Pérdidas Por Creep y Retracción, AASHTO

7/23/2019 Pérdidas Por Creep y Retracción, AASHTO

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Section 5

-

oncrete Structures (SI) i,,;c,,~c:,,"

SPECIFICATIONS COMMENTARY

1'""' In the absenceof more accuratedata, the shrinkage

:.., '.

coefficients may be assumed to be 0.0002 after 28 days . .

and 0.0005

after one year of drying.

When mix-specific

data are not available, estimates

of shrinkage and creep may be made using the

provisions of:

. Articles

5.4.2.3.2

and 5.4.2.3.3,

. The CEB-FIP model code, or

.

ACI 209.

For segmentally onstructed ridges, a more precise

estimate shall be made, including the effect of:

.

Specific rnaterials,

. Structuraldimensions,

. Site conditions,and

. Construction

ethods.

5.4.2.3.2 Creep C5.4.2.3.2

r--. Thecreep oefficient

ay be estimated as: The methods of determining creepand shrinka

specifiedherein and in Article 5.4.2.3.3,are take

.,,(t t): Collins and Mitchell (1991). These methods are

, , on the recommendation of AC' Committee 20

3 5k k ( 1 58 - H ) t 0.118 (t - t,)o.. (5.4.2.3.2-1) modifiedy additionaJ ecently published data.

. c"

120

10 0+ (t-t)o., Other applicable references

nclude Rusch

. I (1983), Bazant and Wittman (1982), and Ghali and

(1986).

for which: The

creep

coeffic;ent ;s applied to the compres

strain caused by perrnanentoads in order to obta

strain due to creep.

k :

~ Creep is influenced by the same

facto

, 42 t' (5.4.2.3.2-2) shrinkage, nd alsoby:

c

. Magnitude and duration

of fue stress,

where:

. Maturityf the concrete at the time of loading, a

H = relativehumidity

percent)

. Temperature f concrete.

kc = factor for the effect of the volume-to-surface

ratio of the component specified in Figure 1 Creep shortening of concrete under permanent

is generally in the range of 1.5 to 4.0 times the

kt = factor for the effect of concrete strength elastic shortening, depending prirnarily on con

maturity at the time of Joading.

t = maturity of concrete (Day)

~ = age of concrete when load is initially applied

(Day)

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-;~f"",:, ::,f;:;'"

Section5 - ConcreteStructures SI)

SPECIFICA IONS COMMENT RY

In the absence

of

better infonl1ation, H may be taken

from Figure 5.4.2.3.3-1.

t'c = specifiedcompressive trengthat 28 days (MPa)

1.4 volume Figure 1 is based on the equation below (PCI 19

surface

rea1.2

~.. 25 mm

I.- 1.0 '..'..38mm t

f

o 8 ::".' 50nw»

. ~ ':...'75mm 2690,Of42CV/S)+t

)[ 1.80 + 1.77S-0.0213Cv/S)

]

g 0.8 ". ~ ~ ...:'...100 mm kc

=

'8

-

~ ..'.150

mm

-. .-

2.587

. .4 45 t

i

0.2 -

r-

+

""-,"',

. (C5.4.2.3

0.01 2 5 10 100 1000 10000

(t . ti> time uooer JDad days)

Th .

VIS

ti '

d

d

.

t maxlmum ra o conSI ere In

development of Figure 1 and Equation C1 was 150 m

Figure

5.4.2.3.2-1

Factorkc for Volume o SurfaceRatio

In determining the maturity of concrete at initíaf

loading, ~, one day of accelerated curing by steam or

radiant heat may be taken as equal to seven days of

normal curing.

The surface area used in determining the volume to ; , ..

area ratio should include only the area that is exposed to ,,\',

atmospheric rying. For poorlyventilatedenclosedcells, ,;: ,

only 50 percentof the interior perimetershould be used"

in

calculating the surface area.

5.4.2.3.3 Shrinkage C5.4.2.3.3

For moist cured concretes devoid of shrinkage-prone Shrinkage of concrete can vary over a wide ran

aggregates, the strain due to shrinkage, EIh' at time, t, from nearly nil if continually immersed in water to

may be taken as: excess of 0.0008 for thin sections made with hig

shrinkage aggregates and sections that are not proper

( t

)

cured.

811= k.k" "3:s:O~ 0.51 10-3 (5.4.~.3.3-1) Shrinkage s affectedby:

8 Aggregate characteristics and proportions,

where:

8 Averagehumidityat the bridgesite,

t = drying ime (Day)

8

Water/cement ratio,

k. = size factor specified in Figure 2

8 Type o, cure,

kn = humidity factor specified in Figure 1 and Table 1

8 Volume o surfacearea ratio of member,and

If the moist-cured concrete is exposed to drying

'"

before five days of curing have elapsed, fue shrinkage as 8 Durabon of drylngpenad.

determined in Equation 1 shourd be increased by 20

percent. Large concrete members may undergo substantial

less shrinkage than that measured by laboratory testin

For steam-cured concrete devoid of shrinkage-prone of small specimens of fue same concrete. The con

agg egates straining effects of reinforcement and composite action

5-14

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Section 5- oncrete Structures (SI>


---

( t ) with other elements of the bridge tend to red

[sil = -kskh 55:o--:;f 0.56 X 10-3 (5.4.2.3.3-2) dimensional hanges n somecomponents.

77 80

.;°Ü70

u

~~

HAWAlI~

~ 7S

Figure5.4.2.3.3-1 AnnualAverageAmbientRelative

Humidity in Percent

~..

volume Figure 2 is based on the equation below (PC

1.4

.. urface

aria

~

1.2

,o 25 mm t

~ 0..8 --- ::::~~::

k =

26eo.0142(VIS) +

t

[ 1064 - 3.70(V/~)

1 .

5

00

-- --- . ...75 mm

I

t 923

:= . '. ..100mm -

u .

45 +

t

.4 -- --- --- . ..125 mm

~ 0.2 ."150 mm (C5.4.2

Q

1 2 5 10 100 1000 10000

rying time (da)'l) The maxlmum VIS ratlo consldered

development 01 Figure 2 and Equation C1 was 1

The values in Table 1 may be approxímate

Figure 5.4.2.3.3-2 - Factor k. for Volume-to-Surface follO"Ning quations:

Ratio

.

For H < 80%

k =.1~

h

70 (C5.4.2.3.3-2)

. ForH;?80%

k = 3(100-H)

h 70 (C5.4.2.3.3-3)

~

5-15

.



Section 5 - Concrete Structures (SI)


Table 5.4.2.3.3-1 Factor~ for

RelativeHumidity

.

AverageAmbient

RelativeHumidity ~

...

.

01:

/0

40 1.43

50 1.29

60 1.14

70 1.00

80 0.86

90 0.43

100 0.00

5.4.2.4 MODULUSOF ELASTICITY

CS.4.2.4

In the absence of more precise data, the modulus of See commentary for specified strength in A

elasticity, Ea, for concretes with densities between 1440 5.4.2.1.

and 2500 kg/m3, rnay be taken as: For normal density concrete with Yc= 2320 kgim

may be taken as

Ec = 0.O43y:.5~ (5.4.2.4-1)

¡r:

= 4800 f (CS.4.2

c

where:

Yc = density of concrete (kg/m3)

l' c = specified strength of concrete (MPa)

5.4.2.5 POISSON'S RATIO C5.4.2.5

Unless determined by physical tests, Poisson's ratio This is a ratio between the lateral and axial strai

may be assumed as 0.2. For components expected o an axially and/or flexurally loaded structural element

be subject to cracking, the effect of Poisson's ratio may

be neglected.

5.4.2.6 MODULUS OF RUPTURE CS.4.2.6

Unless determined by physical tests, the modulus of The given values may be unconservative for te

rupture, fr in MPa, may be taken as: cracking caused by restrained shrinkage. anchor

splittíng, and other such tensile forces caused by e

other than flexure. The direct tensile strength s

. For normaldensityconcrete. . . . . . . . 0.63

~ should be used for these cases.

. Forsand-low-densityoncrete.. . . . . 0.52r:

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Pérdidas Por Creep y Retracción, AASHTO

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