Concrete Solutions 09
Predicting the Deflection of Concrete
Structures in Practice
Doug Jenkins

Interactive Design Services
Introduction
Everything should be made as
simple as possible,
... but not simpler.
Albert Einstein
Introduction
Are the simplified provisions for
the calculation of deflections in
AS3600 “too simple”
It depends
When are Deflections
Important?
Second order effects
Client expectations
Contract conditions
Code compliance
Aesthetics
Clearances
When are Deflections Important?
Sources 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 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 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 Shrinkage
Symmetrical Reinforcement
–
No Load
Effect of Shrinkage
Concrete Shrinkage
–
de

bonded steel
Effect of Shrinkage
Apply compression to steel
Effect of Shrinkage
Re

bond steel and release compression
Effect of Shrinkage
Apply bending below cracking moment
Effect of Shrinkage
Apply bending greater than cracking moment
Calculation of Shrinkage Curvature
Apply “negative” prestress to reinforcement
Effect of Shrinkage
Moment

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
Bending Moment, Knm
Curvature; m^

1
Bending Only
Bending + Shrinkage
Effect 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 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 Study
Case Study
1.
Short term stiffness, gross concrete section
2.
As 1, but age adjusted concrete modulus
3.
As 2, but using Branson equation
4.
As 3, but EC2, β = 1
5.
As 4, but with
M
cr
reduced due to effect of
shrinkage and differential temperature.
6.
As 5, but with β = 0.5
7.
As 6, but with curvature due to shrinkage
included.
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
Bending Moment, kNm
Curvature, m^

1
Crown Deflection, mm

160

140

120

100

80

60

40

20
0
0
0.2
0.4
0.6
0.8
1
Crown Deflection, mm
Load Factor
Run 1
Run 2
Run 3
Run 4
Run 5
Run 6
Run 7
Case 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 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 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
Software
http://newtonexcelbach.wordpress.com/
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