 3.0 0𝑅𝐴 108 6.15 1.0 1075 6.0 38 3.0 0𝑅𝐴 108 1275 RA 1382 kNNB 1525 kNNA 1075 kN6m𝑅𝐴 2002.0𝐻1382 2002.0𝐻WR0.3 mWARAFooting A size: 2.00 3.50 m0.3 mWB0.7 m𝑅𝐴 𝑅𝐵 𝑁𝐴 𝑁𝐵 𝑊𝐴 𝑊𝐵 𝑊𝑅𝑅𝐴 𝑅𝐵 1075 1525 108 153 38𝑅𝐵 2898 𝑅𝐴𝑅𝐵 2898 1382 RA 1516 kNRBHS2mS H 3.46 mm𝑅𝐵 200𝑆21516 200𝑆2 S 2.75 mmFooting B size: 2.75 2.75 m

Example 4: Design of Strap FootingFooting Size ChecksTotal service load 1075 1525 123 132 38 2893 kNArea of footing (2.0 3.5) (2.75 2.75) 14.56 m2Soil pressure 289314.56 199 kN/m2 200 kN/m2 OK

Example 4: Design of Strap FootingNA 1075 kNNB 1525 kN6mR 2893 kNFooting Self WeightX’0.3 m0.3 mWA 123 kNWA 25 (2.0 3.5 0.7) 123 kNWB 25 (2.75 2.75 0.7) 132 kNWR 38 kN2mDistance from resultant force R to centroid of column B:1075 6.0 123 5.15 38 3.0 2893𝑋 ′X’ 2.48 mDistance from centroid of footings to centroid of column B:2.0 3.50 5.15 2.0 3.5 2.75 2.75 𝑋′X’ 2.48 mWB 132 kN2.75 m

Example 4: Design of Strap FootingAnalysisDesign Load:NA (1.35 800) (1.50 275)NB (1.35 1000) (1.50 525)WA 1.35 123WB 1.35 132WR 1.35 38 1493 kN 2138 kN 165 kN 179 kN 52 kNTotal Design Load, Ptotal 4026 kNUltimate soil pressure 𝑃𝑡𝑜𝑡𝑎𝑙𝐴𝑟𝑒𝑎 𝑜𝑓 𝐹𝑜𝑜𝑡𝑖𝑛𝑔 402614.56 276 kN/m2

Example 4: Design of Strap FootingShear Force & Bending Moment Diagram1493 kN2138 kN2.7751.71.2250.30.3525.7276.5 1.2251652.0 3.5 9.1 kN/m 253 3.5 885 kN/m1.40276.5 1792.75 2.75 253 2.75 695 kN/m1077262SFD (kN)237-852-1227-1044.-1004BMD (kNm)-313492522

Example 4: Design of Strap FootingDESIGN OF FOOTING AMain ReinforcementSoil pressure, w 253 2.0 m 506 kN/mMEd0.3 m1.6 m1.6 m𝟏. 𝟔𝑴𝑬𝒅 𝟓𝟎𝟔 𝟏. 𝟔 𝟐 647 kNmw 506 kN/mEffective depth: d h – c – 0.5 bar 700 – 40 – (0.5 16) 652 mm

Example 4: Design of Strap Footing𝐾 𝑀𝐸𝑑𝑓𝑐𝑘 𝑏𝑑2 647 10630 2000 6522 0.025 Kbal 0.167 Compression reinforcement is NOT required𝑧 𝑑 0.25 𝐴𝑠,𝑟𝑒𝑞 𝐾1.134𝑀𝐸𝑑0.87𝑓𝑦𝑘 𝑧 0.98𝑑 0.95d647 1060.87 500 0.95 652 𝟐𝟒𝟎𝟐 mm2/m As,minMinimum & Maximum Area of 𝑛 0.26𝑏𝑑 0.260.0015𝑏𝑑 0.0013𝑏𝑑𝑓𝑦𝑘500 As,min 0.0015bd 0.0015 2000 652 1964 mm2 or 982 mm2/mAs,max 0.04Ac 0.04bh 0.04 2000 700 56000 mm2Main Reinforcement: Provide 14H16 (As,prov 2815 mm2)Secondary Reinforcement: H16-200 (As,prov 1005 mm2/m)

Example 4: Design of Strap Footing(i) Vertical Shear3.52.552Critical shear at 1.0d from face of column:d 0.6522.00.948 Design shear force, VEd 253 0.948 2.0 479.4 kNNote:Bar extend beyond critical section at 948 – 40 908 mm 𝑙𝑏𝑑 𝑑 36 𝑑 36 16 652 1228 mm Asl 0 mm2

Example 4: Design of Strap Footing(i) Vertical Shear𝑘 1 𝜌𝑙 200𝑑 1 200652 1.55 2.0𝐴𝑠𝑙 0𝑏𝑑 𝑉𝑅𝑑,𝑐 0.12𝑘 100𝜌𝑙 𝑓𝑐𝑘 1/3 𝑏𝑑 0.12 1.55 100 0 30 1/3 3500 652 0 N 0 kN 𝑉𝑚𝑖𝑛 0.035𝑘 3/2 𝑓𝑐𝑘 𝑏𝑑 0.035 1.553/2 30 3500 652 484194 𝑁 484.2 kNVEd (479.4 kN) Vmin (484.2 kN) OK

Example 4: Design of Strap FootingCrackingh 700 mm 200 mmMax bar spacingAssume steel stress is under quasi-permanent loading: 𝑝𝑟𝑜𝑣 0.595001.1524022815 219 N/mm2For design crack width 0.3 mm:Maximum allowable bar spacing 200 mmActual bar spacing 2000 2 40 1613 146 mm 200 mmCracking OK

Example 4: Design of Strap FootingDESIGN OF FOOTING BMain ReinforcementSoil pressure, w 253 2.75 m 695.75 kN/mMEd0.3 m1.225 m1.225 m𝟏. 𝟐𝟐𝟓𝑴𝑬𝒅 𝟔𝟗𝟓. 𝟕𝟓 𝟏. 𝟐𝟐𝟓 𝟐 522 kNmw 695.75 kN/mEffective depth: d h – c – 1.5 bar 700 – 40 – (1.5 16) 636 mm

Example 4: Design of Strap Footing𝐾 𝑀𝐸𝑑𝑓𝑐𝑘 𝑏𝑑2522 10630 2750 6362 0.016 Kbal 0.167 Compression reinforcement is NOT required𝑧 𝑑 0.25 𝐴𝑠,𝑟𝑒𝑞 𝐾1.134𝑀𝐸𝑑0.87𝑓𝑦𝑘 𝑧 0.99𝑑 0.95d522 1060.87 500 0.95 636 𝟏𝟗𝟖𝟓 mm2/m As,min 2623 mm2Minimum & Maximum Area of 𝑛 0.26𝑏𝑑 0.260.0015𝑏𝑑 0.0013𝑏𝑑𝑓𝑦𝑘500 As,min 0.0015bd 0.0015 2750 636 2623 mm2As,max 0.04Ac 0.04bh 0.04 2750 700 77000 mm2Main Reinforcement: Provide 15H16 (As,prov 3016 mm2)

Example 4: Design of Strap Footing(i) Vertical Shear2.75d 0.6362.752.161Critical shear at 1.0d from face of column:0.589 Design shear force, VEd 253 0.589 2.75 409.5 kNNote:Bar extend beyond critical section at 589 – 40 549 mm 𝑙𝑏𝑑 𝑑 36 𝑑 36 16 636 1212 mm Asl 0 mm2

Example 4: Design of Strap Footing(i) Vertical Shear𝑘 1 𝜌𝑙 200𝑑 1 200636 1.56 2.0𝐴𝑠𝑙 0𝑏𝑑 𝑉𝑅𝑑,𝑐 0.12𝑘 100𝜌𝑙 𝑓𝑐𝑘 1/3 𝑏𝑑 0.12 1.56 100 0 30 1/3 2750 636 0 N 0 kN 𝑉𝑚𝑖𝑛 0.035𝑘 3/2 𝑓𝑐𝑘 𝑏𝑑 0.035 1.563/2 30 2750 636 653774 𝑁 653.8 kNVEd (409.5 kN) Vmin (653.8 kN) OK

Example 4: Design of Strap FootingCrackingh 700 mm 200 mmMax bar spacingAssume steel stress is under quasi-permanent loading: 𝑝𝑟𝑜𝑣 0.545001.1526233016 204 N/mm2For design crack width 0.3 mm:Maximum allowable bar spacing 200 mmActual bar spacing 2750 2 40 1614 189 mm 200 mmCracking OK

Example 4: Design of Strap FootingDESIGN OF TIE BEAMDesign similar to beam design. Refer to RC1.Moment Designfor FlexuralReinforcement5H32Shear Design forShear LinksH6-150Cracking Checks

DESIGN OF PILEFOUNDATIONS

Design of Pile Foundation To be used when the soil conditions are poor anduneconomical, or not possible to provide adequatespread foundations The piles must extend down to firm soil Load carried by either end bearing, friction orcombination of both

Design of Pile FoundationLoad fromStructurePile CapLower DensityMedium DensityHigh DensityPILEPILEPILEPILE

Design of Pile FoundationSelection of Piles Type Depends on loading, type of structure, soil strata & siteconditions Main types:a) Precast reinforced or pre-stressed concrete pilesb) Cast in-situ reinforced concrete pilesc) Timber pilesd) Steel pilese) Bakau piles

Design of Pile FoundationDetermination of Pile Capacity Safe load:a) Determined from test loading of a pile or using apile formulab) Ultimate load divided by safety factor between 2 &3c) Depends on size & depth, & whether the pile is ofthe end bearing or friction type Pile formula – gives resistance from the energy of thedriving force & the final set or penetration of the pileper blow

Design of Pile FoundationDetermination of Piles Number & Spacing Pile load Single pile capacity Piles are usually arranged symmetrically with respect tothe column axis

Design of Pile FoundationDetermination of Piles Number & SpacingFoundation Subjected to Axial Load OnlyLoad applied at centroid of the group of piles:𝑵 𝑾𝑭𝒂 𝒏N Axial load from columnW Self weight of pile capn Number of piles

Design of Pile FoundationDetermination of Piles Number & SpacingFoundation Subjected to Axial Load & Moment Pile cap assumed to rotate about the centroid of the pile groupPiles load resisting moment vary uniformly from zero at thecentroidal axis to a maximum for the piles farthest away𝑭𝒂𝒊𝑵 𝑾𝑴𝒙𝒊 𝒏𝑰𝒚Fai Load per pile iM Momentxi Distance from pile i to centroid of pile capIy Moment of inertial of pile group 𝑥1 2 𝑥2 2 𝑥𝑛 2

Design of Pile Cap

Design of Pile Cappile cap

Design of Pile CapSize & Thickness Depends of number of piles used, arrangement ofpiles & shape of piles Thickness of the cap sh

Design of Pad Footing Cracking & Detailing Requirements All reinforcements should extend the full length of the footing If 1.5 3 , at least two-thirds of the reinforcement parallel to L y should be concentrated in a band width 3 centred at column where L x & L y and c x & c y are the footing and column dimension in x and y directions