Concrete Solutions 09

siennatearfulUrban and Civil

Nov 25, 2013 (3 years and 11 months ago)

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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/