spread footing shallow footing

8/3/2019 Spread Footing Shallow Footing

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Spread Footing/Shallow Foundation

Analysis and Design

(Part A)

By

U Win Aung Cho

B.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 13

Compiled by U Win Aung Cho

Table of Content

Spread Footing/Shallow Foundation

1 Types of Spreading Footings

1.1 Single Footing

1.2 Combined Footing

1.3 Strip Footing1.4 Grid Foundation

1.5 Mat Footing

2 Behavior of Spread Footing on Soil

3 Various Critical Stages of Footing

3.1 Soil Failure Stage

3.2 Structural Failure Stage

3.3 Strength Failure Stage

3.4 Serviceability Stage

4 Design Requirements for Spreading Footing

4.1 Design Procedure

Ultimate Strength Design (USD)

Allowable Stress Design (ASD)

4.2 Bearing Capacity

4.3 Settlements

4.4 Codes and Standard

4.5 Strength Design

4.6 Factor of Safety

4.6.1 Selection of Total Factor of Safety

4.6.2 Selection of Partial Factor of Safety

5 Design to Accommodate Construction

5.1 Dewatering During Construction5.2 Dealing with Nearby Structures

6 Shallow Foundation Subjected to Vibratory Loading

7 Special Soil Conditions

7.1 Collapsible Soil

7.2 Expansive Clay

7.3 Layered Soil

7.4 Seismic Resisting

7.4.1 Liquefaction

7.4.2 Surface Manifestations

7.4.3 Loss of bearing strength

7.4.4 Ground settlement7.4.5 Foundation ties

8 Work out Examples on Footings

8.1 Determination of Punching Shear

8.2 Single Footing

8.2.1 Footing Size Selection according to UBC

8.2.2 Design and Settlement of Single Footing

8.3 Combined Footing

8.3.1 Design of Combined Footing without Strap Beam

8.4 Mat Footing

8.4.1 Design and Settlement of Mat Footing

9 Analysis of Footing9.1 Rigid Footing


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9.1.1 Bending Moments

9.1.2 Vertical Line Shear

9.1.3 Twisting Moment

9.1.4 Unbalanced Punching Shear

9.2 Flexible Footing

9.2.1 Bending Moments9.2.2 Vertical Line Shear

9.2.3 Twisting Moment

9.2.4 Unbalanced Punching Shear

10 Exercises in Glance

10.1 Bearing Capacity for Layer Soil

10.2 Stability of Footing

10.3 Stability of Overall Structure

10.4 Qualitative Estimation on Strength of Footing

References for Lecture Preparation:

1) Lymon C, Reese, William M. Isenhower, Shin-Tower Wang, Analysis and Design ofShallow and Deep Foundations

2) 2003 Commentary, Foundation Design Requirements3) Robert W. Day. Geotechnical and Foundation Engineering, Design and Construction4) 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 Footing/Shallow Foundation1 Types of Spreading Footings

1.1 Single FootingShape of single footing may be square, rectangle or circular. Trapezoidal or any otherunsymmetrical 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. Rqe

1.3 Strip FootingTwo or more columns may be combined in single direction of line for economy (continuous slab

is 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 it

reduces differential settlement and variation or pressure under foundation.

The continuous foundation such as strip, grid and mat may be designed with or without beam

and pedestals. A footing without beam is flexible and its analysis may request more accurate

method 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 means

of footing.

There are uncertainties in determining the actual distribution of upward pressure and foundation

elements represent themselves massive blocks or thick slab subject to heavy concentrated load

from the structure above. That is why the stresses in foundation can not be determined

accurately. When one uses simplified method in foundation analysis, footing is always assumed

as 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 capacity

Foundation on unstable slope

Support 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 StageWhen 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 Footing

Total 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 stress

design 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 building

gravity load. When seismic effects are considered, the soil capacities can be increased

considering 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 the

edges. The difference between maximum and minimum, that is, differential settlement should be

some fraction of the maximum.

Both total and differential settlements must be considered in design Prediction of immediate and

time-related movement of the foundation should be consistent with the stiffness of the

superstructure.

4.4 Codes and StandardMany of the codes are silent on aspect of the design of foundations, but the engineer will study

carefully any provisions that are given to prevent a violation.

Most of the Uniform Building Code includes requirements for Excavation, Foundations and

Retaining 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 clyc

lxcc =

vc 0.85

24

c

2s d.

bo4

. f'c

psi

. psi.

Vc

1.9 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 max0.02 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 limit

states and serviceability limit states should be considered.

4.6.1 Selection of Total Factor of Safety

The total factor of safety can be expressed as follow.

F = Rmean/Smean

F = factor of safety

Rmean = mean value of resistance

Smean = 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 be

reduced to 2.5 while 3 for single footing.

4.6.2 Selection of Partial Factor of Safety

The partial safety factors are considered separately to reduce the strength of material, to account

for 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 USD

D+L+S 1.4D

D+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)

Where

E = Eh+Ev

Design Consideration fiMoment without axial load

Two-way action, bond and anchorage

Compression member, spiral

Compression member, tied

Unreinforced footings

Bearing on concrete

0.90

0.85

0.75

0.70

0.65

0.70

5 Design to Accommodate Construction

5.1 Dewatering During ConstructionWhen the foundation is placed under water table, pumping from a sump in the excavation is

frequently unacceptable because of the danger of the collapse of the excavation as a result of the

lowered effective stress due to the rising water. The use of well point of good control is

acceptable. 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. Extraordinary

measure must sometimes be taken, including possible underpinning of the foundations of

adjacent structures.

6 Shallow Foundation Subjected to Vibratory Loading

The analysis and design of foundations subjected to machine vibration or impact from

earthquake is a difficult problem because of the complex interaction between the structural

system and supporting soil.

Vibration of sand can cause densification of the sand with consequent settlement of the

foundation. 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 to

vibration.

7 Special Soil Conditions

7.1 Collapsible SoilSuch 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 moderate

loads, however, on becoming saturated, the soil will collapse. Preventions from rising watertable 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 the

swelling potential of clay is expected to be little.

If clay soil is expensive, the thickness of layer is determined and shallow layer should be

removed 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 truss

ground 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 SoilEither the soil is of the same sort but with widely varying properties, or two or more layers exist

in the zone beneath the foundation, bearing may be based on weakest layer or settlement will

control the design.

The shape of the failure surface is modified to reflect the presence of layers with different

characteristics. 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 Liquefaction

It is important to note that soils composed of sands, silts, and gravels are most susceptible to

liquefaction 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 Manifestations

Surface manifestations refer to sand boils and ground fissures on level ground sites. For

structures supported on shallow foundations, the effects of surface manifestations on the

structure could be tilting or cracking.

Well reinforced mat foundations and strongly inter-tied footings have been most effective.

7.4.3 Loss of bearing strength

Loss of bearing strength can occur if the foundation is located within or above the liqefiable

layer. The consequence of bearing failure could be settlement or tilting of the structure.

7.4.4 Ground settlement

For saturated or dry granular soils in a loose condition, the amount of ground settlement could

approach 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 to

evaluate the potential for ground settlement during earthquakes.

Flow failures. Flow failures or flow slides are the most catastrophic form of ground failure that

may 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 are

less than the average shear strengths of liquefied soil on these surfaces. Standard limit

equilibrium static slope stability analyses

7.4.5 Foundation ties

One 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 move

appreciably with respect to another. Structural measures that are used to reduce the hazard

include deep foundations, mat foundations, or footings interconnected with ties should be

considered.


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8 Work out Examples on Footings

8.1 Determination of Punching ShearProblem:

Find punching shear stress for a

footing slab having a thickness of 36

in and following factors.

Material data:

F`c = 3000 psi

Fy = 55000 psi

Column Data:

Breadth = 30 in

Length = 36 in

Pu = 1942.8 kip

Mux = 300.38 kip-ft

Muy = 353.81 kip-ft

Soil Data:Qu = 8.4 ksf

PunchingSHear.mcd

8.2 Single Footing8.2.1 Footing Size Selection according to UBC

Problem:In this example, a spread footing supports a reinforced concrete column. The soil

classification at the site is sand (SW). The following information is given:Zone 4, Ca =0.4,I=1.0,f1 =0.5, and=1.0 for structural system PD=80 kMD=15 k - ft

( PD includes the footing and imposed soil

weight)

PL =30 k ML =6 k - ftPE=40 k VE=30 k ME=210 k -ft(these are theEh loads due to base shearV)

Snow load S =0Wind load W


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Find the following:

1. Determine the design criteria and allowable bearing pressure.

2. Determine footing size.

3. Check resistance to sliding.

Footing Size.mcd


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Work out Examples on Footings

8.1 Determination of Punching Shear

d' 2.5 in. f'c 3000 psi. fy 55000 psi.

Es 29000000 psi.

h 40 in. d h 3.5 in.

d 36.5 in= qu 8.400kip

ft2

. Slab Thickness = 36"

lxc 30 in. lyc 36 in. Column Size

Vu 1942.84 kip. Mux 300.38 kip. ft. Muy 353.81 kip. ft.

box lxc d boy lyc d Vu Vu box boy.( ) qu.Vu 1661.6 kip=

bo box boy( ) 2. box 5.542 ft= boy 6.042 ft=

x1 0 in. y1 0 in. s 40

vx 11

12

3

boy

box.

vx 0.41= clyc

lxcc 1.2=

vy 11

12

3

box

boy.

vy 0.39= i 0 3..

x2

box

2

0 in.

box

2

0 in.

y2

0 in.

boy

2

0 in.

boy

2

L

boy

box

boy

box

x2

33.25

0

33.25

0

in= y2

0

36.25

0

36.25

in=

x3i

Li

d. x2i

.

i

L d.x3 0 in= y3

i

Li

d. y2i

.

i

L d.y3 0 in=

x4box

box0.5. y4

boy

boy0.5.

IxxL

0d

3.

12

d L0

3.

12L

0d. y2

0y3

2. L1

d. y21

y32. L

3d. y2

3y3

2.

L2

d3.

12

d L2

3.

12L

2d. y2

2y3

2.+

...

Spread Footing/Shallow FoundationCom iled b U Win Aun Cho

Solution 8.1 / 1


15/21


IyyL

1d

3.

12

d L1

3.

12L

0d. x2

0x3

2. L1

d. x21

x32. L

3d. x2

3x3

2.

L3

d3.

12

d L3

3.

12L

2d. x2

2x3

2.+

...

Ixy

i

Li

d. x2i

x3. y2i

y3.

Ixx 9284919.427 in4

= Iyy 8179124.552 in4

= Ixy 0 in4

=

j 0 1.. k 0 1..

vuj k,

Vu

bo d.

vx Mux Vu y3 y1( ).( ). Iyy y4k

y3. Ixy x4j

x3..

Ixx Iyy. Ixy2

vy Muy Vu x3 x1( ).( ). Ixx x4j x3. Ixy y4k y3..

Ixx Iyy. Ixy2

+

...

vu176.254

162.803

164.703

151.251psi=

vuj k,

vuj k,

max vu( ) 176.254 psi= Actual Shear Stress

vc 0.85

24

c

2s d.

bo

4

. f'cpsi

. 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+S

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

Because foundation investigation reports for buildings typically specify bearing pressures on

an 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 gross

foundation 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 then

checked 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 L

E

1.4

Pa1 P D P L

P E

1.4Pa1 138.571 kip====

or

Pa2 P D P L

P E

1.4Pa2 81.429 kip====

Ma1 M D M L

M E

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

Ma2 M D M L

ME

1.4Ma2 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

pPa1

A

Ma1

Sp 3.118

kip

ft2

====

or

pPa1

A

Ma1

Sp 0.303

kip

ft2====

Check bearing pressure against gross allowable with the one-third increase for seismic

loads, 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 is

shown 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....

1

a1 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....====

p1Pa

A

Ma

Sp1 1.531 ksf====

p2Pa

A

Ma

Sp2 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 values

are:

Friction coefficient

0.25

Lateral bearing resistance pL = 150 psf/foot depth in feet below grade Assume the footing is

2 feet thick with its base 4 feet below grade. Average resistance on the 2 feet deep by 9 feet

wide 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 l

V 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 to

lateral bearing pressure.

Total resistance = 18.0 + 8.1 = 26.1 > 21.4 kips, o.k.


Solution 8.2.1/4


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4. Determine soil pressure reactions for strength design of footing section.

To obtain the moment and shear actions prescribed in UBC1915.4 and UBC1915.5 for the

strength design of the reinforced concrete footing section, UBC1915.2.1 is interpreted as follows.

The induced reactions necessary to compute the design moments and shears may be obtained byapplying an appropriate factor to the allowable stress design soil pressures found in Part 2 for the

determination of the footing area. The appropriate factor is taken equal to 1.5 for all of the

allowable stress load combinations. This value (which has been approved by the SEAOC

Seismology Committee) provides a reasonably conservative envelope for the strength design load

combinations for the common case where live load L is less than dead load D.

The applicable allowable soil pressures to be considered are due to the following allowable

stress load combinations:

D + L + S = D + L

D + L + E/1.4 = D + L + Eh/1.40.9D E/1.4 = 0.9D Eh/1.4

The corresponding soil pressures have been calculated in Part 2 of this example.

For both simplicity and conservatism, in this example gross value of dead load PD , which

includes the footing and imposed soil weight, will be used.

a. Factored soil pressure due to load combination D + L .

Using the assigned load factor of 1.5, the resulting strength design reaction soil pressures are:

1.5 (1.53 ksf or1.19 ksf )= 2.30 ksf or1.79 ksf

b. Factored soil pressure due to load combination D + L + Eh/1.4 .

The resulting strength design reaction soil pressures are: 1.5 ( 3.12 ksf or 0.30 ksf )= 4.68 ksf or

0.45 ksf


Solution 8.2.1/5


21/21


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 only

0.9D - 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 the

resulting moment and shear actions must be multiplied by 1.1 per Exception 1 of UBC

1612.2.1.

Note also that the factored value of p need not be less than 1.33pa = 3.20 ksf, since it is used as

a 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 footings

without further consideration of the actions on the column. For footings with two or more

columns, 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 each

load case to the factored soil pressure.

spread footing shallow footing

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