Footing Design and Construction

footing design

Footing Design and Construction

বিএসসি ইন সিভিল ইঞ্জিনিয়ারিং পাশ করার পরে ফুটিং ডিজাইন পারা উচিত । তারপরও অনেকে অনুরোধ করেছেন এই কোর্সটার জন্য । হয়ত কোন ব্যাপারে Conflict হয়েছে প্র্যাক্টিস করতে গিয়ে । তবে বিল্ডিং এর Retrofitting Design করতে গিয়ে দেখা গেল অনেক সিভিল ইঞ্জিনিয়ার short term এবং long term bearing capacity বুঝেন না । এই কোর্সে short term and long term bearing capacity, settlement of footing on sand and clay, geotechnical and structural design of combined footing, definition of ultimate, safe and allowable bearing capacity এই বিষয়গুলো বিস্তারিত আছে । এই শর্ট কোর্সটি ছয় বছর আগে যদি বাংলাদেশের সব সিভিল ইঞ্জিনিয়ারদের জন্য বানানো যেত আরো ভাল হত । তাহলে অনেক garments_factory ফাউন্ডেশন Rettrofitting থেকে বেঁচে যেত। যাই হোক নতুন প্রজন্ম এই কোর্স থেকে উপকৃত হয়ে ভবিষ্যতে কাজে লাগাতে পারবে ।

Footing design is not a complicated topic. Yet, many civil engineers requested us to upload this short course. I hope they are learning well now. Footing design should know after passing BSc in Civil Engineering. Even then, many have requested for this course. Maybe there has been a conflict while practicing. However, when designing the retrofitting of the building, it was seen that many civil engineers do not understand the short term and long term bearing capacity. This course covers short term and long term bearing capacity, settlement of footing on sand and clay, geotechnical and structural design of combined footing, the definition of ultimate, safe and allowable bearing capacity. It would have been better if this short course had been made for all the civil engineers in Bangladesh six years ago. Then many garments factory foundations would have survived retrofitting. However, the new generation will benefit from this course and will be able to use it in the future.

What you'll learn

  • Fundamentals of geotechnical engineering
  • Ultimate bearing capacity, Safe bearing capacity and allowable bearing capacity
  • Calculation of bearing capacity of footing
  • Settlement calculation in sand and clay
  • Worked out examples
  • Subgrade modulus calculation and spring constant
  • BNBC 2020 requirements of the settlement

Prerequisite / Eligibility

  • BSc, MSc or PhD in Civil Engineering
  • Level 4 or 4th year student of bachelor’s in civil engineering

Course Teacher

Professor Dr. Jahangir Alam, Department of Civil Engineering, BUET, Dhaka, Bangladesh

Brief Biography of Course Teacher

Education

  • PhD in Geotechnical Earthquake Engineering, the University of Tokyo, Japan, 2005
  • MSc in Civil and Geotechnical Engineering, BUET, Dhaka, Bangladesh, 2002
  • BSc in Civil Engineering, BUET, Dhaka, Bangladesh, 1998

Biography

Professor Dr. Engr. Md. Jahangir Alam is faculty member at the Department of Civil Engineering, BUET, Dhaka-1000, since 1999. He completed his PhD from University of Tokyo in Geotechnical Earthquake Engineering in 2005 as a Monbu-Kagaku-sho Scholar. He was research fellow in Ecole Centrale Paris in 2008. Professor Jahangir did his BSc in Civil Engg with major in Structure and MSc in Civil and Geotechnical Engineering from BUET.

Professor Jahangir has multidisciplinary research interests and has publications in international journals and conferences. His current research topics are “Risk Sensitive Land Use Planning of Mega City”, Physical and Numerical Modeling of Liquefaction Hazard, Mitigation against Seismic Liquefaction, Cyclic Behavior of Non-plastic silt, Reinforced Earth, Earthquake Resistant Foundation in Soft Soil, Climate Resilient Concrete, Climate Resilient Road.

Professor Jahangir was involved in many consultancy projects where he designed/checked high rise RCC buildings, Communication towers, Jetty, Shore Pile, Embankment, Container Terminal, Ground Improvement, Bridge Foundation etc. He supervised many MSc and PhD students. He was involved in pile load testing, pile integrity testing, concrete mix design and development of laboratory and field-testing equipment.

Professor Jahangir actively involved in National and International professional bodies. He is life member and was Treasurer of Bangladesh Society for Geotechnical Engineering (BSGE), which is Bangladesh Chapter of ISSMGE. He is life fellow of Institute of Engineers Bangladesh (IEB). He is life member of Bangladesh Earthquake Society (BES). He was Treasurer of Bangladesh Earthquake Society (BES).

Certificate of Attendance

Certificate of attendance will be awarded after completion of all video lessons and quizzes

Related Courses

Free Courses

Features of ourPROFESSORs.com

Frequently Asked Questions (FAQ)

Course Preview

Detail Course Outline

Bearing Capacity

  • Load combination for settlement and bearing capacity
  • Differences: Maximum settlement, differential settlement, angular settlement, gross and net bearing pressure, ultimate, safe and allowable bearing capacity, bearing capacity vs Bearing pressure.
  • Failure modes of footing: general shear, local shear, punching shear.
  • Effect of ground water table
  • Bearing capacity calculation: general bearing capacity equation, bearing capacity factors, shape factors, depth factors, inclination factors.
  • Examples: ultimate bearing capacity (clay and sand), short term and long-term bearing capacity (soft clay and stiff clay)

Short term and long term bearing capacity of footing

  • Plate load test
  • Use of test results UCS, UU, CU, CD and which condition properly represent the bearing capacity of footing
  • Failure Envelope of Clay in Drained Triaxial Test
  • Effective Stress Friction Angle of Cohesive Soils
  • Important note on Effective Stress Friction Angle of Cohesive Soils

Correlations among soil parameters

  • Comments on Friction Angle ?′
  • Variation of friction angle of river sand with e
  • Correlations for Undrained Shear Strength, Cu
  • Correlations for N60 in: Cohesive Soil, Relative Density, Angle of Friction ?′, Modulus of Elasticity (Es), Shear wave velocity (Vs), Undrained Shear Strength (Su)
  • Split-Spoon Sampling
  • Degree of sample disturbance
  • Hammer efficiency and SPT Correction
  • Correction: N60 in Granular Soil, Borehole Diameter, Sampler Type, Rod Length, Hammer efficiency and SPT Correction, between N60 and Cu
  • Empirical Relations for CN

Interaction of Nearby Footings under Building

  • Introduction and Problem Statement
  • Methodology and Finite Element Model Variable
  • Engineering Properties of Subsoil
  • Point Indication of footing model under building
  • Vertical Settlement of Individual footing model
  • Effect of Footing Interaction Parameter
  • Effect of modulus of elasticity and building size
  • Effect of distance from center of building
  • Effect of pressure on footing

Footing design requirements according to BNBC 2017

  • Service Load Design Method of Foundations: Bearing capacity of the soil, Dimension of footing, Depth of footing, Thickness of Footing, Scour, Mass Movement of Ground in Unstable Areas, Foundation Excavation, Design Considerations, Geotechnical design of shallow foundations, Settlement.

Bearing Capacity of Footing on Sand

  • Allowable Bearing Capacity of footing in Granular Soil and sand
  • Water table correction
  • Bearing capacity from graph, Thumb Rule, by Meyerhof, using SPT-N value,
  • Allowable Bearing Capacity of Footing at Limiting Settlement
  • FoS of Footing on Sand
  • Allowable Bearing Capacity on Sand

Settlement of Foundation on Sand

  • Total settlement: Immediate settlement, Consolidation settlement, Secondary settlement / Creep.
  • Elastic theory in soil mechanics
  • Elastic settlements
  • Worked out Example
  • Bearing Capacity considering Settlement
  • Calculation of: elastic settlement, consolidation settlement, allowable bearing capacity and subgrade modulus.
  • Effect of size ON foundation settlement
  • Variation of Settlement due to variation of size of foundation
  • Calculation of consolidation settlement for Clay
  • Calculation of Elastic settlement for Sand

Structural Design of Footing

  • Structural design of rectangular footing
  • Structural design of combined footing
  • Critical section for moment
  • Distribution of flexural reinforcement
  • Shear in footings
  • Area of footing
  • Factored loads and soil reaction
  • Thickness of footing
  • Footing reinforcement

Bearing capacity calculation

1
Bearing capacity calculation, Part-1

Bearing Capacity

 

 

 

LOAD COMBINATION FOR SETTLEMENT

(b) Shallow foundation design considering settlement shall consider the most unfavourable effect of the following combinations of loading:

Cohesionless D + L

Cohesive soil D + 0.5*L

 

Notes: The values given in the Table may be taken only as a Guide and the permissible Total settlement, Differential settlement and tilt (angular distortion) in each cash should be decided as per requirement of the designer.

L denotes the length of deflected part of wall / raft or centre to centre distance between columns.

H denotes the length of wall from foundation footing.

* For intermediate ratios of L/H, the values can be interpolated. 



LOAD COMBINATION FOR BEARING CAPACITY

Design Load

Shallow foundation design considering bearing capacity due to shear strength shall consider the most unfavorable effect of the following combinations of loading:  

(i) D + L

 (ii) 0.75*(D + L + W or E)

 (iii) 0.9*D + Buoyancy Pressure

 (iv) 0.6*D + W



Ultimate // Safe // Allowable Bearing Capacity

1.           Ultimate bearing capacity = soil pressure at which failure occur

2.           Safe bearing capacity = ultimate/FS; so safety margin exist, no failure; but may have excessive settlement

3.           Allowable bearing capacity = soil pressure at which settlement of footing will be within permitted limit

4.           settlement governs for most of the soils

5.           Ultimate bearing capacity is determined using any formula = 600 kPa

6.           Safe Bearing Capacity = Ultimate / FS = 200 kPa

7.           Say footing size is 3 m x 3 m using safe bearing capacity and calculated settlement is 150 mm

8.           To limit the settlement within allowable limit (say 50 mm), footing size need to be increased. Say, 4 m x 4 m is ok at 100 kPa

9.           So, Allowable bearing capacity = 100 kPa



Bearing capacity vs. bearing pressure

Bearing capacity

1.           Ultimate bearing capacity is determined using any formula = 600 kPa

2.           Safe Bearing Capacity = Ultimate / FS = 200 kPa

3.           Say footing size is 3 m x 3 m using safe bearing capacity and calculated settlement is 150 mm

4.           To limit the settlement within allowable limit (say 50 mm), footing size need to be increased. Say, 4 m x 4 m is ok at 100 kPa

5.           So, Allowable bearing capacity = 100 kPa


Bearing pressure

1.           Bearing pressure = pressure applied on soil at the bottom of footing = soil pressure

2.           Applied load divided by footing area

3.           Bearing pressure may be less, equal or more than Allowable bearing capacity

4.           Bearing pressure should be less than Allowable bearing capacity

 

 

General shear failure

·        When ultimate bearing pressure is reached, footing will undergo a very large settlement

·        Bulging at both side of footing

·        Slip surface extends upto ground level

·        Zone a is pushed down, zone b is pushed laterally and zone c is pushed upward



Local shear failure

·        When ultimate bearing pressure is reached, footing will undergo a very large settlement

·        Small Bulging at both side of footing

·        Slip surface does not extends upto ground level

·        Zone a is pushed down, zone b is pushed laterally and zone c is not developed


Punching shear failure

·        When ultimate bearing pressure is reached, footing will undergo a very large settlement

·        No bulging at both side of footing

·        Slip surface does not form

·        Zone a is pushed down, zone b is pushed down


General Bearing Capacity Equation

The gross ultimate bearing capacity of a footing can be determined by the equation below:


Bearing capacity equation for local shear failure

Use the same equation which is given for general bearing capacity, but modify c and φ

 

Effect of ground water table

Three cases

Case I: above footing

Case II: at footing level

Case II: below footing level

    


General Bearing Capacity Equation

The term B in above equation is the smallest dimension of the mat.

 The net ultimate capacity of a footing is

The factor of safety against bearing capacity failure of mats on sand is very large

Bearing Capacity Factors

 

Ø>0 For cohesive soil and undrained condition, Ø =0.01            

 

Bearing Capacity Factors

 

Bearing Capacity Factors

 

Shape Factors

 

Depth Factors

 

Inclination Factors

 

Safe bearing capacity = Ultimate / FS

< bearing pressure under mat [FS = 3]

 

Settlement must be calculated and compared with allowable limit

 

Ultimate Bearing Capacity Example (Clay)

 

Ultimate Bearing Capacity Example (Sand)

2
All documents of Footing Design
3
Bearing capacity calculation, Part-2
4
Bearing capacity calculation, Part-3
5
Bearing capacity calculation, Part-4
6
Bearing capacity calculation, Part-5
7
Bearing capacity calculation, Part-6
8
Bearing capacity calculation, Part-7

Short term and long term bearing capacity of Footing

1
Short term and long term bearing capacity, Part-1

Footing on Clay


Plate load test may mislead you 

Use of test results – which one?

UCS (Cu = Su = qu/2)

UU triaxial (Cu = Su = ?)

CU triaxial (C and phi)

CD triaxial (C and Phi)


Which condition properly represent

bearing capacity of footing of building?


·        UCS / UU triaxial (most conservative)

·        CU (most appropriate)

·        CD (long term capacity)


UCS or UU Triaxial Test


Consolidated Undrained Triaxial Test Result (CU Test)

NC Clay

Consolidated Drained Triaxial Test Result (CD Test)


OC Clay


Failure Envelope of Clay in Drained Triaxial Test


Peak – and residual- strength envelopes for clay


Effective Stress Friction Angle of Cohesive Soils


Plasticity index (%)

Variation of sin  with plasticity index (PI) for several normally

(Bjerrum and Simons, 1960; Kenney, 1959)


Important note on Effective Stress Friction Angle of Cohesive Soils


Phi (CU) = 0.66*phi (CD) (approx.)

From personal experience


Now you can explain: why some buildings did not fail even it was under designed


Loads are redistributed to adjacent footings if it is subjected excessive settlement

2
Short term and long term bearing capacity, Part-2
3
Short term and long term bearing capacity, Part-3
4
Short term and long term bearing capacity, Part-4

Footing design requirements according to BNBC 2017

1
Footing design requirements, Part-1

BNBC 2017 on Footing , PART 6, CHAPTER 3


DIVISION B : DESIGN OF FOUNDATIONS



ULTIMATE, SAFE AND ALLOWABLE BEARING CAPACITY OF THE SOIL


  1. Ultimate bearing capacity : Ultimate bearing capacity is the maximum pressure that a foundation soil can withstand without undergoing shear failure. Again the Ultimate Bearing Capacity of the soil is the max load which can be applied. It is also defined as the ultimate pressure per unit area of the foundation that can be supported by the soil in excess of the pressure caused by the surrounding soil at the foundation level.
  2. Safe bearing capacity : Safe bearing capacity is the safe extra load the foundation soil is subjected to in addition to initial overburden pressure. Again Safe bearing capacity is the maximum Pressure that a soil bears without shear failure.
  3. Allowable bearing pressure : Allowable bearing pressure is the maximum pressure where the foundation soil is subjected to considering both shear failure and settlement. Again Allowable bearing pressure is the net load intensity at which no failure occurs.



3.8.2 DIMENSION OF FOOTING


Dimension of Footings :

  1. Footings shall generally be proportioned from the allowable bearing pressure and stress limitations imposed by limiting settlement.
  2. The angle of spread of the load from the wall base to outer edge of the ground bearing shall not exceed the following:



3.8.2 Depth of footing


Dimension of Footings :

A footing shall be placed to depth so that:

                   I.           Adequate bearing capacity is achieved,

                II.           In case of clayey soil , shrinkage and swelling due to seasonal weather change is not significant,

             III.           It is below possible excavation close by, and

             IV.           It is at least 500 mm below natural

ground level unless rock or other

weather resistant material is at the surface.

So, Df > 1.5 m



3.8.3 Thickness of Footing


The minimum thickness for different types of footing for light structures, shall be as follows:


Type of Footing ------------------------------------Minimum Thickness ------------------------------------------------Remark

Masonry ---------------250 mm; twice the maximum projection from the face of the wall ------Greater of the two values shall be selected

Plain concrete----------------200 mm, or twice the maximum offset in a stepped footing-----------------------------------------------

Reinforced concrete---------------------------------150 mm,300 mm-----------------------------------Resting on soil,Resting on pile



3.8.6 Minimum Depth of Foundation


The minimum depth of foundation shall be :

       I.           For permanent structures 1.5 m for exterior footing in cohesive soils and 2 m in cohesionless soils.

    II.           For temporary structures the minimum depth of exterior footing shall be 400mm.



3.8.7 Scour


Footings supported on soil shall be embedded sufficiently below the maximum computed scour depth or protected with a scour countermeasure



3.8.8 Mass Movement of Ground in Unstable Areas


In certain areas mass movement of ground may occur from causes independent of the loads applied to the foundation. These include

§ Mining subsidence

§ Landslides on unstable slopes

§ Creep on clay slopes.




3.8.9 Foundation Excavation

1.     Foundation excavation below ground water table shall be made such that the hydraulic gradient at the bottom of the excavation is not increased to a magnitude that would case the foundation soils to loosen due to upward flow of water.

2.     Footing excavations shall be made such that hydraulic gradients and material removal do not adversely affect adjacent structures

3.     Seepage forces and gradients may be evaluated by standard flow net procedures.

4.     Dewatering or cutoff methods to control seepage shall be used when necessary.



3.8.10 Design Considerations for Raft foundation


For raft supports structure consisting of several parts with varying loads and height, it is advisable to provide separate joints between these parts. *****

§ Joints shall also be provided wherever there is a change in the direction of the raft.

§ The minimum depth of foundation shall generally be not less than 1.5 m in cohesive soil and 2 m in cohesionless soils.



Geotechnical Design of Shallow Foundation


3.9.1 General :

The location of the resultant pressure due to seismic and dynamic loads on the base of the footings should be maintained preferably within B/6 of the centre of the footing.



Design Load :

a)     Shallow foundation design considering bearing capacity due to shear strength shall consider the most unfavourable effect of the following combinations of loading:

·        D + L

·        D + L + E or W

·        0.9 D + Buoyancy Pressure


a)     Shallow foundation design considering settlement shall consider the most unfavourable effect of the following combinations of loading:


                                                       I.           SAND

·        D + L

·        D + L + E or W

 

                                                    II.           CLAY

·        D + 0.5 L



Bearing Capacity of Shallow Foundations :


Established bearing capacity equations shall be used for calculating bearing capacity. A factor of safety of between 2.0 to 3.0 shall be adopted to obtain allowable bearing pressure when dead load and normal live load is used.

1.     Allowable increase of bearing pressure due to wind and earthquake forces : The allowable bearing pressure of the soil determined in accordance with this Section may be increased by 33 percent when lateral forces due to wind or earthquake act simultaneously with gravity loads.

2.      Presumptive bearing capacity for preliminary design : For lightly loaded and small sized structures and for preliminary design of any structure, the presumptive bearing values (allowable) as given in next slide may be assumed for uniform soil in the absence of test results.


Soil Description = Safe Bearing Capacity, kPa

1.     Soft Rock or Shale = 440

2.     Gravel, sandy gravel, silty sandy gravel; very dense and offer high resistance to penetration during excavation (soil shall include the groups GW, GP, GM, GC) = 400

3.     Sand (other than fine sand), gravelly sand, silty sand; dry (soil shall include the groups SW, SP, SM, SC) = 200

4.     Fine sand; loose & dry (soil shall include the groups SW, SP) = 100

5.     Silt, clayey silt, clayey sand; dry lumps which can be easily crushed by finger (soil shall include the groups ML,, SC, & MH) = 150

6.     Clay, sandy clay; can be indented with strong thumb pressure (soil shall include the groups CL, & CH) = 150

7.     Soft clay; can be indented with modest thumb pressure (soil shall include the groups CL, & CH) = 100

8.     Very soft clay; can be penetrated several centimeters with thumb pressure (soil shall include the groups CL & CH) = 50

9.     Organic clay & Peat (soil shall include the groups OH, OL, Pt)=To be determined after investigation.

10. Fills=To be determined after investigation.


Two stories or less (Occupancy category A, B, C and D)


50% of these values shall be used where water table is above the base, or below it within a distance equal to the least dimension of foundation



Settlement of Shallow Foundation:

Foundations can settle in various ways and each affects the performance of the structure


a)     Total settlement : Total settlement (ձ) is the absolute vertical movement of the foundation from its as-constructed position to its loaded position.

b)     Secondary consolidation is due to particle reorientation, creep, and decomposition of organic materials.

c)     Secondary compression is always time-dependent and can be significant in highly plastic clays, organic soils, and sanitary landfills, but it is negligible in sands and gravels.



Differential settlement :

Differential settlement is the difference in total settlement between two foundations or two points in the same foundation. This kind of settlement can occur due to the following circumstances:


1.     Non-uniformity in subsoil.*****

2.     Non-uniform pressure distribution.*****

3.     Ground water condition during and after construction.

4.     Loading influence of adjacent structures.

5.     Uneven expansion and contraction due to moisture migration, uneven drying, wetting or softening.


Notes: The values given in the Table may be taken only as a guide and the permissible total settlement, differential settlement and tilt (angular distortion) in each case should be decided as per requirements of the designer.

L denotes the length of deflected part of wall/ raft or centre to centre distance between columns.

H denotes the height of wall from foundation footing.

* For intermediate ratios of L/H, the values can be interpolated



3.9.5 Liquefaction Potential


Soil liquefaction is a phenomenon in which a saturated soil deposit loses most, if not all, of its strength and stiffness due to the generation of excess pore water pressure during earthquake-induced ground shaking.


  1. Sandy and silty soils tend to liquefy; clay soils do not undergo liquefaction except the sensitive clays.
  2. Resistance to liquefaction of sandy soil depends on fines content. Higher the fines content lower is the liquefaction potential. ???
  3. As a rule of thumb, any soil that has a SPT value higher than 30 will not liquefy. ???



1.9.6.3 Raft foundation reactions :

For determining the distribution of contact pressure below a raft both analytical and numerical methods require values of the modulus of subgrade reaction (k) of the soil.

k=0.65×((E_s B^4)/EI)^(1⁄12) E_s/((1-μ^2 ) ) 1/B              

Where, 

E_s = Modulus of elasticity of soil

EI = Flexural rigidity of foundation

B = Width of foundation

μ = Poisson’s ratio of soil



Raft foundation reactions :

 For use in preliminary design, indicative values of the modulus of subgrade reaction (k) for cohesionless soils are given below :

Stiff,Very Stiff,Hard

The values apply to a square plate 300 mm x 300 mm. The above values are based on the assumption that the average loading intensity does not exceed half the ultimate bearing capacity



2
Footing design requirements, Part-2

Correlations among soil parameters

1
Correlations among soil parameters, Part-1

Correlations among Soil Parameters



Effective Stress Friction Angle of Granular Soils

·        The direct shear test yields a higher angle of friction compared with that obtained by the triaxial test


The failure envelope a for a given soil is actually curved. The Mohr-Coilomb failure criterion defined by Eq. (1.81) is only an approximation. Because of the curved nature of the failure envelope, a soil tested at hiaher normal stress will vield a lower value of φ’



Variation of friction angle of river sand with e

For a given value of e, the magnitude of φ' is about to 4 o to 5 o smaller when the confining pressure σ 3 ' is greater than about 70 kN/m2compared with that when σ 3' 70 kN/m2


Consolidated Undrained Triaxial Test Result (CU Test)


Consolidated Drained Triaxial Test Result (CD Test)


Failure Envelope of Clay in Drained Triaxial Test


Peak – and residual- strength envelopes for clay


Effective Stress Friction Angle of Cohesive Soils


Plasticity index (%)

Variation of sin  with plasticity index (PI) for several normally

(Bjerrum and Simons, 1960; Kenney, 1959)


Important note on Effective Stress Friction Angle of Cohesive Soils

The friction angle φ' decreases with the increase in plasticity index 

·        φ' = 38o  For PI = 10

·        φ' = 25o  For PI = 100


* The friction angle (φ') of normally consolidated saturated clays generally ranges from 5 to 20o



Correlations for Undrained Shear Strength, Cuu

Several empirical relationships can be observed between cu and the effiective observed pressure (σ o') in the field. Some of these relationships are summarized in Table 1. 13.

Empirical Equations Related to Cu and (σ o')

(c_u (vst))/φ' _0 = 0.11 + 0.00037 (PI)

 (PI) = plasticity index (%)

cu(VST) = Undrained Shear

Strength From Vane Shear Test


For normally consolidated clay

Skempton (1957)



Bjerrum and Simons (1960)


c_u/φ' _0 =0.45 (PI/100)0.5


For PI >50%


c_u/(φ' _0 )=0.118(LI)0.15


For LI= liquidity index > 0.5


Normally consolidated clay


Mesri (1989)


c_u/φ' _0  = 0.22


Jamiolkowski, et al. (1985)

c_u/φ'_0  = 0.23 ± 0.04


For lightly overconsolidated clays

After Stroud Correlations for N60 in Cohesive Soil

Approximate Correlatiov between CI, N60 and qu


Standard penetration

number, N60 in Consistency       CI           Unconfind compression

strength, qu (kN/m2)

<2          Very soft            <0.5      <25

2-8         Soft to medium 0.5-0.75               25-80

8-15      Stiff       0.75-1.0               80-150

15-30    Very stiff             1.0-1.5 150-400

>30        Hard     >1.5      >400



consistency index (CI)

CI=(LL-w)/(LL-PL)

Szechy and Vargi (1978)



Correction between N60 and Cu

Hara, et al. (1971) suggested the following correlation between the undrained

 shear strength of clay (Cu) & N60

Cu/Pa' = 029 N0.7260

Pa= atmospheric pressure

(= 100 kN/m2 = 2000 Ib/ ft2).



degree of sample disturbance

Area Ratio            AR(% ) (D^2-D^2)/D!^2 = (100)   

Where

AR = area ratio (retio of disturbed area to tatalarea soil)

D0 = outside diameter of the sampling tube

D1 = inside diameter of the sampling tube

Wher the ratio is 10% or less, the sample generally is considered to undisturbed. for a standard split-spoon sampler.

AR(% )=((50.8)^2 - (34.93)^2)/((34.93)^2 ) (100) = 111.5%    



Shelby Tube for Collecting Undisturbed Clay Sample


1.      The system is used to sample soils are particulary sensitive to sampling disturbance as it has a very low wall thikness-to sample area ratio.

2.      This sampler is usually only suitable for cohesive soils up to a fim-to-stiff consistency and free from large particles.

3.      It is not suitable for granular non-cohesive soils



Hammer efficiency and SPT Correction

Er(% ) (actual hammer energy to the samper)/(input energy) x (100)

Teoretical input energy= Wh  

Factors are: 

  1. Borehole diameter,
  2. Sampler type,
  3. Rod length
  4. Hammer type

(Skempton, 1986; Seed, et al., 1985).

W= weight of the hammer = 0.623 kN (140ib)

H= height of drop = 0.76m (30in)



Correction of SPT

Wh = (0.623)(0.76) = 0.474kN –m

In the field, the magnitube of E, can vary from 30to 90%.

The standard practice is to express the N- value to an average energy ratio of 60% (=N60)


N60 = N_ηHηBηSηR/60


Where

N60 = standard penetration number, corrected for field conditions

N = measured penetration number

ŋh = hummer efficiency (%)

ŋB = corrected for borehole diameter

ŋS = sampler corrected

ŋR = corrected for rod length



Correction for N60 in Granular Soil

In granular soils, the value of N is affected by the effective overburden pressure, σ o' For that reason, the value of N60 obtained from field exploration under different effective overburden pressure should be changed to correspond to a standard of σ o', that is,

(N1) 60 = CN N60


Where

(N1) 60 = value of N60 correspond to a standard of

σo' [100  200  )]

(CN) = Correction factor

N60 = value of N obtained from field exploration



Empirical Relations for CN  

Liao and Whitman’s relationship (1986):


pa = atmospheric pressure (= 100 kN/m2 = 2000 Ib/ ft2)

This formula can be used in any consistent unit

Empirical Relations for CN



Empirical Relations for CN

Peck et al.’ s relationship (1974):



SPT Hammer Efficiency

1.      Variation of ŋH


Country-----------------------Hammer type-----------------------Hammer release-----------------------ŋH (%)

Japan-------------------------Donut--------------------------------------Free fall------------------------------78

---------------------------------Donut----------------------------------Rope and pulley-----------------------67

United States---------------Safety ----------------------------------Rope and pulley-----------------------60

---------------------------------Donut----------------------------------Rope and pulley -----------------------45

Argentina--------------------Donut-----------------------------------Rope and pulley-----------------------45

China -------------------------Donut--------------------------------------Free fall-------------------------------60

---------------------------------Donut-----------------------------------Rope and pulley-----------------------50

Auto trip hammer efficiency = 80%



Correction for Borehole Diameter

2. Variation of ŋB

 

Diameter mm-----------ŋB

60-120---------------------1

150------------------------1.05

200--------------------1.15



Correction for Sampler Type

3. Variation of ŋS


Variable---------------------------------------ŋS

Standard sampler--------------------------1.0

With liner for dense sand and clay ---0.8

With liner for loose sand-----------------0.9



Correction for Rod Length

4. Variation of ŋR

Rood length m--------------------ŋR

>10----------------------------------1.0

6-10--------------------------------0.95

4-6---------------------------------0.85

0-4------------------------------------0.75



Correlation between Relative Density and N60

Kulhawy and Mayne (1990) modified an empirical relationship for relative

density that was given by Marcuson and Bieganousky (1977), which can be expressed as

Dr = 12.2 + 0.75[222 N60 + 2311 – 7110CR - 779 ((σ o')/Pa ) – 50cu2] 0.5

Where

Dr = relative densty

σ o' = effective overburden pressure

Cu = Uniformity coefficient of sand

OCR = (preconsolidation pressure,σ c' )/(effective overburden pressure,σ c')

Pa = atmospheric pressure



Correlation between Relative Density and N60


Standard penetration number, (N1) 60---------------Approximate relative density Dr (%)

0-5------------------------------------------------------------------------------0-5

5-10----------------------------------------------------------------------------5-30

10-30---------------------------------------------------------------------------30-60

30-50---------------------------------------------------------------------------60-95



Correlation between Angle of Friction φ' and N60

1. Peck, Hanson, and Thornburn (1974)give a Correlation between N60 and φ' in a graphical form, whoch can be Approximate as (Wolff,1989)

φ' (deg) = 127.1 + 0.3 N60 – 0.00054 [N60]

2. Schmertmann (1975) provided the Correlation between N60, σ 0', and φ' Mathematically, the Correlation can be Approximate as (Kulhawy and Mayne.1990)

3. Hatanaka (1996) provided a simple Correlation between φ' and (N1) 60 that can be expressed as

 φ' = √(20(N1)60+20)


Correlation between Modulus of Elasticity (Es) and N60


A first order estimation for Es was given by Kulhawy and Mayne (1990)


Es/Pa = aN60



Undrained E for Clay



Compression Index (Cc)

The compression index Cc, is the slope of the straight-line portion (the latter part) of the loading curve, or


Skempton (1944) gave an empirical correlation for the compression index in which

Cc = 0.009(LL-10)



Rendon-Herrero (1983):

Cc = 0.141 Gs1.2 ((1+C0)/GS )2.38

Nagaraj and Murty (1985): Cc = 0.2343[ (LL(%))/100] Gs   

Park and Koumoto (2004): Cc = n0/(371.747-4.275n0)   

Where n0= in situ porosity of soil .

Wroth and Word (1978): Cc =0.5GS ((PI(%))/100)   

Typical value of  Gs = 2.7



Kulhawy and Mayne, 1990


Cc = (PI(%))/74   

 

2
Correlations among soil parameters, Part-2

Interaction of Nearby Footings under Building

1
Interaction of Nearby Footings under Building, Part-1

Effect of Interaction of Nearby Footings on Settlement of Foundation under Building



Which option is correct?

1.Settlement of footing under building

= Settlement of individual footing.

2.Settlement of footing under building

≠ Settlement of individual footing.



Engineering Properties of Subsoil

Constitutive model-Mohr-Coulomb

Saturated Unit Weight=18 kN/m3

Initial void ratio=0.800

Modulus of Elasticity=12 – 60 MPa

Poisson’s ratio=0.3

Cohesion=5 kN/m2

Drained Angle of Friction=35 degree


Vertical Settlement of Individual footing model at isolated location


Vertical settlement of Individual footing model under building for 5x5 matrix


Effect of Footing Interaction Parameter


Effect of Footing Interaction Parameter


Effect of Footing Interaction Parameter


Effect of modulus of elasticity and building size


Effect of distance from center of building


Effect of pressure on footing



Conclusions

The following conclusions may be drawn from the results of this parametric study.

1.     Settlement of individual footings under building = 1.5 to 5 times the settlement of individual footing at isolated location.

2.     Settlement individual footings under a building vary with the distance from center of the building. Maximum settlement was found at center of building.

3.     Scenter/Sind is highly sensitive with Footing Interaction Parameter (B/L) and Building size. Scenter/Sind increases with the increase of B/L and building size.

4.     Scenter/Sind α Footing Interaction Parameter.

5.     Scenter/Sind α Building Size For increased pressure, settlement increases. However, Scenter/Sind decreases with the increase of applied pressure on footing.

6.     Scenter/Sind α (1/Applied Pressure)

7.     Scenter/Sind is not sensitive with Modulus of Elasticity. However, settlement increases with the decrease of Modulus of Elasticity. 

2
Interaction of Nearby Footings under Building, Part-2

Bearing Capacity of Footing on Sand using SPT-N Value

1
Bearing Capacity of Footing on Sand, Part-1

Bearing Capacity of Footing on Sand using SPT-N Value




Allowable Bearing Capacity of Granular Soil

•     Water table

•     Foundation width, B (Assume)

•     SPT-N (N60) beneath B from foundation bottom

•     Df= foundation depth

•     Correction factor for overburden pressure (CN)



Allowable bearing capacity from graph (example)

D/B= 10/8=1.25>1.0

So, select graph (a)

Effective overburden pressure = s’= g*h= 120*18=2160 psf=100 kPa

CN=1.0

Cw= 1.0 ( GWT = below the (Df+B))

qall= 100 kPa= 100*0.021 ksf =2.1 ksf

Settlement is 25 mm



Thumb Rule

qall=11N (kPa)= 11*9=99 kPa

For settlement = 25 mm

Allowable Bearing Capacity of Footing at Limiting Settlement using SPT-N value

Bearing capacity by Meyerhof



Allowable Bearing Capacity of Footing at Limiting Settlement Sand


The net allowable bearing capacity for mats constructed over granular soil deposits can be adequately determined from SPT value

qnet= N60/0.08 ((B+0.3)/B)2 Fd (Se/25mm)


N60 = Standard Penetration Resistance

B = Lest dimension of Mat is not to be large

Fb = depth factor = 1+0.33Df/B<1.33

Se = allowable settlement (mm)



Allowable bearing capacity of shallow foundation on Sand by Meyerholf


If allowable settlement is more than 25mm

Allowable settlement = 50 mm

qall= 11N*50/25= 22N

    =22*9=200 kPa

    = 200*0.02

    = 4.0 ksf


Settlement

•     Method of Burland and Burbidge (1985)

•     Empirical expression

•     Normally consolidated course grained soil

S = drained settlement (mm)

N60= average SPT-value within B0.75 beneath for 60% energy

B= width of foundation (m)

q= average pressure applied to the ground by the foundation (kPa)

2
Bearing Capacity of Footing on Sand, Part-2

Settlement of Foundation on Sand

1
Settlement of Foundation on Sand, Part-1

Settlement of Foundation on Sand





Total settlement

•     The settlement of foundations may be regarded as consisting of three separate components of settlement

d= di + dc + ds

d= Total settlement

di = Immediate settlement

dc= consolidation Settlement

ds= secondary settlement



Immediate settlement

Resulting from the constant volume distortion of the loaded soil mass



Consolidation settlement

Resulting from the time dependent flow of water from the loaded area under the influence of the load generated excess pore pressure which itself dissipated by the flow


Secondary settlement / Creep

time dependent but may occur at essentially constant effective stress for longer time



Elastic theory in soil mechanics

Elastic soil parameters

•      Young’s Modulus, E

•      Poison’s ratio, n

As pointed out by Davis and Poulos (1968), the assumption of elastic soil parameters does not imply that real soil behaves as an ideal elastic solid.

·        Elastic-type behaviour may be simulated at small strains under loading conditions

·        Which ensure a high factor of safety against failure



Elastic theory in soil mechanics

The elastic soil constants must be experimentally determined under conditions which simulate the range of stresses

Distributions of stress and displacement in an elastic solid caused by a distributed load are

based on integrations of the effect of a vertical point load



Elastic Pressure Bulb (TENG, 1962)

•     Elastic stress distributions

•     useful qualitative conceptual aid



Elastic settlements

•      As pointed out by Davis and Poulos (1968), in a layered soil the total final settlement may be obtained by summation of the vertical strains in each layer

•      All are increment of stress



Determination of increase in vertical stress under the centre of uniformly loaded flexible footings, after Janbu, Bjerrum and Kjaernslif (1956)



Undrained or immediate settlements of clay

If a saturated clay layer is rapidly loaded locally, the low permeability of the clay retards drainage of water out of the pores and the clay deforms in the undrained or constant volume mode

 Janbu, Bjerrum and Kjaernsli (1956)



Worked out Example-01 (immediate settlement of footing on clay)

•            Square footing, 4mx4m

•            Uniform bearing pressure, q= 100 kN/m2

•            Find the elastic settlement



Modulus of Elasticity of Soil (Es) according to AASHTO


Estimating (Es) from SPT N Value

Soil Type ----------------------------------------------------------------Es (ksi)

Silts, Sandy silts, slightly cohesive mixtures -----------------0.056 N160

Clean fine to medium sands and slightly salty sands -----0.097 N160

Coarse sands and sands with little gravel--------------------0.139 N160

sandy gravel and gravely-----------------------------------------0.167 N160


 Estimating (Es) from qc (static cone resistance )

Sandy soil-------------------------------------------------------------0.028qc



Worked out Example (Elastic Settlement)


q (∶=) 100 kN/( m^(2 ) )

E1 ∶= 10 MN/m^(2 )     I1 ∶= 10m

E2 ∶= 12 MN/m^(2 )     I2 ∶= 10m

E3 ∶= 15 MN/m^(2 )     I3 ∶= 10m

B (∶=) 4 m                     H (∶=) I1 + I2 + I3

(D∶=) 3 m                    L(∶=) 4

(D/B     ∶=) 0.75 m           (H/B ∶=) 7.5    (L/B ∶=) 1

 (I∶=)  μ0 . μ1

 μ0 ∶= 0.75       μ1 ∶= 0.70

(I∶=)  μ0 . μ1


Eavg ∶= (E_(1.) l_1+ E_(2.) l_2+ E_(3.) l_3)/(l_1+l_2+l_3 )    

S1 ∶= (q . B . I)/Eavg=17mm

q (∶=) 100 kN/( m^(2 ) )

E1 ∶= 10 MN/m^(2 )     I1 ∶= 10m   

E2 ∶= 12 MN/m^(2 )     I2 ∶= 10m   

E3 ∶= 15 MN/m^(2 )     I3 ∶= 10m   


B (∶=) 4 m                     H (∶=) I1 + I2 + I3

(D∶=) 3 m                    L(∶=) 4

(D/B     ∶=) 0.75 m           (H/B ∶=) 7.5    □(L/B ∶=) 1      

(I∶=)  μ0 . μ1

μ0 ∶= 0.75       μ1 ∶= 0.70

(I∶=)  μ0 . μ1

Eavg ∶= (E_(1.) l_1+ E_(2.) l_2+ E_(3.) l_3)/(l_1+l_2+l_3 )    




Consolidation of sand

•     Permeability of sand is high

•     Drainage occurs almost instantaneously. The settlement is IMMEDIATE

•     Elastic and consolidation processes cannot be isolated

•     Primary Consolidation is incorporated in the elastic parameters

•     Coarse-grained soils DO NOT undergo consolidation settlement due to relatively high hydraulic conductivity compared to clayey soils

•     Instead, coarse-grained soils undergo IMMEDIATE settlement



Bearing Capacity considering Settlement

Bearing Pressure, qo= 200 kPa


Top layer is a OC clay,

Preconsolidation pressure = 300 kPa

assume Cc=0.15; Cs=0.03

Layer depth

I1 ∶= 3.4 . m    Clay

I2 ∶= 3.3 . m  Sand

I3 ∶= 7 . m       Sand

I4 ∶= 13.8 . m Sand

H ∶= I1 + I2 + I3 + I4 = 27.5m


Ref: Bowels_ Foundation Analysis And Design (Fifth Ed.)


Values of Iand Icompute the Steinbrenner influence factor I1 for use in Eq. (5-16a) for several  N= H/B’ and M= L/B ratios



Settlement is calculated only at corner Point of a foundation


Calculation of elastic settlement


Calculation of consolidation settlement


Calculation of allowable bearing capacity and subgrade modulus


Effect of size ON foundation settlement

Variation of Settlement due to variation of size of foundation


Calculation of consolidation settlement for Clay


Variation of Settlement due to variation of size of foundation


Variation of Settlement due to variation of size of mat


Calculation of Elastic settlement for Sand


settlement calculation for different size of foundation

2
Settlement of Foundation on Sand, Part-2
3
Settlement of Foundation on Sand, Part-3

Structural Design of Footing

1
Structural Design of Footing, Part-1

Structural Design of Footing





Critical section for moment


Distribution of Flexural Reinforcement


Distribution of Flexural Reinforcement


SHEAR IN FOOTINGS

Punching Shear

Beam Shear



One-Way Shear/ Beam Shear


Vu ≤ ∅ Vn

≤∅(2√(fc) bw d)



Two way shear/ Punching shear

Vu ≤ =minimum

(2+( 4)/( β_c ) )=√(f_c) b d

((asd)/( b) +2) √(fc) bd   

4 √(fc) bd


βc = ratio of long side to short side of the column, concentrated load or reaction area

αs = 40 for interior columns

= 30 for edge columns

= 20 for corner columns

bo = perimeter of critical section



Area of Footing

Determine the base area Af required for a square spread footing with the following design conditions:

Service dead load = 350 kips

Service live load = 275 kips

Service surcharge = 100 psf


Assume average weight of soil and concrete above footing base= 130 pcf

Permissible soil pressure = 4.5 ksf


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

Total weight of surcharge = (0.130 × 5) + 0.100 = 0.750 ksf

Net permissible soil pressure = 4.5 - 0.75 = 3.75 ksf

Required base area of footing:

Af = (350 + 275)/ 3.75

= 167 ft2

Use a 13 × 13 ft square footing (Af = 169 ft2)


Factored loads and soil reaction


To proportion the footing for strength (thickness and required reinforcement)

Pu = 1.4 (350) + 1.7 (275) = 957.5 kips

qs =Pu/Af= 957.5/169= 5.70 ksf



Thickness of Footing

fc′ = 3000 psi

Pu = 957.5 kips

qs = 5.70 ksf



1. Beam Shear / One way Shear

Vn = qs x tributary area

Bw 13 ft = 156 in.

Assumed footing thickness,

T = 33 in.

Avg. effective thickness,

d = 28 in.

tributary area = 13 (6.0 - 2.33) = 47.7 ft2  

Vn = 5.7 x 47.7 = 272 kips

  Vn =    

= 0.85  x 156 x28/1000

= 407 kips > Vn O.K.



2. Punching shear/ Two way Shear

Vn = qs x tributary area

tributary area =[(13x13)- ( (30+28)(12+28))/144 ]=152.9 ft2

Vn = 5.70 x 152.9 = 872 kips

 (v)/(√(fc) bd)=minimum

2 +( 4)/(βc )=3.6 (governs)

( asd)/( b0)+2=7.7

4




2. Punching shear/ Two way Shear

b0 = 2 (30 + 28) + 2 (12 + 28) = 96 in.

βc = ( 30)/12 = 2.5

( b_0 )/12d = ( 196)/28 = 7

as = 40 for interior column


2. Punching shear/ Two way Shear

∅Vc = 0.85x 3.6√3000 x 196 x28/1000

= 920 kips > 872 kips O.K.




Footing Reinforcement

fc’ = 3000 psi

fy = 60,000 psi

Pu = 957.5 kips

qs = 5.70 ksf


1. Critical section for moment is at the face of column

Mu = 5.70 × 13 × 62/2 = 1334 ft.-kips

Mu = 5.70 × 62/2 = 102.6 ft.-kips/ft.


2. Compute As (in2/ft.) required


Footing Reinforcement

As = ( M )/(φƒy(d-( a)/2))= ( 102.6*12 )/(0.9*60* (28-( 3)/2))=0.86 in2

 

Mu = 5.70 × 62/2 = 102.6 ft.-kips/ft.


3. Check for compression depth (a)

as = ( A_s   )/(0.85*fc)= ( 0.86*60 )/(0.85*3*12)=1.7 

As = ( M )/(φƒy(d-( a)/2))= ( 102.6*12 )/(0.9*60* (28-( 1.7)/2))=0.84 in2


4. Check minimum reinforcement

rmin= 0.0018 for Grade 60 rebar

= 0.0018*12*33=0.72 in2/ft. < As

5. Spacing of longitudinal rebar

s= (0.5/0.84)*12= f20 @ 7” c/c


As= 0.84 in2/ft.

As,min= 0.72 in2/ft.

s=f20 @ 7” c/c


( Reinforcing in band width )/(Total Reinforcing in short direction )

= ( 2 )/(β +1)= γ                                                ACI: Eqn. 15-1


Band width for steel in the short direction for

rectangular isolated footings.


ACI 318-08 / BNBC 2017

Column = 18”x18”

DL= 185 kip

LL = 150 kip

fy= 60,000 psi

f’c= 4000 psi

qa= 4000 psf

Df= 5 ft.

Pu= 1.2*DL+1.6*LL

f ( torsion and shear) = 0.75



Footing Area and Dimension


1. Assume thickness T= 24” and d= 19.5”

qe = 4000psf – (( 24 in)/(12 in/ft))(150 pcf)- ((36 in)/(12 in/ft)) ( 100 pcf)= 3400 psf

Area required = (185 k+150 k )/(3.4 ksf)=98.5 ft^2

qu ((1.2)(185 k)+ (1.6)(150 k))/〖98.0 ft〗^2 =4.71 ksf

Use 7 ft.× 14 ft.= 98.0 ft2


Thickness of Rectangular Footing


2. Checking Thickness for One-Way Shear

b = 7 ft

Vu1 (7.0 ft) ( 4.625 ft) (4.70 ksf) = 152.49 k

D = ( 152,490 lb )/((0.75)(1.0)(2√(4000 psi))(84 in.))=19.14 in.,h=d+4.5 in.=23.64 in.

Use T= 24”


3. Checking Thickness for Two-Way Shear


18”+19.5”=37.5”=3.125ft.



3. Checking Thickness for Two-Way Shear

b0 = (4) (37.5 in.) = 150in

Vu2 = [98.0 ft^2-(3.125 ft^2 )](4.71 ksf)=415.58 k

d = (415.580 ld )/((0.75)(1.0)(4√(4000 psi))(150 in.))=14.60 in. < 19.5 in

d = (415.580 ld )/((0.75)(( 40 in x 19.5 in)/(150 in.) + 2)(√(4000 psi))(150 in.)) = 8.11 in < 19.5 in

Does not govern



Rebar of Rectangular Footing


4. Design of Longitudinal steel

Lever arm = ( 14 ft )/2- ( 9 in )/(12in/ft )=6.25 ft

Mu = (6.25 ft) (7.0 ft) (4.71 ksf) (( 6.25 ft)/2) = 643.9 ft-k 

Mu = 6.25 × 4.71 x 6.25/2 = 92 ft.-kips/ft.

Compute As (in2/ft.) required

As = ( M )/(φƒy(d-( a)/2))= ( 92*12 )/(0.9*60* (19.5-( 4)/2))=1.17 in2


Mu = 92 ft.-kips/ft.

Check for compression depth (a)

a = ( A_s  f_y )/(0.85*f_c^' )= ( 0.23*60 )/(0.85*4*12)=0.4

 As = ( M )/(φƒy(d-( a)/2))= ( 92*12 )/(0.9*60* (19.5-( 0.4)/2))=0.2 in2


Check minimum reinforcement

rmin= 0.0018 for Grade 60 rebar

= 0.0018*12*24=0.52 in2/ft. > As

rmin= 0.0033

= 0.0033*12*19.5=0.77 in2/ft. > As

Spacing

s= (0.32/0.52)*12= f16 @ 7” c/c

Total bars = 14*12/7+1=25


Total bars = 14*12/7+1=25


( Reinforcing in band width )/(Total Reinforcing in short direction )= ( 2 )/(2+1)= ( 2 )/3   


2/3*25=16 nos. shall be placed in band width

Temperature and shrinkage rebar governed, so this type distribution is not required

However, it is wise to provide flexure minimum in the middle band



Combined Footing


·        Footings support more than one column

·        Necessary when isolated individual footings would run into each other

·        Where a column is close to a property line




Combined Footing Example


qa = 5 ksf

f’c = 3 ksi

fy = 60 ksi

Df = 6 ft



Solution

Assume 27-in. Footing (d=22.5 in.)

qe = 5000 psf- (( 27 in.)/2) (150 pcf) – (( 45 in )/(12 in/ft)) (100 pcf) = 4287 psf


Area required = ((120 k+100 k)+ (200 k+150 k) )/(4287 ksf )=132.96 ft2


Locate Center of Gravity of Column Service Loads

X from c.g. of left column = ((200 k+150 k)+ (12ft) )/((120 k+100 k)+ (200 k+150 k))= 7.37 ft

Distance from property line to c.g. = 0.75 ft + 7.37 ft = 8.12 ft

Length of fooing = (2 x 8.12 ft) = 16.24 ft, 16 ft 3 in.

Required footing width =  ( Area required )/(length )= ( 132.96 ft^2)/(16.25 ft)=8.18 ft


1.Find cg of two column loads

2.Determine length of footing so that cg of footing and load are at approximately same location

3.Determine width of footing for required area


Use 16-ft 3-in. x 8-ft-3-in. footing (A = 134 ft2).


qu ((1.2)(320 k) +(1.6) (250 k ))/(134 ft^2 ) = 5085 ksf


Bearing pressure applied on the footing by soil


Shear and moment diagrams for combined footing


 

Depth Required for One-Way Shear



The largest shear force is 271.1 k at the left face of the right column. At a distance d to the left of this location, the value of shear is


Vu1 271.1 k – 48.26 klf (( 22.5 in )/(12 in/ft)) = 180.61 k


d =   ( v_u1)/(∅2x√(f_c^' ) b)= (415.580 ld )/(0.75 (2) (1) √3000 psi (8.25 in)(12 in/ft.))= 22.2 in < 22.5 in.


Depth Required for Two-Way Shear

Vu2 at right column = 480 k – ((42.5 in)/(12.in/ft))^2 = 406.6 k


d = (406,600 ld )/((0.75) [(4) (10) √3000 psi] (4 x 42.5 in))

= 14.56 in. < 22.5 in. ok


Vu2 at leftt column = 304 k – (( 29.25 in.x 40.5 in.)/(144 in^2/ft^2 ))  = 255.9 k


d = (406,600 ld )/((0.75) [(4) (1.0) √3000 psi] (2 x 29.25 in +40.5 in.))

= 15.73 in. < 22.5 in. ok


Design of Longitudinal Steel


Mu = −729.5 ft-k


As = ( M )/(φƒy(d-( a)/2))= ( 729.5*12 )/(0.9*60* (22.5 - ( 3)/2))=7.72 in2


a = ( A_s  f_y )/(0.85*f_c^' )= (7.72 * 60 )/(0.85 * 3 *8.25*12)=2

As = ( M )/(φƒy(d-( a)/2))= ( 729.5*12 )/(0.9*60* (22.5 - ( 2)/2))=7.5 in2


Design of Longitudinal Steel

 

As,min= 0.0033*b*d


As,min= 0.0033*8.25*12*22.5=7.35 in2


Design of Short-Span Steel Under Interior Column


Assuming steel spread ver width = column width + (2) (( d)/2)   


= 20in. + (2) (( 25.5 in )/2) = 42.5 in.


Design of Short-Span Steel Under Interior Column



8 k/f ((3.29 ft )/2) = 314.9 ft-k


Soil stress used in determining short span steel


Design of Short-Span Steel Under Interior Column


As = ( M )/(φƒy(d-( a)/2))= ( 314.9 * 12 )/(0.9*60* (22.5 - ( 2)/2))=3.25 in2



FEM Modeling of Combined Footing

Combined footing may be easily designed by FEM modeling in ETABS, SAFE or any other software.

  1. Calculate applied pressure (p)
  2. Calculate settlement (s)
  3. Calculate subgrade modulus (p/s)
  4. Determine thickness of footing (beam shear may govern)
  5. Model the footing, analyse and design



Alternative concept of combined footing


1.           Find cg of two column loads

2.           Determine length of footing so that cg of footing and load are at approximately same location

3.           Determine width of footing for required area


1.           If pf is the factored contact pressure of footing

2.           Upward line load below T-beam = pf x footing width

3.           Upward pressure below flange of T-beam = pf

2
Structural Design of Footing, Part-2
3
Structural Design of Footing, Part-3
4
Structural Design of Footing, Part-4
5
Structural Design of Footing, Part-5
6
Structural Design of Footing, Part-6
7
Structural Design of Footing, Part-7
8
Structural Design of Footing, Part-8
9
Quiz on Footing Design and Construction
12 questions
4.7
4.7 out of 5
3 Ratings

Detailed Rating

Stars 5
2
Stars 4
1
Stars 3
0
Stars 2
0
Stars 1
0

{{ review.user }}

{{ review.time }}
 

Show more
Please, login to leave a review
Add to Wishlist
Enrolled: 151 students
Duration: 15 hours
Lectures: 31
Video: 10 hours
Footing Design and Construction
Price:
৳3,000