Concrete Solutions 09Concrete Solutions 09

Predicting the Deflection of Concrete Predicting the Deflection of Concrete Structures in PracticeStructures in Practice

Doug Jenkins - Interactive Design Services

Introduction Introduction Everything should be made as

simple as possible,

... but not simpler.

Albert Einstein

Introduction Introduction Are the simplified provisions for

the calculation of deflections in AS3600 “too simple”

It depends

When are Deflections When are Deflections Important?Important?

Second order effectsClient expectationsContract conditionsCode complianceAestheticsClearances

When are Deflections Important?When are Deflections Important?

Sources of DeflectionSources of Deflection

Short term stress-strain and bond behaviour of the concrete and reinforcement.

Time dependent behaviour of the concrete. Differential strain effects. Construction sequence and other load

sequence effects.

Sources of DeflectionSources of Deflection

Short term stress-strain behaviour:– Concrete flexural tensile strength.– Concrete tension-stiffening effect.

Time dependent behaviour of the concrete– Concrete creep– Concrete shrinkage– Loss of tension stiffening– Loss of flexural tensile strength

Sources of DeflectionSources of Deflection

Differential strain effects.– Differential shrinkage– Differential temperature

Load sequence effects.– Handling, transport and erection– Propping loads– Change in stiffness after overload.– Construction loads on buried structures.– Timing of composite connections.– Effect of varying axial load

Effect of ShrinkageEffect of ShrinkageSymmetrical Reinforcement – No LoadSymmetrical Reinforcement – No Load

Effect of ShrinkageEffect of ShrinkageConcrete Shrinkage – de-bonded steelConcrete Shrinkage – de-bonded steel

Effect of ShrinkageEffect of ShrinkageApply compression to steel Apply compression to steel

Effect of ShrinkageEffect of ShrinkageRe-bond steel and release compressionRe-bond steel and release compression

Effect of ShrinkageEffect of ShrinkageApply bending below cracking momentApply bending below cracking moment

Effect of ShrinkageEffect of ShrinkageApply bending greater than cracking momentApply bending greater than cracking moment

Calculation of Shrinkage CurvatureCalculation of Shrinkage CurvatureApply “negative” prestress to reinforcementApply “negative” prestress to reinforcement

Effect of ShrinkageEffect of ShrinkageMoment-Curvature, without and with shrinkageMoment-Curvature, without and with shrinkage

0

20

40

60

80

100

120

140

160

180

0.00E+00 1.00E-03 2.00E-03 3.00E-03 4.00E-03 5.00E-03

Bend

ing

Mom

ent,

Knm

Curvature; m^-1

Bending Only Bending + Shrinkage

Effect of ShrinkageEffect of Shrinkage

Shrinkage stresses in the concrete will significantly reduce the cracking moment

Shrinkage will cause significant rotations in any asymmetrical section:

– Asymmetrical reinforcement– Cracked section

Case StudyCase Study

Large span pre-cast concrete arch in the UK (approx. 20 m span)

Short term crown deflections under self weight estimated to be about 30 mm

Initial deflections consistent with predictions Deflections after 6 month delay to backfill

increased to 150 mm

Case StudyCase Study

Case StudyCase Study

1. Short term stiffness, gross concrete section2. As 1, but age adjusted concrete modulus3. As 2, but using Branson equation4. As 3, but EC2, β = 1

5. As 4, but with Mcr reduced due to effect of shrinkage and differential temperature.

6. As 5, but with β = 0.57. As 6, but with curvature due to shrinkage

included.

Moment-Curvature (long term)Moment-Curvature (long term)

0

20

40

60

80

100

120

140

160

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007

Bend

ing

Mom

ent,

kN

m

Curvature, m^-1

Crown Deflection, mmCrown Deflection, mm

-160

-140

-120

-100

-80

-60

-40

-20

0

0 0.2 0.4 0.6 0.8 1

Crow

n D

eflec

tion

, m

m

Load Factor

Run 1

Run 2

Run 3

Run 4

Run 5

Run 6

Run 7

Case Study - ConclusionsCase Study - Conclusions

1. Analysis including all relevant effects matched measured deflections

2. Most significant effects:– Reduction in cracking moment due to shrinkage

and differential temperature– Shrinkage curvature

General ConclusionsGeneral Conclusions

Critical cases:– Will much larger than expected deflections have

a significant effect on the design?

If so:– Use conservative estimate of concrete flexural

tensile strength, reduced by shrinkage and tensile differential temperature stresses.

– Allow for section curvature due to shrinkage– Consider possible differential shrinkage– Allow for cumulative second order effects at ULS

General ConclusionsGeneral Conclusions

Structures requiring particular attention:

– Where the maximum bending moment is approximately equal to the concrete cracking moment.

– Asymmetric beams (e.g. Super-T), especially those subject to hot dry conditions.

– Construction sequence effects.

Further Information and Further Information and SoftwareSoftware

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