1 Reinforced Concrete Design II Lecture 13 Dr. Nader Okasha

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Reinforced Concrete Design II

Lecture 13

Dr. Nader Okasha

Footing Design

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Footing

Introduction

Footings are structural elements used to support columns and walls and transmit their

loads to the underlying soil without exceeding its safe bearing capacity below the

structure.

Column

Beam

Loads

Footing

Soil

M

P

L

B

P

L

B

3

The design of footings calls for the combined efforts of geotechnical and structural

engineers.

The geotechnical engineer, on one hand, conducts the site investigation and on the light

of his findings, recommends the most suitable type of foundation and the allowable

bearing capacity of the soil at the suggested foundation level.

The structural engineer, on the other hand, determines the concrete dimensions and

reinforcement details of the approved foundation

Footing

Introduction

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Isolated Footings

Isolated or single footings are used to support single columns. This is one of the most

economical types of footings and is used when columns are spaced at relatively long

distances.

P

L

B C2

C1

P kN

Types of Footing

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Types of FootingWall Footings

Wall footing are used to support structural walls that carry loads for other floors or to

support nonstructural walls.

Wall

Footing

Main reinft.

Secondary reinft

W kN/mW kN/m

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Combined Footings

Combined footings are used when two columns are so close that single footings cannot be used. Or, when one column is located at or near a property line. In such a case, the load on the footing will be eccentric and hence this will result in uneven distribution of load to the supporting soil.

P2P1

P1 kN

P2 kN

C2

C1

C2

C1

L

B

L2L1 L2

Types of Footing

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Combined Footings

The shape of combined footing in plan shall be such that the centroid of the foundation plan coincides with the centroid of the loads in the two columns. Combined footings are either rectangular or trapezoidal. Rectangular footings are favored due to their simplicity in terms of design and construction. However, rectangular footings are not always practicable because of the limitations that may be imposed on its longitudinalprojections beyond the two columns or the large difference that may exist between the magnitudes of the two column loads. Under these conditions, the provision of a trapezoidal footing is more economical.

Types of Footing

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Continuous Footings

Continuous footings support a row of three or more columns

P1

P1 kN

L

B

P2 kN

P3 kN

P4 kNP2 P3 P4

Types of Footing

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Strap (Cantilever ) footings

Strap footings consists of two separate footings, one under each column, connected together by a beam called “strap beam”. The purpose of the strap beam is to prevent overturning of the eccentrically loaded footing. It is also used when the distance between this column and the nearest internal column is long that a combined footing will be too narrow.

P2P1

P1 kN

C2

C1

C2

C1

B1

P2 kN

B2

L1 L2

Strap Beam

prop

erty

line

Types of Footing

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Mat (Raft) Footings

Mat Footings consists of one footing usually placed under the entire building area. They

are used when soil bearing capacity is low, column loads are heavy and differential

settlement for single footings are very large or must be reduced.

L

B

Types of Footing

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Pile caps

Pile caps are thick slabs used to tie a group of piles together to support and transmit

column loads to the piles.

P

L

B

Types of Footing

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Distribution of Soil Pressure

The distribution of soil pressure under a footing is a function of the type of soil, the

relative rigidity of the soil and the footing, and the depth of foundation at level of

contact between footing and soil

For design purposes, it is common to assume the soil pressures are linearly distributed.

The pressure distribution will be uniform if the centroid of the footing coincides with

the resultant of the applied loads

P

L

P

L

P

L

Footing on sand Footing on clay Equivalent uniform distribution

Centroidal axis

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Footing

Pressure Distribution Below Footings

The maximum intensity of loading at the base of a foundation which causes shear

failure of soil is called ultimate bearing capacity of soil, denoted by qu.

The allowable bearing capacity of soil is obtained by dividing the ultimate bearing

capacity of soil by a factor of safety on the order of 2.50 to 3.0.

The allowable soil pressure for soil may be either gross or net pressure permitted on the

soil directly under the base of the footing.

The gross pressure represents the total stress

in the soil created by all the loads above the

base of the footing.

a net soil pressure is used instead of the gross pressure value

P

Dfh

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Footing

Concentrically loaded Footings

If the resultant of the loads acting at the base of the footing coincides with the centroid

of the footing area, the footing is concentrically loaded and a uniform distribution of

soil pressure is assumed in design, as shown in the figure

Centroidal axis

P

L

P/A

B

L

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Footing

Eccentrically Loaded Footings

Footings are often designed for both axial load and moment. Moment may be caused by

lateral forces due to wind or earthquake, and by lateral soil pressures.

Footing is eccentrically loaded if the supported column is not concentric with the

footing area or if the column transmits at its juncture with the footing not only a vertical

load but also a bending moment.

Centroidal axis

P

L

P/A

Pey/I

y

eM

P

L

P/A

My/I

y

Centroidal axis

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Footing

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Footing

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Footing

3

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Footing

In this case, compressive stresses develop over the entire base of thefooting

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Footing

Large eccentricities cause tensile stresses on part of the base area of thefooting. With the dimensions of the footing established and the eccentricity ofthe vertical load known, the distance between the resultant of the appliedload P and the outside edge a can be established. The length of base on which the triangular distribution of soil pressure acts is equal to 3a, where a = L / 2 − e. Equating the resultant of the soil pressure to the applied forces gives

Eccentrically Loaded FootingDesign

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Design Procedure

1.0 1.0

Check service stresses to ensure pressure is all compressive under the footing

If tension stresses develop, resize the footing

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Design Procedure

The critical section for punching shear is located at distance d / 2 from column faces and usually takes the shape of the column.

Calculate Vu using the volume under the trapezoidal shaped stress distribution.

1.2 1.6

= 0.75

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Design Procedure

The critical section for punching shear is located at distance d /2 from column faces and usually takes the shape of the column.

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Design Procedure

= 1.0 for normal weight concrete

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Design Procedure

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Design Procedure

Calculate Mu using the volume under the trapezoidal shaped stress distribution.

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Design Procedure

According to ACI Code 15.4.3, for square footings, the reinforcement is identical in both directions. For rectangular footings, the reinforcement in the long direction is uniformly distributed while the reinforcement in the short direction is concentrated in a band centered on centerline of column and with a width equals to the short dimension of the footing.

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Example 1

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Example 1

In order to have uniform soil pressure under the footing, the footing is to be positioned in such a way to balance the given moment through shifting thecentroid of the footing 0.25 m away from the centroid of the column

Continue the design as a concentrically loaded footing supporting only the axial loads transmitted by the column

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Example 2

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Example 2

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Example 2

Pu = 1.2PD + 1.6PL = 69 tons

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Example 2

Should use as 0.75

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Example 2

Should use as 0.75

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Example 2

Should use as 0.75


Example 2

5

2

5

2

0.85 2 101 1

0.85

0.85 250 2 10 0.871 1 0.00003

4200 0.85 0.9 250 400 (40.9)

c u

y c w

f M

f f b d

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Example 2

Combined FootingDesign

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Combined Footings

Design Procedure

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Combined Footings

Design Procedure

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Combined Footings

ExampleDesign an appropriate footing/footings to support two columns A and B spaced at distance 2.1 m center-to-center. Column A is 20 cm × 30 cm and carries a dead load of 20 tons and a live load of 10 tons. Column B is 20 cm × 40 cm in cross section but carries a dead load of 30 tons and a live load of 15 tons. Width of footing is not to exceed 1.0 m, and there is no property line restriction.

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Combined Footings

Example

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Combined Footings

Example

2.1 m

Pa Pb

x1

R

x2l1 l2

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Combined Footings

Example

Should use DL

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Combined Footings

Example

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Combined Footings

Example

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Combined Footings

Example

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Combined Footings

Example

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Combined Footings

Example

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Combined Footings

Example

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1 Reinforced Concrete Design II Lecture 13 Dr. Nader Okasha