prestressed concrete - Yodebees Consult Limited

lifegunbarrelcityUrban and Civil

Nov 26, 2013 (3 years and 8 months ago)

56 views

PRESTRESSED CONCRETE


INTRODUCTION



Prestresssed concrete is the most recent of the major form
s

of construction to be introduced
into Structural Engineering. The introduction came in the early part of the twentieth century
following the acute shortage of steel that occurred in Europe after t
he Second World War.
The technique of presstressing has several advantages/ applications in Civil Engineering,
notably in prestress concrete where a prestress force is applied

to a concrete member and this
induces an axial compression that counteracts all or part of the tensile stresses set up in the
member by the applied loading.



OBJECTIVES OF PRESTRESSING

1.

Proper prestressing ordinar
i
ly prevent
s

the formation of tension crack under working
load
s
. This is a good reason for prestresssing tanks to avoid leakage or for
prestressing structural members subject to severe corrosion condition
s
.


2.

With lack of cracking, the entire cross
-
section r
emains effective for stress; as such a
small

section normally results. With lighter sections, precasting of longer members
becomes possible.


3.

S
ince prestressing put camber (curves)

into member
s

under dead loading, deflection at
working
load

is greatly redu
ced.


4.

Prestressing reduce
s

diagonal tension stresses at working loads.



ADVANTAGES OF PRESTRESSED CONCRETE


1.

Prestressed
concrete is a

crack
free
under service loads. When

exposed to wea
ther,

e
limination of cracks prevents

corrosion.


2.

A pre
-
stressed member

usually has greater stiffness than non
-

prestressed member
s
.


3.

Precompression of
concrete

reduces the tendency for inclined cracks to be formed.


4.

Shear strength is more co
nsistent than in ordinary reinforced concrete.


5.

Presstressed concrete

has a high abi
lity to absorb energy (
impact

resistance

etc
)
.



DISA
DVANTAGES OF PRESTRESSED CONCRETE

1.

Stronger material
s are used as such
higher unit cost.

2.

More complicated

formwork
s may be necessary
.

3.

Labor cost
s are usual
greater.

4.

More condition
s

must be checked in desi
gn and close
r

contr
ol of every phase is
required et
c
.


BASIC CONCEPTS



Consider a plain concrete beam
for rectangular

cross
-
section


W
L




+
f

(
compres
sion)




WB


h



L


-
f (tension)


b


The bending stress at m
i
d
-

span due to t
he loading condition,



f

=








Since concrete is a poor material in tension, usually

(
-
f) will exceed the tensile strength/stress
of concrete.



Option #1: A
dd steel in the tension zone to carry the tensile stresses as

in reinforced


concrete

Option #2: Pre
compress tension zone as in pre
s
tressed concrete.




Considering option #2




F or

P

Wa


F or

P







W
B


The
stresses at mid
-

span are:







+

=





0 An ideal situation




Stress distribution

The effect

of pre
-
compression her
e is to eliminate all tensile stresses in the concrete
.
However,
the
compressive stress (

+
) applied to the concrete at the top face may
exceed the
permis
sible compressive stress of concrete.




To avoid this
, the
position of F
is
relocate
d
.












F or P





F or P



Sum
med

up the stresses at mid


span

we have,




+


=







SUMMARY:


The objective of prestressing is to lim
it tension in concrete (precompress to
prevent cracks from forming)
. T
he design constraint
is the allowable stress of concrete.





DESIGN CONCEPT

In dealing with the stress in prestressed concrete under service load
conditions, ,three
concept may be applied.

1.

HOMOGENNOUS BEAM CONCEPT


As applied above,

the beam

is assumed

to be made up of one material. T
he
prestressing effectively eliminates cracking.

The combined stress formula is:




Or


this is used to investigate the section.



2.

THE INTERNAL FORCE CONCEPT


It

employ
s

the equilibrium of internal f
orces. Steel takes the tension

and

concrete
takes the compression.
This is analog
ous

to the internal couple method used for non
-


prestressed

reinforced concrete.

At service loads in reinforced concrete
the point
s

of
action of the force
s (C&
T)
, C=T
are independent of the magnitude

of applied bending
moment,
depending only on the cross
-
sectional

dimensions and the modular

ratio M.


This concept
is summarized thus:

i)

A know prestress force put into the steel define T.

ii)

An appl
ied moment M is put on the beam
.

iii)

Knowing the magnitu
de and point of action of the force
C, the stress in the concrete
may be computed as:



f =

3.

LOAD BALANCING

CONCEP
T


The concept visualizes prestressing primarily as a process of balancing loads on the
member. The prestresssing tendons are placed so that the eccentricity of the
prestressing force varies in the same manner as the moment from applied load
s. .I
f
this is done well, zero flexural stress
would

result. Thus only the axial stress

(F is
the horizontal component of the force in the tendon) would

act.






T


T








max


parabolic tendon



L/2



max




Parabolic tendon applied to beam



Force acting on

beam due to prestressing




T



T








The prestressing may be consider
ed as an upward uni
form loads
if the tension is parabolically
draped.
The max prestress moment o
f
*


at mid
-
span can be equated to an equivalent

uniformly loaded beam

mo
ment.

Thus,


*




Therefore

=


If

=




then,

=





And f =



ME
THOD
OF BEAM ANALYSIS


(
Stress analysis by superposition)

Consider a rectangular beam with uniform
load












M





or e


F

F








Stress distribution due to an eccentric load is

f
t

=


f
b

=




or e is +
, if it is below the member centroidal axis

A = cros
s
-
sectional area


And

are the stres
ses at the top and bottom fibers

and
are the section modulli at the top
and bottom

fibers


Compressive stresses
are +

as sagging

Bending Moments.

If an external bending moment is introduced, the additional stress dist
ribution of stresses is
introduced and the resultant stress distribution due to the prestress force and applied bending
moment is found by superposition.



=

…………………………………………………………………(1)



=

…………………………………………………………………(2)

In addition to the applied bending moment at the section there is also an axial load therefore,
the force (F) in equations 1 and 2 is the sum of the prestress force and the applied axial load.

EXAMPLE 1


A simply supported pretensioned concrete beam

has dimension
s

as shown in fig.1 and spans
15m. It has an initial prestress force
of 1100KN

applied to it and carries

a UDL (imposed) of
12KN/m.

Determine the extreme fiber stresses at mid
-

span
:


(1)

Under the self weight of the beam, if the short term losses are 10% and the eccentricity is
325mm below the beam centroid

(2)


Under

the service load,
when the prestress force has been reduced by a further 10%.




a










200





15m



750



a


150



325




Figure 1







0 0 0 200





400










Section A
-
A









SOLUTION


P= 1100KN
; e= 325mm (given)


A =

areas =
2.13 *10


mm
²



I=

Also y

therefore, Z=



=

= 3
5. 12 *10


mm



w
=
24A

=5.1 KN/m




Mi =

143.4KNm (moment due to self weight)

q= w + imposed

load



M
S

=

= 4
80.9KNm (moment due to service load)



= 0.9P = 990KN (for 10% reduction)


= 0.8P= 88OKN (for 20% i.e. further 10% reduction)


(1)


=

=

-
0.43N/mm²







= 4.65 + 9.16


4.08 = 9.73N/
mm²



(ii)

=

= 9.68N/
mm²






= 4
.13 + 8.14


13. 69 =

-

1.42N/mm²



-
0.43 9.68




Transfer stress

service stress









9.73
-

1.42


STRESS DISTRIBUTION FOR EXAMPLE
1

The stress dis
tribution for example 1 exemplifies those in a prestressed concrete member
under max
imum

and min
imum

loads.

This demonstrates
the fact that in prestressed concrete

the minimum load condit
ion is always an important one.

The previous considerations; the

pres
tress force has provided by one layer of tendons,

so that
the resultant prestress force coincide with the physical locat
ion of tendons in prestresed
concrete members.
However
,

there are usually more than one layer of tendons
in prestressed
concrete members
,
in this case the resultant prestress force coincide with the location of the
resultant of all the individual prestressing tendons, even if it not physically possible to locate
a tendon at this position.

For post
-
tensioned members where the duct diameter
is not negligible in comparison with the
section dimension, due allowance for the duct must be made when determining the member
section properties. For pretensioned members, the transformed cross

section should be used.
In practice the section properties
are determined on the basis of the gross cross
-
section.


ADDITIONAL STEEL STRESS DUE TO BENDING

There is no bond between the presstressin
g steel and the surrounding concrete.

In pre
-

tensioned members and grou
ted post


tensioned member
s,

bond is
pres
ent

and bending of
the member induces stress in the steel as in

a reinforced concrete m
ember. It is the bond
between

the steel and concrete
that makes the ultimate loads behavior of pre
-
tensioned and
grou
ted post


tensioned members very similar to that

of reinforced concrete

members and
di
fferent from un
-
g
routed post


tensioned members.


EXAMPLE

Design a rectangular pre
-
tensioned beam to support a live load of 9kN/
m

on a span of 8m. Determine
the dimensions of the beam section, prestressing force and th
e eccentricity.


Final compres
sive strength

of concrete

(
')

=

3.5
/
cm²


Initial compressive strength
(

= 2.8

/
cm²



Tensile
strength of tendons (
) = 189

/
cm²

Solution

Given design data
are shown below;


W
L

=

9.0kN

/
m


L = 8.0m


'
= 3.5

/
cm²



= 2.8

/
cm²


= 189

/
cm²




TRIAL SECTION:

Let


=
20%
of W
L

= 0.2*9 = 1.8kN/m


Therefore (W) =


+

W
L

= 9+1.8 = 10.8

/m




=

= 10.8 *8² = 86.4kNm




Since б =

=
fc
'
=





=

2469cm
3


Assume b=



Z =


=


*


=

= 2469cm







h = 28cm

30 cm


Try 20cm x

30cm




Z =


=

3000cm
3

>
. (hence dimensions are adequate)




= {0.2*0.3*1} 24 = 1.44kN/m
1.8kN/m


w= 9+1.44
= 10.44
kN/m



Actual

=
= 83.52kNm




Actual
)
=
= 2386c
m
3
3
000cm
3

o.k.



ACI
DESIGN

SPECIFICATIONS

Permissible stress
:

a)

Initial co
ndition: compression =

= 0.6(2.8) = 1.68kN/cm
2



Tension


=

= 0.13kN/
cm²


b)

Final condition:

compression =

0.45

= 1
. 58kN/cm
2




Tension =

= 0.31kN/
cm²



c)

Steel stress:


Immediate stress after transfer (
)

= 0.7
f
pu

= 132. 3kN/
cm²


Assume 18% loss for pre
-

tensioning


Total loss
)

=

23.81kN/
cm²



Effective stress

(
)

=


-


= 108.49kN/
cm²


If immediate stress
loss (
) =

0.5




Immediate

stress loss
(
) = 11.9kN/
cm²


Immediate stress
(
)

=

-


= 120.4kN/
cm²

The ratio of



=




= 1.11F

Determine

force and eccentricity for maximum tension at the bottom

of the beam










-








=
2.474

----
------------------

(
equation
1)



Determine

force and eccentricity for minimum tension at the top (initial condition of self
weight)







Where
,

Mb


=

=
11.52kNm




But,

=
1.11F









=
-
0.463

----------------

(
equation
2)


Solving equation
s

1 & 2 together

=
2.474


0.463



F = 603.3KN

To obtain the value of the eccentricity (e), substitute the value of F = 603.3kN
into equation
(1)



e = [
2.474

-
]

=

7
.30cm







SELECTION OF STRANDS

Try 8

nos
ϴ
10mm strands.


G
iving
the following:




=

189kN/
cm²


F = 603.
3kN




e

= 7.30cm



Calculate area of strands =

8

2

= 6.28cm²


F = A
rea

of strands *




F = 681.32kN

>603.3
kN



Stran
ds

selected are

adequate








= 7.30cm