8/19/2019 Effects of Column Creep

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TITLE NO 66 83

Effects of Column Creep

and Shrinkage

in

Tall

Structures

Prediction of Inelastic Column Shortening

By M RK FINTEL and F ZLUR

R

KH N

A

procedure

for prediction

of the

amount of

creep

and shrinkage strains

s

outlined based

on

the present

state

of the art. Consideration s given

to

the loading history of columns

n

multistory

buildings which receive their load n as many

n-

crements as

there are

stories

n the

building, thus

considerably reducing the

creep

as

compared

to

a

single load application. Also, volume-to-surface

ratio of sections and the

effect

of reinforcement

on the

creep

and shrinkage

s

considered.

Keywords columns supports);

creep

properties;

frames; high-rise buildings; loads forces); multi

story buildings; reinforced concrete; shrinkage;

strains; structural design.

• WITH INCREASING HEIGHT of

buildings, the

im

portance

of time-dependent

shortening

of

columns

and shear

walls)

becomes

more

critical

due

to

the cumulative nature

of

such

shortening. t is

known

that

columns

with

varying percentage of

reinforcement and varying volume-to-surface ra

tio will

have different

creep

and shrinkage strains.

n

increase in

percentage

of reinforcement

and

in

volume-to-surface ratio reduces strains due to

creep and shrinkage under similar

stresses.

In

a multistory building, adjacent columns may

have different

percentage of

reinforcement due to

different

tributary

areas or

different

wind loads.

As a result, the differential inelastic shortening of

CI

JOURN L DECEMBER 969

adjacent columns

will produce

moments in the

connecting

beams

or slabs and

will

cause load

transfer

to

the

element

that

shortens

less. As

the

number

of stories increases, the

cumulative dif

ferential

shortening also increases and

the related

effects become more severe. A common example

is the case of a large, heavily reinforced

column

attracting

additional

loads from the adjacent shear

wall

which has higher creep

and

shrinkage due

to

lower percentage of

reinforcement

and lower

volume-to-surface

ratio.

Significant differential

shortening m ay occur

due

to a time gap between

a slipformed

core and

the slabs.

In this

case

the

columns

are subjected

to the full

amount

of

creep

and shrinkage while the core

may have

had the

bulk

of its

inelastic shortening occurring prior to

casting

of the adjacent column.

Although

a large amount of research

informa

tion is available on

shrinkage

and creep strains,

it

is

not directly

applicable to

columns

of high

rise buildings. The available shrinkage

data

can

not

be

applied

without modification since

it

is

obtained

from small

standard prisms

or

cylinders

stored in

a controlled

laboratory

environment.

The available creep

research

is based on applica

tion of

loads

in

one

increment. Such

creep

in-

9 7

8/19/2019 Effects of Column Creep

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ACI member Mark Fintel is director, Engineering Design and

Standards Department, Portland Cement Association, Skokie,

ill. He has been with PCA since 1961. He received his Dip .

lng. from

the

Munich Institute

of

Technology in 1950. Between

1950 and 1961 he worked on the design of reinforced con

crete structures, mainly in the fields

of

multistory and s p e i ~ l

structures. He is head

of

the PCA earthquake investigation

team.

Mr.

Fintel

is

a registered structural

engineer In

Illinois.

Currently, he is chairman

of ACI

Committee 422, Response

of

Buildings to lateral Forces, a member

of ACI-ASCE

Committee

421, Reinforced Concrete Slabs.

ACI

member

Fazlur

R.

Khan

is

associate partner, Skidmore,

Owings and

Merrill, architects

and

engineers, Chicago,

Ill.

He

received his PhD from the University

of

Illinois in 1955.

Dr.

Khan has been responsible for the design of many high-rise

buildings, among them the 714-ft high 52-story One Shell

Plaza Building in Houston.

He is

a registered structural en

gineer

in Illinois. Currently, he

is

a member

of ACI

Committee

118, Use of Computers, and

ACI

Committee 442 Response

of

Building to lateral Forces.

formation,

therefore,

is

applicable

to

flexural

ele

ments of reinforced

concrete

and

to

elements

of

prestressed

concrete.

In

the construction of

a

high-rise

building, columns

are loaded in

as

many

increments

as there are stories above

the

level

under

consideration.

The

significance

of

incre

mentalloading became

apparent during the

design

of

the

52-story

Shell

Oil

Building in

Houston.

Although

creep

and

shrinkage in columns

have

a

similar effect in

that

they

cause

length

shorten

ing,

they should

be considered separately

with

respect

to time.

The length of construction time

has

a pronounced effect on the

amount

of creep,

while shrinkage proceeds independently

of

the

construction time.

Only after the creep

and shrink

age strains

have

been computed separately and

modified for

the

conditions

of the

designed

struc

ture, can

their combined effect on

the structure

be considered.

In

view

of the

basic difference

in loading

his

tory between

high-rise

and low-rise

buildings

and

the difference

between

the

actual

column

size as

compared to laboratory specimens,

two

categories

of information

are

required to develop a

rational

design

method

to

incorporate

the effects of creep

and shrinkage in

columns. These

are:

1.

The amount of

creep and shrinkage

occurring

in columns and shear walls with consideration

of

the

loading

history,

size of

the

member, per

centage of reinforcement, and environment.

2.

Analytical procedures

to

consider the struc

tural

effects

of

a

known amount

of

differential

elastic

and

inelastic

shortenings

of vertical load

carrying members in

a

structure.

The authors present in this

paper

a proce

dure

to

predict the

inelastic

(creep and shrink

age) shortening

as a function of

the incremental

loading

sequence, the volume-to-surface ratio, and

the effect

of

the percentage of reinforcement.

The method presented

is

based on the large body

9 8

of available research information on both shrink

age

and the

single

loading

type of creep. Re

sults of a 6 -year observation of creep and

shrinkage shortening of

a

number

of

36-story col

umns

will be

reported

separately,

together

with

an

n lyticql

procedure

to

design for structural

effects

of differential

column

shortening.

EFFE T

OF INCREMENT L LO DS

ON REEP STR INS

During the initial period

the rate

of creep

is

significant.

The

rate

diminishes

as

time progresses

until

it

eventually approaches zero. Fig.

la

shows

a typical

creep

versus

time

curve

drawn on

a

standard

scale.

The

same

curve plotted on semi

logarithmic graph

paper is shown

in

Fig.

lb with

time on the

logarithmic abscissa.

Creep

consists

of two

components:

1. Basic (or true) creep occurring under con

ditions

of hygral

equilibrium, which

means that

no moisture movement occurs to

or from

the

ambient medium.

In the

laboratory basic

creep

can

be

reproduced

by

sealing

the

specimen

(e.g.,

in

copper

foil), or

by keeping the specimen

in

a

fog room.

2. Drying

creep

resulting

from exchange of

moisture between

the stressed

member and

its

environment. Drying

creep has its

effect

only dur

ing

the initial period under

load.

Creep

of

concrete is a

linear function

of

stress

up

to stresses which

are about 40 percent

of

the ultimate strength.

This

includes all practical

ranges of stresses in columns and

walls.

Beyond

that

level,

creep

becomes a

nonlinear function of

stress.

For

structural engineering

practice, it is con

venient to consider specific creep,

cc', which

is

defined

as the ultimate creep

strain per unit of

sustained stress.

For

a given mix of concrete

the amount

of

creep

depends not only on

the

total

stress

but

also to a

great extent

on

the loading history. t

is

well established

by experimental research that

a

concrete

specimen

with its load applied at an

early age

exhibits

a much

larger

specific

creep

than

a

specimen loaded

at

a

later age

(Fig.

2).

Since creep decreases

with

age

of

the

concrete

at

load

application,

each subsequent incremental

loading contributes

a

smaller

specific

creep

to

the

final average

specific

creep of the column.

The postulated

1

and confirmed

2

-

5

principle

of

superposition of

creep states that:

Strains produced in

concrete

at

any

time by

a

stress increment are independent of the

effects of

any stress applied either earlier or later. The stress

increment

may be

either positive or negative,

but

stresses which approach the

ultimate strength are

excluded.

ACI

JOURNAL

DECEMBER 969

8/19/2019 Effects of Column Creep

3/11

Thus, each

load

increment causes

a

creep strain

corresponding

to

the strength-to-stress

ratio at

time of its application, as

if

it were the only

loading

to

which

the column is subjected.

DETERMIN TION OF SPECIFIC REEP

The specific creep values

corresponding

to

the

ages at which incremental loadings are applied in

an

intended

multistory structure can be obtained

by extrapolation

from

a

number

of

laboratory

sam

ples

prepared in

advance

from the

actual

mix

to

be

used

in

the

structure.

I t

is obvious

that

suf

ficient time for such

tests

must be allowed prior

to

the start

of construction,

since reliability

of

the

prediction

improves

with length

of time over

which creep

is

actually

measured.

0.20

0.15

/

/

'

:'

::

'

0.10

.

I

'

'

0.05

40days

80

120 160

200

(a)

Standard scale

'

:

:n

c.

.,

.,

u

An alternate

method to predict basic

creep

(withou t testing) from the elastic modulus of

elasticity has

been recently

proposed by

Hickey

6

based on long-time

creep

studies

at

the Bureau of

Reclamation in

Denver. Results of

the limited

tests

on normal weight concrete indicate that

creep can be predicted from the initial modulus

at time of load application.

Curves in

Fig. 3 give

the creep

magnitude

as related to

the

initial mod

ulus

of elasticity for different load durations.

For

design purposes, the 20-year creep can be

regarded

as

the ultimate

creep. Thus,

from the

specified

28-day strength, the basic specific creep for load

ing at 28

days

can be determined and then mod

ified

for construction

time, member size,

and

percentage of reinforcement as presented later

in this paper.

0.20

v

,-

/

v

v

0.1 5

0.10

v

120

31r.

0.05

lday 3 7

14

28

90

180 I

yr.

2yr. 5yr.

(b) Semilogorithmic scale

Fig. 1-Creep strains versus time under load

I J)

a.

0.35

4.97

c

0.30

c

10

0.25

. .

0

a.

8/19/2019 Effects of Column Creep

4/11

Specific creep

E

x ro·•cm/cm/kg/cmz

7

142 4 26 7 II 9 95 12 8 15 63

18 5

49.2

~ ~

\\

\

\

\

::

\

I I 1

Test results _

---Extrapolation

b ~ o

_ e

0

 .s

s ....

Jflrt

42.2

35.2

N

E

u

28.1 '

...

...

....

e o , . i " - . . , . ~ o d

r----.

1

eo .

-

...

. . .

14.1

...__

--

1 - - -

--

..........

---

1' ·······•·,.30

days

- - - -

--

-· ·-

~ d

7.0

0

o.I

0 2 o 3

o 4 o 5 o s

o r

o a

o 9

1 0 1.1 1 2 r 3

r 4

Specific

creep xi0

6

in./in./psi

Fig.

3-Prediction

of basic creep from elastic modulus

2.0

I ..

'

~

.5

~

'

:

1.0

0

t:l

'

........

.....

'

.5

0

120

I day 3 7 14 28

90

180 lyr.

Age at

loading,days

Fig. 4-Creep versus age at loading

EFFE T

OF ONSTRU TION

TIM

ON

REEP

The exponential expression for creep, repre

sented graphically in Fig. lb,

has

a particular

advantage

for

the structural

engineer.

t

allows

interpolation and extrapolation with as

few

as

two points, since beyond

about

10 days it is repre

sented as a straight line when time is plotted

on

a

logarithmic

scale.

The

curve in Fig. 4, giving

the relationship

be

tween

creep and age at loading, has been plotted

using available information from

many

tests.

The

coefficient aaue relates

the

creep for

any

age

at

96

loading to the

creep

of a specimen loaded at

the

age of

28 days. The 28-day creep is

used

as a basis

for comparison

(with

aage 2s

=

1.0).

The total creep

strain

for

an incrementally

loaded column

N

stories below

the

roof will be:

(1)

where

c ~ E c i

are creep strains produced by

the stress

increments f c ~ . Individual values for

specific

creep

E

can be obtained either from Fig. 3 or

from the

creep of a test specimen

loaded

at 28 days

and

then

modified for

the

various

ages

at

loading using

the coefficients aaue from Fig. 4.

Where

load increments are

unequal,

the

weighted average of the specific creep (weighted

corresponding to the

stress

magnitudes) will

be

2)

For N equal load increments, each corresponding

to a specific

creep

of

E

N

E

1

c1

(

E

c.ave=

--r

3)

For the

cases of

average

specific

creep of

Eq.

2)

and

(3), the total

creep strain will

be:

Ec ==

t

.at:efc

4)

where fc

is

the total stress

on

the concrete

section

from all incremental loadings.

The coefficient

aave

plotted in Fig. 5, is used to

convert the

28-day

creep into the average

specific

creep

for a

column

loaded

with

equal

load incre

ments at equal time intervals. The

curve in

this

ACI

JOURNAL

DECEMBER

1969

8/19/2019 Effects of Column Creep

5/11

C i

>

0

'd

.

o>

c

'0

0

0

E

c

4>

E

u

c

...

0

-

E

4>

u

4>

o·

.)

1.3

1.2

1.1

1.0

0.9

0.8

0..7

0.6

0

\

\

1\

40

~

\

\

\.

f

f- -

"

i -._

-....

'-.

'-...

1-o.....

.......... ..........

..........

r--

80 120

160 200

240 280 320 360 400

Time

o

construction,T, days

Fig.

5-Creep

versus construction time

figure shows

the

relationship

between creep and

the total time

of construction

T during which

equal load

increments have

been applied. The

curve

is a

solution

of Eq.

(3)

using

the

curve in

Fig. 4 for

the

values of creep for

various

ages

at

loading.

Thus,

for

example,

if a

column receives

56 load increments, and

the progress of

construc

tion is

three

floors

per

2 weeks, it takes:

14

T

=

56

X

3

=

262 days

to apply

the 56 equal

load

increments. From

Fig.

5

we see that

a coefficient

of aave

= 0.72

has

to

be

applied to

the

28-day specific

creep

obtained

either

in the

laboratory on a 6 in. (15.24 em) sealed

cylinder or

from

Fig. 3.

We can

also

see

from

the

curve

that

if the entire load

were applied

to the

column at

7 days,

it would have twice the creep

aave =

1.4)

than in incremental loading over

a

period of

262

days.

EFFE T OF MEMBER SIZE ON REEP

Creep is less sensitive to

member

size

than

shrinkage since only

the

drying creep component

of

the total creep

is

affected by

size

and shape

of members, whereas

basic

creep

is

independent

ACI

JOURNAL

DECEMBER

969

of size and shape. I t

appears from

a laboratory

investigation

8

that drying

creep has its effect

only

during the initial

3 months.

Beyond 100

days,

the rate

of creep

is

equal

to

the

basic creep.

In

Fig. 6

the relationship

between creep

and

volume-to-surface ratio has been plotted

for

Elgin

gravel

aggregate concrete

based on a laboratory

investigation.

8

Also plotted in Fig. 6 is

the

curve

based

on

European experience.

7

The

curves

are

almost

identical. I t is seen

from

the curves

that

in

members

with

a

volume-to surface ratio of

10,

drying creep

is negligible and only basic

creep

occurs.*

SHRINKAGE STRAINS ADJUSTED FOR

COLUMN SIZE

Shrinkage

of concrete is caused by

evaporation

of moisture from the

surface.

Similar

to

creep,

the rate of shrinkage

is

high at early

ages,

de

creasing

with

increase

of age,

until the curve be

comes

asymptotic

to

the

final value of

shrinkage.

Since

evaporation occurs only from

the

surface

of

members,

the volume-to-surface ratio of

a

mem-

*The effect of the ambient relative humidity and

the

effects

of

t m p r ~ t u r

and

humidity

variations

on drying

creep has

not

been

considered due

to the

lack

of

information. Preliminary re

sults of a field investigation indicate that creep of members

subjected to varying temperature and humidity

may

be

con

siderably higher than creep

in

a controlled environment.

96

8/19/2019 Effects of Column Creep

6/11

ber

has

a

pronounced effect

on

the amount

of

its

shrinkage.

The

amount of shrinkage decreases as

the size of

specimen increases.

Much

of

the shrink

age data

available in

the literature is obtained

on 11

in. (27.9 em)

long prisms

of a 3 x 3-in.

(7.6 x 7.6 em) section (volume-to-surface ratio,

VIS

0.75 in.,

or 1.91

em)

or

on in. (15.24 em)

diameter cylinders VIS= 1.5

in.,

or 3.81 em).

Obviously,

such data cannot be applied

to

usual

size

columns without

considering

the

size effect.

The

relationship between

the

magnitude

of

shrinkage and the

volume-to-surface

ratio has

U >

l : j

a:

0

2

-

 

Q)

< >

._

a;

0

< >

Q)

N

Ui

1.8

1.7

1.6

1.5

1.4

1.3

I. 2

1.1

1.0

0.9

0

254

7.62

•

\

em

1270

1778

2286

Elgin grovel

aggregate

8)

European.-

[)---.

_

urve ?)

1 .

2 3 4 5 6 7 8 9 10

Volume to surface

ratio,

n.

Fig.

6-Creep

versus volume-to-surface ratio

1.0

0.8

been.

plotted in

Fig. 7 based on

laboratory

data.

8

Also

plotted in

Fig. 7

is

a

curve from Reference

7

based

on European iiwestigations.

I t

is interesting

to

note

that

the European curves both for shrink

age

and

creep and

those for

the Elgin

gravel ag

gregate concrete are almost identical.

The

coef

ficient

a v;s shown in

Fig. 7 is

used

to

convert

shrinkage data obtained

on 6-in. (15.24

em)

cylinders VIS = 1.5 in., or 3.81 em) to any

other

size columns. A

similar

curve

can

also

be plotted

to

convert laboratory data obtained from

3 x 3-in.

(7.6 x

7.6

em)

prisms VIS =

0.75 in.,

or

1.91

em).

'>

t

._

._

Q)

0

< >

Q)

N

Ui

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0

2 54 762

\

r\

\

'

~

em

1270

......

1778

2286

European

curve

7l7

· ~

Elgin grove I j

-

...

aggregate (8)

2 3 4 5 6 7 8 9 10

Volume to surfoce

ratio,

in.

Fig.

7-Shrinkage

versus column-to-surface ratio

v

_,.

/

/ '

/

/

v

l>

0.6

0>

0

..,.;

c

..c

( /)

96

0.4

v

.2

/

.0

100

90 80 70 60

50

40

Relative

humidity, %

Fig.

8-Shrinkage

versus relative humidity

30 20

ACt

JOURNAL DECEMBER

969

8/19/2019 Effects of Column Creep

7/11

Thus

the amount of

shrinkage fs

of a

nonrein-

 

forced column is:

5)

where fs test is the shrinkage

obtained from

6 in.

15.24 em cylinder specimens made of the con-

crete mix to be used in the

structure

and stored

under job-site conditions and a ,;s is the coef-

ficient from

Fig. 7 for the

volume-to-surface ratio

of

the

column being

designed.

EFFE T

OF REL TIVE

HUMIDITY

ON SHRINK GE

Since

the rate

and

amount

of

shrinkage greatly

depend upon the

relative

humidity of the en

vironment,

the

shrinkage specimen should be

stored under

conditions

similar

to those for the

actual structure.

f

this is not possible, the shrink

age

results

of a specimen not

stored under

field

humidity conditions must then be modified to ac-

count

for

the

humidity conditions

of

the

structure

as

in

Fig. 8. This figure shows the effect of rela

tive humidity of the environment on the amount

of

shrinkage.

Alternating the ambient

relative

humidity with

in

two limits results in

higher shrinkage

and creep

than

that

obtained at a constant humidity within

the given

limits. Laboratory tests,

therefore,

may

underestimate creep and shrinkage under

condi-

tions of

practical

exposure.

PROGRESS OF REEP ND SHRINK GE

WITH TIME

Both

creep and shrinkage have

a similarity re

garding

the rate of progress

with respect

to time.

1.0

0.9

0.8

0.7

Q

_

()

_

0

0.6

Q

0>

0.5

0

>

8/19/2019 Effects of Column Creep

8/11

The change

in

stress

in

the

concrete f .fc, and

in the

steel,

f .j., due

to

creep and

shrinkage

can

be

calculated

with the

following formulas:

oo,n

Afc

=

fo +

::

)(

1 -

e-

(pnfl+Pn)ec Ec) 6)

f .j

 

= ~

= fc +;a/Eo

1 _ (pn/l+Pn)e, Ec)

·=

fc£/

+

Es)

1

_

-

(pnfl+pn)ec Ec)

7)

peo

in which

initial elastic stress

in the

co,ncrete

total

shrinkage

strain of plain concrete

adjusted

for

VIS

ratio

:::e

-

6

Q

E

Q

0

....

0

-

 

5

Q

....

0

0

-

...

Q

4

>

£/

= ultimate

specific

creep of plain concrete

in.

per

in.

per

psi)

Ec modulus of

elasticity of

concrete

reinforcement ratio of

the

section

n modular ratio E

 

/Eo

The

above formulas have been checked out

against several specimens of normal weight

and

lightweight

concrete with various ratios of rein

forcement and

have

shown reasonably good agree

ment.12

The total creep and shrinkage

strains

of the

nonreinforced column are

8)

The residual

creep and

shrinkage strains

of a

reinforced concrete column are equal to the ad-

1 ~ L ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

0.30 0.40

0.50

0.60

0.70

0.80

0.90

R t

. residual

strain

a

10

=

total strain

Fig.

10-Ratio

of residual creep and shrinkage of a reinforced column

to

the

total

creep and shrinkage of a plain

Concrete column

96

ACI JOURNAL

DECEMBER

969

8/19/2019 Effects of Column Creep

9/11

ditional

strain

of

the

steel and

can therefore be

derived from the

change

in steel

stress

)

Ll fs

1l fs f =

9)

The ratio

of residual creep and shrinkage

strains

of a reinforced column to the total creep and

shrinkage strain of

the

identical

column without

reinforcement is presented on

the

bottom of Fig.

10 for various

percentages of reinforcement,

vary

ing specific creep and

modulus

of elasticity of

concrete. I t is

evident from the curves that the

residual creep and shrinkage decreases with in

creased

percentage

of reinforcement.

The function

1 - e-

2

Although the magnitude of creep and shrink

age of

plain

concrete

specimens may vary

con

siderably, the final inelastic strains in reinforced

concrete columns and walls have much less varia

tion

due to the restraining effect of the reinforce

ment.

3 Elements which receive a substantial loading

at early

ages,

such

as prestressed elements and

columns in the

upper

stories of

tall

structures or

columns

of

low-rise

structures,

are prone

to

higher

shrinkage and

creep

strains.

4 Lower story columns of

tall

structures

have

considerably smaller creep

and shrinkage strains

than

commonly assumed as a

result

of:

a) Incremental

loading

over a longer

period

of

time which reduces creep.

(b) A substantial volume-to-surface ratio which

reduces shrinkage.

c) A substantial percentage of

reinforcement

which

reduces

both shrinkage and

creep.

5 In

a

tall structure the relative

vertical

move

ment

between

columns

and adjacent

walls

can

cause

structural and architectural

distress unless

proper design

and

details are provided.

>

w

-

1 1

.

I

Q)

I

Fig. I -Computation of residual strains

CI

JOURN L

DECEMBER

989

96

8/19/2019 Effects of Column Creep

10/11

REFERENCES

1. McHenry, D., A New Aspect of Creep in Con

crete

and

its

Application to Design,

Proceedings,

ASTM,

V. 43, p. 1069.

2. Ross, A. D., Creep

of

Concrete Under Variable

Stress, ACI JouRNAL,

Proceedings

V. 54 No. 9

Mar.

1958, pp. 739-758.

3. Backstrom, S., Creep and

Creep

Recovery of

Cement

Mortar, Preliminary

Publication, Fifth Con

gress

of

the International

Association

for Bridge and

Structural

Engineering,

Zurich, 1956, pp. 77-83.

4. Seed, H. B.,

Creep and Shrinkage in Reinforced

Concrete Structures,

Reinforced

Concrete

Review

(London),

1948, pp. 253-267.

5.

Davies,

R. D., Discussion of Creep of Concrete

Under Variable Stress by A. D. Ross, ACI JoURNAL

Proceedings

V. 54 1958, pp. 1279-1280.

6.

Hickey, K. B., Creep of Concrete Predicted from

Elastic

Modulus Tests, Report No. C-1242,

Department

of the

Interior,

Bureau of

Reclamation,

Denver, Jan.

1968, 27 pp.

7.

Recommendations

for an

International Code

of

Practice for

Reinforced

Concrete,

Comite Europeen du

Beton,

Paris, 1964. (English translation

available

from

the Cement and Concrete Association and

American

Ooncrete Institute,

155

pp.)

8. Hansen, T. C.,

and

Mattock, A. H., Influence

of Size

and

Shape of

Member on the

Shrinkage and

Creep of Concrete, ACI JouRNAL,

Proceedings

V. 63

No. 2

Feb.

1966, p. 267.

9.

Troxell, G. E.; Raphael,

J.

M.;

and

Davis, R. E.,

Long-Time Creep and Shrinkage Tests of Plain and

Reinforced Concrete,

Proceedings,

ASTM, V.

58

1958,

pp. 1101-1120.

10.

Dischinger,

F.,

Investigations on Resistance

to

Buckling, Elastic Deformation and Creep of o n ~ r e t e

in Arch

Bridges (Untersuchungen

ueber

die

Knick

sicherheit, die elastische

Verformung

und das Kriechen

des

Betons bei

Bogenbruecken) , Der Bauingenieur

(Berlin),

V. 18 No. 39/40, Oct. 1937, pp. 595-621.

11. Morsch, E.,

Static

der

Gewalbe

und

Rahmen,

Verlag

von Konrad

Wittwer,

Stuttgart,

1947.

12. Pfeifer, D. W., Reinforced Lightweight Concrete

Columns, Proceedings,

ASCE, V. 95 ST1, Jan. 1969,

pp. 57-82.

Given

PPENDIX

DESIGN EX MPLE

Assume

an inside column 36

stories below

the roof.

Floor

to floor

height

is

9.0 ft

(2.74 m). The

20

x 49-in.

(50.80 x 124.5 em) column is reinforced with 26

11

bars

( 40.6 sq. in., or 261.9 cm2)

equals

4.15

percent

of

A431; fy

=

75,000 psi (5280 kg/cm2).

Concrete: fc 5000

psi

(352 kg/cm2) at 28 days,

normal weight

Ec

33w31ZV

f< = 4.05

X

106

n

=

Es Ec

=

7.2

Transformed

column area:

9

At

Ag+

n-1)As

20

X

49

(7 .2- 1) X 40.6

1232 sq in. (7950 cm2)

The planned construction progress

is one

floor

in 8

calendar

days.

Planned total time for 36 floors (load

increments) is T

= 36

X 8

=

288 days.

The

dead load of the typical floor is 37 kips (16,800

kg).

Since

time did

not permit long-time shrinkage

and

creep test cylinders, 20-year specific basic creep for

loading

at

28

days

was

estimated from

Fig.

3 to

be

Ec' =

0.33

X 10-6

in. per in. per psi (4.7

X 10-6

em/em/

kg/cm2) for Ec = 4.05

X

106

psi

(28.5

X

104 kg/cm2).

Shrinkage determined

on

the

same mix of a

previous

job was 630 X 10-6 in. per in. during the first 90

days.

The

6-in. (15.24 em) cylinders were moist cured

for

7

days and then stored in

the

laboratory in

50

percent

relative

humidity and 70

F.

Required

Compute the

ultimate

residual creep and shrinkage

strains

of the

reinforced concrete

column

and

the

ad

ditional stress in reinforcing steel.

The

following

steps will be carried out:

1. Compute

for

the plain concrete column the total

ultimate

creep

strains, considering effects

of incre

mental loading and of column size; and shrinkage

considering volume-to-surface ratio.

2.

Compute

the

additional stress in the vertical

reinforcing steel

due

to

creep

and

shrinkage.

3. Compute for the reinforced

concrete

column the

residual creep

and shrinkage strains.

Solution

Creep strains for

nonreinforced

concrete

column

Conversion of specific creep

for

loading

at

28 days

to consider

incremental

loading over a

period

of

=

288 days using a.ave

=

0.70 from Fig. 5:

c ave

E . c ~ 2 8 U a v e

=

0.33 X 10-6 X 0.70

=

0.231

X

10-G in. per in.

per

psi

Modification of specific creep

for

size effect

using

Fig.

6.

Volume-to-surface ratio:

20

X 49

VIS =

2

(

20

49

) = 7.1 in.

from

which

a.c,

  8

= 1.06.

Ec'

0.231

X

10-6

X

1.06

0.245 x 10-G in. per in.

per

psi

Sustained

stress on the

concrete:

p

fc

At

=

36

x

37,ooo

=

1080

psi

1232

Total creep strain:

Ec :.= Ec X

fc

0.245 X 10-6 X 1080

265

X 10-6

in. per

in.

Shrinkage

strains for

nonreinforced

concrete

column

Conversion of 90-day measured shrinkage to ultimate

shrinkage

(coefficient from Fig. 9

representing

the

ratio of shrinkage

at

90 days to ultimate shrinkage):

630 X 10-

6

0.61

1035 x

10-6

per in. per in.

ACI

JOURNAL

I

DECEMBER

969

8/19/2019 Effects of Column Creep

11/11

Conversion of shrinkage measured on the 6-in.

cylinder to

account

for size of real

column

using

Fig.

7:

from which

a v;s = 0.57.

s = 1035 X lO-G X 0.57

= 590 x

10-6

in. per in.

Total creep

and

shrinkage strains for nonreinforced

column:

E

c s

265 590)

10-6

= 855 X lO-G in. per in.

Additional

stresses

in the

vertical reinforcing

steel

For specific

creep

Ec = 0.245 X lO-G in. per in. per

ps i nd fo r

Ec=4.05XlO-G psi,

the f u n c t i o n

e- (pnf l+pn)< cEc) = 0.203 (from Fig. 11). The addi

tional

stress in

steel

from Eq. (7) are:

Llf

855 X lO-G X 0.203

s = 0.0415

X

0.245

X

10-6

17,050 psi

Residual

creep

and shrinkage

strains for

column

with

a

reinforcing

steel ratio

of 4 15 percent using

Eq. (9)

Llfs'

Ll(e:c+Es) =

Es

17

•

050

= 588 x 10-n in. per in.

29 X

10-6

R t' Residual strains

a

10

Total

strains

588 X

10-6

855 X

10-6

0.69

The above ratio means that the total strains have

been

reduced

by

the reinfoTcing by 31 percent. This

can be seen also

in

approximation from Fig. 10.

A

similar

design

example

carried

out on

a 14 in.

thick wall

of

the

same

concrete having 1.5 percent

vertical reinforcement and a dead load stress of 600

psi

shows

a residual creep and shrinkage stTain

of

645 X lO-G as compared to 588

x 10-6

in. per

in.

for

the column.

For

the

height of the entire building of 324 ft 98.76

m), the

differential

shortening

between the

column

and

the

wall (assuming

the

same shortening for all

36 stories) will

be

0.222 in. 0.563 em).

At

Ec

NOTATION

area

of gross column section

modulus

of elasticity of

concrete

at initial

loading

Es

modulus of elasticity of

steel

f

c

initial

elastic stress

in concrete

fci

stress in concrete due to incremental load

fs

stress in vertical

column

reinforcement

n modular

ratio Es Ec

p reinforcement ratio of section

Uage

=

coefficient

to conside-r the effect

on

creep

of

age at loading

aave = coefficient to consider the effect on creep of

duration of

load application (construction

time)

ACI

JOURNAL DECEMBER

969

acv/s

= coefficient

to

consider

the

effect of

volume-to

surface

ratio

on creep

a•v;s

coefficient to ..consider

the

effect of

volume-to

surface ratio on shrinkage

E

c

stTain, in. per in.

creep strain

Ec specific

creep of plain concrete,

in.

per

in. per

psi, i.e., creep per

unit stress

• .

t

specific creep corresponding to incremental load

= total

shrinkage

strain of plain

concrete

s

This paper was received by the Institute July 22, 1968.

Sinopsis Resume Zusammenfassung

Efectos del Flujo Plcistico y

Ia

Contracci6n en

Columnas de Estructuras

Altas Predicci6n

del

Acortamiento lnelcistico de Columna

Se detalla un procedimiento para predecir la

cantidad de deformaci6n

por

flujo plastico y

contracci6n con

base

en

el

estado

actual del

conocimiento.

Se toma en

consideraci6n

la

historia de

carga de las

columnas

en edificios de varios niveles las

cuales reciben sus caTgas en incrementos a medida que

se construye el edificio,

reduciendo considerablemente

el

flujo plastico

comparada con una sola aplicaci6n

de la carga. Tambien se consideran la relaci6n

volumen/superficie de las secciones y el efecto del

refuerzo en el flujo plastico y la contracci6n.

Effet de Fluage et Retrait de Colonnes

de Grands Immeubles Prediction du

Retrait de Colonnes lnelastiques

Un precede

pour

prediction de 'amplitude des forces

de fluage

et

Tetrait

est

detaille

sur

la

base des

realisations

actuellement construites. Une

consideration

est

donnee

a

'experience

acquise

dans

la

construction d'immeubles

a

etages

multiples

dans

lesquels la

repartition

des charges intervient dans les

nombreux increments

de

construction d'un immeuble

a etages multiples,

reduisant ainsi considerablement le

fluage par

comparaison

a

une

application avec chaTge

simple. Egalement le

rapport

volume-surface des

sections

et l 'effet

d'armature

sur le fluage et retrait

sont consideres

Der Einfluss des Kriechens und Schwindens der

Saulen in hohen

Gebauden die

Vorherbestimmung

der anelastischen Saulenverkiirzung

Eine Vorherbestimmungsmethode flir die Grosse

von

Kriech-

und Schwindverformungen

wird

gegeben, die

auf

den

derzeitigen Wissenstand auf

diesem

Gebiete

aufbaut. Dabei wird die Belastungsgeschichte der

Saulen in hohen Gebauden beriicksichtigt.

Die

Last

wird

in

ebenso

vielen

Stufen

aufgebracht,

wie

das

Bauwerk Stockwerke

enthalt. Damit wird

die

Kriechverformung im

Vergleich zu

einer einmaligen

Beanspruchung mit de-r

Gesamtlast

wesentlich

reduziert. Auch

das

Verhaltnis

von

Volumen zu

Oberflache der Querschnitte

und der Einfluss

der

Bewehrung auf

das

Kriechen und Schwinden werden

beriicksichtigt.

9 7