Shallow Footing

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Spread Footing/Shallow Foundation

Analysis and Design

(Part A)

ByU Win Aung ChoB.E.Civil (Y.T.U)

M.Civ.Engg. (Hannover)

Date: 14-Oct-2006


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U Win Aung Cho 10/13/2006

Lecture on Spread Footing/Shallow Foundation Analysis and Design 14Compiled by U Win Aung Cho

9.1.1 Bending Moments9.1.2 Vertical Line Shear 9.1.3 Twisting Moment9.1.4 Unbalanced Punching Shear

9.2 Flexible Footing

9.2.1 Bending Moments9.2.2 Vertical Line Shear 9.2.3 Twisting Moment9.2.4 Unbalanced Punching Shear

10 Exercises in Glance10.1 Bearing Capacity for Layer Soil10.2 Stability of Footing10.3 Stability of Overall Structure10.4 Qualitative Estimation on Strength of Footing

References for Lecture Preparation:1) Lymon C, Reese, William M. Isenhower, Shin-Tower Wang, Analysis and Design of

Shallow and Deep Foundations 2) 2003 Commentar y, Foundation Design Requirements 3) Robert W. Day. Geotechnical and Foundation Engineering, Design and Construction 4) SEAOC Seismic Design Manual (UBC Version) Volume I, Errata No. 2, 3/18/025) Joseph E. Bowles, P.E. S.E . Foundation Analysis and Design (fifth edition)6) Nilson H. Design of Concrete Structure (twelfth edition)


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Spread Foot ing/Shallow Foundation1 Types of Spreading Footings1.1 Single Footing

Shape of single footing may be square, rectangle or circular. Trapezoidal or any other unsymmetrical shape should be avoided.

1.2 Combined FootingTwo columns may be combined because of the area limitation of one column due to existent of

property line or other structure.


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b2

b1

3 n m( ). l

2 l. 3 n m( ).

b1 b2( )2 R .

qe l.

c1 l b1 2 b2.( ).3 b1 b2( ).

c2l 2 b1. b2( ).

3 b1 b2( ).

b1R

qe

2 2 m( ). l2

l1 l1 l2( ).

b2R

l2 qe.l1 b1.

l2

l1 b1. l2 b2. R qe

1.3 Strip FootingTwo or more columns may be combined in single direction of line for economy (continuous slabis cheaper then cantilever slab) and to reduce differential settlement between adjacent columns.

1.4 Grid FoundationTwo orthogonal sets of strip footing are combined in two directions of lines.1.5 Mat FootingAll the foundation slabs are merged into one resulting mat footing. Rigidity is better and itreduces differential settlement and variation or pressure under foundation.The continuous foundation such as strip, grid and mat may be designed with or without beamand pedestals. A footing without beam is flexible and its analysis may request more accuratemethod such as finite element or finite difference methods.


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2 Behavior of Spread Footing on Soil

Load from super-structure is spread to satisfactory soil directly underlies the structure by meansof footing.There are uncertainties in determining the actual distribution of upward pressure and foundationelements represent themselves massive blocks or thick slab subject to heavy concentrated loadfrom the structure above. That is why the stresses in foundation can not be determinedaccurately. When one uses simplified method in foundation analysis, footing is always assumedas a rigid plate which is not bent and pressure under footing is assumed as linearly varied or

uniformly distributed.


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3 Various Critical Stages of Footing 3.1 Soil Failure StageWeak bearing capacityFoundation on unstable slopeSupport yielding under side load

Ground water table Liquefaction

3.2 Structural Failure StageUnbalanced conditions between acting loads and bearing pressure under individual footing

Assumed pressure distribution is not enough for equilibriumOver all stability of building and its footings

Overturning Sliding

3.3 Strength Failure Stage

When stress analysis is not accurate, One-way shear failure Two-way shear failure Flexural moment failure

3.4 Serviceability Stage Total settlement is larger then allowable Differential settlement is not acceptable

4 Design Requirements for Spreading FootingTotal Settlement of the structure be limited to a tolerable amount and differential settlement of the various parts of the structure be eliminated as nearly as possible. To limit settlements, the

strength of the soil stratum underneath the footing must be sufficient and spread the load over asufficient area to minimize bearing pressure.

4.1 Design Procedure Ultimate Strength Design (USD) Allowable Stress Design (ASD)Foundation design procedures typically provide soil bearing pressures on an allowable stressdesign basis while seismic forces in the 1997 UBC, and in most concrete design under ACI 318,are on a strength design basis. This requires that the designer make a transition from the ASD

procedure used to size the footing to the USD procedures used to design the footing.

4.2 Bearing CapacityThe building foundation without seismic forces applied must be adequate to support the buildinggravity load. When seismic effects are considered, the soil capacities can be increasedconsidering the short time of loading and the dynamic properties of the soil.Following factors should be included in bearing capacity calculations.

Eccentricity Load inclination factors Base and ground inclination Shape factor Depth factor Water table location


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4.3 SettlementsMaximum settlement should occur under the center of foundation and the minimum under theedges. The difference between maximum and minimum, that is, differential settlement should besome fraction of the maximum.Both total and differential settlements must be considered in design Prediction of immediate andtime-related movement of the foundation should be consistent with the stiffness of thesuperstructure.

4.4 Codes and Standard Many of the codes are silent on aspect of the design of foundations, but the engineer will studycarefully any provisions that are given to prevent a violation.Most of the Uniform Building Code includes requirements for Excavation, Foundations andRetaining Walls in chap 29.

4.5 Strength Design

Some ACI 318 Provisions are mentioned as follow.Allowable for Two-Way Shear Allowable for One-Way Shear

s 40 c lyclxc

c =

vc 0.85

24

c

2s d.

bo4

. f'c psi

. psi.

Vc1.9 f'c. 2500 .

Vu d.

Mu. b. d.

3.5 f'c b. d..

Allowable Bearing at Base of Column


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Pn0.85 . f'c. A1.

A2

A1.

0.85 . f'c. A1. 2.

AllPu min Pn( )

Dowel Bars

Minimum dowel bar length for developement length ls max 0.02 db. fy. f'c.

0.0003db. fy.

Minimum lapped splice length ls 0.0005db. fy.

Minimum dowel steel area At 0.005A1.

4.6 Factor of SafetyThe engineer must refer to the building code covering the project for a list of requirements. A

study to determine the quality of data related to the design can help to decide factor of safety.The idea of limit states provides the basic consideration of factor of safety. All of ultimate limitstates and serviceability limit states should be considered.4.6.1 Selection of Total Factor of SafetyThe total factor of safety can be expressed as follow.

F = Rmean/SmeanF = factor of safetyRmean = mean value of resistanceSmean = mean value of loads

Soil resistance should be selected lower-bound values with the service loads which lead to either overstressing a component of foundations or excessive deflection. The safety factor should be

increased in local failure of soil (loose soil).In allowable bearing capacity estimation, total safety factor is mostly used and it is assumed

between 2.5 and 3. For the fairly stiff footing such as grid and mat factor of safety may bereduced to 2.5 while 3 for single footing.4.6.2 Selection of Partial Factor of SafetyThe partial safety factors are considered separately to reduce the strength of material, to accountfor deficiencies in fabrication and for inadequacies in the theory or model of design.Some partial safety factors are expressed according to ACI318 and UBC.

ASD USDD+L+S 1.4DD+L+E/1.4 1.2D+1.6L for D > L0.9DE/1.4 1.2D+0.5L+0.5CaID+ Eh


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0.9D-(0.5CaID+ Eh)WhereE = Eh+Ev

Design Consideration fiMoment without axial loadTwo-way action, bond and anchorageCompression member, spiralCompression member, tiedUnreinforced footingsBearing on concrete

0.900.850.750.700.650.70

5 Design to Accommodate Construction 5.1 Dewatering During ConstructionWhen the foundation is placed under water table, pumping from a sump in the excavation isfrequently unacceptable because of the danger of the collapse of the excavation as a result of thelowered effective stress due to the rising water. The use of well point of good control isacceptable. Make an attention to nearby building not to be affected by lowering the water level

beneath the building. 5.2 Dealing with Nearby StructuresAn excavation with a substantial depth for a mat could create several problems. Extraordinarymeasure must sometimes be taken, including possible underpinning of the foundations of adjacent structures.6 Shallow Foundation Subjected to Vibratory LoadingThe analysis and design of foundations subjected to machine vibration or impact fromearthquake is a difficult problem because of the complex interaction between the structuralsystem and supporting soil.Vibration of sand can cause densification of the sand with consequent settlement of thefoundation. If the relative density of the sand close to unity, vibration is likely not to be a

problem. Therefore soil-improvement method must be implemented to make the sand tovibration.7 Special Soil Conditions7.1 Collapsible Soil Such soil consist of thick strata of windblown fine grains, deposited over long periods of time,and reinforced by remains of vegetation or by cementation. The will remain under moderateloads, however, on becoming saturated, the soil will collapse. Preventions from rising water table and saturation are essential.7.2 Expansive ClayDuring dry weather, there will be seen cracks in the surface soil and may extend several feet

below ground surface. There is a suggestion that a plasticity index of 15 or less means that theswelling potential of clay is expected to be little.If clay soil is expensive, the thickness of layer is determined and shallow layer should beremoved out. The improvement can be treated using chemicals such line.If the stratum is thick to remove or stabilize, engineer must use stiffened slab on grade or trussground beam with deep foundation.

To avoid uplift from expending clay, beams and floors should not be contact to such soil.


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7.3 Layered Soil Either the soil is of the same sort but with widely varying properties, or two or more layers existin the zone beneath the foundation, bearing may be based on weakest layer or settlement willcontrol the design.The shape of the failure surface is modified to reflect the presence of layers with differentcharacteristics. A more favorable approach is to employ finite element method.7.4 Seismic ResistingIn most codes permit a 33% increase in allowable pressure when the effects of wind or earthquake are included. But following should be encountered in judgments.7.4.1 LiquefactionIt is important to note that soils composed of sands, silts, and gravels are most susceptible toliquefaction while clayey soils generally are not susceptible to liquefaction phenomenon.Liquefaction hazard evaluation, should be consulted when

Gravelly soils are encountered, For soils containing more than 35 percent fines,

The weight of soil particles finer than 0.005 mm is less than 15 percent of the dry weightof a specimen of the soil, The liquid limit of soil is less than 35 percent, and The moisture content of the in-place soil is greater than 0.9 times the liquid limit.

If these criteria are not met, the soils may be considered no liquefiable.7.4.2 Surface Manifestation sSurface manifestations refer to sand boils and ground fissures on level ground sites. For structures supported on shallow foundations, the effects of surface manifestations on thestructure could be tilting or cracking.Well reinforced mat foundations and strongly inter-tied footings have been most effective.

7.4.3 Loss of bearing strengt hLoss of bearing strength can occur if the foundation is located within or above the liqefiablelayer. The consequence of bearing failure could be settlement or tilting of the structure.7.4.4 Ground settlementFor saturated or dry granular soils in a loose condition, the amount of ground settlement couldapproach 3 to 4 percent of the thickness of the loose soil layer in some cases. This amount of settlement could cause tilting or cracking of a building, and therefore, it is usually important toevaluate the potential for ground settlement during earthquakes.Flow failures. Flow failures or flow slides are the most catastrophic form of ground failure thatmay be triggered when liquefaction occurs. They may displace large masses of soils tens of meters. Flow slides occur when the average static shear stresses on potential failure surfaces areless than the average shear strengths of liquefied soil on these surfaces. Standard limitequilibrium static slope stability analyses

7.4.5 Foundati on tiesOne of the prerequisites of adequate performance of a building during an earthquake is the

provision of a foundation that acts as a unit and does not permit one column or wall to moveappreciably with respect to another. Structural measures that are used to reduce the hazardinclude deep foundations, mat foundations, or footings interconnected with ties should beconsidered.


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Work out Examples on Footings

IyyL1 d

3.

12

d L13.

12L0 d

. x20 x32. L1 d

. x21 x32. L3 d

. x23 x32.

L3 d 3.

12

d L33.

12L2 d

. x22 x32.+

...

Ixy

i

Li d . x2i x3

. y2i y3.

Ixx 9284919.427 in 4= Iyy 8179124.552 in 4= Ixy 0 in 4=

j 0 1.. k 0 1..

vu j k ,Vu

bo d .

vx Mux Vu y3 y1( ).( ). Iyy y4k y3. Ixy x4 j x3

..

Ixx Iyy. Ixy2

vy Muy Vu x3 x1( ).( ). Ixx x4 j x3. Ixy y4k y3..

Ixx Iyy. Ixy2+

...

vu176.254

162.803

164.703

151.251 psi=

vu j k , vu j k , max vu( ) 176.254 psi= Actual Shear Stress

vc 0.85

24

c

2 s d . bo

4

. f'c psi

. psi. vc

248.301

337.618

186.226

psi= Allowable Shear Stress

min vc( ) 186.226 psi=

Shear Ratiomax vu( )

min vc( )0.946= OK it less then 1

If Shear Ratio > 1, Provide Shear Reinforcement

Spread Footing/Shallow FoundationCom iled b U Win Aun Cho

Solution 8.1 / 2


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Solution:

1. Determine the design criteria and allowable bearing pressure.

Following load combinations are choosed. (UBC 1612.3.2.)

D+L+SD+L+E/1.40.9D+E/1.40.9D-E/1.4

Because foundation investigation reports for buildings typically specify bearing pressures onan allowable stress design basis, criteria for determining footing size are also on this basis.The earthquake loads to be resisted are specified,

E= Eh +Ev

Since Ev = 0 for allowable stress design, reduces to

E= Eh=(1.0)Eh

Table 18-1-A of UBC 1805 gives the allowable foundation pressure, lateral bearing pressure,and the lateral sliding friction coefficient. These are default values to be used in lieu of site-specific recommendations given in a foundation report for the building. They will be used in this example.

For the sand (SW) class of material and footing depth of 4 feet, the allowable grossfoundation pressure pa is pa = 1.50 +(4 ft -1 ft)(0.2)(1.50)=2.40 ksf

One-third increase in pa is permitted for the load combinations that include earthquake load.2. Determine footing size.

The trial design axial load and moment will be determined for load combination and thenchecked for the other combinations. Earthquakes loads are in both directions, but the

positive values are used in this calculation to create the largest bearing pressures.pa 2.4 ksf .... V E 30 kip....

P D 80 kip.... P L 30 kip.... P E 40 kip....

M D 15 kip.... ft.... M L 6 kip.... ft.... M E 210 kip.... ft....

Pa D LE

1.4

Pa1 P D P LP E

1.4Pa1 138.571 kip====

or

Pa2 P D P LP E

1.4Pa2 81.429 kip====

Ma1 M D M LM E

1.4Ma1 171 kip ft....====

Ma2 M D M LM

E1.4

Ma2 129 kip ft....====

Lecture on Spread Footing/Shallow Foundation Analysis and DesignCompiled by U Win Aung Cho

Solution 8.2.1/1


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Select trial footing size.

Try 9 ft x 9 ft footing size, Footing area A and section modulus S are computed as

B 9 ft.... L 9 ft.... A B L....

SB L 2....

6S 121.5 ft 3====

Calculated soil pressures P due to axial load and moment using the largest values of Pa and M a are

pPa1A

Ma1S

p 3.118 kip

ft 2====

or

pPa1

A

Ma1

Sp 0.303 kip

ft 2====

Check bearing pressure against gross allowable with the one-third increase for seismicloads, 3.12 ksf


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L

61.5 ft====

Since the magnitude of e = 1.63 or - 3.15 > 1.5, there is partial uplift, and a triangular pressure distribution is assumed to occur.

For the footing free-body:

Pa Rpp

23 a....( ).... B.... Rp = Pressure resultant

Note that Rp must be co-linear with Pa such that the length of the triangular pressure distribution is equal to 3a.

For the load combination 0.9D - E/1.4, the load combinations with Pa = 43.4 kips and Ma = -136.5 k - ft or with Pa = 100.6 kips and Ma = 163.5 k - ft , must be checked. This isshown below.

for e1 1.626 ft==== a1L

2e1 a1 2.874 ft====

for e2 3.143 ft==== a2 L2

e2 a2 1.357 ft====

Pap

23 a.... L....( ).... a

for e1 1.626 ft==== the bearing pressure is

p12

3Pa1....

1a1 L....

.... p1 2.592 ksf ====


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Pa D L Ma M D M L

Pa P D P L Pa 110 kip====

Ma MD

ML

Ma 21 kip ft....====

p1 PaA

MaS

p1 1.531 ksf ====

p2PaA

MaS

p2 1.185 ksf ====

All applicable load combinations are satisfied, therefore a 9ft x 9ft footing is adequate.

3. Check resistance to sliding.

Unless specified in the foundation report for the building, the friction coefficient and lateral bearing pressure for resistance to sliding can be determined from Table 18-1-A. These valuesare:

Friction coefficient 0.25

Lateral bearing resistance pL = 150 psf/foot depth in feet below grade Assume the footing is2 feet thick with its base 4 feet below grade. Average resistance on the 2 feet deep by 9 feetwide footing face is (300 + 600 )/2 = 450 psf

p L 0.450 ksf ....

Load combination of 0.9D will be used because it has the lowest value of vertical load ( 0.9D= 0.9PD ). The vertical and lateral loads to be used in the sliding resistance calculations are:P = 0.9PD = 0.9 (80)= 72 kips

Lateral Load F lV E

1.4

The resistance due to friction is 0.9 P D.... .... 18 kip====

The resistance from lateral bearing is p L 2.... ft.... B.... 8.1 kip====

The total resistance is then the sum of the resistance due to friction and the resistance due tolateral bearing pressure.Total resistance = 18.0 + 8.1 = 26.1 > 21.4 kips, o.k.

Lecture on Spread Footing/Shallow Foundation Analysis and DesignCompiled by U Win Aung Cho

Solution 8.2.1/4


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c. Factored soil pressure due to load combination 0.9D Eh 1.4.

Noting that 0.9D + Eh 1.4 is governed by D + L + Eh 1.4 , then only0.9D - Eh 1.4 needs to be considered. The resulting strength design soil pressure reactions for the triangular distribution are: 1.5 ( 2.38 ksf or 0)= 3.57 ksf or 0

The factored soil pressures due to the D + L + Eh/1.4 load combination governs. Note that theresulting moment and shear actions must be multiplied by 1.1 per Exception 1 of UBC1612.2.1.

Note also that the factored value of p need not be less than 1.33pa = 3.20 ksf, since it is used asa load for concrete section design rather than for determining footing size.

The 1.5 factor method shown above can be used for the design of individual spread footingswithout further consideration of the actions on the column. For footings with two or morecolumns, however, the method may result in unstable solutions. This is because the soil

bearing pressure has a 1.5 load factor, while dead, live, and earthquake loads factors are 0.9 or 1.2 for dead, f1 or 1.6 for live, and 1.0 for earthquake. Thus, static equilibrium very likely willnot be achieved. In this situation, the designer may need to determine the contribution of eachload case to the factored soil pressure.

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