INTRODUCTION 1 INTRODUCTION Footings are structural members used to support columns and walls and transmit their loads to the underlying soils Reinforced concrete is a material admirably suited for ID: 541035 Download Presentation

Download Presentation - The PPT/PDF document "FOOTINGS" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.

152 views

155 views

132 views

## Presentation on theme: "FOOTINGS"— Presentation transcript

Slide1

FOOTINGSINTRODUCTION

1Slide2

INTRODUCTION Footings are structural members used to support columns and walls and transmit

their loads

to the underlying soils. Reinforced concrete is a material admirably suited for

footings and is used as such for both reinforced concrete and structural steel buildings, bridges, towers, and other structures.

The permissible pressure on a soil beneath a footing is normally a few tons per square foot. The compressive stresses in the walls and columns of an ordinary structure may run as high as a few hundred tons per square foot. It is therefore necessary to spread these loads over sufficient soil areas to permit the soil to support the loads safely.

Not only is it desired to transfer the superstructure loads to the soil beneath in a manner that will prevent excessive or uneven settlements and rotations, but it is also necessary to provide sufficient resistance to sliding and overturning.

2Slide3

INTRODUCTION To accomplish these objectives, it is necessary to transmit

the supported loads to

a soil

of sufficient strength and then to spread them out over an area such that the unit pressure is within a reasonable range. If it is not possible to dig a short distance and find a satisfactory soil, it will be necessary to use piles or caissons to do the job. These latter subjects

are not considered within the scope of this text. The closer a foundation is to the ground surface, the more economical it will be to construct. There are two reasons, however, that may keep the designer from using very shallow foundations. First, it is necessary to locate the bottom of a footing below the ground freezing level to avoid vertical movement or heaving of the footing as the soil freezes and expands in volume. This depth varies from about 3 to 6

feet. Second, it is necessary to excavate a sufficient distance so that a satisfactory bearing material is reached, and this distance may on occasion be quite a few feet.3Slide4

TYPES OF FOOTINGS Among the several types of reinforced concrete footings in common use are the wall, isolated, combined

, raft, and pile cap types. These are briefly introduced in this section;

the remainder

of the chapter is used to provide more detailed information about the simpler types of this group.1. A

wall footing is simply an enlargement of the bottom of a wall that will sufficiently distribute the load to the foundation soil. Wall footings are normally used around the perimeter of a building and perhaps for some of the interior walls.

2. An isolated or single-column footing is used to support the load of a single column. These are the most commonly used footings, particularly where the loads are

relatively

light and the columns are not closely spaced.

4Slide5

TYPES OF FOOTINGS

5Slide6

TYPES OF FOOTINGS3. Combined footings

are used to support two or more common

loads. A combined footing might be economical where two or more heavily loaded columns are so spaced that normally designed single-column footings would run into each other

. Single-column footings are usually square or rectangular and, when used for columns located right at property lines, would extend across those lines. A footing for such a column combined with one for an interior column can be designed to fit within the property lines.4. A

mat or raft or floating foundation is a continuous reinforced concrete slab over a large area used to support many columns and walls. This kind of foundation is used where soil strength is low or where column loads are large but where

piles or caissons are not used. For such cases, isolated

footings

would be

so large

that it is more economical to use a

continuous

raft or mat under the entire area.

6Slide7

TYPES OF FOOTINGS

7Slide8

TYPES OF FOOTINGS5. The cost of the formwork for a mat footing is far less than is the

cost

of the

forms for a large number of isolated footings. If individual footings are designed for each column and if their combined area is greater than half of the area contained

within the perimeter of the building, it is usually more economical to use one large footing or mat. The raft or mat foundation is particularly useful in reducing differential settlements between columns—the reduction being 50% or more. For these types

of footings the excavations are often rather deep. The goal is to remove an amount of earth approximately equal to the building weight. If this is done, the net soil pressure after the building is constructed will

theoretically equal what it was before the

excavation was made

. Thus the building

will

float

on the raft foundation.

6.

Pile

caps

are slabs of reinforced concrete used to

distribute column loads

to groups of piles.

8Slide9

ACTUAL SOIL PRESSURES The soil pressure at the surface of contact between a footing and the soil is assumed to

be uniformly

distributed as long as the load above is applied at the center of gravity of

the footing. This assumption is made even though many tests have shown that soil pressures are unevenly distributed due to variations in soil properties, footing rigidity

, and other factors. A uniform-pressure assumption, however, usually provides a conservative design since the calculated shears and moments are usually larger than those that actually occur.

9Slide10

ACTUAL SOIL PRESSURES

10Slide11

ACTUAL SOIL PRESSURES As an example of the variation of soil pressures, footings on sand and clay soils are considered

. When footings are supported by sandy soils, the pressures are larger under

the center

of the footing and smaller near the edge. The sand at the edges of the footing does not have a great deal of lateral support and tends to move from underneath the

footing edges, with the result that more of the load is carried near the center of the footing. Should the bottom of a footing be located at some distance from the ground surface, a sandy soil will provide fairly uniform support because it is restrained from lateral movement. Just the opposite situation is true for footings supported by clayey soils. The clay under the edges of the footing sticks to or has cohesion

with the surrounding clay soil. As a result, more of the load is carried at the edge of the footing than near the middle.11Slide12

ACTUAL SOIL PRESSURES The designer should clearly understand that the assumption of uniform soil pressure underneath

footings is made for reasons of simplifying calculations and may very

well have

to be revised for some soil conditions. Should the load be eccentrically applied to a footing with respect to the center of gravity of the footing, the soil pressure is assumed to vary uniformly in proportion to

the moment, will be discussed later.12Slide13

ALLOWABLE SOIL PRESSURES The allowable soil pressures to be used for designing the footings for a particular structure are

desirably obtained by using the services of a geotechnical engineer. He or she will

determine safe

values from the principles of soil mechanics on the basis of test borings, load tests, and other experimental investigations. Because such investigations often may not be feasible, most building codes

provide certain approximate allowable bearing pressures that can be used for the types of soils and soil conditions occurring in that locality. Next table shows a set of allowable values that are typical of such building codes. It is thought that these values usually provide factors of safety of approximately 3 against severe settlements.13Slide14

ALLOWABLE SOIL PRESSURES

14Slide15

ALLOWABLE SOIL PRESSURES Section 15.2.2 of the ACI Code states that the required area of a footing is to be determined by

dividing the anticipated total load, including the footing weight, by a

permissible soil

pressure or permissible pile capacity determined using the principles of soil mechanics. It will be noted that this total load is the un-factored load, and yet the design

of footings described in this chapter is based on strength design, where the loads are multiplied by the appropriate load factors. It is obvious that an ultimate load cannot be divided by an allowable soil pressure to determine the bearing area required. The designer can handle this problem in two ways. He or she can determine the bearing area

required by summing up the actual or un-factored dead and live loads and dividing them by the allowable soil pressure. Once this area is determined and the dimensions are selected, an ultimate soil pressure can be computed by dividing the factored or ultimate load by the area provided. The remainder of the footing can then be designed by

the

strength method using this ultimate soil pressure. This simple procedure is used for

the footing

examples here.

15Slide16

ALLOWABLE SOIL PRESSURES An alternate method for determining

the footing

area required that will give exactly the same answers as the procedure just

described. By this latter method the allowable soil pressure is increased to an ultimate value by multiplying it by a ratio equal to that used for increasing the magnitude of the service loads. For instance, the ratio for

D and L loads would be

The resulting ultimate soil pressure can be divided into the ultimate column load to

determine the

area required.

16Slide17

DESIGN OF WALL FOOTINGS The theory used for designing beams is applicable to the design of footings with only a few modifications

. The upward soil pressure under the wall footing

tends

to bend the footing into the deformed shape shown. The footings will be designed as shallow beams for the moments and shears involved. In

beams where loads are usually only a few hundred pounds per foot and spans are fairly large, sizes are almost always proportioned for moment. In footings, loads from the supporting soils may run several thousand pounds per foot and spans are relatively short. As a result, shears will almost always control depths.

17Slide18

DESIGN OF WALL FOOTINGS

18Slide19

DESIGN OF WALL FOOTINGS It appears that the maximum moment in this footing occurs under the middle of the wall

, but tests have shown that this is not correct because of the

rigidity of such walls

. If the walls are of reinforced concrete with their considerable rigidity, it is considered satisfactory to compute the moments at the faces of the walls (ACI Code 15.4.2). Should a footing

be supporting a masonry wall with its greater flexibility, the Code states that the moment should be taken at a section halfway from the face of the wall to its center. (For a column with a steel base plate, the critical section for moment is to be located halfway from the face of the column to the edge of the plate.)19Slide20

DESIGN OF WALL FOOTINGS To compute the bending moments and shears in a footing, it is necessary to compute only

the net upward pressure

q

u caused by the factored wall loads above. In other words, the weight of the footing and soil on top of the footing can be neglected. These items cause

an upward pressure equal to their downward weights, and they cancel each other for purposes of computing shears and moments. In a similar manner, it is obvious that there are no moments or shears existing in a book lying flat on a table. Should a wall footing be loaded until it fails in shear, the failure will not occur on a vertical plane at the wall face but rather at an angle of approximately 45 with the wall, as shown

in next figure. Apparently the diagonal tension, which one would expect to cause cracks in between the two diagonal lines, is opposed by the squeezing or compression caused by the downward wall load and the upward soil pressure. 20Slide21

DESIGN OF WALL FOOTINGS

Outside this zone the compression effect is negligible in its effect on diagonal tension. Therefore, for

non pre-stressed

sections shear may be calculated at a distance

d from the face of the wall (ACI Code 11.1.3.1) due to the loads located outside the section.21Slide22

DESIGN OF WALL FOOTINGSThe use of stirrups in footings is usually considered impractical and uneconomical. For this reason, the effective depth of wall footings is selected so that

V

u

is limited to the design shear strength φV

c that the concrete can carry without web reinforcing, that is, (from ACI Section 11.3.1.1 and ACI Equation 11-3). The following expression is used to select the depths of wall footings:

22Slide23

DESIGN OF WALL FOOTINGS The design of wall footings is conveniently handled by using 12-in. widths of the wall

, as shown in

figure below.

Such a practice is followed for the design of a wall footing in next example. It should be noted in Section 15.7 of the Code that the depth of a footing above the bottom reinforcing bars may be no less than 6 in. for footings on soils and 12 in. for those on piles. Thus total minimum practical depths are

at least 10 in. for the regular spread footings and 16 in. for pile caps.

23Slide24

DESIGN OF WALL FOOTINGS The design of a wall footing is illustrated in next example. Although the

example problems

use

various values, 3000 and 4000 psi concretes are commonly used for footings and are generally quite economical. Occasionally, when it is very important to minimize footing depths and weights, stronger concretes may be used. For most cases, however, the extra cost of higher strength

concrete will appreciably exceed the money saved with the smaller concrete volume.24Slide25

DESIGN OF WALL FOOTINGSExample

Solution

25Slide26

DESIGN OF WALL FOOTINGS

26Slide27

DESIGN OF WALL FOOTINGS

27Slide28

DESIGN OF WALL FOOTINGS

28Slide29

DESIGN OF

29Slide30

DESIGN OF WALL FOOTINGS

30Slide31

DESIGN OF WALL FOOTINGS The determination of a footing depth is a trial-and-error

procedure.

The designer assumes an effective depth d, computes the d required for shear, tries another d, computes the d

required for shear, and so on, until the assumed value and the calculated value are within about 1 in. of each other. You probably get upset when a footing size is assumed here. You say, “Where in the world did you get that value?” We think of what seems like a reasonable footing size and start there. We compute the d required for shear and probably find we’ve missed the assumed value

quite a bit. We then try another value roughly two-thirds to three-fourths of the way from the trial value to the computed value (for wall footings) and compute d. (For column footings we probably go about half of the way from the trial value to the computed value.) Two trials are usually sufficient.

31Slide32

32Slide33

DESIGN OF SQUARE ISOLATED FOOTINGS Single-column footings usually provide the most economical column foundations.

Such footings

are generally square in plan, but they can just as well be rectangular or even

circular or octagonal. Rectangular footings are used where such shapes are dictated by the available space or where the cross sections of the columns are very pronounced rectangles.

Most footings consist of slabs of constant thickness, such as the one shown in next figure, but if calculated thicknesses are greater than 3 or 4 ft, it may be

economical to use stepped footings. The shears and moments in a footing are obviously larger near the column, with the result that greater depths are required in that area as compared to the outer parts of the footing. For very large footings, such as

for bridge

piers,

stepped footings

can give appreciable savings in concrete quantities.

33Slide34

DESIGN OF SQUARE ISOLATED FOOTINGS

34Slide35

DESIGN OF SQUARE ISOLATED FOOTINGS Occasionally, sloped footings

are

used instead of the stepped ones,

but labor costs can be a problem. Whether stepped or sloped, it is considered necessary to place the concrete for the entire footing in a single pour to ensure the construction of a

monolithic structure, thus avoiding horizontal shearing weakness. If this procedure is not followed, it is desirable to use keys or shear friction reinforcing between the parts to ensure monolithic action. In addition, when sloped or stepped footings are used, it is necessary to check

stresses at more than one section in the footing. For example, steel area and development length requirements should be checked at steps as well as at the faces of walls or columns.

Before a column footing can be designed, it is necessary to make a few comments

regarding shears

and moments.

35Slide36

DESIGN OF SQUARE ISOLATED FOOTINGS Two shear conditions must be considered in column footings, regardless of their

shapes. The

first of these is one-way or beam shear, which is the same as that considered in

wall footings in the preceding section. For this discussion, reference is made to the footing of next figure. The total shear (

Vu1) to be taken along section 1–1 equals the net soil pressure qu times the hatched area outside the section.

Shears In the expression to follow, bw

is the

whole width

of the footing. The

maximum value

of

V

u

1

if stirrups

are

not

used

equals

φ

V

c

,

which is

and

the maximum depth required is as follows:

36Slide37

DESIGN OF SQUARE ISOLATED FOOTINGS

Shears (Cont’d)

37Slide38

DESIGN OF SQUARE ISOLATED FOOTINGSShears (Cont’d)

The

second shear condition is two-way or punching shear, with reference being

made to the next figure. The compression load from the column tends to spread out into the

footing, opposing diagonal tension in that area, with the result that a square column tends to punch out a piece of the slab, which has the shape of a truncated pyramid. The ACI Code (11.12.1.2) states that the critical section for two-way shear is located at a distance d/2 from the face of the column.

The shear force Vu2 consists of all the net upward pressure q

u

on the hatched

area shown

, that is, on the area outside the part tending to punch out. In the expressions to

follow,

b

o

is the perimeter around the punching area, equal to

4(

a

+

d

)

. The nominal

two-way shear strength of the concrete

V

c

is specified as the smallest value

obtained by

substituting into the applicable equations that follow.

38Slide39

DESIGN OF SQUARE ISOLATED FOOTINGSShears (Cont’d)

39Slide40

DESIGN OF SQUARE ISOLATED FOOTINGSShears (Cont’d)

The first expression is the usual punching shear strength:

Tests have shown that when rectangular footing slabs are subjected to bending in

two directions

and when the long side of the loaded area is

more than two times the length of the short side, the shear strength Vc =

may

be much too high. In the

expression to

follow,

β

c

is the ratio of the long side of the column to the short side of the

column, concentrated

load, or reaction area.

40Slide41

DESIGN OF SQUARE ISOLATED FOOTINGSShears (Cont’d)

The

shear stress in a footing increases as the ratio

bo

/d decreases. To account for this fact ACI Equation 11-34 was developed. The equation includes a term αs which is used to account

for variations in the ratio. In applying the equation αs is to be used as 40 for interior columns (where the perimeter is four-sided), 30 for edge columns (where the perimeter is three-sided), and 20 for corner columns (where the perimeter is two-sided).

The

d

required for two-way shear is the

largest value

obtained from the

following expressions

:

41Slide42

DESIGN OF SQUARE ISOLATED FOOTINGSMoments

The

bending moment in a

square reinforced concrete footing is the same about both axes due

to symmetry. It should be noted, however, that the effective depth of the footing cannot be the same in the two directions because the bars in one direction rest on top of the bars in the other direction. The effective depth used for calculations might be the average for the two directions or, more conservatively, the value for the bars on top. This

lesser value is used for the examples in this text. Although the result is some excess of steel in one direction, it is felt that the steel in either direction must be sufficient to resist the moment in that direction. It should be clearly understood that having an excess of steel in one direction will not make up for a shortage in the other direction at a

90˚

angle.

The

critical section for bending is taken at the face of a reinforced concrete column

or halfway

between the middle and edge of a masonry wall or at a distance halfway from

the edge

of the base plate and the face of the column if structural steel columns are

used (Code

15.4.2).

42Slide43

DESIGN OF SQUARE ISOLATED FOOTINGSMoments

The determination of footing depths by the procedure described here will often

require several cycles of a trial-and-error procedure. There are, however, many tables

and handbooks available with which footing depths can be accurately estimated. One of these is the previously mentioned CRSI Design Handbook. In addition, there are many rules of thumb used by designers for making initial thickness estimates, such as 20% of the footing width

or the column diameter plus 3 in. The reinforcing steel area calculated for footings will often be appreciably less than the minimum values

and

specified

for flexural members

in ACI

Section 10.5.1. In Section

10.5.4, however

, the Code states that

in slabs of

uniform thickness

the minimum area and maximum spacing of

reinforcing bars in the direction

of bending

need only be equal to those required for

shrinkage and temperature

reinforcement.

43Slide44

DESIGN OF SQUARE ISOLATED FOOTINGSMoments

The maximum spacing of this reinforcement may not exceed the lesser of

three times the footing thickness, or 18 in

. Many designers feel that the combination of high shears and low ρ

values that often occurs in footings is not a good situation. Because of this, they specify steel areas at least as large as the flexural minimums of ACI Section 10.5.1. This is the practice we also follow herein. Example 12.2 illustrates the design of an isolated column footing.

44Slide45

DESIGN OF SQUARE ISOLATED FOOTINGSExample 12.2

Solution

45

Solution

Assume depth = 24 insSlide46

DESIGN OF SQUARE ISOLATED FOOTINGSExample 12.2

46Slide47

DESIGN OF SQUARE ISOLATED FOOTINGSExample 12.2

47Slide48

DESIGN OF SQUARE ISOLATED FOOTINGSExample 12.2

48Slide49

DESIGN OF SQUARE ISOLATED FOOTINGS

49Slide50

FOOTINGS SUPPORTING ROUND OR REGULARPOLYGON-SHAPED COLUMNS

50Slide51

FOOTINGS SUPPORTING ROUND OR REGULARPOLYGON-SHAPED COLUMNS Sometimes

footings are designed to support round columns or regular

polygon-shaped columns

. If such is the case, Section 15.3 of the Code states that the column may be replaced with a square member having the same area as the round or polygonal one

. Then the equivalent square is used for locating the critical sections for moment, shear, and development length.51Slide52

LOAD TRANSFER FROM COLUMNS TO FOOTINGS All forces acting at the base of a column must be satisfactorily transferred into the

footing. Compressive

forces can be transmitted directly by bearing, whereas uplift or

tensile forces must be transferred to the supporting footing or pedestal by means of developed reinforcing bars

or by mechanical connectors (which are often used in precast concrete). A column transfers its load directly to the supporting footing over an area equal to the cross-sectional area of the column.

The footing surrounding this contact area, however, supplies appreciable lateral support to the directly loaded part, with the result that the loaded concrete in the footing can support more load. Thus for the same grade of concrete, the footing can carry a larger bearing load than can the base of the column.

In checking the strength of the lower part of the column, only the concrete is

counted. The

column reinforcing bars at that point cannot be counted because they are not

developed unless

dowels are provided or

unless the bars themselves are extended into the footing

.

52Slide53

LOAD TRANSFER FROM COLUMNS TO FOOTINGS At the base of the column, the permitted bearing strength

is

(where

φ is 0.65, but it may be multiplied by for bearing on the footing (ACI Code 10.17). In these expressions, A

1 is the column area, and A2 is the area of the portion of the supporting footing that is geometrically similar and concentric with the columns. (See Figure 12.12.)

If the computed bearing force is higher than the smaller of the two allowable values, it will be necessary to carry the excess with dowels or with column bars extended into the footing. Should the computed bearing force be less than the allowable value, no dowels

or extended

reinforcing are theoretically needed, but the Code (15.8.2.1) states that

there must

be a minimum area of dowels furnished equal to no less than 0.005 times the

gross cross-sectional

area of the column or pedestal.

53Slide54

LOAD TRANSFER FROM COLUMNS TO FOOTINGS The development length of the bars must be sufficient to transfer the compression

to the

supporting member, as per the ACI Code (12.3). In no case may the area of the

designed reinforcement or dowels be less than the area specified for the case where the allowable bearing force was not exceeded. As a practical matter in placing dowels, it should

be noted that regardless of how small a distance they theoretically need to be extended down into the footing, they are usually bent at their ends and set on the main footing reinforcing, as shown in figure below. There the dowels can be tied firmly in place and not be in

danger of being pushed through the footing during construction, as might easily happen otherwise. The bent part of the bar does not count as part of the compression development length (ACI Code 12.5.5). The reader should again note that the bar details shown in this figure are

not satisfactory for seismic areas as the bars should be bent inward

and not outward.

54Slide55

LOAD TRANSFER FROM COLUMNS TO FOOTINGS An alternative to the procedure described in the preceding paragraph is to place

the footing

concrete without dowels and then to push straight dowels down into the

concrete while it is still in a plastic state. This practice is permitted by the Code in its Section 16.7.1 and

is especially useful for plain concrete footings. It is essential that the dowels be maintained in their correct position as long as the concrete is plastic. Before the engineer approves the use of straight dowels as described here, he or she must be satisfied that the dowels will be properly placed and the concrete satisfactorily compacted around them.

55Slide56

LOAD TRANSFER FROM COLUMNS TO FOOTINGS If the computed development length of dowels is greater than the distance

available from

the top of the footing down to the top of the tensile steel, three possible solutions

are available. One or more of the following alternatives may be selected:

1. A larger number of smaller dowels may be used. The smaller diameters will result in smaller development lengths.2. A deeper footing may be used.

3. A cap or pedestal may be constructed on top of the footing to provide the extra development length needed.

Should

bending moments or uplift forces have to be transferred to a footing such

that the

dowels would be in tension, the development lengths must satisfy the requirements

for tension

bars. For tension development length into the footing, a hook at the bottom of

the dowel

may be considered effective.

56

If there is moment or uplift, it will be necessary for the designer to conform to

the splice

requirements of Section 12.17 of the Code in determining the distance the

dowels must

be extended up into the wall or column

.Slide57

LOAD TRANSFER FROM COLUMNS TO FOOTINGSExample 12.3

Solution

57Slide58

LOAD TRANSFER FROM COLUMNS TO FOOTINGS

58Slide59

LOAD TRANSFER FROM COLUMNS TO FOOTINGSExample 12.4

Solution

59Slide60

LOAD TRANSFER FROM COLUMNS TO FOOTINGS

60Slide61

61Development of deformed bars and deformed wire in tension

1. Development length for deformed bars and deformed wire in tension, shall be determined from either 12.2.2 or 12.2.3 and applicable modification factors of 12.2.4 and 12.2.5, but

shall not be less than 12in.

2. For deformed bars or deformed wire, shall be as follows:Slide62

62Development of deformed bars and deformed wire in tension

3. For deformed bars or deformed wire, shall be

In which the confinement term shall not be taken greater than 2.5, and

where n is the number of bars or wires beings spliced of developed along the plane of splitting. It shall be permitted to use as design simplification even if transverse reinforcement is present.Slide63

63Development of deformed bars and deformed wire in tension

4

. The factors used in the expressions for development of deformed bars and deformed wires in tension in 12.2 are as follows:

a. where horizontal reinforcement is placed such than more than 12 in. of fresh concrete is cast below the development length or splice,

ᴪt = 1.3. For other situations, ᴪt = 1.0. b. For epoxy-coated bars, zinc and epoxy dual-coated bars, or epoxy-coated wires with cover less than 3db, or clear spacing less than 6db,

ᴪe = 1.5. For all other epoxy-coated bars, zinc and epoxy dual-coated bars, or epoxy-coated wires, ᴪe = 1.2. For uncoated and zinc-coated (galvanized) reinforcement, ᴪe = 1.0.

However, the product

ᴪ

t

ᴪ

e

need not be greater than 1.7.Slide64

64Development of deformed bars and deformed wire in tension

c. For No. 6 and smaller bars and deformed wires,

ᴪ

s = 0.8. For no 7 and larger bars, ᴪs = 1.0.

d. Where lightweight concrete is used, λ shall not exceed 0.75 unless fct is specified (see 8.6.1). Where normal weight concrete is used, λ = 1.0.5. Reduction in

ld shall be permitted where reinforcement in a flexural member is in excess of that required by analysis except where anchorage or development for fy is specifically required or the reinforcement is designed under provisions of 21.1.1.6 ………………….. (As required)/(As

provided).

Excess Reinforcement Slide65

65Development of deformed bars and deformed wire in Compression

1. Development length for deformed bars and deformed wire in compression,

l

dc, shall be determined from 12.3.2 and applicable modification factors of 12.3.3, but l

dc shall not be less than 8 in.2. For deformed bars and deformed wire, ldc shall be taken as the larger of and with λ as given in 12.2.4(d) and the constant 0.0003 carries the unit of in.²/lb.

3. Length

l

dc

in 12.3.2 shall be permitted to be multiplied by the application factors for:

a. Reinforcement in excess of that required by analysis ………….

(As required)/(As provided)Slide66

66Development of deformed bars and deformed wire in Compression

b. Reinforcement enclosed within spiral reinforcement not less than ¼ in. diameter and not more than 4 in. pitch or within No.4 ties in conformance with 7.10.5 and spaced at not more than 4 in. on center ……………………………………. 0.75.