Spread Footing Analysis and Design

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

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 Footing 1.4 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 Construction 5.2 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 settlement 7.4.5 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 Footing 9.1 Rigid Footing



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 Moments 9.2.2 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 of Shallow and Deep Foundations

2) 2003 Commentary, 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, 3/18/02 5) Joseph E. Bowles, P.E. S.E. Foundation Analysis and Design (fifth edition) 6) Nilson H. Design of Concrete Structure (twelfth edition)



Spread Footing/Shallow Foundation 1 Types of Spreading Footings 1.1 Single Footing Shape of single footing may be square, rectangle or circular. Trapezoidal or any other unsymmetrical shape should be avoided.

1.2 Combined Footing Two columns may be combined because of the area limitation of one column due to existent of property line or other structure.



b2b1

3 n m( ). l2 l. 3 n m( ).

b1 b2( ) 2 R.

qe l.

c1 l b1 2 b2.( ).

3 b1 b2( ).

c2 l 2 b1. b2( ).

3 b1 b2( ).

b1Rqe

2 2 m( ). l2l1 l1 l2( ).

b2R

l2 qe.l1 b1.

l2

l1 b1. l2 b2. Rqe

1.3 Strip Footing Two 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 Foundation Two orthogonal sets of strip footing are combined in two directions of lines. 1.5 Mat Footing All 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.



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.



3 Various Critical Stages of Footing 3.1 Soil Failure Stage Weak bearing capacity Foundation on unstable slope Support yielding under side load

• Ground water table • Liquefaction

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

• Assumed pressure distribution is not enough for equilibrium Over 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 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 a sufficient 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 Capacity The 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



4.3 Settlements Maximum 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 Standard Many 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 αs 40 βc lyc

lxcβc =

φvc 0.85

2 4βc

2 αs d.

bo

4

. f'cpsi

. psi.

Vc1.9 f'c. 2500 ρ. Vu d.

Mu. b. d.

3.5 f'c b. d..

Allowable Bearing at Base of Column



φPn0.85 φ. f'c. A1. A2

A1.

0.85 φ. f'c. A1. 2.

AllPu min φPn( )

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 0.005 A1.

4.6 Factor of Safety The 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 > L 0.9D±E/1.4 1.2D+0.5L+0.5CaID+ρEh



0.9D-(0.5CaID+ρEh) Where E = ρEh+Ev

Design Consideration fi Moment 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 Construction When 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 Structures An 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 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 moderate loads, however, on becoming saturated, the soil will collapse. Preventions from rising water table and saturation are essential. 7.2 Expansive Clay During 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.



7.3 Layered Soil Either 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 Resisting In 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 weight

of 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.



8 Work out Examples on Footings 8.1 Determination of Punching Shear Problem: 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 Footing 8.2.1 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 ρ = 1.0 for structural system PD = 80 k M D

=15 k - ft ( PD includes the footing and imposed soil weight) PL = 30 k ML = 6 k - ft PE = ± 40 k VE = 30 k ME = ± 210 k - ft (these are the Eh loads due to base shear V ) Snow load S = 0 Wind load W < Eh/1.4

To properly apply load combinations when the interaction of axial load P and flexural load M is involved, it is necessary to define a sign convention:

Axial load P is positive (+) when acting downward on the top of the footing.

Flexural load M is positive (+) when acting clockwise on the top of the footing.

Note that when the applied seismic forces on the structure are acting in the left-to-right direction, the resulting seismic actions PE and M E are both positive (+). For the right-to-left force direction, both PE and M E are negative (-). The loads given above follow this sign convention.



Find the following:

1. Determine the design criteria and allowable bearing pressure. 2. Determine footing size.

3. Check resistance to sliding.

Footing Size.mcd

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 8.400 kip

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. αs 40

γvx 1 1

1 23

boybox

.

γvx 0.41= βc lyclxc

βc 1.2=

γvy 1 1

1 23

boxboy

.

γvy 0.39= i 0 3..

x2

box2

0 in.

box2

0 in.

y2

0 in.

boy2

0 in.

boy2

L

boy

box

boy

box

x2

33.25

0

33.25

0

in= y2

0

36.25

0

36.25

in=

x3 i

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.

IxxL0 d3.

12

d L03.

12L0 d. y20 y3 2. L1 d. y21 y3 2. L3 d. y23 y3 2.

L2 d3.

12

d L23.

12L2 d. y22 y3 2.+

...

Spread Footing/Shallow FoundationCompiled by U Win Aung Cho

Solution 8.1 / 1


IyyL1 d3.

12

d L13.

12L0 d. x20 x3 2. L1 d. x21 x3 2. L3 d. x23 x3 2.

L3 d3.

12

d L33.

12L2 d. x22 x3 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.γvx Mux Vu y3 y1( ).( ). Iyy y4k y3. Ixy x4j x3..

Ixx Iyy. Ixy2

γvy 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

φvc 0.85

2 4βc

2 αs d.

bo

4

. f'cpsi

. psi. φvc

248.301

337.618

186.226

psi= Allowable Shear Stress

min φvc( ) 186.226 psi=

Shear Ratiomax vu( )min φvc( )

0.946= OK it less then 1

If Shear Ratio > 1, Provide Shear Reinforcement

Spread Footing/Shallow FoundationCompiled by U Win Aung Cho

Solution 8.1 / 2


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 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=ρρρρEh +Ev

Since Ev = 0 for allowable stress design, reduces to

E=ρρρρEh=(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 E1.4

Pa1 P D P LP E1.4

Pa1 138.571 kip====

or

Pa2 P D P LP E1.4

Pa2 81.429 kip====

Ma1 M D M LM E1.4

Ma1 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


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....

S B L2....

6S 121.5 ft3====

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

p Pa1A

Ma1S

p 3.118 kip

ft2====

or

p Pa1A

Ma1S

p 0.303 kip

ft2====

Check bearing pressure against gross allowable with the one-third increase for seismic loads, 3.12 ksf <1.33pa =1.33 ( 2.40)= 3.20 ksf, o.k.

Check for the next load combination

Pa 0.9 D.... E1.4

or Pa 0.9 D.... E1.4

Pa1 0.9 P D....P E1.4

Pa1 100.571 kip====

or

Pa2 0.9 P D....P E1.4

Pa2 43.429 kip====

Ma1 0.9 M D....M E1.4

Ma1 163.5 kip ft....====

or

Ma2 0.9 M D....M E1.4

Ma2 136.5 kip ft....====

Note that according to the stated sign convention, the positive (+) values for PE and ME correspond to an applied seismic force loading from left to right, and minus (-) values are due to the right to left load direction. A positive (+) PE cannot occur at the same time as minus (-) M E since each sign corresponds to the particular direction of the applied seismic force loading.

e1 Ma1Pa1

e1 1.626 ft====

e2 Ma2Pa2

e2 3.143 ft====

Check for partial uplift. This occurs when the magnitude of e exceeds L/6, where

L = width of footing and L/6 is the limit of the kern area


Solution 8.2.1/2


L6

1.5 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 Rp p2

3 a....( ).... B.... Rp = Pressure resultantNote 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==== a1 L2

e1 a1 2.874 ft====

for e2 3.143 ft==== a2 L2

e2 a2 1.357 ft====

Pa p2

3 a.... L....( ).... a

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

p123

Pa1.... 1a1 L....

.... p1 2.592 ksf==== <1.33 pa.... 3.192 ksf====

for e2 3.143 ft==== the bearing pressure is

p223

Pa2.... 1a2 L....

.... p2 2.371 ksf==== <1.33 pa.... 3.192 ksf====

If p had been greater than 1.33pa , the footing size would have to be increased. Finally, check the gravity load combination for p < pa = 2.40 ksf .


Solution 8.2.1/3


Pa D L Ma M D M L

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

Ma M D M L Ma 21 kip ft....====

p1 PaA

MaS

p1 1.531 ksf====

p2 PaA

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 values are:

Friction coefficient µµµµ 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 lV E1.4

The resistance due to friction is 0.9 P D.... µµµµ.... 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.

No sliding occurs


Solution 8.2.1/4


No sliding occurs

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 by applying 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


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 will not be achieved. In this situation, the designer may need to determine the contribution of each load case to the “factored” soil pressure.


Solution 8.2.1/6

Documents

Spread Footing Analysis and Design