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Introduction: Structural Design of Spread Footings

1

Se

Sc

Ss

S = Se+Sc+Ss

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Basis for Design Methods:

1. Design Loads:

Geotechnical Engineers design footing width (B) and footing depth (D)

and bearing capacity based on ASD method (un-factored loads)

Structural Engineers design footing thickness and reinforcement (size,

number and spacing) based on LRFD method (factored loads)

2. Foundation Failure Mode:

Shear failure: one way or two way shear failure

Flexural failure

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LRFD Design Concept

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Square Footing: Design for shear

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Square Footing: Design for Flexural

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Square Footing: Design for shear

a. One-way shear failure:Critical shear failure located a distance d from theface of column

b. Two-way shear failure:Critical shear failure located a distance d/2 from the face of column

The footing design is satisfactory for shear when it satisfies the following condition:

factored shear force on critical surface

nominal shear capacity on critical surface

resistance factor for shear = 0.75

Considered = 0

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One way shear failure:

1. Critical shear failure located a distance d from the face of column

2. Two way shear always governs the design of square footings subjected onlyvertical load. However, if applied shear or moment loads are present, bothkinds of shear need to be checked

3. Factored shear force on critical shear surface:

Required shear strength:

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One way shear failure:

The nominal one way shear load capacity on the critical section is (ACI 11.3.1.1):

Vn = nominal one way shear capacity on the critical section (kN)

Vc = nominal one way shear capacity of concrete (kN)

bw = length of critical shear surface = B (m)

d = effective depth (m)

fc = 28 day compressive strength of concrete (MPa)

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Two way shear failure (punching shear):

1. Critical shear failure located a distance d/2 from the face of column

2. Inner block and outside block: located inside and outside critical shearsurface

3. The percentage of normal force applied at center of inner block has to passthrough critical shear failure and enter the soil beneath

Required shear strength:

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Two way shear failure (punching shear):

For square footing supporting square or circular columns located in the interior of thefooting (not edge or corner), the nominal two way shear capacity is (ACI 11.12.2.1):

Vn = nominal two way shear capacity on the critical section (kN)

Vc = nominal two way shear capacity of concrete (kN)

b0 = length of critical shear surface (m)

c = column width (m)

d = effective depth (m)

fc = 28 day compressive strength of concrete (MPa)

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Square Footing: Design for Flexural

A square footings bend in two perpendicular directions.Yet for practical purposed, footings are designed as 1way slab:

- It is appropriate to design foundations moreconservative than the superstructure

- The flexural stresses are low, the amount of steelrequired is normally governed by minimumreinforcement ratio (min)

- The additional cost due to this simplified approachis nominal

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Square Footing: Design for Flexural

Required moment strength:

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Square Footing: Design for Flexural

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1. Minimum steel required:

- For 275000 kPa 415000 kPa yield strength steel: As 0.0020 Ag

- For 415000 kPa and above yield strength steel: As 0.0018 Ag

Where Ag= gross cross sectional area

Clear space between bar must be larger than 25 mm

2. Development length:

c = spacing or cover dimensiondb = bar diameter

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Square Footing: Design for Flexural

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Rectangular Footing: Design for Shear

Rectangular footings with width B and length L that support onlyone column are similar to square footings. Design them as follow:

1. Check both one-way shear and two-way shear using the critical shear surfacesshown below. Determine the minimum required d and T to satisfy both.Remember to substitute L for B in appropriate manner.

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Rectangular Footing: Design for Flexural

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Rectangular Footing: Design for Flexural

b. Design the long and short steel (Fig 9.16b) by substitute L for B appropriatelyin square footings formula. Since the central position of the footing takes alarger portion of the short direction, place more of short steel in this zone. Thetotal short steel area to be placed in inner zone is:

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Continuous Footing: Design for One wayShear Failure

1. One way is the only practical failure type in this case. Critical shear failurelocated a distance d from the face of column

2. Factored shear force on critical shear surface:

Setting Vu = Vn and solve for concrete depth d:

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Continuous Footing: Design for One wayShear Failure

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Continuous Footing: Design for Flexural

Longitudinal reinforcement: provide a minimum reinforcement (0.0018 or0.0020 Ag) to prevent shrinkage, soft spots in the soils, etc.

Transverse steel (run perpendicular to the wall) to resist the flexural stresses atthe critical section

The required moment strength of this section:

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Example

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Example 1:

Wall footing: support 30 cm thick wallDepth D = 1.5 mSoil Unit weight: = 19.2 kN/m3

DL = 150 kN/mLL = 187.5 kN/mConcrete compressive strength: fc = 20.7 MPaReinforcement yield strength: fy = 415 MPaAllowable bearing pressure: 240 kN/m2

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Example

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Example 2:

Square footing support a column: 45 cm x 45 cmTop of the footing covered with:

15 cm basement floor 15 cm soil with Unit weight: = 19.2 kN/m3

Basement load = 4.8kN/m2DL = 1800 kNLL = 1200 kNConcrete compressive strength: fc = 20.7 MPaReinforcement yield strength: fy = 415 MPaAllowable bearing pressure: 288 kN/m2

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Example

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Example 3:

Rectangular footing support a column: 45 cm x 45 cmFooting dimension: 2.75 m x 4.3 mThickness T = 0.85 mFactored net soil pressure: q = 350 kPaConcrete compressive strength: fc = 20.7 MPaReinforcement yield strength: fy = 415 MPa

Chapter 5: Allowable Bearing Capacity and Settlement

References:

a. Principles of Foundation Engineering, Braja M.Das, SI 7th

Edition

b. Foundation Design: Principles and Practices, DonaldP.Coduto, 2nd Edition

c. Foundation Analysis and Design, Joseph E.Bowles, 5th

Edition

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