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Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design -1

FOUNDATION DESIGN Proportioning Elements for: • Transfer of Seismic Forces • Strength and Stiffness • Shallow and Deep Foundations • Elastic and Plastic Analysis

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 2

Load Path and Transfer of Seismic Forces soil pressure Pile supporting structure Force on a pile

deflected shape

soil pressure

Unmoving soil

EQ on unloaded pile

deflected shape

soil pressure

Inertial force

deflected shape

soil pressure

EQ Motion

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 3

Load Path and Transfer of Seismic Forces foundation force transfer

Passive earth pressure

Shallow

Friction

EQ motion

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 4

Load Path and Transfer of Seismic Forces soil to foundation force transfer

Deep

Motion

Soil pressure

Bending moment

EQ Motion Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 5

Load Path and Transfer of Seismic Forces vertical pressures - shallow Overturning moment

EQ motion Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 6

Load Path and Transfer of Seismic Forces vertical pressures - deep

Overturning moment

EQ Motion

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 7

Outside face of concrete column or line midway between face of steel column and edge of steel base plate (typical) (a) Critical section for flexure extent of footing (typical)

d

(b) Critical section for one-way shear

Reinforced Concrete Footings: Basic Design Criteria (concentrically loaded)

(c) Critical section for two-way shear d/2 (all sides) Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 8

P M (a) Loading (b) Elastic, no uplift (c) Elastic, at uplift (d) Elastic, after uplift

Footing Subject to Compression and Moment: Uplift Nonlinear

(e) Some plastification

(f) Plastic limit

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 9

7 Bays @ 25'-0" = 175'-0"

1'-2"

5 Bays @ 25'-0" = 125'-0"

1'-2"

1'-2"

N

Example 7-story building: shallow foundations designed for perimeter frame and core bracing

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 10

Shallow Footing Examples Soil parameters: • Medium dense sand • (SPT) N = 20 • Density = 120 pcf • Friction angle = 33o

Gravity load allowables • 4000 psf, B < 20 ft • 2000 psf, B > 40 ft Bearing capacity (EQ) • 2000B concentric sq. • 3000B eccentric • φ = 0.7

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 11

Footings proportioned for gravity loads alone

Corner: 6'x6'x1'-2" thick

Interior: 11'x11'x2'-2" thick Perimeter: 8'x8'x1'-6" thick

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 12

Design of footings for perimeter moment frame

5 at 25'-0"

7 at 25'-0"

N

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 13

7 Story Frame, Deformed

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 14

Combining Loads

• • •

Maximum downward load: 1.2D + 0.5L + E Minimum downward load: 0.9D + E Definition of seismic load effect E: E = ρ1QE1 + 0.3 ρ2QE2 +/- 0.2 SDSD ρx = 1.0 ρy = 1.0 and SDS = 1.0

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 15

Reactions Grid

Dead

Live

Ex

Ey

A-5

P Mxx Myy

203.8 k

43.8 k

-3.8 k 53.6 k-ft -243.1 k-ft

21.3 k -1011.5 k-ft 8.1 k-ft

A-6

P Mxx Myy

103.5 k

22.3 k

-51.8 k 47.7 k-ft -246.9 k-ft

-281.0 k -891.0 k-ft 13.4 k-ft

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 16

Reduction of Overturning Moment

• •

•

NEHRP Provisions allow base overturning moment to be reduced by 25% at the soilfoundation interface For a moment frame, the column vertical loads are the resultants of base overturning moment, whereas column moments are resultants of story shear Thus, use 75% of seismic vertical reactions

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 17

Additive Load w/ Largest eccentricity

•

• • •

Combining loads on footings A-5 and A-6, applying the 0.75 multiplier for overturning effects to the axial loads, and neglecting the weight of the foundation and overlying soil, P = 256 kips Mxx = -6,717 ft-kips Myy = -126 ft-kips (which is negligible)

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 18

Counteracting Load w/ Largest e

• • • •

Again combining loads on footings A-5 and A-6, including the overturning factor, and neglecting the weight of the footing and overlying soil, P = 8 kips Mxx = -5,712 ft-kips Myy = -126 ft-kips (negligible)

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 19

Elastic Response

•

•

Objective is to set L and W to satisfy equilibrium and avoid overloading soil Successive trials usually necessary

L P

M

W

R e

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 20

Additive Combination Given P = 256 k, M =6717 k-ft Try 4.5 foot around, thus L = 34 ft, B = 9 ft • Minimum W = M/(L/2) – P = 139 k = 455 psf Try 2 foot soil cover & 3 foot thick footing • W = 214 k; for additive combo use 1.2W • Qmax = (P + 1.2W)/(3(L/2 – e)B/2) = 9.74 ksf • φQn = 0.7(3)Bmin = 18.9 ksf, OK by Elastic Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 21

Plastic Response

• •

Same objective as for elastic response Smaller footings can be shown OK thus

L P

M

W

R e

Instructional Materials Complementing FEMA P-751, Design Examples

R

Foundation Design - 22

Counteracting Case Given P = 8 k; M = 5712 Check prior trial; W = 214 k (use 0.9W) • e = 5712/(214 + 8) = 25.7 > 34/2 NG New trial: L = 40 ft, 5 ft thick, 2 ft soil cover • W = 360 k; e = 17.2 ft; plastic Qmax= 8.78 ksf • φQn = 0.7(3)4.1 = 8.6 ksf, close • Try plastic solution, L’ = 4.2 ft, φQn = 8.82 ksf • MR = (0.9(360)+8)(40/2-4.2/2) = 5943 > 5712 Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 23

Additional Checks

• • •

Moments and shears for reinforcement should be checked for the overturning case Plastic soil stress gives upper bound on moments and shears in concrete Horizontal equilibrium: Hmax< φµ(P+W) in this case friction exceeds demand; passive could also be used

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 24

Results for all Seismic Resistant System Footings Middle: 5'x30'x4'-0"

Side: 8'x32'x4'-0"

Corner: 9'x40'x5'-0" w/ top of footing 2'-0" below grade

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 25

Design of footings for core-braced 7 story building

25 foot square bays at center of building Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 26

Solution for Central Mat Very high uplifts at individual columns; mat is only practical shallow foundation

Mat: 45'x95'x7'-0" with top of mat 3'-6" below grade

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 27

Bearing Pressure Solution

12.2 ksf ~

12 4

(a) Plastic solution

Plastic solution is satisfactory; elastic is not

16 (b) 8 Elastic solution 0 pressures (ksf)

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 28

Pile/Pier Foundations Pile cap

Passive resistance (see Figure 4.2-5)

Pile

p-y springs (see Figure 4.2-4)

View of cap with column above and piles below

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 29

Pile/Pier Foundations Pile Stiffness: • Short (Rigid) • Intermediate • Long Cap Influence Group Action

Soil Stiffness • Linear springs – nomographs e.g. NAVFAC DM7.2 • Nonlinear springs – LPILE or similar analysis

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 30

Sample p-y Curves 100,000

Soil resistance, p (lb/in.)

10,000 1,000 100 Site Class C, depth = 30 ft Site Class C, depth = 10 ft

10

Site Class E, depth = 30 ft Site Class E, depth = 10 ft

1 0.0

0.1

0.2

0.3

0.4 0.5 0.6 0.7 Pile deflection, y (in.)

Instructional Materials Complementing FEMA P-751, Design Examples

0.8

0.9

1.0

Foundation Design - 31

P/Pult

Passive Pressure 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0

0.01

0.02

0.03 0.04 δ/H

0.05

Instructional Materials Complementing FEMA P-751, Design Examples

0.06

Foundation Design - 32

Group effect factor

Group Effect Factor

Group Effect 1.0

s = 7D

0.8

s = 5D

0.6

s = 3D

0.4

s = 2D 0.2

0.0 1

2

3

4

5

6

7

8

Pile group size (number of rows)

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 33

Pile Shear: Two Soil Stiffnesses 0 5

Depth (ft)

10 15 20 25

Site Class C Site Class E

30 -5

0

5 10 Shear, V (kip)

15

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 34

0

Pile Moment vs Depth

5

Depth (ft)

10 15 20 25

Site Class C Site Class E

30 -1000

-500 0 Moment, M (in.-kips)

500

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 35

Pile Reinforcement 4" pile embedment 6'-4"

(6) #5

21'-0"

23'-0"

A

#4 spiral at 3.75 inch pitch

Section A (6) #5

B

#4 spiral at 7.5 inch pitch

Section B (4) #5

C

• Site Class C • Larger amounts where moments and shears are high • Minimum amounts must extend beyond theoretical cutoff points • “Half” spiral for 3D

#4 spiral at 11 inch pitch

Section C

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 36

Pile Design

12'-4"

4" pile embedment

(8) #7

A

#5 spiral at 3.5 inch pitch

20'-0"

Section A (6) #7

B

#5 spiral at 3.5 inch pitch

32'-0"

Section B

• Site Class E • Substantially more reinforcement • “Full” spiral for 7D • Confinement at boundary of soft and firm soils (7D up and 3D down)

(4) #7

C

#4 spiral at 11 inch pitch

Section C

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 37

Other Topics for Pile Foundations

• • • •

Foundation Ties: F = PG(SDS/10) Pile Caps: high shears, rules of thumb; look for 3D strut and tie methods in future Liquefaction: another topic Kinematic interaction of soil layers

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 38

Tie between pile caps 2" clear at sides

(3) #6 top bars #4 ties at 7" o.c.

3" clear at top and bottom

(3) #6 bottom bars

• Designed for axial force (+/-) • Pile cap axial load times SDS/10 • Oftentimes use grade beams or thickened slabs on grade Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 39

Questions

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 40

Title Slide

Foundation Design - 1

The subtitles are effectively a table of contents, although the topics are not really treated in that specific order. This unit is primarily aimed at the structural engineering of foundations, not at the geotechnical engineering. This presentation relates to example computations in Chapter 5 of the FEMA P752, NEHRP Recommended Provisions: Design Examples.

Foundation Design - 2

First model: soil pressures in unmoving soil caused by force at top of deep pile; most of stress resisted at top of pile; only small stresses below about twice the characteristic length of pile. Second model: unloaded pile subject to earthquake ground motion; small stresses induced by upper levels of soil lagging behind deep motion. Note opposing directions of “push”. Third model: both types of force act on pile. The lag of structure induces inertial forces at top of pile similar to static force in first model; net force shape similar to static situation.

Foundation Design - 3

As building lags behind ground motion, induced inertial forces must be transferred between footing and soil. Design may consider that inertial forces are transferred as passive earth pressure on face of footing, friction on bottom of footing, or both.

Foundation Design - 4

Same single story structure; now on deep pile foundation. One leg shows pile displacements; other shows resulting earth pressures; third diagram shows bending moment in pile. One reference that has long been used for laterally loaded piles is the Navy Design Manual 7.2, Foundations and Earth Structures. However, it and most other older methods are based upon assumptions of linear behavior in soil. Over the past two decades considerable progress has been made in developing design tools rooted in the strongly nonlinear behavior of soil. “LPILE” is one widely used example that allows the user to specify soil parameters that model resistance of soil to lateral movement of piles.

Foundation Design - 5

As aspect ratio of building height to width increases, overturning moment becomes significant; induced vertical forces must be transferred in addition to horizontal pressures. (Similar vertical forces in footing result from column moments not specifically related to overturning.) Slide shows overturning moment being resisted below basement of medium sized building; horizontal pressures are transferred at the basement walls.

Foundation Design - 6

This example of tall building with shear wall continuing through deep basement shows that the horizontal and vertical forces can be resisted by different portions of foundation structure. Basement wall resists horizontal forces near ground surface; vertical forces resisted by piles at base of wall.

Foundation Design - 7

Reinforced concrete footings are proportioned according the provisions of ACI 318, Building Code Requirements for Structural Concrete. It is often opined that foundations should not yield, due to the high cost of foundation repair. However, nonlinear soil behavior is common in strong ground shaking, and it is traditional to design foundations for the reduced forces computed with the response modification factor, R, used for the superstructure. Neither the NEHRP Recommended Provisions nor earlier model building codes required the use of amplified forces for foundation design.

Foundation Design - 8

ASCE 41 has a good discussion of the plastic behavior of soil beneath eccentrically loaded footings. Just as for analysis of structural members, plastic analysis of a footing is simple “by hand”, but not so with a computer. Both uplift and nonlinear behavior introduce complications in conventional analysis. Many commercially available software packages for structural analysis now handle the uplift case; a smaller set can also handle nonlinear behavior.

Foundation Design - 9

Title slide for 7-story building showing plan of steel building.

Foundation Design - 10

The gravity load allowables are set to control settlements. The values between 20 and 40 feet should be interpolated. The bearing capacity is the classic value from theoretical soil mechanics (normal gravity loads are checked). The subject of strength design in soils is in its infancy, and many geotechnical professionals are not yet comfortable with strength design concepts. Note that the term phi is Resistance Factor for bearing capacity. B is the footing width.

Foundation Design - 11

The size of the square footing is controlled by the allowable bearing pressure at total loads, and the thickness is controlled by two-way shear at the critical section (“punching shear”). The point of this information is primarily for later comparison with footings designed for seismic loads.

Foundation Design - 12

The only portion of the steel frame that resists lateral forces is at the perimeter, thus, the only footings that will be affected by the seismic load are at the perimeter.

Foundation Design - 13

The image is taken from the RAM Frame analysis used to design the steel moment resisting frame for seismic loads.

Foundation Design - 14

Load combinations for strength-based design, which is the fundamental method for earthquake resistant design. Greek rho is the redundancy factor. Q is the effect of horizontal seismic motions. The 0.2SdsD is an approximation for the effect of vertical earthquake motions. For the footings, the horizontal motions produce vertical and horizontal forces, as well as bending moments, at the base of each column. Dead and Live loads are taken to produce only vertical forces in this example.

Foundation Design - 15

Grid A-6 is at the lower left corner of the plan, and A-5 is adjacent. (Go back three slides to show the location on the plan.) Recall that the seismic reactions can be positive or negative; what is given here is for motion in the positive x and y directions. Carefully note that subscripts x and y on the load effect E refer to the global north-south and east-west, respectively, but the subscripts x and y on the moments at the column bases refer to the local strong and weak axes, respectively, which is just the opposite as the global directions, unfortunately. The most significant point of this slide is that seismic uplift at A-6 exceeds the dead load by a considerable margin. It is possible to place a footing with sufficient size to resist the uplift and the overturning moment, but it is much more economical to combine one footing for the two locations. These reactions include the effects of horizontal torsion on the system. Also recall that the footing must resist horizontal forces.

Foundation Design - 16

The Provisions allow an overturning moment reduction of 25% at the soil-foundation interface.

Foundation Design - 17

None of these loads include the weight of the footing. P is positive in compression. M is positive by the local right hand rule. This is not the maximum downward load; it is the maximum ratio of moment to axial load for the additive combos.

Foundation Design - 18

Note that the net vertical load is upward without the weight of the footing. It so happens that this combo also gives the maximum eccentricity, when combined with the weight of footing and soil.

Foundation Design - 19

Slide is drawn for the case with substantial moment, such that uplift will occur at the heel. Note that eccentricity e changes as W changes. For our footing, L will exceed 25 feet by some margin, given that the two columns are 25 feet apart.

Foundation Design - 20

Initial approximation of W is simply to keep the resultant of earth pressure within the footing. It must be somewhat larger in order to control the bearing pressures. Note that the load factor on W does not include the amplifier for vertical seismic acceleration; this is the author’s interpretation of the NEHRP Provisions. The minimum B used to find the nominal bearing capacity is found by comparing the width of the footing and the half length of the loaded area. The half length is used because the soil pressure is not uniform.

Foundation Design - 21

Slide shows basis of plastic design of foundation.

Foundation Design - 22

Note how much larger the footing must be for the counteracting case. Also, it would have been even larger if the elastic solution were used in lieu of the plastic solution.

Foundation Design - 23

Notes for additional checks for foundation design.

Foundation Design - 24

Given the combined footing strategy, footing sizes are more strongly influenced by the uplift on columns at the ends of frames than by the moments transmitted by the columns. Note that a complete perimeter grade beam would be a very feasible solution for this project, especially in cold climates where a continuous perimeter wall for frost control is necessary. A 4 ft by 4 ft continuous grade beam would be sufficient.

Foundation Design - 25

The screen capture is from the RAM Frame analysis of the structure, and the small plan is based on the same grids used for the 7 story moment frame. The braced frames appear to be 8 stories high, because there is a small penthouse over the core.

Foundation Design - 26

The fundamental method is the same as used in the previous example: Determine the total applied vertical and horizontal loads and the moments. The complicating factor here is that the bending is significant about two axes simultaneously. Elastic solutions can be found from software that has the capacity for compression-only springs; SAP2000 was used in this case. Plastic solutions typically need to be done “by hand,” although spreadsheets are a great asset for the successive trial nature of the solution.

Foundation Design - 27

Slide shows the results from “hand” analysis for plastic distribution and for SAP2000 elastic solution. See Chapter 5 of FEMA P-751 for more detail on the solution, as well as the design of the footing cross section for moment and shear.

Foundation Design - 28

Title slide for pier foundations.

Foundation Design - 29

Most pile analysis for lateral loads is performed assuming linear response in the pile itself, although it is now common to consider nonlinear soil response. Some “byhand” plastic techniques do make use of the classic pile stiffness idealizations.

Foundation Design - 30

Note the logarithmic scale on the vertical axis.

Foundation Design - 31

This passive pressure mobilization is useful for inclusion of the pile cap. It is from ASCE 41. Delta/H is the imposed displacement as a fraction of the minimum dimension of the face being pushed into the soil mass.

Foundation Design - 32

Plots of group effect factors computed based on Rollins et al., “Pile Spacing Effects on Lateral Pile Group Behavior: Analysis,” Journal of Geotechnical and Geoenvironmental Engineering, October 2006. The plot shows four curves, each for a different spacing (in terms of pile diameter). The horizontal axis is the number of rows of piles, and the vertical axis is the Group Effect Factor.

Foundation Design - 33

Note that the shear forces in the pile (as well as deformations and bending moments) carries to greater depths in soft soils than in firm soils. Pile (or pier) foundations are often used in stiff soils to control settlement of heavy structures or heave of expansive soils.

Foundation Design - 34

See Chapter 5 of FEMA P-751.

Foundation Design - 35

Diagram and notes indicate requirements for pile reinforcement. “D” is pile diameter.

Foundation Design - 36

The drawing shows one of the piles with detail of reinforcement. “D” is pile diameter. See Chapter 5 of FEMA P-751.

Foundation Design - 37

Additional considerations for Pile Foundations. The equation is from ASCE 7-10 Section 12.13.5.2, where F is the design tension/compression force in the foundation tie beam and PG is the load in the pile.

Foundation Design - 38

Required iin higher seismic design categories for softer soils. It is designed for “pure” axial force. Fundamental objective is to prevent relative lateral displacement between column bases. It “fixes” the column bases for translation, but it is not intended to restrain rotation at the column bases.

Foundation Design - 39

Slide to initiate questions from the participants.

Foundation Design - 40

Instructional Material Complementing FEMA P-751, Design Examples

Foundation Analysis and Desing 5 Foundation Analysis and Design Michael Valley, S.E.

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design -1

FOUNDATION DESIGN Proportioning Elements for: • Transfer of Seismic Forces • Strength and Stiffness • Shallow and Deep Foundations • Elastic and Plastic Analysis

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 2

Load Path and Transfer of Seismic Forces soil pressure Pile supporting structure Force on a pile

deflected shape

soil pressure

Unmoving soil

EQ on unloaded pile

deflected shape

soil pressure

Inertial force

deflected shape

EQ Motion

Instructional Materials Complementing FEMA P-751, Design Examples

5 – Foundation Design

soil pressure

Foundation Design - 3

1

Instructional Material Complementing FEMA P-751, Design Examples

Load Path and Transfer of Seismic Forces foundation force transfer

Passive earth pressure

Shallow

Friction

EQ motion

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 4

Load Path and Transfer of Seismic Forces soil to foundation force transfer

Deep

Motion

Soil pressure

Bending moment

EQ Motion Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 5

Load Path and Transfer of Seismic Forces vertical pressures - shallow Overturning moment

EQ motion Instructional Materials Complementing FEMA P-751, Design Examples

5 – Foundation Design

Foundation Design - 6

2

Instructional Material Complementing FEMA P-751, Design Examples

Load Path and Transfer of Seismic Forces vertical pressures - deep

Overturning moment

EQ Motion

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 7

Outside face of concrete column or line midway between face of steel column and edge of steel base plate (typical) (a) Critical section for flexure extent of footing (typical) (b) Critical section for one-way shear

d

Reinforced Concrete Footings: Basic Design Criteria (concentrically loaded)

(c) Critical section for two-way shear d/2 (all sides) Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 8

P M (a) Loading (b) Elastic, no uplift (c) Elastic, at uplift (d) Elastic, after uplift

Footing Subject to Compression and Moment: Uplift Nonlinear

(e) Some plastification

(f) Plastic limit

Instructional Materials Complementing FEMA P-751, Design Examples

5 – Foundation Design

Foundation Design - 9

3

Instructional Material Complementing FEMA P-751, Design Examples

7 Bays @ 25'-0" = 175'-0"

1'-2"

5 Bays @ 25'-0" = 125'-0"

1'-2"

1'-2"

N

Example 7-story building: shallow foundations designed for perimeter frame and core bracing

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 10

Shallow Footing Examples Soil parameters: • Medium dense sand • (SPT) N = 20 • Density = 120 pcf • Friction angle = 33o

Gravity load allowables • 4000 psf, B < 20 ft • 2000 psf, B > 40 ft Bearing capacity (EQ) • 2000B concentric sq. • 3000B eccentric • = 0.7

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 11

Footings proportioned for gravity loads alone

Corner: 6'x6'x1'-2" thick

Interior: 11'x11'x2'-2" thick Perimeter: 8'x8'x1'-6" thick

Instructional Materials Complementing FEMA P-751, Design Examples

5 – Foundation Design

Foundation Design - 12

4

Instructional Material Complementing FEMA P-751, Design Examples

Design of footings for perimeter moment frame

5 at 25'-0"

7 at 25'-0"

N

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 13

7 Story Frame, Deformed

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 14

Combining Loads

• • •

Maximum downward load: 1.2D + 0.5L + E Minimum downward load: 0.9D + E Definition of seismic load effect E: E = 1QE1 + 0.3 2QE2 +/- 0.2 SDSD x = 1.0 y = 1.0 and SDS = 1.0

Instructional Materials Complementing FEMA P-751, Design Examples

5 – Foundation Design

Foundation Design - 15

5

Instructional Material Complementing FEMA P-751, Design Examples

Reactions Grid

Dead

Live

Ex

Ey

A-5

P Mxx Myy

203.8 k

43.8 k

-3.8 k 53.6 k-ft -243.1 k-ft

21.3 k -1011.5 k-ft 8.1 k-ft

A-6

P Mxx Myy

103.5 k

22.3 k

-51.8 k 47.7 k-ft -246.9 k-ft

-281.0 k -891.0 k-ft 13.4 k-ft

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 16

Reduction of Overturning Moment

• •

•

NEHRP Provisions allow base overturning moment to be reduced by 25% at the soilfoundation interface For a moment frame, the column vertical loads are the resultants of base overturning moment, whereas column moments are resultants of story shear Thus, use 75% of seismic vertical reactions

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 17

Additive Load w/ Largest eccentricity

•

• • •

Combining loads on footings A-5 and A-6, applying the 0.75 multiplier for overturning effects to the axial loads, and neglecting the weight of the foundation and overlying soil, P = 256 kips Mxx = -6,717 ft-kips Myy = -126 ft-kips (which is negligible)

Instructional Materials Complementing FEMA P-751, Design Examples

5 – Foundation Design

Foundation Design - 18

6

Instructional Material Complementing FEMA P-751, Design Examples

Counteracting Load w/ Largest e

• • • •

Again combining loads on footings A-5 and A-6, including the overturning factor, and neglecting the weight of the footing and overlying soil, P = 8 kips Mxx = -5,712 ft-kips Myy = -126 ft-kips (negligible)

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 19

Elastic Response

•

•

Objective is to set L and W to satisfy equilibrium and avoid overloading soil Successive trials usually necessary

L P

M

W

R e

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 20

Additive Combination Given P = 256 k, M =6717 k-ft Try 4.5 foot around, thus L = 34 ft, B = 9 ft • Minimum W = M/(L/2) – P = 139 k = 455 psf Try 2 foot soil cover & 3 foot thick footing

• W = 214 k; for additive combo use 1.2W • Qmax = (P + 1.2W)/(3(L/2 – e)B/2) = 9.74 ksf • Qn = 0.7(3)Bmin = 18.9 ksf, OK by Elastic Instructional Materials Complementing FEMA P-751, Design Examples

5 – Foundation Design

Foundation Design - 21

7

Instructional Material Complementing FEMA P-751, Design Examples

Plastic Response

• •

L

Same objective as for elastic response Smaller footings can be shown OK thus

P

M

W

R e

Instructional Materials Complementing FEMA P-751, Design Examples

R

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Counteracting Case Given P = 8 k; M = 5712 Check prior trial; W = 214 k (use 0.9W) • e = 5712/(214 + 8) = 25.7 > 34/2 NG New trial: L = 40 ft, 5 ft thick, 2 ft soil cover • W = 360 k; e = 17.2 ft; plastic Qmax= 8.78 ksf • Qn = 0.7(3)4.1 = 8.6 ksf, close • Try plastic solution, L’ = 4.2 ft, Qn = 8.82 ksf • MR = (0.9(360)+8)(40/2-4.2/2) = 5943 > 5712 Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 23

Additional Checks

• • •

Moments and shears for reinforcement should be checked for the overturning case Plastic soil stress gives upper bound on moments and shears in concrete Horizontal equilibrium: Hmax< (P+W) in this case friction exceeds demand; passive could also be used

Instructional Materials Complementing FEMA P-751, Design Examples

5 – Foundation Design

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8

Instructional Material Complementing FEMA P-751, Design Examples

Results for all Seismic Resistant System Footings Middle: 5'x30'x4'-0"

Side: 8'x32'x4'-0"

Corner: 9'x40'x5'-0" w/ top of footing 2'-0" below grade

Instructional Materials Complementing FEMA P-751, Design Examples

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Design of footings for core-braced 7 story building

25 foot square bays at center of building Instructional Materials Complementing FEMA P-751, Design Examples

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Solution for Central Mat Very high uplifts at individual columns; mat is only practical shallow foundation

Mat: 45'x95'x7'-0" with top of mat 3'-6" below grade

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Instructional Material Complementing FEMA P-751, Design Examples

Bearing Pressure Solution Plastic solution is satisfactory; elastic is not

12.2 ksf ~

12 4

(a) Plastic solution

16 (b) 8 Elastic solution 0 pressures (ksf)

Instructional Materials Complementing FEMA P-751, Design Examples

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Pile/Pier Foundations Pile cap

Passive resistance (see Figure 4.2-5)

Pile

p-y springs (see Figure 4.2-4)

View of cap with column above and piles below

Instructional Materials Complementing FEMA P-751, Design Examples

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Pile/Pier Foundations Pile Stiffness: • Short (Rigid) • Intermediate • Long Cap Influence Group Action

Soil Stiffness • Linear springs – nomographs e.g. NAVFAC DM7.2 • Nonlinear springs – LPILE or similar analysis

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Instructional Material Complementing FEMA P-751, Design Examples

Sample p-y Curves 100,000

Soil resistance, p (lb/in.)

10,000 1,000 100 Site Class C, depth = 30 ft Site Class C, depth = 10 ft Site Class E, depth = 30 ft

10

Site Class E, depth = 10 ft 1 0.0

0.1

0.2

0.3

0.4 0.5 0.6 0.7 Pile deflection, y (in.)

0.8

0.9

Instructional Materials Complementing FEMA P-751, Design Examples

1.0

Foundation Design - 31

P/Pult

Passive Pressure 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0

0.01

0.02

0.03 0.04 /H

0.05

0.06

Instructional Materials Complementing FEMA P-751, Design Examples

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Group effect factor

Group Effect Factor

Group Effect 1.0

s = 7D

0.8

s = 5D

0.6

s = 3D

0.4

s = 2D 0.2

0.0 1

2

3

4

5

6

7

8

Pile group size (number of rows)

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Instructional Material Complementing FEMA P-751, Design Examples

Pile Shear: Two Soil Stiffnesses 0 5

Depth (ft)

10 15 20 25

Site Class C Site Class E

30 -5

0

5 10 Shear, V (kip)

15

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 34

0

Pile Moment vs Depth

5

Depth (ft)

10 15 20 25

Site Class C Site Class E

30 -1000

-500 0 Moment, M (in.-kips)

500

Instructional Materials Complementing FEMA P-751, Design Examples

Foundation Design - 35

Pile Reinforcement 4" pile embedment 6'-4"

(6) #5

21'-0"

23'-0"

A

#4 spiral at 3.75 inch pitch

Section A (6) #5

B

#4 spiral at 7.5 inch pitch

Section B (4) #5

C

• Site Class C • Larger amounts where moments and shears are high • Minimum amounts must extend beyond theoretical cutoff points • “Half” spiral for 3D

#4 spiral at 11 inch pitch

Section C

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Instructional Material Complementing FEMA P-751, Design Examples

Pile Design

12'-4"

4" pile embedment

(8) #7

A

reinforcement

#5 spiral at 3.5 inch pitch

20'-0"

Section A (6) #7

B

#5 spiral at 3.5 inch pitch

Section B 32'-0"

• Site Class E • Substantially more • “Full” spiral for 7D • Confinement at boundary of soft and firm soils (7D up and 3D down)

(4) #7

C

#4 spiral at 11 inch pitch

Section C

Instructional Materials Complementing FEMA P-751, Design Examples

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Other Topics for Pile Foundations

• • • •

Foundation Ties: F = PG(SDS/10) Pile Caps: high shears, rules of thumb; look for 3D strut and tie methods in future Liquefaction: another topic Kinematic interaction of soil layers

Instructional Materials Complementing FEMA P-751, Design Examples

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Tie between pile caps 2" clear at sides

(3) #6 top bars #4 ties at 7" o.c.

3" clear at top and bottom

(3) #6 bottom bars

• Designed for axial force (+/-) • Pile cap axial load times SDS/10 • Oftentimes use grade beams or thickened slabs on grade Instructional Materials Complementing FEMA P-751, Design Examples

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Instructional Material Complementing FEMA P-751, Design Examples

Questions

Instructional Materials Complementing FEMA P-751, Design Examples

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