11 CHAPTER 11: FOOTINGS

Transcription

1 CHAPTER ELEVEN FOOTINGS 1 11 CHAPTER 11: FOOTINGS 11.1 Introuction Footings are structural elements that transmit column or wall loas to the unerlying soil below the structure. Footings are esigne to transmit these loas to the soil without exceeing its safe bearing capacity, to prevent excessive settlement of the structure to a tolerable limit, to minimize ifferential settlement, an to prevent sliing an overturning. The settlement epens upon the intensity of the loa, type of soil, an founation level. Where possibility of ifferential settlement occurs, the ifferent footings shoul be esigne in such away to settle inepenently of each other. Founation esign involves a soil stuy to establish the most appropriate type of founation an a structural esign to etermine footing imensions an require amount of reinforcement. Because compressive strength of the soil is generally much weaker than that of the concrete, the contact area between the soil an the footing is much larger than that of the columns an walls. 11. Footing Types The type of footing chosen for a particular structure is affecte by the following: 1. The bearing capacity of the unerlying soil.. The magnitue of the column loas. 3. The position of the water table. 4. The epth of founations of ajacent builings. Footings may be classifie as eep or shallow. If epth of the footing is equal to or greater than its with, it is calle eep footing, otherwise it is calle shallow footing. Shallow footings comprise the following types:

2 CHAPTER ELEVEN FOOTINGS 1- Isolate Footings: (a) (b) Figure 11.1: (a) Square isolate footing; (b) Rectangular isolate footing An isolate footing is use to support the loa on a single column. It is usually either square or rectangular in plan. It represents the simplest, most economical type an most wiely use footing. Whenever possible, square footings are provie so as to reuce the bening moments an shearing forces at their critical sections. Isolate footings are use in case of light column loas, when columns are not closely space, an in case of goo homogeneous soil. Uner the effect of upwar soil pressure, the footing bens in a ish shape form. An isolate footing must, therefore, be provie by two sets of reinforcement bars place on top of the other near the bottom of the footing. In case of property line restrictions, footings may be esigne for eccentric loaing or combine footing is use as an alternative to isolate footing. Figure 11.1 shows square an rectangular isolate footings Depth of Footing The epth to which founations shall be carrie is to satisfy the following: a. Ensuring aequate bearing capacity.

3 CHAPTER ELEVEN FOOTINGS 3 b. In the case of clay soils, footings are to penetrate below the zone where shrinkage an swelling ue to seasonal weather changes are likely to cause appreciable movement. c. The footing shoul be locate sufficiently below maximum scouring epth.. The footing shoul be locate away from top soils containing organic materials. e. The footing shoul be locate away from unconsoliate materials such as garbage. All footings shall exten to a epth of at least 0.50 meter below natural groun level. On rock or such other weather-resisting natural groun, removal of the top soil may be all that is require. In such cases, the surface shall be cleane, so as to provie a suitable bearing. Usually footings are locate at epths of 1.5 to.0 meters below natural groun level Pressure Distribution Below Footings The istribution of soil pressure uner a footing is a function of the type of soil, the relative rigiity of the soil an the footing, an the epth of founation at level of contact between footing an soil. A concrete footing on san will have a pressure istribution similar to Figure 11..a. When a rigi footing is resting on sany soil, the san near the eges of the footing tens to isplace laterally when the footing is loae. This tens to ecrease in soil pressure near the eges, whereas soil away from the eges of footing is relatively confine. On the other han, the pressure istribution uner a footing on clay is similar to Figure 11..b. As the footing is loae, the soil uner the footing eflects in a bowl-shape epression, relieving the pressure uner the mile of the footing. For esign purposes, it is common to assume the soil pressures are linearly istribute. The pressure istribution will be uniform if the centroi of the footing coincies with the resultant of the applie loas, as shown in Figure 11.. (a) (b) (c) Figure 11.: Pressure istribution uner footing; (a) footing on san; (b) footing on clay; (c) equivalent uniform istribution

4 CHAPTER ELEVEN FOOTINGS Ultimate Bearing Capacity of Soil The maximum intensity of loaing at the base of a founation which causes shear failure of soil is calle ultimate bearing capacity of soil, enote by q u Allowable Bearing capacity of Soil The intensity of loaing that the soil carries without causing shear failure an without causing excessive settlement is calle allowable bearing capacity of soil, enote by shoul be note that q a. It q a is a service loa stress. The allowable bearing capacity of soil is obtaine by iviing the ultimate bearing capacity of soil by a factor of safety on the orer of.50 to 3.0. The allowable soil pressure for soil may be either gross or net pressure permitte on the soil irectly uner the base of the footing. The gross pressure represents the total stress in the soil create by all the loas above the base of the footing. These loas inclue: (a) column service loas; (b) the weight of the footing; an (c) the weight of the soil on the top of the footing, or q q + q + q ( 11.1) gross soil footing column For moment an shear calculations, the upwar an ownwar pressures of the footing mass an the soil mass get cancelle. Thus, a net soil pressure is use instea of the gross pressure value, or q net q q q ( 11.) gross footing soil Figure 11.3 shows schematic representation of allowable gross an net soil pressures.

5 CHAPTER ELEVEN FOOTINGS 5 (a) (b) Figure 11.3: Gross an net soil pressures; (a) gross soil pressure; (b) net soil pressure 11.5 Concentrically loae Footings If the resultant of the loas acting at the base of the footing coincies with the centroi of the footing area, the footing is concentrically loae an a uniform istribution of soil pressure is assume in esign, as shown in Figure The magnitue of the pressure intensity is given by P q ( 11.3) A where A is the bearing area of the footing, an P is the applie loa. Figure 11.4: Concentrically loae footing

6 CHAPTER ELEVEN FOOTINGS Design of Isolate Footings Design of isolate rectangular footings is etaile in the following steps. 1- Select a trial footing epth. Accoring to ACI Coe 15.7, epth of footing above reinforcement is not to be less than 15 cm for footings on soil. Noting that 7.5 cm of clear concrete cover is require if concrete is cast against soil, a practical minimum epth is taken as 5 cm. - Establish the require base area of the footing. The allowable net soil pressure is q all where ( net) q ( gross) γ ( h ) γ ( h ) all h c is assume footing epth, surface between footing base an soil, ensity of soil on top of footing. c c s f c f is istance from groun surface to the contact γ c is weight ensity of concrete, an γ s is weight Base on ACI Coe 15.., base area of footing is etermine from unfactore forces an moments transmitte by footing to soil an the allowable soil pressure evaluate through principles of soil mechanics. The require base area of the footing is obtaine by iviing the column service loas by the allowable net soil pressure of the soil, or A req P q D + all P L ( net) (11.4) where PD an P L are column service ea an live loas respectively. Select appropriate L, an B values, if possible, use a square footing to achieve greatest economy. 3- Evaluate the net factore soil pressure. Evaluate the net factore soil pressure by iviing the factore column loas by the chosen footing area, or qu ( net) 1. PD P L (11.5) L B 4- Check footing thickness for punching shear. Since large soil pressures are present uner footings, high shear stresses are prouce an since shear reinforcement is not normally use, shear rather than moment commonly

7 CHAPTER ELEVEN FOOTINGS 7 etermines the minimum require epth of footing. The epth of the footing must be set so that the shear capacity of the concrete equals or excees the critical shear forces prouce by factore loas. As iscusse in Chapter 4, the critical section for punching shear is locate at istance / from column faces an usually takes the shape of the column. Footing thickness is aequate for resisting punching shear once V u Φ V C The critical punching shear force can be evaluate using one of the two following methos: ( net) [( L) B ( C + )( C )] Vu qu 1 + (11.6.a) ( 1. P P ) q ( net)( C + )( C ) Vu D L u 1 + (11.6.b) where C 1 an C are column cross sectional imensions, shown in Figure 1.5. Figure 11.5.a: Critical sections for punching an beam shears (square footings)

8 CHAPTER ELEVEN FOOTINGS 8 Figure 11.5.b: Critical sections for punching an beam shears (rectangular footings) Punching shear force resiste by concrete V c is given as the smallest of: Vc Vc 0.53 f' c 1 λ bo β + (11.7) λ f' c bo (11.8) α V 0.7 s c + λ f' c bo b (11.9) o When β, equations (11.7) an (11.8) give the same value, if β > Eq. (11.7) gives smaller value than that evaluate using Eq. (11.8). Since there are two layers of reinforcement, an average value of may be use. The average effective epth is given as avg h 5 c 7. cm b, where b is bar iameter. Increase footing thickness if aitional shear strength is require. 5- Check footing thickness for beam shear in each irection. If V u Φ V C, thickness will be aequate for resisting beam shear without using shear reinforcement. The critical section for beam shear is locate at istance from column faces.

9 CHAPTER ELEVEN FOOTINGS 9 a- In the short irection: The factore shear force is given by L C Vu qu ( net) B (11.10) The factore shearing force resiste by concrete is given as V f B (11.11) c c b- In the long irection: The factore shear force is given by B C1 ( net) L Vu qu (11.1) The factore shearing force resiste by concrete is given as V f L (11.13) c c Increase footing thickness if necessary until the conition V ΦV is satisfie. u C 6- Compute the area of flexural reinforcement in each irection. The critical section for bening is locate at face of column, or wall, for footings supporting a concrete column or wall, as specifie by ACI Coe Figure 11.6 shows critical sections for flexure for footings supporting concrete columns, masonry walls, an columns with steel base plates. M M a- Reinforcement in the long irection: B L C u qu ( net) (11.14) b- Reinforcement in the short irection: L B C1 u qu ( net) (11.15)

10 CHAPTER ELEVEN FOOTINGS 10 (a) (b) (c) Figure 11.6: Critical section for moment (a) concrete column or wall; (b) masonry wall; (c) column with steel base plate The reinforcement ratio is calculate base on rectangular section esign, where the minimum reinforcement ratio ρ min is not to be less than (a)

11 CHAPTER ELEVEN FOOTINGS 11 (b) Figure 11.6: Flexural reinforcement; (a) square footing; (b) rectangular footing Accoring to ACI Coe , for square footings, the reinforcement is ientical in both irections as shown in Figure 11.6.a, neglecting the slight ifference in effective epth values in the two irections. For rectangular footings, ACI Coe specifies that the reinforcement in the long irection is uniformly istribute while portion of the total reinforcement in the short irection, γ s A s is to be istribute uniformly over a ban with, centere on centerline of column, equal to the length of the short sie of footing. Remainer of reinforcement require in short irection, ( 1 γ s ) As is to be istribute uniformly outsie center ban with of footing as shown in Figure 11.6.b. where A s is the total reinforcement require in the short irection, β equals the ratio of the long sie to the short sie of the footing an γ s is given as γ s (11.16) 1 + β 7- Check for bearing strength of column an footing concrete. All forces applie at the base of a column or wall must be transferre to the footing by bearing on concrete an/or by reinforcement. Tensile forces must be resiste entirely by the reinforcement. Bearing on concrete for column an footing must not excee the concrete bearing strength. The joint coul fail by crushing of the concrete at the bottom of the column where the column bars are no longer effective or by crushing the concrete in the footing uner the column.

12 CHAPTER ELEVEN FOOTINGS 1 For a supporte column, the bearing capacity ( 0.85 f A ) 1 Φ Pn is Φ P Φ (11.17) where n c f c compressive strength of the column concrete A 1 column cross-sectional area Φ strength reuction factor for bearing 0.65 For a supporting footing, A Φ Pn Φ ( 0.85 f c A1 ).0Φ ( f c A1 ) (1.18) A where 1 f c compressive strength of the footing concrete A area of the lower base of the largest frustum of a pyrami, cone, or tapere wege containe wholly within the footing an having for its upper base the loae area, an having sie slopes of 1 vertical to horizontal. When bearing strength is exceee, reinforcement in the form of owel bars must be provie to transfer the excess loa. A minimum area of reinforcement must be provie across the interface of column or wall an footing, even where concrete bearing strength is not exceee. For columns, minimum owel reinforcement is given by ACI Coe as As, min A g (11.19) where A g column gross cross-sectional area Require owel reinforcement is given by A ( P Φ P ) u n s, req (11.0) Φ f y 8- Check for anchorage of the reinforcement. Both flexural an owel reinforcement lengths are checke for anchorage to prevent bon failure of the owels in the footing an to prevent failure of the lap splices between the owels an the column bars, as shown in Figure 11.7.

13 CHAPTER ELEVEN FOOTINGS 13 Figure 11.7: Anchorage of reinforcement 9- Prepare neat esign rawings showing footing imensions an provie reinforcement. Example (11.1): Design an isolate square footing to support an interior column 40 cm 40 cm in cross section an carries a ea loa of 80 tons an a live loa of 60 tons. Use 50 kg / cm, f c D f 1. 5 m. f y 400 kg / cm, ( gross).0 kg / cm q all, 3 γ soil 1.7 t / m, an Figure 11.8.a: Footing imensions

14 CHAPTER ELEVEN FOOTINGS 14 Solution: 1- Select a trial footing epth: Assume that the footing is 50 cm thick. - Establish the require base area of the footing: ( net) ( 17. ) 0. 5 (. 5) t/m q all A P req qall ( net) m For a square footing, B m Use 85 cm 85 cm 50 cm footing, as shown in Figure 11.8.a. 3- Evaluate the net factore soil pressure: ( 80) ( 60) 19 tons P u 1.0 P ( ) u 19 q u net 3.64 t/m B (.85) 4- Check footing thickness for punching shear: Average effective epth cm The factore shear force ( 3.64) [(.85)(.85) ( 0.809)( 0.809) ] tons V u ( ) 33. cm b 4 6 o Φ V c is the smallest of: Φ Vc 0.53Φ f' c 1 + λ bo β ( ) ()( )( 40.9) / tons Φ Vc Φ λ f' c bo ( 33.6) ( 40.9) tons Φ Vc 0.7Φ α s bo + λ f' c bo

15 CHAPTER ELEVEN FOOTINGS 15 ( 40.9) ( 0.75) ( 33.6)( 40.9) / tons Φ V c tons < tons Increase footing thickness to 55 cm, an repeat punching shear check. Average effective epth cm The factore shear force ( 3.64) [(.85)(.85) ( 0.859)( 0.859) ] tons V u ( ) cm b o 4 Φ Vc Φ λ f' c bo ( )( 45.9) tons Φ V c tons > tons i.e. footing thickness is aequate for resisting punching shear. 5- Check footing thickness for beam shear in each irection: Figure 11.8.b: Critical sections for beam shear an moment

16 CHAPTER ELEVEN FOOTINGS 16 ( 0.53) 50 ( 85)( 45.9) / tons Φ V c 0.75 Maximum factore shear force in Figure 11.8.b, or: ( 3.64)(.85)( 0.766) tons 8. tons V u < V u is locate at istance from faces of column, as shown 6- Compute the area of flexural reinforcement in each irection: The critical section for moment is locate at column faces, as shown in Figure 11.8.b, or: 1.5 Mu ρ ( 3.64)(.85) ( ) t. m ( 50).353( 10) ( 50.55) 1 1 ( 0.9)( 85)( 45.9) ( 50) ( 85)( 45.9) 9.8 cm A s 0.008, use 15 φ 16 mm in both irections. Figure 11.8.c: Critical section for bearing 7- Check for bearing strength of column an footing concrete: For column, ( 0.85)( 50)( 40)( 40) / tons 19 tons Φ P n 0.65 > A s cm i.e. use minimum owel reinforcement, ( )( ) Use 4φ 16 For footing, mmfor owel reinforcing bars. ( 60) ( 40) Φ Pn 0.65( 0.85)( 50)( 40)( 40) / tons > 44 tons

17 CHAPTER ELEVEN FOOTINGS 17 i.e. Φ P n 44 tons > 19 tons 8- Check for anchorage of the reinforcement: Bottom reinforcement ( φ 16 mm ): ψ t ψ e λ 1 an ψ s 0. 8 c b is the smaller of: cm, or ( ) 9.58 cm, i.e., c b 8.3 cm cb + Ktr >.5, taken as.5 b 1.6 f yψ tψ eψ s 400 ( 0.8) l b cm c K 3.5 (.5) b + tr f' λ c b Available length cm > cm a- Dowel reinforcement ( φ 16 mm ): fy b λ f' c ( 1.6)( 400) f y b l cm, or 50 ( 1.6)( 400) 9.57 cm cm l > 0 Available length cm > cm b- Column reinforcement splices: ( 1.6)( 400) cm l sp , taken as 50 cm. 9- Prepare neat esign rawings showing footing imensions an provie reinforcement: Design rawings are shown in Figure

18 CHAPTER ELEVEN FOOTINGS 18 Figure 11.8.: Design rawings Example (11.): Design an isolate rectangular footing to support an interior column 40 cm 40 cm in cross section an carries a ea loa of 80 tons an a live loa of 60 tons. Use f c 50 kg/cm, f y 400 kg/cm, q all ( gross). 0kg/cm, 3 γ soil 1. 7 t/m, an D f 1. 5 m. Space limitations are such that one lateral imension cannot excee.5m. Solution:

19 CHAPTER ELEVEN FOOTINGS 19 Figure 11.9.a: Critical section for punching shear 1- Select a trial footing epth: Assume that the footing is 55 cm thick. - Establish the require base area of the footing: ( net) ( 17. ) 0. 55(. 5) t/m q all A P req qall ( net) 8.03m 8.03 Let B.5 m, L 3. 1 m.5 Use 35 cm 50 cm 55 cm footing. 3- Evaluate the net factore soil pressure: ( 80) ( 60) 19 tons P u 1.0 P 19 q u L B ( net) u 3.63 t/m 4- Check footing thickness for punching shear: The critical section for punching shear is shown in Figure 11.9.a. Average effective epth cm

20 CHAPTER ELEVEN FOOTINGS 0 The factore shear force ( 3.63) [( 3.5)(.5) 0.859( 0.859) ] tons V u ( ) 343. cm b 4 6 o Φ V c is the smallest of: Φ Vc 0.53Φ f' c 1 + λ bo β ( 0.75) 50 1 ()( )( 45.9) / tons Φ Vc Φ λ f' c bo ( )( 45.9) tons Φ Vc 0.7Φ α s bo + λ ( 45.9) f' c bo ( 0.75) Φ V c 187.0tons > tons ( )( 45.9) / tons i.e. footing thickness is aequate for resisting punching shear. 5- Check footing thickness for beam shear in each irection: a- In the short irection: ( 0.53) 50 ( 50)( 45.9) / tons Φ V c 0.75 Maximum factore shear force V u is locate at istance from faces of column, ( 3.63)(.5)( 0.966) tons 7.1 tons V u < b- In the long irection: ( 0.53) 50 ( 35)( 45.9) / tons Φ V c 0.75 Maximum factore shear force ( 3.63)( 3.5)( 0.591) tons tons V u < V u is locate at istance from faces of column,

21 CHAPTER ELEVEN FOOTINGS 1 Figure 11.9.b: Critical section for beam shear (short irection) Figure 11.9.b: Critical section for beam shear (long irection) 6- Compute the area of flexural reinforcement in each irection: a- Reinforcement in long irection: The critical section for bening is shown in Figure Figure 11.9.: Critical section for bening (long irection) 1.45 Mu ρ ( 3.63)(.5) ( ) t. m ( 50).353( 10) ( 59.98) 1 1 ( 0.9)( 50)( 45.9) ( 50) ( 50)( 45.9) 35.69cm A s , use 15 φ 18 mm in the long irection. b- Reinforcement in short irection:

22 CHAPTER ELEVEN FOOTINGS Figure 11.9.e: Critical section for bening (short irection) The critical section for bening is shown in Figure 11.9.e Mu ρ ( 3.63)( 3.5) ( ) 4.33 t. m ( 50).353( 10) ( 4.33) 1 1 ( 0.9)( 35)( 45.9) ( 50) ( 35)( 55) 3.17 cm A s,min γ s A s cm 1 35 / 50 + Central ban reinforcement ( ) Use 14 φ 16 mm in the central ban. For each of the sie bans, Use A s.10 cm φ 16 mm in each of the two sie bans. 7- Check for bearing strength of column an footing concrete: For column, ( 0.85)( 50)( 40)( 40) / tons 19 tons Φ P n 0.65 > i.e. use minimum owel reinforcement, ( )( ) Use 4φ 16 For footing, mmfor owel reinforcing bars. A s cm.

23 CHAPTER ELEVEN FOOTINGS 3 ( 60) ( 40) Φ Pn 0.65( 0.85)( 50)( 40)( 40) / tons > 476 tons i.e. Φ P n 476 tons > 19 tons 8- Check for anchorage of the reinforcement: a- Reinforcement in long irection ( φ 18 mm): ψ t ψ e λ 1 an ψ s 0. 8 c b is the smaller of: cm, or cb + Ktr b cm, i.e., c b 8.40 cm 15 ( ) >.5, take it equal to fyψ tψ eψ s 400 ( 0.8) l b cm c K 3.5 (.5) b + tr f' λ c b Available length cm > 43.7 cm b- Reinforcement in short irection ( φ 16 mm ): ψ t ψ e λ 1 an ψ s 0. 8 c b is the smaller of: cm, or ( ) 8.34 cm, i.e., c b 8.3 cm cb + Ktr b >.5, take it equal to fyψ tψ eψ s 400 ( 0.8) l b cm c K 3.5 (.5) b + tr f' λ c b Available length cm > cm

24 CHAPTER ELEVEN FOOTINGS 4 c- Column reinforcement splices: ( 1.6)( 400) cm l sp , taken as 50 cm. 9- Prepare neat esign rawings showing footing imensions an provie reinforcement: Design rawings are shown in Figure 11.9.f. Figure 11.9.f: Design rawings 11.7 Problems P11.1 Design a circular footing to support a column 40 cm in iameter, an carries a service ea loa of 60 tons, an a service live loa of 0 tons. Use 300 kg / cm, f c D f 1. 5 m. f y 400kg / cm, ( ) q all gross 1.7kg / cm, γ soil t / m, an P11. Design an isolate footing to support a column 5 cm 60 cm in cross section. The column carries a service ea loa of 60 tons, an a service live loa of 30 tons, in aition to a service ea loa moment of 8 t.m, an a service live loa moment of 4 t.m.

25 CHAPTER ELEVEN FOOTINGS 5 Use 300 kg / cm, f c f y 400kg / cm, an ( net) 1.7kg / cm q all.