Cracking, Deflections and Ductility Code Provisions and Recent Research

transcript

Cracking, Deflections and DuctilityCode Provisions and Recent

Research

October 2006

Serviceability and DuctilityServiceability and DuctilityThe Other Limit StatesThe Other Limit States

Cracking, Deflections and DuctilityCode Provisions and Recent Research

Overview– Code provisions for ductility

– Background to the study

– Codes: AS3600, AS5100, EC2, BS5400, BS8110, CEB-FIP 1990, ACI 318

– Background to prediction of cracking and deflections

– Code provisions for crack widths and stress limits

– Code provisions for deflections

– Recent research

– Conclusions

Code provisions for ductility

Detailing Capacity Factors

Ductile Capacity

Ductility Limits

AS 3600

AS 5100

BS5400

BS8110

CEB-FIP

ACI 318

Background to the study

Prediction of cracking and deflection:– Why is it important?– Why is it difficult?– What do the codes say?

Prediction of Cracking and DeflectionsWhy is it important?

Second order effects Load distribution and transfer Loads on non-structural members Durability Code compliance Contract conditions Client expectations Aesthetics Clearances, ponding etc.

Why is it difficult?

Uncertain or unknown material properties Inconsistent and incomplete code provisions Inherently random nature of cracking Unknown manufacture procedures and

construction programme Variations in curing procedures and

environmental effects Complex loading history

Uncertain or unknown material properties

Concrete tensile strength; creep rupture? Concrete stiffness under tension; non-

linearity? Concrete creep and shrinkage properties Concrete behaviour under unloading/

reloading

Inconsistent and incomplete code provisions

Tensile strength of concrete Effect of shrinkage on tensile strength Tension stiffening Loss of tension stiffening Effect of uncracked parts of structure Effect of shrinkage

Unknown manufacture procedures and construction

programme Concrete age at loading? Time before application of loads or restraints? Effect of steam curing

– Locked in thermal stresses? Storage, curing

– Differential shrinkage?

Complex loading history

Critical sections subject to may be sagging, hogging, sagging, hogging

Effect of axial load Calculation of non-recoverable deflections

(eg creep)

What do the codes say?

Compare AS3600, AS5100, EC2, BS5400, BS8110, CEB-FIP 1990, ACI 318

Differing and inconsistent provisions No one code covers all significant effects

Background to prediction of cracking and deflections

Formation and propagation of cracks Relationship between cracking and section

stiffness– Tension stiffening– Loss of tension stiffening

Time related effects– Creep– Shrinkage– Differential shrinkage

Calculating deflections from section stiffness

Background to prediction of cracking and deflections

Recommended reading:Concrete Structures– Stresses and Deformations– Ghali Favre and Elbadry

Formation and propagation of cracks

Relationship between cracking and section stiffness

Tension stiffening Displacement of Neutral Axis Loss of tension stiffening

Time related effects Creep

– General agreement on mechanism and analysis approach

– Amount and rate of creep variable Shrinkage

– Affects both section curvature and effective cracking stress

– No agreed approach to analysis of either effect Differential shrinkage

– May have a large effect on section curvature and deflections

– Not specifically covered by any of the codes studied

Calculating deflections from section stiffness

Two approaches in codes– “Effective stiffness” approach (ACI and Australian

codes) - Branston equation– Average of cracked and uncracked section

stiffness.– Integrate section curvature along the length of the

member.

Code provisions for stress limits AS 3600, AS 5100 and EC2

– Crack control by stress limits governed by bar diameter and spacing

– AS 5100 has much lower stress limits applicable to stresses due to permanent loads in exposure classifications B2, C or U

– EC2 limits related to specified crack widths under quasi-static loading

– AS 3600 limits similar to EC2 limits for 0.4 mm crack width for bar diameter, and 0.3 mm for bar spacing

– AS 5100 limits for exposure classification B2 and higher similar to EC2 limits for 0.2 mm crack width

– The specified stress limits will result in substantially higher design crack widths with increased cover.

Code provisions for stress limitsStress Limits for Maximum Bar Diameter

Bar Dia AS 3600 AS 5100mm Cw =0.4 Cw =0.3 Cw =0.26 450 340 450 400 3208 400 305 400 360 28010 360 275 360 32012 330 250 320 280 24016 280 215 280 240 20020 240 185 24024 210 160 200 16028 185 14032 160 125 200 16036 140 11040 120 95 160

Code provisions for stress limits Stress Limits for Maximum Bar Spacing

Spacing AS 3600 AS 5100mm Cw =0.4 Cw =0.3 Cw =0.250 360 280 360 280

100 320 240 360 320 240150 280 200 320 280 200200 240 160 280 240 160250 200 120 240 200300 160 80 200 160

Code provisions for stress limits Design crack widths for maximum stress

40 36 32 28 24 20 16 12 10

Crack width to EC2, cover = 40 mm

50 100 150 200 250 300

40 36 32 28 24 20 16 12 10

Crack width to EC2, cover = 85 mm

50 100 150 200 250 300

40 36 32 28 24 20 16 12 10

Crack width to BS5400, cover = 85 mm

50 100 150 200 250 300

Code provisions for crack widths

AS 3600 and AS 5100– No requirement for calculation of crack widths

Code provisions for crack widths EC2

Code provisions for crack widths -EC2

Code provisions for crack widths EC2 - Notes:

– Crack spacing is mainly related to cover depth– Crack width is directly proportional to crack spacing– Tension stiffening is limited to 40% of steel strain without

stiffening– Coefficient for long term tension stiffening is reduced by 1/3

(0.6 to 0.4)

Design surface crack width:Design surface crack width:

BS 5400BS 5400 BS8110BS8110

91 101

cssrssk lw 22max

CEB-FIP 1990 (MC 90)CEB-FIP 1990 (MC 90)Design crack width:Design crack width:

maxsl Length over which slip between concrete and steel occursLength over which slip between concrete and steel occurs

Steel strain under a force causing stress equal to concrete Steel strain under a force causing stress equal to concrete tensile strength over concrete tension area x empirical tensile strength over concrete tension area x empirical coefficientcoefficient

Free shrinkage of concrete (generally negative)Free shrinkage of concrete (generally negative)

Steel strain at the crackSteel strain at the crack

ACI 318 - 89, 99, Gergely-Lutz equationACI 318 - 89, 99, Gergely-Lutz equation

x)-x)/(d-(h

3 Adfz cs

unitsmNzw 12max 1011

ACI requirements based on stress limits derived from theACI requirements based on stress limits derived from theGergely-Lutz equation:Gergely-Lutz equation:

Crack Width vs Steel StressSpacing 125 mm

0 50 100 150 200 250 300 350

Steel Stress, MPa

EC2 BS5400 BS5400 BS8100 CEB_FIP_1990 ACI318_99

0 50 100 150 200 250 300 350

Steel Stress, MPa

0 50 100 150 200 250 300 350

Steel Stress, MPa

0 50 100 150 200 250 300 350

Steel Stress, MPa

0 50 100 150 200 250 300 350

Steel Stress, MPa

Crack Width vs CoverSpacing 125 mm

20 30 40 50 60 70 80 90 100

Cover, mm

20 30 40 50 60 70 80 90 100

Cover, mm

20 30 40 50 60 70 80 90 100

Cover, mm

20 30 40 50 60 70 80 90 100

Cover, mm

20 30 40 50 60 70 80 90 100

Cover, mm

Crack Width vs Spacing (constant area, constant stress)

0 50 100 150 200 250 300 350

Bar Spacing, mm

0 50 100 150 200 250 300 350

Bar Spacing, mm

0 50 100 150 200 250 300 350

Bar Spacing, mm

0 50 100 150 200 250 300 350

Bar Spacing, mm

0 50 100 150 200 250 300 350

Bar Spacing, mm

Crack Width vs Spacing (Constant area, max stress)

0 50 100 150 200 250 300 350

Bar Spacing, mm

0 50 100 150 200 250 300 350

Bar Spacing, mm

0 50 100 150 200 250 300 350

Bar Spacing, mm

0 50 100 150 200 250 300 350

Bar Spacing, mm

0 50 100 150 200 250 300 350

Bar Spacing, mm

Code provisions for deflections AS 3600, AS 5100, and ACI 318

Code provisions for deflections AS 3600, AS 5100, and ACI 318 - Notes

– Code provisions based on the “Branson Equation” ACI 318 is differently formulated, but gives the same results.

– Ief is the average effective stiffness, applied over the full length of the member.

– Ms is determined at the critical section(s) specified in the code.

– AS 5100 provisions are identical to AS 3600, (other than a typographical mistake!)

– In the Australian codes the cracking moment is reduced by a factor dependent on the concrete shrinkage. ACI 318 makes no adjustment to the cracking moment.

– AS 3600 and AS 5100 provide a factor kcs to account for the effects of creep and shrinkage:

kcs = [2 - 1.2(Asc / Ast )] >= 0.8

Code provisions for deflections AS 5400 and 8110

– Deflections calculated from integration of section curvatures– Cracking moment and curvature of cracked sections allows

for a short term concrete tensile stress of 1 MPa, reducing to 0.55 MPa in the long term.

– Shrinkage curvature determined from the free shrinkage strain, and the first moment of area of the reinforcement about the cracked or uncracked section, as appropriate.

– BS 5400 tabulates factors based on the compression and tension reinforcement ratios.

Code provisions for deflections Eurocode 2 and Eurocode 2 and CEB-FIP 1990 (MC 90)CEB-FIP 1990 (MC 90) Members which are expected to crack should behave in a

manner intermediate between the uncracked and fully cracked conditions and, for members subjected mainly to flexure, an adequate prediction of behaviour is given by Expression (7.18):

Code provisions for deflections Eurocode 2 and Eurocode 2 and CEB-FIP 1990 (MC 90)CEB-FIP 1990 (MC 90)

Code provisions for deflections Eurocode 2 and Eurocode 2 and CEB-FIP 1990 (MC 90)CEB-FIP 1990 (MC 90) Shrinkage curvatures may be assessed using

Expression (7.21):

Code provisions for deflections SummarySummary

– Australian and American codes based on the Branson Australian and American codes based on the Branson equation, using a uniform average effective stiffness value.equation, using a uniform average effective stiffness value.

– Australian codes allow for loss of tension stiffening through a Australian codes allow for loss of tension stiffening through a reduction of the cracking moment related to the free concrete reduction of the cracking moment related to the free concrete shrinkage.shrinkage.

– Allowance for shrinkage curvature in the Australian codes is Allowance for shrinkage curvature in the Australian codes is simplified and will underestimate curvature in symmetricaly simplified and will underestimate curvature in symmetricaly reinforced sections.reinforced sections.

– British codes allow only a low tension value for cracked British codes allow only a low tension value for cracked sections, which is further reduced for long term deflectionssections, which is further reduced for long term deflections

– European codes adopt an intermediate approach for cracked European codes adopt an intermediate approach for cracked sections, with an allowance for loss of tension stiffening.sections, with an allowance for loss of tension stiffening.

– British and European code provisions for shrinkage curvature British and European code provisions for shrinkage curvature are essentially the sameare essentially the same

Code provisions for deflections SummarySummary

– None of the codes included in this study None of the codes included in this study make specific provision for differential make specific provision for differential shrinkage for monolithic construction.shrinkage for monolithic construction.

– Recent research suggests that loss of Recent research suggests that loss of tension stiffening takes place within a few tension stiffening takes place within a few days, and reduced tension stiffening values days, and reduced tension stiffening values should be used in almost all casesshould be used in almost all cases

Ief vs Bending MomentNo shrinkage

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

3.00E-03

3.50E-03

4.00E-03

4.50E-03

0 20 40 60 80 100 120 140 160 180 200

AS3600 EC2 BS5400 BS8110 No Tens-Stiff

Ief vs Bending Moment300 Microstrain shrinkage

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

3.00E-03

3.50E-03

4.00E-03

4.50E-03

0 20 40 60 80 100 120 140 160 180 200

AS3600 EC2 BS5400 BS8110 No Tens-Stiff

Crown Deflections v Load FactorNo shrinkage

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Load Factor

Deflectio

DX1 BS8110 DX2 AS3600 Offset DY2 S7DX EC2

Crown Deflections v Load Factor300 Microstrain shrinkage

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Load Factor

Deflectio

DX1 BS8110 DX2 AS3600 Offset DY2 S7DX EC2

Recent Research Beeby, Scott and JonesBeeby, Scott and Jones

– Loss of tension occurs much more quickly than Loss of tension occurs much more quickly than has previously been assumed, within 20-30 dayshas previously been assumed, within 20-30 days

– Mechanism is cumulative damage, resulting from Mechanism is cumulative damage, resulting from loss of tensile strength under load, creep plays an loss of tensile strength under load, creep plays an insignificant partinsignificant part

– Evidence that final tension stiffening may be Evidence that final tension stiffening may be largely independent of concrete strength.largely independent of concrete strength.

Conclusions Cracking and deflections may be highly Cracking and deflections may be highly

variable, even under nominally identical variable, even under nominally identical conditionsconditions

Codes do not make specific provisions Codes do not make specific provisions for all the relevant factors for all the relevant factors

AS 3600 and AS 5100 stress limits may AS 3600 and AS 5100 stress limits may result in substantially greater crack result in substantially greater crack widths than allowed in other codeswidths than allowed in other codes

Conclusions In spite of similar approaches, different code In spite of similar approaches, different code

methods for crack width calculation give methods for crack width calculation give highly variable results.highly variable results.

Eurocode 2 appears to be the most Eurocode 2 appears to be the most consistentconsistent

Predicted deflections are also highly variable.Predicted deflections are also highly variable. Shrinkage effects are significant, even in Shrinkage effects are significant, even in

symmetrically reinforced sections.symmetrically reinforced sections. Allow for loss of tension stiffeningAllow for loss of tension stiffening Consider the possibility of differential Consider the possibility of differential

shrinkageshrinkage

Cracking, Deflections and Ductility Code Provisions and Recent Research

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