sabp-q-002

Previous Issue: 31 August 2002 Next Planned Update: 1 February 2009 Primary contact: Abu-Adas, Hisham on phone 874-6908 Page 1 of 43

Best Practice

SABP-Q-002 31 January 2005 Spread Footings Design

Document Responsibility: Onshore Structures

Spread Footings Design

Developed by: Hisham Abu-Adas Developed Date: 31 July 2002 Civil Engineering Unit/M&CED Consulting Services Department

Document Responsibility: Onshore Structures SABP-Q-002 Issue Date: 31 January 2005 Next Planned Update: 1 February 2009 Spread Footings Design

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SPREAD FOOTINGS DESIGN

Table of Contents Page

1 Introduction.............................................................................................. 4

1.1 Purpose............................................................................................. 4

1.2 Scope................................................................................................. 4

1.3 Disclaimer........................................................................................ 4

1.4 Conflicts with Mandatory Standards............................................ 4

2 References.................................................................................................. 5

2.1 Industry Codes and Standards....................................................... 5

2.2 Saudi Aramco Best Practices.......................................................... 5

2.3 Saudi Aramco Standards................................................................ 5

3 General...................................................................................................... 6

4 Loadings..................................................................................................... 6

5 Footing Design.......................................................................................... 7

5.1 Sizing................................................................................................ 7

5.2 Reinforced Concrete Footing Design........................................... 11

6 Pedestal Design........................................................................................ 14

7 Anchor Bolts............................................................................................ 15

8 Procedure for Footing Design................................................................ 16


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List of Figures 1 Uniaxial Loading

2 Biaxial Loading

3 Tributary Area for Wide Beam & Two-Way Action Shear

4 Shear Strength of Concrete in Footing

5 Distribution of Flexural Reinforcement

Attachments: Attachment 1: List of Forms....................................................................... 18

1 Design Input – Uniaxial Loading

2 Sample Input Data – Uniaxial Loading

3 Design Input – Biaxial Loading

Attachment 1a: Soil Pressure for Biaxial Footings................................... 20

Attachment 2:................................................................................................ 21 Spread Footing Design – Example 1 (Manual Calculations)

Attachment 3:................................................................................................ 27 Spread Footing Design – Example 1 (In-House Developed Spreadsheet)

Attachment 4:................................................................................................ 30 Spread Footing Design – Example 2 (Manual Calculations)

Attachment 5:................................................................................................ 33 Spread Footing Design – Example 2 (In-House Developed Spreadsheet)

Attachment 6: List of Tables...................................................................... 38

1 Reinforcing Bars Diameters & Cross Sections

2 Basic Development Length of Standard 90° Hooks in Tension

3 Basic Development Length in Compression

4 Minimum Straight Tension Development Length (Bottom Bars)

5 Minimum Straight Tension Development Length (Top Bars)

6 Minimum Percent Reinforcement Required for Footing Design


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1 Introduction

1.1 Purpose

The purpose of this practice is to provide the engineer and designer with guidelines for spread footing design for use by engineers working on Saudi Aramco projects and Saudi Aramco engineers.

1.2 Scope

This design guide defines the minimum requirements for the analysis and design of reinforced spread footings in process industry facilities at Saudi Aramco sites. It covers general design philosophy and requirements to be used in the analysis and design of spread footings. Section 2.0 of this instruction includes reference codes and Saudi Aramco standards. Combined footings, mats and pile foundations are beyond the scope of this guideline. The Design Input Forms 1 and 2 (Attachment 1) for foundation input loads presented in this guideline are valid for either square or rectangular footings subject to either uniaxial or biaxial overturning forces.

1.3 Disclaimer

The material in this Best Practices document provides the most correct and accurate design guidelines available to Saudi Aramco which comply with international industry practices. This material is being provided for the general guidance and benefit of the Designer. Use of the Best Practices in designing projects for Saudi Aramco, however, does not relieve the Designer from his responsibility to verify the accuracy of any information presented or from his contractual liability to provide safe and sound designs that conform to Mandatory Saudi Aramco Engineering Requirements. Use of the information or material contained herein is no guarantee that the resulting product will satisfy the applicable requirements of any project. Saudi Aramco assumes no responsibility or liability whatsoever for any reliance on the information presented herein or for designs prepared by Designers in accordance with the Best Practices. Use of the Best Practices by Designers is intended solely for, and shall be strictly limited to, Saudi Aramco projects. Saudi Aramco® is a registered trademark of the Saudi Arabian Oil Company. Copyright, Saudi Aramco, 2005.

1.4 Conflicts with Mandatory Standards

In the event of a conflict between this Best Practice and other Mandatory Saudi Aramco Engineering Requirement, the Mandatory Saudi Aramco Engineering Requirement shall govern.


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2 References

The latest edition of the following applicable codes, standards, specifications, and references in effect on the date of contract offer shall be used, except as otherwise specified. Short titles will be used herein when appropriate.

2.1 Industry Codes and Standards

American Concrete Institute (ACI)

ACI 318-02 Building Code Requirements for Reinforced Concrete and Commentary

American Society of Civil Engineers (ASCE)

ASCE 7-02 Minimum Design Loads for Buildings and Other Structures

International Conference of Building Officials

Uniform Building Code, 1997 Edition

2.2 Saudi Aramco Best Practices SABP-Q-001 Anchor Bolt Design and Installation SABP-M-006 Wind Loads on Pipe Racks & Open Frame

Structures

2.3 Saudi Aramco Standards

Saudi Aramco Engineering Standards (SAES)

SAES-A-113 Geotechnical Engineering Requirements SAES-A-114 Excavation and Backfill SAES-A-204 Preparation of Structural Calculations SAES-M-001 Structural Design Criteria for Non-Building

Structures SAES-Q-001 Criteria for Design and Construction of Concrete

Structures SAES-Q-005 Concrete Foundations


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3 General

3.1 The design and specifications for construction of spread footings shall be adequate for the structure intended use, in accordance with commonly accepted engineering practice, Saudi Aramco Standard SAES-Q-005 Section 4.0, and this guideline.

3.2 A geotechnical investigation is required for all new structures and foundations as described in SAES-A-113. (Ref. SAES-Q-005, Para. 4.1.1)

3.3 The allowable soil bearing pressure shall be based on the results of the geotechnical investigation, and a consideration of permissible total and differential settlements. Soil pressures shall be calculated under the action of vertical and lateral loads using load combinations that result in the maximum soil pressures. The maximum soil pressure shall not exceed the applicable allowable value. (Ref. SAES-Q-005, Para. 4.1.2)

3.4 Foundations shall be founded on either undisturbed soil or compact fill and at least 600 mm below the existing or finished grade surface, unless a detailed soils investigation indicated otherwise. In the case of foundations supported on compacted fill, the geotechnical investigation and/or SAES-A-114 shall govern the type of fill material and degree of compaction required. (Ref. SAES-Q-005, Para. 4.1.3)

3.5 The design and construction of all concrete foundations shall comply with the requirements of SAES-Q-001. (Ref. SAES-Q-005, Para. 4.3.1)

3.6 The top of concrete pedestal shall be a minimum of 150 mm above finished grade for all columns supporting process equipments and pipe racks. (Ref. SAES-Q-005, Para. 4.3.2.a)

3.7 The design concrete compressive strength of concrete shall be 27.6 MPa (4000 psi) at 28 days. (Ref. SAES-Q-005, Para. 4.3.2.b)

3.8 The structural calculations shall be prepared in accordance with the requirements of SAES-A-204.

4 Loadings

4.1 Loads and load combinations for spread footing design shall conform to Sections 5 and 6 of SAES-M-001 "Structural Design Criteria for Non-Building Structures" and Chapter 16 of International Building Code (IBC 2003).


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4.2 The loads used for footing design shall be service load reactions obtained from an elastic analysis of the superstructure. In computing footing soil pressures the service load reactions are used. The weight of the footing and soil overburden shall be combined with the service loads. The effect of buoyancy shall be considered in footing design.

4.3 In computing moments and shears for footing slab design, the service load soil pressures are factored. In designing the pedestal, load factors are applied to the service load reactions and the pedestal is designed in accordance with the ACI Code.

5 Footing Design

5.1 Sizing

5.1.1 General

a) Generally, spread footings should be square or rectangular and sized in 6-inch (150 mm) increments. The footing Length (L) to Width (W) ratio of rectangular footings shall conform to the following range 0.5 < L/B < 2.

b) Footings must be designed to safely resist the effects of the applied factored axial loads, shears and moments. Provisions of Chapter 15 of ACI Code apply primarily for design of footings supporting a single column (isolated footings).

c) The size of spread footings may be governed by stability requirements, sliding, soil bearing pressure, or settlement. A discussion of each of these considerations follows.

5.1.2 Foundation Stability

a) All foundations subject to buoyant forces shall be designed to resist a uniformly distributed uplift equal to the full hydrostatic pressure. The minimum safety factor against floatation shall be 1.20, considering the highest anticipated water level (Ref. SAES-Q-005, Para. 4.2.7).

b) The minimum safety factor against overturning for load combinations which include wind forces shall be 1.5; (Ref. SAES-Q-005, Para. 4.2.1). Overturning caused by earthquake shall be checked in accordance with SEI/ASCE 7, Chapter 9; (Ref. SAES-Q-005, Para. 4.2.2).


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5.1.3 Foundation Sliding

The minimum safety factor against sliding for service loads other than earthquake shall be 1.5. The coefficient of friction used in computing the safety factor against sliding for cast-in-place foundations shall be 0.40, unless specified otherwise in a detailed soil investigation. Passive earth pressure from backfill shall not be considered in computing these safety factors (ref. SAES-Q-005, Para. 4.2.6).

5.1.4 Soil Bearing Pressure

A common assumption in the design of soil bearing footings is that the footing behaves as a rigid unit. Hence, the soil pressure beneath a footing is assumed to vary linearly when the footing is subjected to axial load and moment. The ensuing rectangular footing formulas are based on the linear pressure assumption. We will consider the following conditions:

Case 1 - Resultant is within middle third of footing e ≤ L/6 The resultant R consists of the applied vertical load plus the weight of the footing.

In this case, all of footing area in compression, and the direct soil pressure PT/A is larger than the bending pressure Mc/I = M/S.

When bending occurs about one axis only (Figure 1 – Case 1), and the entire footing is subjected to pressure,

Qmax = PT/A + M/S = PT/BL (1 + 6e/L) Uniaxial Loading Eq. 5-1

Qmin = PT/A - M/S = PT/BL (1 - 6e/L) Uniaxial Loading Eq. 5-2

Eccentricity e = ΣM/ΣPT = (M + H x h) /PT Eq. 5-3


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When bending occurs about both the x and y axis, and the entire footing is subjected to pressure (i.e., eccentricity of the footing ex and ey lie within their respective kern points),

qmax = PT/A + My/Sx + Mx/Sy = PT/BL (1 + 6ex/L + 6ey/B) Biaxial Loading Eq. 5-4

qmin = PT/A - My/Sx - Mx/Sy = PT/BL (1 - 6ex/L - 6ey/B) Biaxial Loading Eq.5-5

ex = ΣMy/ΣPT Eq. 5-6

ey = ΣMx/ΣPT Eq. 5-7


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where

A = Area of footing = (L) (B)

L = Footing Length – Dimension Parallel to X-Axis

B = Footing width – dimension parallel to Y-axis

PT = Vertical design load including soil overburden, foundation weight, and buoyancy

Mx = Moment About X-Axis of Footing Plan

My = Moment About Y-Axis of Footing Plan

Sx = L (B2/6) Ix = L B3/12

Sy = B (L2/6) Iy = B L3/12

The values of ex and ey are obtained using equation 5-6 and 5-7 first about the x-axis and then about the y-axis

Case 2 - Resultant is outside middle third of footing e>L/6 The resultant R consists of the applied vertical load plus the weight of the footing and soil overburden.

When bending occurs about one axis only:

In this case, as the load acts outside the middle third, tensile stress results at the left side of the footing as shown in Figure 1- Case 2.

Figure 1 - Case 2 shows the distribution of soil pressure beneath the footing when the resultant is outside the middle third of the base. According to the laws of static, the total upward force must be equal to and collinear with R. These two conditions may be expressed by

R = (qmax B x) / 2 Eq. 5-8 and

x/3 = (L/2) - e2 x = 3 (L/2 – e2) Eq. 5-9

qmax = 2PT/3B (L/2 – e2) Eq. 5-10

When bending occurs about both the x and y axis, and the values of ex and ey are obtained using equation 5-6 and 5-7 first about the x-axis and then about the y-axis. If the resulting point of application of eccentricity e falls outside of the kern of the section (as labeled in Figure 2), a special case exists and the points of zero pressure must be determined by trial. It should be noted that tension cannot exist between the soil and the footing.


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For the spread footings that are subject to biaxial bending with the resultant lies outside or inside the kern, numerical solutions can be found in many soil mechanics textbooks. Commercial software is also available for this situation. Attachment 1A is a design aid that is based on accurate numerical solutions and graphically provides the results.

5.1.5 Settlement

Footings shall be designed so that under sustained loads (operating loads) the total settlement and the differential settlement between footings do not exceed the established limits. The maximum allowable amount of total settlement and differential settlement is typically set by the Project Structural Engineer based on the sensitivity of the equipment or structure being supported.

5.2 Reinforced Concrete Footing Design

5.2.1 General


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a) Reinforced concrete footing design shall conform to the requirements of ACI 318. The strength method shall be used for all reinforced concrete footings design.

b) The footing thickness is generally controlled by shear or rigidity requirements. However, thickness may be controlled by flexural considerations where the thickness is increased to avoid tension top steel or to keep ρ less than ρbal. In any case, the minimum thickness of a soil bearing footing shall be 12 inches.

5.2.2 Flexural Considerations

a) Footings shall be designed considering two-way action. The procedures outlined in ACI 318, Chapter 15 shall be followed for footing design.

b) The strength method outlined in ACI 318, Chapter 10 shall be used for all design.

c) For square footings, reinforcing steel shall be placed continuously across the entire footing in a grid pattern. For rectangular footings, placement of steel shall conform to ACI 318, Section 15.4.4. All reinforcement shall be fully developed in compliance with ACI 318 criteria.

d) The minimum amount of bottom steel (grade 60 ksi) shall not be less than the minimum shrinkage reinforcement:

As (min) = 0.0018 b h

where

b = width of footing

d = distance from top of footing to center of bottom bars

h = depth of footing

e) If a footing has uplift, there will be a moment at the heel that will cause tension in the top of footing. Provide top steel to account for the moment resulting from the footing weight and soil overburden weight. Development length of top steel shall be per Table 5. The bars may be hooked 90° downward to achieve the required development length if straight embedment is not adequate. If top reinforcing is required, minimum reinforcing shall be #3 at 12 inches on center, each way.


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5.2.3 Shear Considerations

Both wide-beam action and two-way action must be checked to determine the required footing depth. Beam action assumes that the footing acts as a wide beam with a critical section across its entire width. Two-way action for the footing checks "punching" shear strength. The critical section for punching shear is a perimeter bo around the supported member with the shear strength computed in accordance with ACI Code Sect. 11.12.2.1. Tributary areas and corresponding critical sections for wide-beam action and two-way action for an isolated footing are illustrated in Figure 3 below:

Figure 3 – Tributary Area for Wide-Beam and Two-Way Action Shear (Adapted from Notes on ACI 318 - 02 by PCA)

Tributary Areas and Critical Sections for Shear

For footing design, the depth must be selected so that shear reinforcement is not required. The shear strength equations may be summarized as follows:


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Figure 4 – Shear Strength of Concrete in Footings

6 Pedestal Design

6.1 Pedestals shall be designed using the strength method and moment magnification. The pedestal shall be assumed to be a cantilever with K factor of 2.0. The service loads acting on the pedestal shall be factored, and the pedestal shall be designed as a column or cantilever beam in accordance with ACI 318 provisions.

6.2 Use reinforcing dowels to transfer the column loads to the footings. Minimum dowel projections should be that required for a tension splice in accordance with ACI 318.

6.3 Transfer of Force at Base of Column

All forces applied at the base of a column (supported member) must be transferred to the footing (supporting member) by bearing on concrete and/or by reinforcement. Tensile forces must be resisted entirely by reinforcement.


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Bearing on concrete for both supported and supporting member must not exceed the concrete bearing strength permitted by ACI Code Section 10.17.

For a supported column, the bearing capacity φPnb is

φPnb = φ(.85 f 'c A1) ACI – Sect. 10.17.1

f 'c = compressive strength of the column concrete

A 1 = loaded area (column area)

φ = 0.65

For a supporting footing,

φPnb = φ(.85 f 'c A1) 12/AA ≤ 2φ(.85 f 'c A1)

f 'c = compressive strength of the footing concrete

A2 = area of the lower base of the largest frustum of a pyramid, cone, or tapered wedge contained wholly within the footing and having for its upper base the loaded area, and having side slopes of 1 vertical to 2 horizontal (see ACI Code Fig. R10.17).

When bearing strength is exceeded, the bearing area must be increased.

A minimum area of reinforcement 0.005Ag (Ag = gross area of column) must be provided across the interface of column or wall and footing. The minimum reinforcement for column shall be in accordance with the ACI Code Sect. 10.9 and R10.8.4.

The shear-friction design method of ACI Code Sect. 11.7.4 should be used for horizontal force transfer between columns and footings. Consideration of some of the lateral force being transferred by shear through a formed shear key is questionable. Considerable slip is required to develop a shear key. Shear keys, if provided, should be considered as an added mechanical factor of safety only, with no design shear force assigned to the shear key. Net tension across the shear plane shall be resisted by additional reinforcement.

7 Anchor Bolts

Anchor bolts design requirements shall be in accordance with SAES-Q-005 and SABP-Q-001.


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8 Procedure for Footing Design

The following sequence of steps can be used in the design of spread footings:

8.1 Determine the gross allowable soil bearing pressure based on soil investigation report or available exiting soil data.

8.2 Size the foundation pedestal based on strength requirements, anchor bolt pattern and required clearances.

8.3 Determine the primary service load cases and the critical load combinations acting on the footing.

8.4 Calculate eccentricity e = ΣM/PT (Eq. 5-3) to determine if the resultant is in middle third (e ≤ L/6) or outside middle third (e > L/6).

8.5 Assume a trial footing size and use service load combinations to calculate the maximum soil bearing pressure (qmax) and minimum soil bearing pressure (qmin) based on the location of eccentricity. Adjust footing size so that qmax does not exceed the maximum gross allowable soil bearing pressure.

8.6 Calculate safety factor against overturning by dividing resisting moment by overturning moment. The resultant Safety Factor should be 1.5 minimum, otherwise increase footing size.

8.7 Calculate safety factor against sliding by dividing resisting shear by actual shear. The resultant Safety Factor should be 1.5 minimum.

8.8 Assume footing thickness and determine the required effective depth of the section that has adequate beam shear capacity at a distance d from the support face for one way shear and punching shear at a distance d/2 for two-way action.

8.9 Calculate the controlling factored moment Mu on a plane at the face of the column support. Find Mn = Mu/0.9. Select a total reinforcement area As based on Mn and the applicable effective depth. Ensure that the area of steel in each principal direction of the footing plan exceeds the minimum value required for temperature and shrinkage: As = 0.0018 bw h (bw = width of footing, h = total thickness).

8.10 Determine the size and spacing of the flexural reinforcement in the long and short directions. In one-way footings and two-way square footings, flexural reinforcement shall be distributed uniformly across the entire width of the footing. For two-way rectangular footings, the reinforcement must be distributed as shown in Figure 5 below.


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Figure 5 – Distribution of Flexural Reinforcement

(Adapted from Notes on ACI 318-02 by PCA)

8.11 Check development length and anchorage available to verify that bond requirements are satisfied (ACI Code Chapter 12 and attached Tables 2 through 5).

8.12 Check the bearing stresses on the column and the footing at their area of contact.

8.13 Check shear friction steel requirements at the footing and pedestal interface and determine the number and size of the dowels required.

Revision Summary 31 July 2002 New Saudi Aramco Best Design Practice. 31 January 2005 Revision 1 to comply with ACI-318-02 and revised SAES-Q-005.


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Attachment 1: List of Forms


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Attachment 1A: Soil Pressure for Biaxial Footings

Location of Smax

d

b

Smax = K (P/bd)

Load P

e2

e1

K coefficient

RATIOe1/d

0.40

0.38

0.02

0.00

12 010 9 8 7 6 5 4 3 2 111

12 010 9 8 7 6 5 4 3 2 111

0.36

0.34

0.32

0.30

0.28

0.26

0.24

0.22

0.20

0.18

0.16

0.14

0.12

0.10

0.08

0.06

0.04

0.40

0.38

0.02

0.00

0.36

0.34

0.32

0.30

0.28

0.26

0.24

0.22

0.20

0.18

0.16

0.14

0.12

0.10

0.08

0.06

0.04

e2 /b = 0.40

0.3750.35

0.3250.30

e2 /b = 0.0

0.2750.25

0.225

0.05

0.100.15

0.20

0.175


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Attachment 2: Spread Footing Design – Example 1 (Manual Calculations)

Spread Footing Design – Example 1

Given: PD = 300 Kips Soil Weight = 115 pcf PL = 250 Kips

f’c = 4,000 psi fy = 60,000 psi

Allowable Soil Bearing Pressure qs = 4.0 ksf (gross) Assume footing width restricted to 10 feet


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Step 1: Determine base area required

The base area of the footing is determined using service (unfactored) loads with the net permissible soil pressure.

Total weight of surcharge = 0.115 X 4.5 ft = 0.52 ksf

Net permissible soil pressure qs = 4.0 – 0.52 = 3.48 ksf

Required base area of footing: Af = (300 + 250) / 3.48 = 158.05 ft²

Use 10 ft X 16 ft footing (Af = 160 ft² > 158.05) O.K.

Step 2: Factored loads and soil reaction

Pu = 1.2 (300) + 1.6 (250) = 760 kips

qu = Pu / Af = 760 / 160 = 4.75 ksf

Step 3: Check beam shear (wide beam action) – see Figure below

Assume footing thickness = 30 in. and average effective thickness d=26.5 in. = 2.21 ft

ΦVn ≥ Vu ACI – Eq. 11-1

Vu = qu x tributary area

Tributary area = 10 (8.0 – 1.25 –2.21) = 45.40 ft²

Vu = 4.75 x 45.40 = 215.65 kips

ΦVn = = Φ(2 cf ' bw d) ACI - Eq. 11-3

ΦVn = 0.75 (2 4000 x 120 x 26.5)/1000

ΦVn = 301.72 kips > 215.65 O.K.

Ratio = 215.65 / 301.72 = 0.71 < 1.0 O.K.

Step 4: Check Two-way action (punching shear)- see Figure below

Check punching shear along tributary perimeter area (per Figure below)

Vu = qu x Tributary area

Tributary Area = (Lx * Ly) – ((30 + d) (12 + d)/144)


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Tributary area = [(10 x 16) – (30 + 26.50)(12 + 26.50)/144] = 144.89 ft²

Vu = 4.75 x 144.89 = 688.23 kips

ΦVn ≥ Vu (Vn = Vc) ACI – Eq. 11-1

Vc shall be the smallest of :

Vc = (2 + 4/βc) cf ' bo d ACI Eq. 11-33

Vc = (αsd/bo+ 2) cf ' bo d ACI Eq. 11-34

Vc = 4 cf ' bo d ACI Eq. 11-35

bo = 2(30 + 26.5) + 2(12 + 26.5) = 190 in.

βc = 30 / 12 = 2.50

bo / d = 190 / 26.50 = 7.17

αs = 40 for interior columns

In Eq. 11-33 (2 + 4/βc) = 2 + 4/2.50 = 3.60 Governs Design

In Eq. 11-34 (αsd/bo+ 2) = 40*26.50/190 + 2 = 7.58

In Eq. 11-35 4

ΦVc=0.75x(2 + 4/βc)x cf ' bo d=0.75 x 3.6 x 4000 x190x26.50/1000 = 859.79 kips

ΦVc = 859.79 kips > 688.23 kips O.K. (Footing thickness is adequate)

Ratio = 688.23 / 859.79 = 0.80 < 1.0 O.K.


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Beam Shear & Punching Shear in Footing:

Step 5: Design Footing Reinforcement

Ultimate moment Mu:

Mu = Wl2/2 = 4.75 x 10 ft x (6.752 /2) = 1082.11 k –ft

Mn = 1082.11 /0.9 = 1202.34 k-ft


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F = bd2/12,000 = (10x12) x 26.52 / 12,000 = 7.02

Kn = Mn /F = 1202.34 / 7.02 = 171.27

ρreqd = 0.0030 (From Table 6) > ρ min = 0.0018 As = ρ x b x d

As = 0.0030 x 120 x 26.50 = 9.54 in²

Use 14 # 8 bars As = 11.06 in2 > 9.54 ok

Use #8 @ 8 ¾ inches

Reinforcement in Perpendicular Direction:

Mu = 4.75 x 16x (4.5)2/2 = 769.50 k-ft

Mn = 769.50/0.9 = 855.00 k-ft

F = bd2/12,000 = (16x12) x 262 / 12,000 = 10.82

Kn = Mn /F = 855.00 / 10.82 = 79.02

ρreqd = 0.0013 (From Table 6) < ρ min = 0.0018

Use ρ min = 0.0018 (min. shrinkage reinf.)

As = ρ x b x h

As = 0.0018 x 16 x 12 x 30 = 10.37 in²

Distribution to 10 ft width:

As1 = (2 / 1 + β) x As

As1 = (2/ 1 + 16/10) x 10.37 = 7.97 in²

Use 14 # 7 As1 = 8.40 in2 > 7.97 ok Region 2 (middle) 120 inch

Distribution to each end of footing ends:

As2 = (As – As1) / 2 = (10.37 – 7.97 ) / 2 = 1.20 in²

Use 2 # 7 As2 = 1.20 in² > or = 1.20 ok Region 1 and 3 (ends) 36 inch


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Step 6:Check force transfer at column base:

Bearing Strength of Column:

φPnb = φ(.85 f 'c A1) ACI – Sect. 10.17.1

0.65 (0.85 x 4) x (12 x 30) = 795.60 Kips > 760.0 Kips - O.K.

Bearing Strength of Footing:

φPnb = φ(.85 f 'c A1) 12/AA

12/AA > 2 Use 2

φPnb = 0.65 ( 0.85 x 4) x (12 x 30) x 2 = 1591.20 kips > 760.0ips Ok.

Use minimum column dowels:

0.005 x 12 x30 = 1.8 in² Use 4 # 6 As = 1.76 in²

Step 7: Check development length for column dowels and for footing bottom bars

Column Vertical Dowels:

For # 6 dowels: Required compression development length

ld (required) = 14.2 in (per Table 3) < 26 in available O.K.

Footing Bottom Bars:

Footing Bottom bars development length required ld for # 8 = 57 in. (per Table 4) < (81 –3) = 78” Available - O.K.

Footing Bottom bars development length required ld for #7= 50 in. (per Table 4) < (54 – 3) = 51 in. Available – O.K.


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Attachment 3:


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Attachment 4: Spread Footing Design – Example 2 (Manual Calculations)

Based on STAAD III output, the following is the critical service load combination. See detailed load combinations from STAAD III output (not included).

Given: P = 27.25 Kips Soil Weight = 115 pcf H = 4.93 Kips M = 54.55 Kip - ft

f’c = 4,000 psi fy = 60,000 psi

Allowable Soil Bearing Pressure qs = 3.0 ksf (gross)


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Step 1: Determine base area required & maximum soil bearing pressure

The base area of the footing is determined using service (unfactored) loads:

Footing & Pedestal weight = (8.0x5.0x1.5x0.15) + (2.5x1.67x3.0x0.15) = 9.00 + 1.88 = 10.88 Kips

Weight of Soil = ((8.0x5.0) – (2.5x1.67)) x 2.50 x 0.115 = 10.30 kips

Total P = 27.25 + 10.88 + 10.30 = 48.43 Kips

Overturning Moment (O.M.)= (H x h) + M = (4.93 x 4.5) + 54.55 = 76.74 k-ft

Resisting Moment (R.M.) = ∑P x Lx/2 = 48.43 x 8/2 = 193.71 k-ft

S.F. against overturning =R.M./O.M.= MR/MO = 193.71 / 76.74 = 2.52 > 1.5 O.K.

S.F. against sliding = P x 0.4 / H = 48.43 x 0.4 / 4.93 = 3.93 > 1.5 O.K.

Check location of eccentricity e: e = MO / P = 76.74 / 48.43 = 1.58 ft > L/6 = 8/6 = 1.33

Resultant is outside the middle third of footing.

Use equations 5-8 and 5-9 for calculating maximum gross soil bearing pressure

X/3 = (Lx/2 ) – e = (8.0 /2) – 1.58 = 2.42 Eq. 5-9

X = 7.26 ft

qmax = (P x 2) / Ly x X = (48.43 x 2) / (5.0 x 7.26) = 2.67 ksf < 3.0 O.K. Eq. 5-8

qnet = 2.67 – (4.0 x 115)/1000 = 2.67 – 0.46 = 2.21 ksf

Step 2: Factored loads and soil reaction

Critical factored load combination based on STAAD III computer output

Pu = 39.36 kips

Add weight of footing and soil:

Pu = 39.36 + 1.2(10.88 + 10.30) = 64.78 KIPS

Hu = 8.19 kips

Mu = 91.38 k - ft


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Add additional moment from horizontal load Mu = 91.38 + (8.19 x 4.5) = 128.24 k-ft

e = Mu /Pu = 128.24 / 64.78 = 1.98 > L/6 = 1.33

Resultant outside middle third – use Eq. 8 and 9:

X/3 = (Lx/2 ) – e = (8.0 /2) – 1.98 = 2.02 Eq. 5-9

X = 6.06 ft

qmax = (P x 2) / Ly x X = (64.78 x 2) / (5.0 x 6.06) = 4.28 ksf Eq. 5-8

qnet = 4.28 – 1.2 (10.88 + 10.30) / (8.0 x 5.0) = 4.28 – 0.64 = 3.64 ksf

With factored soil bearing pressure qnet = 3.64 ksf, repeat steps 3 to 6 as in example 1.

Also, see In-House developed Spreadsheet (Attachment 4).

q at face of column = (4.28/6.06) * (6.06 –2.75) = 2.34 ksf

qnet = 2.34 – 1.2 (10.88 + 10.30) / 8.0 x 5.0 = 2.34 – 0.64 = 1.70 ksf

Max. Moment at face of column:

Mu = (1.70*2.752)/2 + (3.64-1.70) *2.75 * 0.5 * 2.75 *2/3

Mu = 6.43 + 4.89 = 11.32 k-ft /ft Mn = 11.32 / 0.9 = 12.58 k-ft / ft

Mu (total) = 11.32 * 5.0 = 56.60 k-ft Mn (tot) = 56.60 / 0.9 = 62.89 k-ft


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Attachment 5:


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Attachment 6: List of Tables


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TABLE 6 – Minimum Percent Reinforcement Required for Footing Design

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