Control of Crack Widths

Shear Behaviour of Large, Lightly-Reinforced Control of Crack Widths Concrete Beams and One-Way Slabs

232

CHAPTER 6: CONTROL OF CRACK WIDTHS

“Surface cracking is inevitable but, with proper structural design and detailing, the cracks are very narrow and barely perceptible.” -A.M. Neville This chapter describes a series of experiments designed to investigate the effects of bar diameter of skin reinforcing steel on crack widths in the webs of large flexural elements. This chapter also describes experiments to investigate the effects of skin reinforcement on the shear behaviour of flexural elements, and whether the shear strength is related to the vertical spacing between skin reinforcing bars. It is found that the diameter of skin reinforcing bars has a clear effect on crack widths, and that the ACI skin reinforcement provisions should specify a minimum bar diameter. It is also found that the shear strength of large members is not entirely related to the vertical spacing between skin reinforcement, and a modified method by which the SMCFT should calculate sx is recommended, based on the effective depth of the member.

6.1 General

The low tensile strength of concrete relative to its compressive strength means that most

non-prestressed concrete in service is cracked to some degree. In zones of tension, the

steel reinforcement is engaged primarily when a crack occurs, and design of reinforced

concrete structures is carried out based on the fact that significant portions of the

structure are cracked. However, the widths of these cracks must be limited for

appearance, durability and structural integrity.

It is important to limit crack width so as to ensure adequate shear behaviour. As crack

widths increase, their ability to transfer shear stresses by aggregate interlock decreases.

Members in which there is insufficient reinforcement to control crack widths are at risk

of developing wide cracks that may result in a premature shear failure. This is of

particular concern for very thick members without stirrups, as cracks widths within the

web can be considerably greater than those at the level of the steel. It is an aspect that

has typically not been addressed by previous studies on crack widths in reinforced


233

concrete, as the focus has generally been on the effects of crack widths on durability and

appearance.

The 1995 version of the ACI-318 code included provisions for crack control based on

crack width limits of 0.4mm (0.016in.) and 0.33mm (0.013in.) for interior and exterior

applications, respectively. However, ACI Committee 318 is now of the opinion that

crack width is not directly related to long-term durability, with cover depth and concrete

quality being of greater importance (ACI Committee 224, 1993). Furthermore, ACI

Committee 318 now believes that, given the inherent variability of crack widths in

concrete structures, it can be misleading to use a design method that purports to

effectively calculate crack widths. Hence, crack control requirements in the ACI code

have evolved over ten years, with the 2005 crack control requirements representing a

considerable departure from the 1995 requirements.

A particular aspect of the 2005 requirements that is worthy of further study is the skin

reinforcement requirements. Skin reinforcement is provided within the web of thick

members so as to control the width of flexural cracks as they extend above the tension

steel. See, for example, the three 20M bars provided on each face of the transfer girders

described in Figure 1-4. However, as discussed in the following sections, the 2005 ACI

318 code no longer requires a minimum bar diameter for skin reinforcement, based on

research suggesting that spacing of skin reinforcing bars is the primary variable affecting

flexural crack widths in the webs of thick members. It is thus possible to use, for

example, D4 wires in place of No. 5 skin reinforcing bars, at the same spacing, and still

meet the 2005 ACI 318 skin reinforcement requirements. This is despite the fact that the

area of steel has been reduced by 87%.

Based on the above discussion, the intention of this chapter is to investigate the skin

reinforcement requirements of the 2005 ACI-318 code. The effects of crack control

reinforcement on the shear behaviour of thick slabs will also be investigated, and the

ability of the 2004 CSA A23.3 code to account for these effects will be assessed.


234

6.2 Crack Control in the ACI-318 Code

6.2.1 Crack Control at the Level of the Tensile Steel

In the 1995 ACI-318 code, crack control requirements at the level of the tensile

reinforcement were based on the well-known Gergely-Lutz expression (Gergely and Lutz,

(1968)), which was derived from regression analyses on data from several crack width

studies:

s3

bb RfAt0.076w = (6.1)

where wb = crack width on the bottom (soffit) of the member, tb = cover from bottom of member to centre of lowest level of steel= dc, R = (h-kd)/((1-k)d) = factor to account for strain gradient (ratio between strain at bottom of member and strain at level of reinforcement) fs = steel stress A = 2b’(h-d)/m = effective area of concrete in tension surrounding the reinforcement b’ = width of member at centroid of steel m = number of tensile reinforcing bars

In their analysis of flexural crack widths at the level of the reinforcement and on the

bottom face of the member, Gergely and Lutz found that:

“1. The steel stress is the most important variable. 2. The cover thickness is an important variable but not the only consideration. 3. The bar diameter is not a major variable. 4. The size of the side crack width is reduced by the proximity of the compression zone in flexural members. 5. The bottom crack width increases with the strain gradient. 6. The major variables are the effective area of concrete, Ac, the number of bars, m, the side or bottom cover, and the steel stress.”

Point 3 appears to be counterintuitive, but the effect of bar diameter is, in fact, taken into

account by other parameters. Reducing the bar diameter by using a large number of

small diameter bars (at a reduced spacing) would be expected to produce smaller crack

widths than would the use of a small number of large diameter bars at the same steel area


235

and steel stress. This effect is accounted for by the variable m. The bar diameter also

affects crack widths when the total steel area is reduced by using smaller diameter bars,

and this effect is accounted for by use of the steel stress term fs, which will increase.

Equation (6.1) was developed to calculate the most probable crack width on the bottom

of the flexural member. A second expression was also derived to calculate the most

probable crack width on the side face of the member at the level of the reinforcement.

The ACI implementation of the Gergely-Lutz expression used R=1.2 and required the

calculation of a “z-factor” as outlined below, in which z was limited to 175kips/in for

interior exposure and 145kips/in for exterior exposure. These limits correspond to crack

widths of 0.016 and 0.013in (0.4 and 0.33mm). The CSA-A23.3 code also uses the z-

factor for controlling crack widths at the tensile reinforcement, with z being limited to

30,000N/mm and 25,000N/mm for interior and exposure conditions respectively.

3cs Adfz = (6.2)

A challenge posed by the z-factor is that it promotes the use of smaller covers below the

level of the reinforcement so as to reduce dc. Yet, it is generally understood that larger

covers are very effective at improving long-term durability, possibly even more effective

than limiting crack widths (ACI Committee 224 (1993)). Furthermore, while a range of

dc values from 0.75-3.31in. (19 – 84mm) was used by Gergely and Lutz to derive their

expression for bottom-face cracking, there were only three data points with a cover

greater than 2.5in (64mm). As such, it can be difficult to meet the requirements of Eq.

(6.2) at covers exceeding 2in (50mm). The commentary to Clause 10.6.1 in the CSA

code suggests that in situations with large covers, it is not necessary to use a value for

clear cover greater than 50mm when calculating dc and A. In these situations, it is better

to allow thicker covers at the expense of wider surface crack widths. In these cases,

crack widths at the level of the steel will remain small, with the wider surface crack

widths therefore becoming essentially an aesthetic issue. This simple solution was not

implemented in the ACI code.


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Frosch (1999) noted the difficulty in meeting the requirements of the z-factor for larger

covers, and developed a new approach to crack control at the level of tension

reinforcement. Reviewing the work of Broms (1965), Frosch noted that the spacing of

cracks depends on the concrete cover, and calculates the crack spacing as follows:

*sc dΨS = (6.3)

where Sc = crack spacing, d* = controlling cover distance (Figure 6-3) Ψs = crack spacing factor =1.0 for minimum crack spacing =1.5 for average crack spacing =2.0 for maximum crack spacing Noting that the crack width at the level of the reinforcement wc=εsSc, Frosch derived an

equation for the maximum crack width on the bottom of the beam as follows:

22c

s

sc (s/2)dβ

Ef

2w += (6.4)

where Es = Young’s Modulus of steel, β = equivalent to Gergely-Lutz R-value = 1.0 + 0.08dc as a simplification.

Frosch rearranged this equation to solve for the permissible bar spacing, s, as a function

of the permissible maximum crack width, wc:

2c

2

s

sc dβ2f

Ew2s −⎟⎟

⎠

⎞⎜⎜⎝

⎛= (6.5)

A permissible crack width of between 0.016 and 0.021in (0.4-0.53mm) was chosen by

Frosch, a service load steel stress of 0.6fy was assumed, and simplified design curves

generated as shown in Figure 6-2 (Frosch Design Curves).

Figure 6-1: Controlling Cover Distance


237

0

2

4

6

8

10

12

14

16

18

0 1 2 3 4 5 6 7Concrete Cover, dc (in.)

Rei

nfor

cem

ent S

paci

ng, s

(in.

)Grade 60 Steel

Frosch Design Curve

ACI-318 Design CurveEq. 6-6, No. 8 Bar

Eq. 6-5, wc=0.016in.Eq. 6-5, wc=0.021in.

0

2

4

6

8

10

12

14

16

18

0 1 2 3 4 5 6 7Concrete Cover, dc (in.)

Rei

nfor

cem

ent S

paci

ng, s

(in.

)

Frosch Design Curve

ACI-318 Design CurveEq. 6-6, No. 8 Bar

Eq. 6-5, wc=0.016in.

Grade 75 Steel

Eq. 6-5, wc=0.021in.

Figure 6-2: Rebar Spacing Requirements –Eq. 6-5 and Simplified Design Expressions

In implementing the design recommendation of Frosch (1999), ACI Committee 318

chose more conservative design curves as shown in Figure 6-2 (ACI Design Curves), and

the expression for calculating minimum bar spacing is shown below (in ksi, inch units).

The ACI expression is formulated in terms of the clear cover, cc, and entered use in the

1999 ACI-318 design code.

( )scs

f36122.5cf

540s ≤−= (6.6)

where s = centre-to-centre spacing of tension reinforcement fs = calculated stress in longitudinal reinforcement at service loads (in ksi). In lieu of direct calculation, it is permitted to take fs=60% of the specified yield strength cc = clear cover from surface to tensile steel.

ACI Committee 318 now believes that, given the inherent variability of crack widths in

concrete structures, it can be misleading to use a design method that purports to

effectively calculate crack widths (ACI Committee 224, 1993). Frosch (1999), for

example, notes that crack spacing (and, hence, crack widths) can vary by a factor of 2.

The 1978 CEB-FIP code (CEB 1978) suggests that the 95th percentile of crack widths is

equal to 1.7 times the average crack width. A distinction is no longer made between

interior and exterior exposure conditions, as the committee has accepted that crack widths

are not directly related to durability.


238

Due to changes in φ-factors and load combinations in the 2002 version of the ACI code,

Equation (6-6) was reformulated for the 2005 version of the code to take into account the

higher service load stresses in flexural steel:

( )scs

f40122.5cf

15(40)s ≤−= (6.7)

where fs = calculated stress in longitudinal reinforcement at service loads (in ksi). In lieu of direct calculation, it is permitted to take fs=2/3 of the specified yield strength

Despite an increase in service load stresses of 10%, the required spacing of the tensile

reinforcement was not changed. For the case of a 2in. (50mm) clear cover, the required

spacing in both versions of the expression is 10 in. (254mm). The maximum spacing for

tensile reinforcement is 12 in. (300mm).

6.2.2 Skin Reinforcement

It has long been recognized that flexural crack widths can increase in width as the cracks

extend into the web of a deep member (Figure 6-3), and it is argued in Chapter 5 that this

is the primary cause of the size effect in shear. The 1977 version of the ACI-318 code,

for example, required that an area of steel equal to 10% of the tensile reinforcement be

distributed along the side faces of deep members to control crack widths in the web.

Figure 6-3: Side-Face Cracking in Large Beams (adapted from Frantz and Breen (1980))


239

The logic of this requirement in the 1977 ACI code is weak, however, as identified by

Frantz and Breen (1976, 1980a,b). For a given factored moment, increasing the effective

depth of a member will result in a lower area of tensile steel and a lower area of skin

reinforcement, where in fact a deeper section would logically require at least the same, or

probably additional, skin reinforcement. Thus, Frantz and Breen carried out an extensive

series of tests in which crack widths in deep flexural members with various skin

reinforcement configurations were measured and analyzed, and recommended a design

procedure for skin reinforcement. They found a very clear relationship between the skin

reinforcement ratio, ρsk, and the maximum crack width in the web. They recommend that

the expression described in Figure 6-4 be used when determining the required amount of

skin reinforcement.

For 30 < d < 100inches, ρsk = 0.00024 (d-30) d > 100inches, ρsk = 0.011 + 0.000058d

Figure 6-4: Frantz and Breen (1980a) Skin Reinforcement Requirements

ACI 318-02

The results of Frantz and Breen’s study formed the basis of the ACI skin reinforcement

requirements up until the 2002 ACI-318 design code. As shown in Figure 6-5, it is

reflected in the requirement that that the spacing, ssk, between skin reinforcing bars not

exceed 1000Ab/(d-30), where Ab is the area of an individual bar. In previous versions of

the code this requirement was formulated such that the area of skin reinforcement per

foot height of web per side exceed 0.012(d-30) in2/ft. Both expressions, however, are


240

mathematically equivalent. No distinction was made between interior and exterior

exposure conditions, unlike the z-factor for the flexural steel.

10.6.7 — If the effective depth d of a beam or joist exceeds 36in., longitudinal skin reinforcement shall be uniformly distributed along both side faces of the member for a distance d/2 nearest the flexural tension reinforcement. The spacing ssk between longitudinal bars or wires of the skin reinforcement shall not exceed the least of d/6, 12in. and 1000Ab/(d-30). It shall be permitted to include such reinforcement in strength computations if a strain compatability analysis is made to determine stress in the longitudinal bars or wires. The total area of longitudinal skin reinforcement in both faces need not exceed one-half of the required flexural tensile reinforcement.

Figure 6-5: ACI 318-02 Skin Reinforcement Requirements

The ACI 318-02 maximum spacings, ssk, are shown in Figure 6-6a) as a function of the

beam depth, d, for various bar diameters. The resulting skin reinforcement ratios, ρsk, are

shown in Figure 6-6b) for a value of cc+0.5db=2in, where ρsk is calculated as Abar/(ssk x

(2cc+db)), as opposed to the method by which Frantz and Breen calculate ρsk. This is the

method used to calculate ρsk in the CSA code, and ρsk calculated using this method can be

converted to Frantz and Breen’s ρsk by multiplying it by the ratio (No. of bars per side

/(No. of bars per side + 1). The Frantz and Breen expressions are also shown in Figure

6-6b), and have been modified for the different method of calculating ρsk.

Inspection of Figure 6-6a) will show that, for all bar sizes, the maximum spacing initially

increases as a function of the depth by virtue of the d/6 spacing limit, until the point at

which the 1000Ab(d-30) limit governs. At this point, the required spacing decreases.

The d/6 limit thus serves to prevent designs with both large bar spacings and large bar

diameters at effective depths close to 36in. An efficient use of steel would result by

using No. 3 bars as skin reinforcement for depths from 36-48in., No. 4 bars for depths

from 48-60in., and No. 5 bars for depths exceeding 60in. (Figure 6-6b)).


241

0

2

4

6

8

10

12

0 12 24 36 48 60 72 84 96 108 120

Effective Depth, d

Req

uire

d Sp

acin

g of

Ski

n R

einf

orce

men

t, s

0

50

100

150

200

250

300

0 1000 2000 3000

D4D10

No. 3

No.4

No. 5

d/6 Limit

Skin Rft. not req'd in either code

(in.)

(mm)

(in.) (mm)1000Ab

(d-30)Limit

d=55in.

ACI-318-05

c c =3in.

c c =2in.

c c <1.2in.

ACI-318-02

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 12 24 36 48 60 72 84 96 108 120

Effective Depth, d

Skin

Rei

nfor

cem

ent R

atio

, ρsk

(%)

0 1000 2000 3000

(in.)

(mm)

D4

D10No. 3

No. 5CSA Exterior

CSA Interior

Range of ρsk

for d=55in.

d=55in.

No. 4

Frantz&Breen -D4

Frantz&Breen -No.5

ACI-318-02

Figure 6-6: ACI 318-02 and ACI-318-05 Skin Reinforcement Requirements

ACI 318-05

In an attempt to unify the flexural reinforcement spacing requirements of clause 10.6.4

and the skin reinforcement spacing requirements of clause 10.6.7, Frosch (2002)

undertook a review of Frantz and Breen’s study. In the review, Frosch suggested that the

spacing of skin reinforcing bars has a far greater effect on the crack widths in the web of

flexural elements than does the diameter of the bars. In deriving a new design method for

skin reinforcement, Frosch (2002) predicts that “the bar size does not significantly affect

crack width” and that “any size bar can be used successfully.” Frosch also quotes

Gergely and Lutz, who found that the bar diameter was not major variable. The clear

effect of ρsk found by Frantz and Breen was thus suggested by Frosch to be a result

primarily of changes in the bar spacing rather than the bar diameter.

a) b)


242

Based on further analytical work, Frosch found that the crack widths on the side face of

deep flexural elements are related to their distances from the bars. As shown below,

Frosch developed an equation for the side face crack width, ws, at a distance x below the

neutral axis (Figure 6-7):

*xxss dεΨw = (6.8)

where ws = crack width located a distance x below the neutral axis, εx = longitudinal strain at a distance x below the neutral axis dx* = controlling cover distance at a distance x below the neutral axis = 2

s2 d+)'x(

Ψs =1.0 for minimum crack spacing, =1.5 for average spacing, =2.0 for max spacing x` =vertical distance from point x to nearest reinforcing bar

The depth of the neutral axis, c, is calculated based on an elastic analysis of the

transformed section.

Figure 6-7: Effect of Skin Reinforcement According to Frosch (2002)

The effect of side face steel on crack widths is modelled by the reduction of the

controlling cover distance, dx*. Cracks are thus predicted to be locally wider at s/2 from

a skin reinforcing bar, and locally narrower directly beside a bar (where x’=0). Noting

that side face cracks exhibit considerable variability in widths, it was suggested that the

largest crack width can be calculated using Ψs=2, and the narrowest crack width

calculated using Ψs=1. Showing generally good agreement between predicted and


243

experimental crack widths from the Frantz and Breen study, Frosch recommended that

Equation (6-7) be applied to the design of skin reinforcement in addition to flexural

reinforcement. Clause 10.6.7 was thus rewritten for the 2005 version of the ACI code

based on the work of Frosch (2002). See Figure 6-8.

Code Commentary 10.6.7 — Where h of a beam or joist exceeds 36in., longitudinal skin reinforcement shall be uniformly distributed along both side faces of the member. Skin reinforcement shall extend for a distance h/2 from the tension face. The spacing s shall be as provided in 10.6.4, where cc is the least distance from the surface of the skin reinforcement or prestressing steel to the side face. It shall be permitted to include such reinforcement in strength computations if a strain compatibility analysis is made to determine stress in the individual bars or wires.

R10.6.7 — For relatively deep flexural members, some reinforcement should be placed near the vertical faces of the tension zone to control cracking in the web.10.20,

10.21 (See Fig. R10.6.7.) Without such auxiliary steel, the width of the cracks in the web may exceed the crack widths at the level of the flexural tension reinforcement. This section was modified in the 2005 edition to make the skin reinforcement spacing consistent with that of the flexural reinforcement. The size of the skin reinforcement is not specified; research has indicated that the spacing rather than bar size is of primary importance.10.21 Bar sizes No. 3 to No. 5 (or welded wire reinforcement with a minimum area of 0.1 in.2 per foot of depth) are typically provided. (emphasis added)

Figure 6-8: ACI 318-05 Skin Reinforcement Requirements

The code clause no longer specifies a minimum ρsk or bar diameter, since ACI

Committee 318 believes, as identified in the commentary, that bar size is, at best, of

secondary importance.

The skin reinforcement bar spacings based on the 2005 ACI code are shown in Figure

6-6a), where it can be seen that, for example, for a 2in. cover, a spacing of 10in. is

required. However, unlike the 2002 code provisions, this spacing is independent of the

bar size, db, and thus the skin reinforcement ratio, ρsk. In the case of a 55in. deep beam

with a clear cover of 2in., the 2002 code would have required an unreasonably small

maximum spacing of 1.6in for a D4 deformed wire (Abar=0.04in2), while the 2005 code

requires a maximum spacing of 10in. In this case, the 2005 code suggests that, using D4

skin reinforcement, a skin reinforcement ratio of about 15% that recommended by the

2002 code will sufficiently control crack widths.


244

While the commentary suggests that No. 3 to No. 5 bars are generally used, this is not a

mandatory code requirement. Furthermore, the commentary also suggests that welded

wire reinforcement with an area of 0.1in2/foot of depth is also typical. For a 55in. deep

beam with a cover of, say, 1.2in., the 2002 code would have required a spacing of 4in. for

D10 bars, resulting in an ρsk of 0.9%. For the same beam using D10 bars as skin

reinforcement, the 2005 code requires a spacing of 12in., resulting in an ρsk of 0.3%. In

this case, the 2005 code suggests that one-third of the steel that was required in the 2002

is sufficient.

6.2.3 Skin Reinforcement –CSA Code

The CSA code has also used the work of Frantz and Breen for its skin reinforcement

requirements. However, the code requires a constant ρsk of 0.8% for interior conditions

and 1% for exterior conditions in flexural members where h exceeds 750mm (29.5in.)

(Figure 6-9). The CSA code further limits the maximum spacing of skin reinforcing bars

to 200mm (7.9in.). The CSA values are plotted in Figure 6-6b). The 2002 ACI required

ρsk values exceed the CSA interior requirement at d=62in. (1575mm), and exceeds the

CSA exterior requirement at d=71in.

Figure 6-9: CSA Skin Reinforcement


245

6.3 Skin Reinforcement Study

6.3.1 General

The previous discussion has shown that the ACI-318-05 skin reinforcement requirements

have been considerably changed from earlier versions. A particularly significant change

has been the elimination of a minimum bar diameter, and reformulation based solely on

bar spacing. Yet common sense would dictate that it is, at best, counter-intuitive that the

bar diameter would have no effect on crack width at a constant bar spacing and cover. It

was thus decided to investigate the effects of these changes by adding skin reinforcement

to a series of specimens in the test program described in Chapter 5, as well as construct a

series of specimens to investigate the effect of skin reinforcement on the shear behaviour

of large reinforced concrete flexural elements.

6.3.2 Experimental Program

The design of the skin reinforcement is shown in Figure 6-10. Four closed steel hoops

were added to the midspan region in specimens L-10H, L-10HS, L-50N1 and L-50N2.

The hoops in L-10H and L-50N1 were constructed out of D4 deformed wire, with a

cross-sectional area of 0.04in2 (25.8mm2), and a diameter of 0.226in. (5.7mm). The

hoops in L-10HS and L-50N2 were constructed out of 15M rebar with a cross-sectional

area of 200mm2 (0.31in2) and a diameter of 16mm (5/8in.). The clear cover to the skin

reinforcement in these four specimens was 2in (50mm), thus Clause 10.6.7 of the 2005

ACI code states that a maximum spacing of 10in. (254mm) must be provided. The hoops

measured 60in. (1525mm) long, and were centered below the line of application of the

load. They were suspended in the middle of the formwork using thin steel wire at five

locations along the 60in. length of the hoops (labeled (a) in Figure 6-10). Three D4 bars

were tied to each hoop (labeled (b) in Figure 6-10), with each bar cut long enough to bear

against the sides of the formwork so as to maintain the clear cover of the hoops. The

hoops were tied tightly by steel wire to the bottom longitudinal reinforcement.


246

As the crack control steel was contained well within dv=1260mm from the edge of the

loading plate, it can not be expected to have a significant impact upon the shear

behaviour of specimens L-10H, L-10HS, L-50N1 and L-50N1. The crack patterns at

failure are consistent with this.

The 90o bends had an inside radius of 2in (50mm) in the 15M bars and an inside radius of

1in (25mm) in the D4 bars. The side clear cover to the flexural steel was 30mm in L-

10HS and 55mm in the other specimens. The skin reinforcement ratio for the specimens

reinforced with D4 deformed wire was 0.095%, and it was 0.67% for the specimens

reinforced with 15M bars. These ratios are calculated by the CSA method for calculating

ρsk=Abar/((db+2cc)s). They correspond to 0.07% and 0.5% based on Frantz and Breen’s

method of calculating ρsk=3Abar/((db+2cc)dsk), where dsk=4s.

An additional large specimen (L-20D) was constructed, as well as two small specimens

(S-20D1 and S-20D2). Specimen L-20D was constructed with four 30M bars at an

effective depth of 1450mm, and with 2-10M longitudinal bars spaced at 225mm over the

height of the specimen. The clear cover to this skin reinforcement was 50mm, and the

skin reinforcement extended the full length of the specimen. The skin reinforcement ratio

for this specimen was 0.4% based on the CSA method, and 0.3% based on Frantz and

Breen’s method. This full length skin reinforcement was hung using thin steel wires.

Taking into account the skin reinforcement in the bottom h/2 of the specimen results in

an effective depth of 1371mm and a longitudinal reinforcing ratio ρw=0.84% for

Specimen L-20D. The specimen as-built width was 295mm, and it was tested like the

other large specimens in this study at a span of 8100mm, resulting in an a/d ratio of 2.95.

Specimens L-20D and S-20D1/D2 will be described in more detail in Section 6.6, but

some of the results from L-20D will be used in this section.


247

Figure 6-10: Design of Skin Reinforcement

Support of Skin Reinforcement in Formwork

(b)

(a)


248

The crack control steel in the mid-span regions of L-10H, L-10HS, L-50N1 and L-50N2

was designed to investigate the effects of the bar diameter and ρsk, at a constant clear

cover, on flexural crack widths. Thus, crack widths in the middle 48in. (1220mm) of the

specimens were measured at various stages as they were loaded to shear failure. They

were measured visually using a crack comparator gauge with a precision of 0.05mm

(0.002in.) The zurich targets were used to confirm the visually measured horizontal

crack widths at midheight when only one crack occurred between adjacent targets. No

special adjustment was made to account for the slope of the crack. Crack widths were

calculated from the zurich target data assuming all strain measured between targets

occurred at the crack.

According to clause 12.5 of the ACI code, the development length for the 90o 15M hooks

is 6.9in. (175mm), while it is 6in. (150mm) for the D4 hooks. Cracks located outside the

middle 48in were thus not considered, so as to avoid any issues with regards to

inadequately developed reinforcement. This also reduced the likelihood that locally

increased tensile stresses at the locations of the bends would affect the crack widths.

Since the hoops were supported by steel wire, considering only the middle 48in.

eliminates any inaccuracies in the exact placing of the hoops, in case they shifted slightly

during the concrete pour.

6.3.3 Experimental Results

A summary of measured crack widths is provided in Table 6-1. Diagrams of the cracks

on the south faces of the specimens are presented in Figure 6-11 for mid-span steel

stresses of between 209-237MPa (30.3-34.4ksi). These steel stresses are reasonably

constant, hence comparison of crack patterns between specimens can be made. These

stresses are 51-52% of the specified yield stress, and thus represent a probable service

load stresses. The steel stress is calculated based on an elastic analysis of the transformed

section, in which the depth to the neutral axis, c, is calculated as:


249

( )( )dnρ-n)(ρ+n2ρ=kd=c w2

ww (6-9)

where ρw = As/bwd n=Es/Ec 'cc f57,000=E (psi units) (clause 8.5.1, ACI-318)

'cc f4734=E (MPa units)

While the actual yield strength of the flexural reinforcement was 452 MPa, (65.5ksi), in

this section, the US specified yield stress of 414MPa (60ksi) will be used.

Specimens L-10N1 and L-10N2, without skin reinforcement, exhibited wide flexural

cracking at this steel stress, with midspan cracks of up to 0.4 to 0.5mm in width (0.016-

0.020in). Aesthetically, these cracks are far too wide, and skin reinforcement is required.

Provision of D4 wires at 10in reduced the maximum crack widths to about 0.3 to 0.35mm

(specimens L-10H and L-50N1). While this is a decrease in maximum crack width of

about 25% and represents some improvement, in the opinion of this author, these cracks

are still too wide. This is particularly the case when considering that the stress in the

steel represents only about 3/4 of the maximum service load steel stress. Increasing the

steel stress by about one-third will increase the crack widths by a similar amount,

resulting in cracks of about 0.4 to 0.45mm.

Provision of 15M rebars at 10in. has resulted in much narrower cracks. The widest

flexural crack in the midspan region of L-10HS and L-50N2 is 0.15mm, representing a

decrease in maximum crack width of about 67% versus no skin reinforcement. The bar

diameter thus appears to have had a considerable impact on flexural crack widths.


250

Figure 6-11: Crack Widths in Middle of Specimens at fs Ranging from 209 to 237MPa (30.3-31.3ksi)


251

Table 6-1: Crack Width Data

(kN) (MPa) (GPa) Es/Ec (%) (MPa) Avg. Avg.225 38.4 29.3 6.82 0.83 0.285 0.90 122 - - 0.217 - - 0.217 - - 0.20 - - 0.20 0.298 0.20350 180 - - 0.347 - - 0.347 - - 0.30 - - 0.30 0.428 0.35388 197 - - 0.373 - - 0.373 - - 0.35 - - 0.35 0.460 0.40430 216 - - 0.418 - - 0.418 - - 0.40 - - 0.40 0.520 0.50475 237 - - 0.436 - - 0.436 - - 0.40 - - 0.40 0.538 0.50500 249 - - 0.480 - - 0.480 - - 0.45 - - 0.45 0.589 0.50160 40.3 30.0 6.66 0.83 0.282 0.91 93 - - - - - - - - - - - - 0.088 0.10225 122 - - 0.249 - - 0.249 - - 0.15 - - 0.15 0.296 0.25350 179 0.171 0.339 - - 0.255 0.10 0.20 - - 0.15 0.427 0.35420 211 0.188 0.360 - - 0.274 0.10 0.25 - - 0.18 0.499 0.40450 225 0.228 0.396 - - 0.312 0.20 0.30 - - 0.25 0.528 0.40187 73.6 40.6 4.92 0.83 0.248 0.92 104 - - 0.100 (1) 0.100 - - 0.10 - - 0.10 - - 0.10225 121 - - 0.100 - - 0.100 - - 0.10 - - 0.10 - - 0.10350 177 0.150 0.100 - - 0.125 0.15 0.10 - - 0.13 - - 0.25420 209 0.198 0.150 - - 0.174 0.20 0.15 - - 0.18 - - 0.30450 222 0.242 0.150 - - 0.196 0.25 0.15 - - 0.20 - - 0.35450 71.2 39.9 5.01 1.33 0.305 0.90 142 - - 0.094 0.039 0.067 0.10 0.05 - - 0.08 0.169 0.15700 214 - - 0.169 0.077 0.123 0.10 0.05 - - 0.08 - - 0.15942 283 - - 0.196 0.113 0.155 0.15 0.05 - - 0.10 - - 0.201200 357 0.039 0.211 0.152 0.134 0.20 0.10 0.05 0.12 - - 0.25193 41 30.3 6.60 0.83 0.281 0.91 108 - - - - - - 0.05225 122 0.058 0.038 - - 0.048 0.10 0.05 - - 0.08 - - 0.15350 179 0.202 0.202 - - 0.202 0.20 0.20 - - 0.20 0.28 0.25420 211 0.258 0.302 - - 0.280 0.20 0.25 - - 0.23 0.35 0.30225 40.1 30.0 6.67 0.83 0.282 0.91 122 0.000 - - 0.05 - - 0.05 0.089 0.10350 179 0.110 0.134 - - 0.122 0.10 0.10 - - 0.10 0.148 0.15420 211 0.119 0.180 - - 0.150 0.10 0.10 - - 0.10 0.174 0.15450 225 0.147 0.197 - - 0.172 0.10 0.15 - - 0.13 0.207 0.15500 248 0.137 0.214 - - 0.176 0.10 0.15 - - 0.13 0.205 0.20225 35.8 28.3 7.06 0.84 0.290 0.90 129 - - - - - - - - - - - - - - - - 0.127 0.10350 189 0.099 0.125 0.145 0.123 0.05 0.10 0.05 0.07 0.213 0.15450 237 0.136 0.192 0.207 0.178 0.05 0.15 0.10 0.10 0.319 0.25550 285 0.195 0.282 0.287 0.255 0.10 0.20 0.20 0.17 - - 0.30650 334 0.204 0.336 0.341 0.294 0.20 0.20 0.25 0.22 - - 0.30

L-50N1 D4@10in. ρsk=0.09%

L-50N2 15M@10in. ρsk=0.67%

L-20D 10M@9in. ρsk=0.39%

App. Load

L-10HS 15M@10in. ρsk=0.67%

L-10H D4@10in. ρsk=0.09%

L-10N1 No skin rft.

L-10N2 No skin rft.

n ρs kSpecimen

Ecf'c Measured VisuallyCrack Widths Crack Widths

jBased on Zurich Targets

fs

Crack Widths at Mid-Height (mm) Max. Crack Width (mm)

Zurich Visual

6.3.4 Crack Widths as a Function of Steel Stress

Maximum Crack Widths

The maximum single crack widths measured at any point in the 48in. wide midspan

regions of specimens L-10N1 + L-10N2 (no skin reinforcement), L-50N1 (D4@10in.), L-

50N2 (15M@10in.) and L-20D ([email protected].) are plotted in Figure 6-12a) versus the

steel stress at midspan. The maximum single crack widths measured at any point in the

48in. wide midspan regions of specimens L-10H (D4@10in.) and L-10HS (15M@10in.)

are plotted in Figure 6-12b). The crack widths in Figure 6-12 were measured visually

using a crack comparator gauge at load stages. The steel stresses were calculated based

on an elastic analysis of the section at midspan. Since all specimens in Figure 6-12 other


252

than L-20D and L-10HS failed prior to the steel stresses reaching the maximum service

load steel stress of 67% of fy, linear extrapolations have been added to the data. Also

shown is the ACI 318-99 maximum crack width of 0.016in. (0.4mm) for interior

exposure. ACI 318-99 required that crack widths not exceed this width at service loads.

Figure 6-12 Maximum Crack Widths in 48in. Wide Midspan Region, Measured Visually

It can be clearly seen in Figure 6-12 that unacceptably wide cracks occurred in L-10N1

and L-10N2 under service loads. For example, at the maximum service load steel stress

(0.67fy) the widest crack in L-10N1 would be expected to be about 0.6mm (0.024in.).

Indeed, the maximum crack widths in L-10N1 and L-10N2 reached 0.4mm (0.016in.) at a

steel stress of about 50% of fy. Clearly, members of this depth are in need of additional

reinforcement to control crack widths at service loads.

However, the provision of D4 bars spaced at 10in. did not provide adequate control of

crack widths. Based on the linear extrapolations in Figure 6-12, it is expected that the

maximum crack width in both L-50N1 and L-10H would reach 0.45mm at a steel stress


253

of 67% of the yield stress. Unacceptably wide cracks thus occurred in the midspan

regions of L-50N1 and L-10H, even though these regions contained skin reinforcement

designed to conform to ACI 318-05.

Using 15M bars spaced at 10in. successfully controlled crack widths in specimens L-

50N2 and L-10HS. Compare the crack widths measured in L-50N2 to those measured in

L-50N1, and the crack widths measured in L-10HS to those measured in L-10H. The

maximum measured crack width in L-10HS was 0.25mm at a steel stress of 31.8ksi

(357MPa), representing 86% of the yield stress. Using 10M bars at 8.9in. also

successfully controlled crack widths in L-20D. Any differences in the crack widths

between L-20D and L-50N2 fall within the precision of the crack comparator gauge.

Crack Widths at Midheight

The averages of the crack widths at the midheight (h/2) of the 48in. wide midspan regions

are plotted in Figure 6-13 and Figure 6-14 versus the midspan steel strains. The averages

of the crack widths measured using the comparator gauge are plotted in Figure 6-13,

while the average based on the zurich target data are plotted in Figure 6-14.

The maximum crack widths in the middle 48in. of the specimens did not occur at mid-

height, but, rather, were found to occur at between 450mm and 670mm (18-26.5in.) from

the bottom face. Nevertheless, the average crack widths at the midheight of the beams

without skin reinforcement were unacceptably wide. Provision of D4 skin reinforcement

reduced the average crack widths at mid-height, though the 15M skin reinforcement was

far more effective.

The analysis of crack widths plotted in Figure 6-12, Figure 6-13 and Figure 6-14 has

shown that that the D4 skin reinforcement had only a small impact on flexural crack

widths. Crack widths were still unacceptably wide in the specimens with D4 skin

reinforcement, even though this skin reinforcement met the requirements of ACI 318-05.

Skin reinforcement consisting of 15M bars at the same spacing and bar cover, however,

was extremely effective at controlling crack widths.


254

Figure 6-13 Average Crack Width at Midheight of Midspan Region, Measured Visually

Figure 6-14 Average Crack Widths at Midheight Midspan Region, -Zurich Target Data


255

6.3.5 Crack Widths at Maximum Service Load Steel Stress

While crack widths below the maximum service load are useful to investigate, the crack

widths at the ACI maximum service load steel stress of 0.67fy are the most useful. Since

a number of the specimens shown in the previous figures failed at loads below those

corresponding to a steel stress of 0.67fy, it is necessary to estimate the crack widths at

fs=0.67fy had the beams not failed. This was accomplished using the extrapolations

shown in Figure 6-12, and the resulting estimated maximum crack widths at fs=0.67fy are

shown in Figure 6-15. Extrapolated crack widths for specimens L-20N1, L-20N2, L-

40N1 and L-40N2 are also shown. Using an extrapolation is an appropriate method for

estimating the maximum crack width at fs=0.67fy since a stable crack pattern formed in

the specimens, in which existing cracks widened with increasing load, with few new

cracks forming.

Figure 6-15 clearly shows that at a constant clear cover and a constant spacing of 10in.,

decreasing the skin reinforcement ratio by decreasing the bar diameter can result in

unacceptably wide cracks at service loads. At a constant spacing and cover, the bar

diameter thus has a very clear effect on flexural crack widths.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0 0.4 0.8 1.2 1.6 2Skin Reinforcement ratio, ρsk

0

0.004

0.008

0.012

0.016

0.02

0.024

0.028L-10N SeriesL-20N SeriesL-40N Series

Max

imum

Exp

ecte

d C

rack

Wid

th a

t fs=

0.67

f y (mm) (in.)

Normal f'cSeries

High f'cSeries

Range in Crack Widths at ρsk=0 c=2in (50mm)

Figure 6-15: Expected Crack Widths at fs=0.67fy

(L-50N Series, L-20D) (L-10H, L-10HS)


256

The concrete strengths in the specimens without skin reinforcement ranged from 28.1-

41MPa (4075-5945psi), resulting in neutral axis depths of 393-426mm (15.5-16.8in.).

Thus, some of the scatter in crack widths at ρsk=0 might be expected to have occurred due

to differences in the concrete strength. An increase in concrete strength is associated

with a decrease in neutral axis depth, resulting in slightly larger longitudinal strains

below the neutral axis and consequent crack widths at otherwise constant crack spacings

and steel strains. While the differences in concrete strengths between the specimens

would result in only very small differences in longitudinal web strains, this effect is

evident in the data at ρsk=0 and ρsk=0.095%, in that there is a general trend of increasing

crack widths with increasing concrete strengths. An opposite effect is noted, however, at

ρsk=0.67%. Other researchers, however (for example, Hognestad (1962)) have not found

that concrete strength affects crack widths beyond the initial cracking load.

In specimens of similar concrete strength, the maximum expected crack width decreases

by about 20% in specimen L-50N1 (reinforced with D4 wires) relative to specimens L-

10N1 and L-10N2 (with no skin reinforcement). Nevertheless, it is instructive to note

that the crack widths in the specimens reinforced with D4 wire fall within the scatter of

maximum crack width data from specimens without skin reinforcement. It thus

interesting to note that provision of D4 skin reinforcement at a spacing of 10in. was about

as effective at reducing crack widths as reducing the concrete strength by about 30%.

6.3.6 Predictions of Web Crack Width

Crack Width Profiles

The widths of the single widest flexural crack in the six specimens shown in Figure 6-11

are plotted in Figure 6-16. Using the cracking model developed by Frosch (2002) and

described by Equation 6-8 and in Figure 6-7, it is possible to predict the measured crack

width profiles shown in Figure 6-16.


257

The predicted widest (Ψ=2) and narrowest (Ψ=1) cracks in specimens L-10N1 and L-

10N2 are shown in Figure 6-16a) and b). It can be seen that Frosch’s model is generally

good at calculating the overall width profile of the widest cracks in these specimens.

While the maximum crack width was observed to occur lower in the section than what is

predicted by Frosch’s model, this maximum width was calculated reasonably accurately

using Ψ=2 in Equation 6-8.

The predicted crack width profiles for the specimens with D4 reinforcement are shown in

Figure 6-16c) and d). The predicted crack width profiles for the specimens with 15M

reinforcement are shown in Figure 6-16e) and f). Two sets of predictions have been

generated. The first set, shown in solid lines, is for the case where the controlling cover

distance, dx* in Equation 6-8, is calculated based on skin reinforcement provided at

10inch spacing. Since all four specimens in Figures 6-18c)-f) have skin reinforcement

present, these are the predictions that apply to these beams. The second set, shown in the

dashed lines, was generated neglecting the skin reinforcement, and resemble the crack

width predictions for L-10N1 and L-10N2. The predicted effect of reducing the

controlling cover distance, dx*, by providing skin reinforcement can be clearly seen by

comparing these two sets of predictions. It is predicted (Figure 6-7) that cracks will

locally widen between skin reinforcing bars, but the overall width is predicted to be

considerably reduced.

It can be seen in Figure 6-16e) and f) that the measured crack widths in the specimens

with 15M skin reinforcement are considerably smaller than those measured in L-10N1

and L-10N2 (Figure 6-16a) and b)). For these two beams, calculating dx* based on the

presence of the skin reinforcement resulted in accurate predictions of the maximum crack

width from Frosch’s model. While the precision of the crack comparator gauge did not

allow for the detailed mapping of the variation in crack widths over the height of

specimens L-10HS and L-50N2, the maximum crack width was accurately calculated

using Ψs=2.


258

Figure 6-16: Widest Crack in Midspan Region and Crack Width Predictions by Eq. 6-8


259

Figure 6-16c) and d) indicate that calculating dx* based on the presence of skin

reinforcement did not accurately predict the crack widths and overall crack width profiles

in the two specimens with D4 skin reinforcement. For L-10H and L-50N1, the measured

crack widths fell well outside the band of expected crack widths defined by 1<Ψs<2. For

example, the maximum measured width in these specimens was 0.3mm, and in both this

maximum width was observed to occur directly beside a skin reinforcing bar, where

Frosch’s model predicts a local narrowing of the crack. By observation, in fact, it can be

seen that the predicted crack width profiles generated neglecting the presence of the D4

bars (the dotted lines) more accurately predict the measured crack width profiles.

When using Frosch’s model to predict the flexural crack widths in the two beams with

D4 skin reinforcement, it appears that it is more accurate to neglect the skin

reinforcement than it is to consider it in the model.

Experimentally Determined Ψs Values

At each load stage, it is possible to calculate an experimentally-determined Ψs value. It

can be calculated by dividing the maximum crack width measured at any point on the

crack by the largest width on the predicted crack width profile generated using Ψs = 1.

Separate experimental Ψs values can be determined by both considering and neglecting

the skin reinforcement.

To further examine how the crack widths measured in L-10H and L-50N1 lie outside the

range of crack widths predicted by Frosch’s model, Figure 6-17 was created. Each data

point represents the average of experimentally-determined Ψs values for load stages

where the steel stress exceeded one-third of the yield stress. This limit on the steel stress

was chosen to ensure a stable crack pattern had formed. This figure shows that the

maximum measured crack widths in specimens with ρsk=0.4% and 0.67% lie within the

scatter band defined by Frosch, with experimental Ψs values ranging from 1.3 to 1.6.

Likewise, the maximum measured crack widths for ρsk=0% lie within the scatter band.


260

The maximum measured crack widths in the specimens reinforced with D4 wire lie well

outside the expected range of Ψs values, with Ψs values of 2.4 and 2.5. However, the key

to this figure is to note that the maximum measured crack widths in these specimens

actually fall within the range of Ψs values generated assuming no skin reinforcement. In

this case, the experimental values of Ψs are both 1.23. Thus, when using Frosch’s model

to predict the crack widths in the specimens with D4 skin reinforcement, assuming that

no skin reinforcement is present produces more accurate predictions of the maximum

crack width than assuming skin reinforcement to be present.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.2 0.4 0.6 0.8 1.0

Skin Reinforcement Ratio, ρsk (%)

Expe

rimen

tal C

rack

Spa

cing

Fac

tor, Ψ

s

Range of Ψs in Frosch Model

Assuming no Skin Reinforcement Provided

Assuming Skin Reinforcement Provided

Figure 6-17: Experimentally Determined Values of Ψs

2.5 2.4

1.23


261

6.3.7 Another Look at Frantz and Breen

Average and Maximum Crack Widths Frantz and Breen tested a total of 44 inverted-T specimens, studying numerous

combinations of web depths, flange depths, reinforcement ratios ρw and ρsk, web widths,

bar diameters and clear covers. The majority of them were “reduced segment” specimens,

which were 72in. (1830mm) long, and which were loaded using hydraulic rams to

directly apply tension to the main reinforcing bars and compression above the neutral

axis. The location of the compression force was determined by an analysis of the cracked

transformed section. The specimens were thus loaded in pure moment, and were tested

upside-down to facilitate observations of the cracks.

Despite the impressively large number of specimens in the test program, only one series

of five specimens was tested in which all variables were kept constant, with only db being

varied. Results from this series of tests are summarized in Figure 6-18, in which average

and maximum web crack widths are plotted as a function of steel stress. In these

specimens, the centre-to-centre bar spacing, clear cover and section dimensions were kept

constant, while the skin reinforcement was varied from Swedish Grade 77 deformed

6mm bars (Specimen A-7) to No. 3 bars and No. 4 bars (Specimens A-8 and A-9). These

bars resulted in ρsk values of 0.34%, 0.81% and 1.34%. Two specimens, A-1 and A-2,

were tested without skin reinforcement.

In reviewing the data summarized in Figure 6-18, Frosch (2002) notes that there was

essentially no difference between the measured crack widths in the specimens reinforced

with No. 3 bars and No. 4 bars, and thus concludes that any bar size can be successfully

used to control crack widths. The considerably wider cracks in the specimen reinforced

with 6mm bars were attributed by Frosch to the fact that the bars were Swedish, with

deformations that were less pronounced than the No. 3 and 4 bars, and which, according

to Frosch, did not conform to the ASTM A615 standard on deformations. Thus, the

increase in crack widths was attributed by Frosch to differing bond properties between

the Swedish and US bars. The fact that smaller deformations can be used on smaller bars


262

because of the larger ratio of perimeter to cross-sectional area (and thus inherently better

bond properties) is not addressed. Also note that the accuracy of the gauge used to

measure the crack widths in Frantz and Breen’s experimental program was 0.001in.

Hence, the maximum crack widths in A-9 (No. 4 bars) were larger than those in A-8 (No.

3 bars) by only one increment on the gauge.

0.00

0.10

0.20

0.30

0.40

0.50

25 30 35 40 45Bar Stress

Cra

ck W

idth

0

4

8

12

16

20170 210 250 290

#3 Bars ρsk=0.81%

(mm)

(x10

-3in

.)

(ksi)

(MPa)

#4 Bars ρsk=1.41%

6mm Bars ρsk=0.34%

No Skin Rft. ρsk=0%

a) Average Web Crack Width

0.00

0.10

0.20

0.30

0.40

0.50

25 30 35 40 45Bar Stress

Cra

ck W

idth

0

4

8

12

16

20170 210 250 290

#3 Bars

(mm)

(x10

-3in

.)

(ksi)

(MPa)

#4 Bars

6mm Bars

No Skin Rft.

Crack Width Gauge Resolution=0.001in.b) Maximum Web Crack Width

Figure 6-18: Effect of Bar Diameter on Crack Width in Web (Frantz and Breen, 1976)

Crack Magnification Ratio and Extension of Cracks into the Web The ratios of the average web crack width (wweb) to the average crack width at the level

of the steel (wsteel) for all of Frantz and Breen’s specimens are plotted in Figure 6-19a) for

a steel stress of 35ksi. Frantz and Breen refer to wweb/wsteel as the crack magnification

ratio. The crack magnification ratios for specimens A-1, A-2, A-7, A-8 and A-9 have

been identified with open symbols. The crack magnification ratios for specimens A-7, A-

8 and A-9 are plotted in Figure 6-19b) at steel stresses of 25, 30, 35 and 40ksi. Figure

6-20 plots the percentage of the cracks at the level of the steel that extended into the web

in specimens A-1, A-2, A-7, A-8 and A-9, and crack diagrams have been reproduced.


263

It can be seen in these figures that, in fact, using #4 bars instead of #3 bars affected

cracking in the webs in two important ways. Firstly, the crack magnification ratio was

lower in A-9 than in A-8 for all steel stresses. Although crack widths in the webs of A-8

and A-9 were similar, cracks at the level of the steel in A-9 were, on average, about 15%

wider than they were in A-8. The use of #4 bars reduced their widths in the web to

widths that were similar to the widths measured in A-8, resulting in the reduced crack

magnification ratios. It is interesting to note that a curve of best fit drawn through the

cloud of data points in Figure 6-19a) might be drawn almost right on top of the curve

connecting the points for A-7, A-8, A-9 and the average of A-1 and A-2.

Secondly, and more importantly, a considerably greater number of cracks extended into

the web in specimen A-9 than in A-8. Frantz and Breen report that twenty-eight cracks

occurred at the level of the steel in specimens A-7, A-8 and A-9 (counted on both sides of

the specimen), while twenty-six were counted in A-2 and nineteen in A-1. Sixteen of

these cracks extended into the web in A-9, versus ten in A-8, nine in A-7 and six in

specimens A-1 and A-2. The crack patterns reproduced in Figure 6-20 clearly indicate

how closely spaced the cracks were in A-9 as compared to other specimens. This

behaviour corresponds with Frantz and Breen’s findings with regards to all of their

specimens, whereby the percentage of flexural cracks that extended into the web

increased in direct proportion to the total area of skin reinforcing bars provided.

The fact that A-9 had 60% more cracks in the web than A-8, yet had web cracks that

were similar in width, leads to the conclusion that the longitudinal strain in the web was

considerably greater than it was in A-8. Specimens A-1 through A-9 were all loaded in a

similar manner, with the location of the hydraulic ram modified based on an elastic

analysis of the cross-section. Thus any differences in the strain profiles would be due to

differences in the locations of the neutral axes due to differences in the concrete strengths.

The concrete strength of A-9 was 5231psi (36.1MPa) and was greater than the concrete

strength of A-8, which was 4580psi (31.6MPa). However, this difference resulted in a

neutral axis depth in A-9 that was 97% of the neutral axis depth in A-8, an

inconsequential difference.


264

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 0.5 1 1.5 2 2.5 3Skin Reinforcement Ratio, ρsk (%)

No Skin Rft. (A-1, A-2)

6mm bars(A-7)

#3 Bars (A-8)

#4 Bars (A-9)

wwebwsteel

Cross-Section

Other Specimens

0.0

0.5

1.0

1.5

2.0

2.5

20 25 30 35 40 45

Steel Stress, fs (MPa)

6mm Bars(A-7)

#3 Bars(A-8)

#4 Bars(A-9)

wwebwsteel

Figure 6-19: Effect of Bar Size on Crack Magnification Ratio (Frantz and Breen, 1976)

10%

20%

30%

40%

50%

60%

70%

80%

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Skin Reinforcement Ratio, ρsk (%)

6mm bars

Perc

ent o

f Cra

cks

at L

evel

of S

teel

Ext

endi

ng In

to W

eb

No Skin Rft.

#3 Bars

#4 Bars

Vetical spacingbetween bars = 4.125in.

Figure 6-20: Effect of Bar Size on Crack Extension into Web

a) fs=35ksi b) Beams A-7, A-8 A-9

fs=35ksi

Note: Frantz and Breen (1976) present crack width data for fs=25, 30, 35 and 40ksi. Data not available for A-9 at fs=35ksi.


265

It is not entirely clear why, with considerably more cracks in the web of A-9 than in A-8,

the average web crack widths were measured to be about the same. There is an inherent

scatter associated with crack widths in the webs of concrete members, and it is a

considerable challenge to measure crack widths accurately and uniformly. However, it is

a far more straight-forward exercise to simply visually identify the locations of cracks

and to mark them with pens. The crack diagrams shown in Figure 6-20 can thus be

regarded as a very accurate representation of the effect of increasing the skin

reinforcement bar diameter to a No. 4 from a No. 3, without the inherent variability

associated with visual crack width measurements.

There is a considerable amount of scatter in the data presented in Figure 6-19a), due in

part to the large number of variables considered in the experimental program. There is

even a considerable amount of scatter in crack magnification ratios between nominally

identical specimens tested with ρsk =0.22%, and this is illustrative of the type of scatter

inherent in the phenomenon of cracking in concrete. However, the data in this figure

indicates that a small amount of crack control reinforcement may have a significant

impact on web crack widths, but that this effect is unreliable. As the value of ρsk is

increased, web crack widths decrease, but at a decreasing rate. The behaviour of the

cracks exhibited in specimen A-9, in which the majority of cracks at the level of the steel

extend well into the web, is far preferable to the behaviour of the cracks in the other

specimens, including those in A-8. In the other specimens, most of the cracks at the level

of the steel coalesced into a smaller number of wider cracks in the web.

The data in Figure 6-19a) is reproduced in Figure 6-21 based on the CSA method of

calculating ρsk. It can be seen that beyond a skin reinforcement ratio of about 1%, cracks

in the webs tended to stay narrower than 1.7 times the widths of the cracks at the flexural

steel. One notable exception is specimen A-6, which contained skin reinforcement

consisting of one No. 6 (19mm diameter) rebar on either side of the specimens spaced at

13.375in. (340mm) from the tensile steel. The spacing of this single bar exceeded the

maximum spacing of 12in. (300mm) allowed in the ACI 318-05 skin reinforcement


266

provisions by only 1.375in (35mm), yet considerably wider cracks occurred in the web

than at the level of the steel. Commenting on the cracks in this specimen, Frantz and

Breen note that “…the bars in A-6 are located too far away from the crack development

zone…to significantly influence the crack formation.”

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 0.5 1 1.5 2 2.5 3Skin Reinforcement Ratio, ρsk (%)

wwebwsteel

skb

barsk )sd+(2c

A=ρ

A-6

ρsk>1%

Figure 6-21: Effect of ρsk on Crack Magnification Ratio

6.3.8 Suggested Modifications to ACI Code

The experimental program described in this chapter has shown that the bar size has a

clear effect on crack widths in the webs of thick flexural elements. It seems that, at the

very least, a minimum bar diameter must be specified in clause 10.6.7 of the ACI code

(Figure 6-8). Describing commonly-used bar sizes in the commentary is not sufficient.

The crack widths measured in the current experimental program were successfully

controlled using both 10M bars at 225mm (about equivalent to #3 bars at 9in.), resulting

in an ρsk value of 0.4%, and 15M bars at 255mm (about equivalent to #5 bars at 10in.),


267

resulting in an ρsk value of 0.68%. Furthermore, Frosch’s model generally was accurate

at predicting the maximum crack widths for these specimens.

Referring to Figure 6-21, it can be seen that specimens in the Frantz and Breen study

exhibited relatively narrower cracks in the webs for ρsk values exceeding about 1%, so

long as the vertical spacing between the skin reinforcing bars was not too great. Based

on specimen A-6, it appears that the maximum spacing of 12 in. for skin reinforcing bars

may be too large.

It is suggested that the ACI 318-05 code require at least a No. 5 rebar for skin reinforcing

bars, and that the vertical spacing between layers of skin reinforcement, s, be calculated

as follows, with the maximum spacing being 10 inches (254mm) for a steel stress of

40ksi, rather than 12 inches (300mm):

( )scs

f40102.5c-f

15(40)s ≤= (6-10)


268

6.4 Effect of Crack Control Steel on Shear Strength

6.4.1 General

It has been suggested that the ACI code’s inability to account for the size effect in shear

can be partially or fully addressed by the use of skin reinforcement. For example, narrow

beams with sufficiently large skin reinforcing bars such that cracks remain narrow and

closely spaced within the web have been shown to exhibit higher shear strengths (Collins

and Kuchma (1996)). However, the preceding sections have shown that deep sections

with skin reinforcement designed in conformance with the ACI code may still exhibit

wide cracks, since the code does not mandate a minimum bar diameter or skin

reinforcement ratio. Furthermore, wide slabs with a large width to depth ratio may still

experience wide cracking well away from the skin reinforcement. The 1978 CEB-FIP

code, for example, suggests that a rebar controls crack widths only within 7.5db from the

centre of the bar.

As discussed in Chapter 2, the 2004 CSA code suggests that the crack spacing parameter,

sz, can be taken to be equal to the vertical spacing between layers of distributed

longitudinal reinforcement, if the total area of steel in a layer (Alayer) exceeds 0.3% of bwsz.

The reduced value of sz can be used instead of 0.9d or 0.72h, and is designed to model the

effect that distributed longitudinal reinforcement has on the spacing of cracks in the web.

Specifically including bw when calculating the required area of steel requires the designer

to specify larger bars for wider members if it is desired to use the reduced value of sz. To

be effective, the bars in each layer must be spaced closer than 600mm (24in.) horizontally

(Lubell et. al. (2004)). In the context of calculating sz, this distributed longitudinal

reinforcement is referred to as crack control reinforcement, and this is a more accurate

description of the role that this reinforcement plays.

Previous tests of beam specimens with crack control steel reported by Collins and

Kuchma (1999) involved values of Alayer/bwsz of between 0.61% and 1.19%, and there are

no tests to be found in the literature on thick beams with only just the minimum quantity


269

of crack control reinforcement to use the reduced value of sz. Furthermore, a number of

the larger specimens with crack control steel reported by Collins and Kuchma failed at

ratios of vexp/vCSA of less than 1. The average value of vexp/vCSA for the eight tests

(including three repeated tests) with an effective depth of 920mm or greater was 0.9, with

the lowest value being 0.77.

It was thus decided to investigate the shear behaviour of a large beam specimen with

distributed longitudinal steel designed to just meet the 0.003bwsz requirement. It was also

decided to investigate whether this quantity of crack control steel could control crack

widths to such an extent that the size effect could be essentially eliminated. In order to

simplify discussion, it is proposed that a new parameter, ρd, be defined, where

ρd=Alayer/bwsz, where Alayer is the area of steel in a layer of crack control reinforcement.

6.4.2 Experimental Program

The specimens are described in Figure 6-10. Specimen L-20D was designed to be

300mm wide, 1510mm high and 9000mm long. It was constructed with 4-30M rebars at

a depth of 1450mm from the top face of the specimen, and six layers of two 10M

longitudinal bars spaced at 225mm over the height of the specimen. The as-built width

was 295mm, resulting in a ρd value of 200/(295 x 225)=0.301%, and this is almost

exactly the minimum required value of ρd to use a reduced sz value.

The CSA code and AASHTO-LRFD both specify that the area of flexural tension

reinforcement, As, includes all longitudinal reinforcement in the flexural tension half of

the member. Counting the layers of 10M crack control steel below h/2 results in an

effective depth of 1370mm, an area of steel of 3400mm2, a reinforcement ratio of 0.84%

and an a/d ratio of 2.96. Cross sectional properties were chosen such that the

reinforcement ratio was similar to the ten equivalent specimens that were tested as part of

the aggregate interlock study which had a reinforcement ratio of 0.83%.


270

The specimen was cast at the same time as L-20L (discussed in Chapters 5 and 7), with

normal strength concrete and a maximum aggregate size of 19mm (3/4in.). Because of

the use of crack control steel, the 2004 CSA code states that sz can be taken as the vertical

spacing between the layers of steel, namely 225mm. The crack control steel was hung in

place with a series of small-gauge steel wires tied to the bars and to supports spanning

over the top of the forms. Photographs of the cage under construction are provided in

Figure 6-22.

Figure 6-22: Photographs of L-20D Cage Under Construction

The 225mm centre-to-centre spacing of the crack control steel is 12.5% greater than the

200mm maximum spacing in the CSA code. However, the ACI code maximum spacing

was 254mm (10in.). To make the specimen applicable to the study of both codes, the

average of the code spacings was used.

Specimen L-20D was designed to be shear critical, and was tested in three point bending

under the Baldwin test frame in the Huggins structures laboratory in the Department of

Civil Engineering at the University of Toronto. The test setup was identical to that used

to test the other L-series of specimens described in Chapter 5 of this thesis, with


271

associated zurich targets and LVDTs to measure vertical deflection and shear strains.

After the specimen failed on the east side, this side was clamped together with a series of

externally placed Dywidag bars, and the beam was retested to failure on the west side (L-

20DR).

Two small specimens, S-20D1 and S-20D2 were constructed at the same time as L-20D

to represent small members with identical effective crack spacing parameters, sxe. They

nominally measured 96mm wide, 280mm high and 1800mm long, and were reinforced

with two 10M rebars at an effective depth of 250mm. They were loaded to failure in

three point bending under a displacement-controlled MTS actuator in a setup similar to

that used for the S-Series of specimens described in Chapter 5, with associated LVDTs to

measure midspan vertical displacements and shear strains (Figure 6-23).

Specimens S-20D1 and S-20D2 were supported on 30mm wide supports spaced 1480mm

apart, had a nominal reinforcement ratio of 0.83% and were constructed with normal

strength concrete and a maximum aggregate size of 19mm (3/4in.). They had an sxe value

of 0.9(250) = 225mm.

Figure 6-23: Test Setup –Specimens S-20D1 and S-20D2

Specimens S-20D1, S-20D2 and L-20D were each designed to have identical sxe values

and identical a/d and ρw values. Thus, the CSA code predicts that each specimen should

fail at identical values of β=V/bwd(f’c)0.5 and hence that there should be no size effect

between the large and small specimens.


272

6.4.3 Experimental Results

As built dimensions and key experimental results are presented in Table 6-2. Average

experimental results from the ten equivalent L-series specimens without crack control

steel are provided for comparison. Load vs. mid-span displacement curves are presented

in Figure 6-24. Also shown in Figure 6-24 are the failure loads predicted by the

simplified MCFT and ACI Eq. 11-5.

The average failure shear force of L-20D and L-20DR was 356kN, which is 32% greater

than the average failure shear force of the ten equivalent specimens without the crack

control reinforcement.

The behaviour of L-20D under load was characterized by the formation of cracks in the

web that were narrower and more numerous than those formed in the ten equivalent L-

series specimens without crack control steel. See, for example, Figure 6-25, which

compares the cracking patterns of L-20D and L-20N1. It can be seen that, for L-20N1,

the three widest cracks measured 0.4mm, 0.6mm and 1.0mm when the load was 500kN,

whereas for L-20D the three widest cracks all measured 0.3mm when the load was

650kN. These loads correspond to midspan steel strains of 1250με and 1670με

respectively, based on an elastic analysis of the cracked sections. Furthermore, note that

the average longitudinal spacing of the cracks at midheight of the beams decreased from

about 700mm (0.5d) to 400mm (0.3d), and the number of cracks at midheight increased

from seven to thirteen. It can thus be seen that at considerably higher steel strains, the

crack control steel caused narrower, more numerous cracks to form in specimen L-20D.

The crack control steel in L-20D also resulted in final failure cracks that were flatter than

those in the specimens without crack control steel. The crack angle calculated by the

SMCFT (Eq. 2-22) is shown in Figure 6-25, and it can be seen that this equation

provides a good estimate of the actual crack angle in these specimens.


273

Table 6-2: As-Built Properties and Experimental Results, L-20D and S-20D Series

bw d a/d ρw f'c(1) ag,eff sxe Pexp Vexp(2) vexp Δult/0.5L γult εs,max wmax

(mm) (mm) (%) (MPa) (mm) (mm) (kN) (kN) (MPa) x10-3 x10-3με (mm)

S-20D1 98 252 2.94 0.81 40.6 19 227 49.5 24.8 1.00 4.5 0.87 2160 0.15S-20D2 96 250 2.96 0.83 40.8 19 225 51.6 25.8 1.08 4.3 0.43 2340 0.15

L-20D 295 1370 2.96 0.84 35.8 19 225 668 350 0.87 2.8 0.60 1620 0.30L-20D-R 295 1370 2.96 0.84 35.8 19 225 689 361 0.89 - - 0.61 1660 0.35

0.53L-Avg(3) 300 1400 2.89 0.83 39.5 0-51 1071-2756 509 270 0.64 2.1 0.65 1255

SpecimenSpecimen Properties (as-built) Experimental Observations

Notes:(1) day of test(2) Calc. at d from face of loading plate, incl. self-weight (vexp = Vexp/bwd)(3) Average of L-10H, 10N1, 10N2, 20N1, 20N2, 40N1, 40N2, 50N1, 50N2, 50N2-R

0

100

200

300

400

500

600

700

800

0 2 4 6 8 10 12Mid-Span Deflection, Δ (mm)

App

lied

Load

(kN

)

ACI

SMCFT

L/800

4-30Mρw=0.84%

2-10M @ 225 Failure LoadL-20DR

L-20D

0

10

20

30

40

50

60

0.0 1.0 2.0 3.0 4.0Mid-Span Displacement, Δ (mm)

App

lied

Load

(kN

)

L/480

S-20D2

S-20D1

ACI -D2ACI -D1

SMCFT -D2SMCFT -D1

2-10Mρw=0.82%

Figure 6-24: Load vs. Midspan Displacement Curves, L-20D, S-20D1, S-20D2


274

Figure 6-25: Failure Crack patterns in L-20D and L-20N1


275

It is interesting to note that the ratio of Δ/0.5L to the shear strain, γult, in L-20D was 21%,

while the average for the specimens without crack control steel was 31% (with the lowest

value being 23%). Less of the total mid-span displacement was caused by shear strains in

L-20D and it exhibited a higher shear stiffness than the specimens without crack control

reinforcement. See Figure 6-26, in which the measured shear stress vs. shear strain

curves at the quarterspans are plotted for specimens L-20DR and L-20N2.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 0.2 0.4 0.6 0.8 1Shear Strain (mm/m)

Shea

r Str

ess,

v (M

Pa)

L-20DR

L-20N2

L-20D Failure on East End

Figure 6-26: Shear Stress vs. Shear Strain for Specimens L-20DR and L-20N2,

Measured at Quarterspan

The stiffer response of L-20D compared to specimens without crack control steel can also

be seen by comparing the midspan deflections. At an applied load of 500kN, the

measured midspan deflection for L-20D was 7.2mm, and this is 22% less than the

average measured midspan deflection for L-20N1 and L-20N2 at the same load. Yet the

transformed moment of inertia for L-20D was 94,300x106mm4, versus an average value

of 95,500x106mm4 for L-20N1 and L-20N2.


276

6.4.4 Effect of Dowel Action and Aggregate Interlock

It is suggested that the considerable increase in shear strength exhibited in L-20D and L-

20DR was primarily a result of the formation of narrower cracks that were better able to

transfer shear due to aggregate interlock. A portion of the increase can also be attributed

to increased dowel resistance.

Bhide and Collins (1987) note that a large number of small size bars offers a larger dowel

resistance than a small number of large bars, for the same reinforcement ratio and dowel

displacement, where the dowel displacement is calculated as “…the component of the

crack width in the direction at right angles to the reinforcing bar under consideration.”

Put another way, a large number of small bars offers a stiffer response than does a small

number of large bars. Thus, beams in which some of the longitudinal steel area

concentrated in the bottom has instead been distributed over the height would be

expected to exhibit a stiffer shear response, and this behaviour was observed in L-20D

and L-20DR. It would also be expected that a greater proportion of the total shear at a

section in such a beam would be carried by dowel action, for three reasons:

1) the cracks in the web are at a flatter angle than at the level of the main reinforcement,

with a larger component of the crack width oriented in the vertical direction. Analysis

of the cracks at the level of the main reinforcement in all the large specimens tested

indicated a wide range of crack angles ranging from perfectly vertical to identical to

the angle of the crack in the web. In general, however, the cracks in the web were

observed to be flatter than the cracks at the level of the main reinforcement.

2) cracks in the web are wider than they are at the level of the main steel. This would

only be the case if the longitudinal crack spacing in the web was not reduced to a

degree such that crack widths reduced from a maximum at the steel to zero at the tips

of the cracks.


277

3) reduced longitudinal stiffness in the main reinforcement results in wider cracks at the

level of the reinforcement, with the components of the widths in the vertical direction

increasing as a consequence.

At a load of 650kN, a total of eight 10M crack control bars crossed the critical shear

cracks in L-20D and L-20DR. Combined with the four 30M bars in the bottom of the

specimen, this resulted in a total cross-sectional area of 3600mm2 of steel crossing the

crack that was available to resist shear by dowel action. This cross-sectional area is 3%

greater than the area of steel crossing the crack in the specimens without crack control

steel, but more importantly there was a total of twelve bars crossing the crack as opposed

to five.

Bhide and Collins (1987) derived a series of expressions to estimate the dowel force in a

bar crossing a crack of width w. The dowel force, Fd, versus dowel displacement, δ,

relationships for a 10M and a 30M bar are shown in Figure 6-27, in which the cracking

pattern in L-20D at P=650kN has been reproduced. The measured crack widths at a

single crack are shown as well. This crack was inclined at about 60o, and measured

0.25mm wide over most of its height. At the level of the main reinforcement, it was

about 0.15mm wide. Based on comparisons with crack patterns in the other L-series of

specimens, had this beam not contained crack control steel, it likely would have failed at

this crack at a load that was considerably smaller than 650kN.

Figure 6-27: Analysis of Dowel Action in Specimen L-20D


278

The component of the crack widths in the vertical direction were 0.125mm and 0.075mm

in the web and at the main reinforcement, respectively. These dowel displacements

resulted in dowel forces of 2.5kN and 5.9kN in the 10M bars and 30M bars, respectively,

and a total of about 8 x 2.5 + 4 x 5.9 = 44kN of shear being transferred by dowel action at

the section. This represents 13% of the total shear at the section. Had five 30M bars

been placed in the bottom layer without crack control steel, and the same crack pattern

formed with identical inclinations and crack widths, the shear transferred by dowel action

would have been about 5 x 5.9 = 30kN, representing 9% of the total shear at the section.

Indeed, a slightly narrower crack might be expected to have formed at the level of the

steel due to the presence of an additional 30M bar, reducing the dowel forces slightly.

We thus see that increased dowel action may have accounted for about 44kN-

30kN=14kN of the total additional shear of (0.5x650 – 0.5x500) = 75kN. This represents

19% of the total increase in shear force. The geometry of the cracking patterns in L-20D

and L-20DR generally resembled the geometry of the cracking patterns in L-10N2, in

which about 24% of the total shear force was transferred in the uncracked compression

zone, and it is unlikely that crack control steel significantly alters this proportion.

We are therefore left with the conclusion that the majority of the additional shear strength

exhibited by L-20D and L-20DR, about (100%-24%-19%)=57%, was due to enhanced

aggregate interlock capacity along the narrower cracks.

6.4.5 Code Estimates of the Shear Strength

It can be seen in Figure 6-24 that both the ACI and SMCFT generally provided accurate

estimates of the failure loads of the small beams, but both methods were somewhat

unconservative when estimating the failure loads of the two large specimens. For these

large beams, the average ratio of vexp/vACI was 0.86, while the average ratio of vexp/vSMCFT

was 0.91.


279

Providing skin reinforcement spaced closer than that required by ACI 318-05 thus did not

completely eliminate the size effect in shear. Had bars of a diameter smaller than that of

a 10M rebar been used as skin reinforcement, such as #3 US rebar or small deformed

wires, the shear strength would have been reduced. Application of the ACI skin

reinforcement provisions, which do not require a minimum bar diameter, does not,

therefore, ensure that the size effect will be adequately accounted for when designing

slender beams and slabs without shear reinforcement.

The failure shear stresses of L-20D, L-20DR, S-20D1 and S-20D2 are plotted in Figure

6-28 versus the effective crack spacing, and have been normalized by (f’c)0.5 and the CSA

strain effect term. The CSA size effect term, 1300/(1000+sze), has been plotted as well,

along with the experimental points from the other S- and L- series specimens. This figure

shows that the size effect has not been completely eliminated through the use of crack

control steel with ρd=0.3%. Interestingly, the difference between the normalized shear

strengths of S-20D1/2 and L-20D/R resembles the difference between the normalized

shear strengths of the small and large specimens tested with stirrups (see Chapter 7).

Based on these observations, it seems that, while the CSA shear provisions perhaps need

to be improved for members with distributed reinforcement, it is unclear whether

increasing ρd will adequately address the situation.

Table 6-3 compares experimental results from fifteen tests of continuous and simply-

supported beams of various depths reported by Collins and Kuchma, all of which

contained crack control steel with ρd values well in excess of 0.3%, with the four tests in

the D series of this thesis. Examination of the vexp/vsmcft values indicates that a number of

the specimens failed at shear strengths that were less than those predicted by the SMCFT.

BHD100, BND100 and SE100B-45, for example, failed at shears that were 78%, 83%

and 77%, respectively, of the SMCFT predicted failure shears. With the exception of

SE50B-45, generally the deeper specimens exhibited reduced shear strengths. These

specimens had ρd values considerably higher than that used in L-20D as a result of both

smaller vertical spacings between the layers of crack control steel and larger bar


280

diameters, yet failed at lower ratios of vexp/vsmcft. Furthermore, these specimens were

shallower than L-20D. Thus, requiring a higher ρd value before sz can be set equal to the

vertical spacing between layers of crack control steel does not appear to be the correct

modification.

Figure 6-28: Size-Effect Factors for Members with Distributed Longitudinal Steel


281

Table 6-3: Summary of Experiments of Beams with Crack Control Reinforcement

bw d ρw ρd sd f'c(1) ag,eff Vexp vexp vACI vexp sxe vSMCFT vexp sxe vSMCFT vexp

(mm) (mm) (%) (%) (mm) (MPa) (mm) (kN) (MPa) (MPa) vACI (mm) (MPa) vSMCFT (mm) (MPa) vSMCFT

Continuous BeamsSE100B-45 295 920 1.36 1.04 195 50 9.5 281 1.04 1.16 0.99 268 1.35 0.77 547 1.18 0.88SE100B-45R 295 920 1.36 1.04 195 50 9.5 316 1.16 1.16 1.00 268 1.35 0.86 547 1.18 0.99SE50B-45 169 445 1.20 0.61 195 53 9.5 87 1.16 1.19 0.97 268 1.28 0.90 268 1.28 0.90

SE100B-83 295 920 1.36 1.04 195 86 0 365 1.34 1.36 0.99 427 1.38 0.97 872 1.15 1.17SE100B83R 295 920 1.36 1.04 195 86 0 364 1.34 1.36 0.99 427 1.38 0.97 872 1.15 1.17SE50B-83 169 445 1.20 0.61 195 91 0 101 1.34 1.35 0.99 427 1.28 1.05 427 1.28 1.05

3-Point Bending BeamsB100D 300 925 1.19 1.18 170 36 9.5 320 1.15 1.02 1.13 233 1.11 1.04 480 0.99 1.17BND100 300 925 1.19 0.78 170 37 9.5 258 0.93 1.03 0.90 233 1.12 0.83 480 1.00 0.93BND50 300 460 1.09 0.78 85 37 9.5 163 1.18 1.02 1.15 117 1.15 1.02 119 1.15 1.02BND25 300 225 1.48 1.19 40 37 9.5 112 1.66 1.04 1.59 55 1.33 1.25 55 1.33 1.25

BHD100 300 925 1.19 0.78 170 99 0 278 1.00 1.38 0.73 372 1.28 0.78 764 1.09 0.92BHD100R 300 925 1.19 0.78 170 99 0 334 1.20 1.38 0.87 372 1.28 0.94 764 1.09 1.11BHD50 300 460 1.09 0.78 85 99 0 193 1.40 1.37 1.02 186 1.35 1.04 190 1.35 1.04BHD50R 300 460 1.09 0.78 85 99 0 205 1.49 1.37 1.08 186 1.35 1.10 190 1.35 1.10BHD25 300 225 1.48 1.19 40 99 0 111 1.64 1.40 1.18 88 1.60 1.03 88 1.60 1.03

S-20D1 98 252 0.81 0 - - 40.6 19 24.8 1.00 1.08 0.93 227 0.99 1.01 227 0.99 1.01S-20D2 96 250 0.83 0 - - 40.8 19 25.8 1.08 1.08 0.99 225 1.00 1.07 225 1.00 1.07L-20D 295 1370 0.84 0.3 225 35.8 19 350 0.87 1.02 0.85 225 0.96 0.90 685 0.78 1.11L-20DR 295 1370 0.84 0.3 225 35.8 19 361 0.89 1.02 0.87 225 0.96 0.92 685 0.78 1.13

Average: 1.01 0.97 1.06COV: 17% 12% 9%

Specimen Properties and Experimental Observations

SMCFT -Modified sxSMCFTSpecimen

ACI Method

The values of vexp/vsmcft from Table 6-3 are plotted in Figure 6-29 for the different ρd and

effective depth values. There is a general trend indicating that vexp/vsmcft decreases as the

effective depth increases. This relationship with the effective depth can also be seen in

Figure 6-30, where generally the CSA size effect term becomes more unconservative as

the effective crack spacing increases. The shape of the experimentally determined size

effect curves for the BND and BHD data, in particular, do not match the shape of the

CSA size effect curve.

Failure cracks in members with crack control steel can be expected to be flatter than in

members without crack control steel (see Figure 6-25). However, as cracks become

flatter, longitudinal crack control steel will become less effective at controlling crack

widths. (This is in contrast to members with stirrups, in which flatter crack angles result

in increased stirrup effectiveness.) It appears that this reduced effectiveness was

sufficient to overcome the beneficial effects of large crack control bar diameters in

members summarized in Table 6-3.


282

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.0 0.3 0.6 0.9 1.2 1.52Abar/bwsz

Vexp

VCSA

(%)

CSA-04 Minimum

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 10 20 30 40 50 60Effective Depth, d

0 500 1000 1500

(in.)

(mm)VexpVCSA

Trendline

Figure 6-29: Shear Strengths of Members with Crack Control Steel

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

-200 0 200 400 600 800 1000 1200

L-20DS-20DBNDBHDB100DSE-45SE-84

Effective Crack Spacing, sze (mm)

Test Series

Figure 6-30: CSA Size Effect Term for Members with Crack Control Steel

x

'c

vw

c

1500ε+10.4

f

dbV

a) b)

d=445-460mm

d=925mm

d=1370mm


283

6.4.6 Suggested Modifications to CSA Code

It is suggested that the method by which sz, the crack spacing parameter, is calculated be

modified to account for the lower values of vexp/vsmcft values at higher effective depths. It

is recommended that it be calculated as follows:

For d < 450mm, sz = sd

For d ≥ 450mm, sz = 450d

sd ≤ 0.9d or 0.72h, whichever is larger (6-11)

where sd is the vertical centre-to-centre spacing between layers of crack control steel having a

minimum area of 0.003bwsd per layer. See Figure 6-31.

Figure 6-31: Definition of sd in Eq. 6-11

A number of different factors of varying complexity by which sd could be multiplied

were examined, but it is felt that the (d/450) factor is appropriately simple for design

situations.

The vexp/vsmcft values presented in Figure 6-29 are recalculated and plotted in Figure 6-32

using the modified method to calculate sz. As summarized in Table 6-3, the average

value of vexp/vsmcft for the experiments is 1.09 with a COV of 9% using the modified value

of sz, versus 0.97 and 12% based on sz=sd. Using the modified method to calculate sz

results in a slight upwards trend in the vexp/vsmcft values as the effective depth increases.

As there is a lack of experimental data for members with effective depths exceeding

1400mm with crack control steel, it is appropriate to be conservative when extrapolating

beyond the range of experimental data.


284

Referring to Figure 6-33, it can be seen that the experimentally determined values of the

size effect term and the shapes of the experimentally determined size effect curves more

accurately follow the CSA size effect curve. Note, for example, that test series with

formerly one value for sze (the SE series and the S- and L- series reported here) now have

different sze values, with variations in the normalized shear strength that more closely

match the CSA size effect term. While the line for the SE-45 series falls below the CSA

curve, the slope of the line matches the slope of the CSA curve.

The crack spacing parameter in the CSA code, sz, is intended as a measure of the crack

spacing at mid-depth of a member. For members without stirrups or crack control steel,

it is equal to 0.9d, and is analogous to a “characteristic crack spacing”. Shioya et. al.

(1989) found in their tests that the average crack spacing at midheight was generally

about 0.5d in specimens without stirrups or crack control steel, and similar crack spacings

were found in this experimental program. The CEB-FIP code defines a characteristic

crack width, wk, as the width that 5% of cracks will exceed, and it is equal to 1.7 times

the mean crack spacing, wm. The characteristic crack spacing, sk, therefore, is equal to

1.7 times the mean crack spacing, wm. For a mean crack spacing of 0.5d, the

characteristic crack spacing is 1.7 x 0.5d = 0.85d, which is about equal to the CSA crack

spacing parameter.

In specimen L-20D, the mean measured crack spacing was 400mm, resulting in a

characteristic crack spacing of 1.7x400=680mm. The crack spacing parameter for

specimen L-20D calculated using Eq. 6-11 is equal to 685mm, and thus corresponds to

the characteristic crack spacing.


285

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.0 0.3 0.6 0.9 1.2 1.52Abar/bwsz

Vexp

VCSA

(%)

CSA-04 Minimum

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 10 20 30 40 50 60Effective Depth, d

0 500 1000 1500

(in.)

(mm)VexpVCSA

Trendline

Figure 6-32: Shear Strengths of Members with Crack Control Steel Based on Eq. 6-11

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

-200 0 200 400 600 800 1000 1200

L-20DS-20DBNDBHDB100DSE-45SE-84

Effective Crack Spacing, sze (mm)

Test Series

Figure 6-33: Size Effect Term for Members with Crack Control Steel Based on Eq. 6-11

x

'c

vw

c

1500ε+10.4

f

dbV


286

6.5 Concluding Remarks

The experiments described in this chapter have shown the importance of proper structural

detailing in minimizing the negative effects of cracking in reinforced concrete structures.

The skin reinforcement study has shown that it is incorrect to state that any sized rebar

can be used effectively to control flexural crack widths in the webs of large members.

The study on the shear strength of elements with crack control steel has shown that shear

strength can be enhanced through the use of a sufficiently large quantity of well

distributed longitudinal steel.

In tests of reinforced concrete elements subjected to pure tension, in which covers and

bar spacings were kept constant, Williams (1986) showed that small bars were unable to

control crack widths. When a crack first formed, the tensile force in the concrete, Acfcr,

exceeded the yield strength of the small bars. Hence, further straining occurred at the

cracks due to bar yielding rather than by the formation of additional cracks. Even in

elements with larger bars, where yielding did not immediately occur, elements with lower

steel areas exhibited more widely spaced cracks, as the small area of steel crossing the

crack had a low stiffness, AsEs, that was insufficient to restrain widening of the crack.

Likewise, in the case of skin reinforcement, small diameter bars spaced far apart are not

able to restrain the widening of cracks, as the longitudinal stiffness of the steel crossing

the crack will be insufficient. While Frosch quotes Gergely and Lutz’s statement that

“the bar diameter is not a major variable,” (as discussed on page 241) in fact, Gergely and

Lutz state that “the steel stress is the most important parameter.” Very small bars with a

low ρsk value are highly stressed at the locations of flexural cracks. The steel stress is,

indeed, the primary variable, and the stress will be increased considerably through the use

of small diameter bars.

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Control of Crack Widths