Losses in Prestressing Concrete

8/13/2019 Losses in Prestressing Concrete

1/10

UN T 4 LOSSES OF PR STR SS NON RETE

Structure

4.1 IntroductionObjectives

4 2 Loss .of Prestress Due to Elastic Shortening

4 3 Loss of Prestress During the Tensioning Process Due to Friction

4 4 Loss of Prestress Due to Anchorage Slip

4 5 Loss of Prestress Due to Creep of Concrete

4 6 Loss of Prestess Due to Shrinkage of Concrete

4 7 Loss of Prestress Due to Relaxation of Steel

4.8 Total Loss of Prestress

4.9 Summary

4.10 Answers to SAQs

4 1 INTRODU TION

In prestressed concrete the most important parameter is the prestressing force. Ifthe prestressing force reduces with time prestresses also get reduced.

Even at the time of the transfer of prestress to the concrete member there is a

drop of the prestressing force from the recorded value in the jack gauge. Variousreductions of the prestressing force are termed as the losses in prestress.

A loss of prestress will affect the stress distribution on a section of the member. Itis therefore necessary to estimate the probable loss of prestress that may beincurred in a prestressed member. Total loss of prestress consists of those losseswhich are instantaneous at the transfer stage as well as those which are timedependent.

Types of osses

mmediate Time Dependent

Elastic Shortening Friction nchorage Slip

Creep Shrinkage Relaxation

Objectives

After studying this unit you should be able to

understand why losses of prestress occur in prestressed concretemembers

know various reasons behind such losses of prestress


2/10

Prestressed oncrete appreciate relative variations of losses of prestress in pre andpost-tensioned structural elements, and

calculate such losses of prestress.

4 2 LOSS OF PRESTRESS DUE TO EL STIC

SHORTENING

At the transfer of prestress, tensile stresses of tendons are transferred to concretcin the form of compressive stresses. Due to this compression, elastic shorteningof length takes place in concrete. As the length of concrete member gets reduced,;an equal length reduction or strain takes place in tendons. Consequently, stressesin tendons are lost by a magnitude corresponding to this strain. This loss ofprestress is called as loss due to elastic shortening of concrete.

Let fcgp = Concrete stress at the location of centre of gravity of prestressingsteel due to the prestressing force at transfer and the self-weight of

the member at the section of maximum moment,s = Modulus of elasticity of steel, and

c Modulus of elasticity of concrete

Strain in concrete at the level of steel = k]Stress variation in steel corresponding to this strain

= Loss of prestress

The prestress loss due to elastic shortening in pretensioned members is taken asthe product of the concrete stress at the centroid of the prestressing steel attransfer, fcgpand the ratio of the modulus of elasticities of the prestressing steeland the concrete at transfer.

So, loss of prestress due to elastic shortening = ( 1/ sAs modular ratio m) =c

So, loss in stress in steel = fcgp

Loss of prestress due to elastic shortening definitely occurs in pre-tensionedconcrete members. But in post-tensioned members it does not occur if all thetendons across a cross-section are simultaneously stretched, anchored and theirprestresses transferred to concrete. In this case, jacks which stretch tendons buttagainst the ends of members. So the prestressing force which is to be transferredby tendons in already felt by the concrete member through the jacks. Butpost-tensioned members are subjected to this loss of prestress if all the tendonsare not simultaneously tensioned. In that case, every tendon being stretched shallproduce a loss of prestress in all the tendons which have already been tensioned.


3/10

-4 3 LOSS OF PRESTRESS DURING THE

Losses of Prestress

i n o n c r e t e

TENSIONING PROC ESS DUE TO FRICTION

Thi s loss occurs only in post-tensioned mem bers. There always exists a certainam ount of friction in the jacking and anch oring system and on the walls of the

duct.. So, the actual stress in the ten don is less than w hat is indicated by thepressure gauge.

Conside rable frictional loss takes place du e to friction between the tendon andthe material surrounding it, namely the concrete or the sheathing. Loss due tofriction may be classified as below.

( a) loss due to length effect, and

(b) loss due to curvature effect.

The length effect represents the effect of friction for a straight tendon d ue toslight imperfections of the duct. In practice, the duct meant for the straighttendon is not absolutely straight. Hence the cable will touch the duc t or concrete

This loss is also called the loss due to wobbing eBect.In the case of curved ducts, the loss of prestress depends upon the radius o fcurvature R of the duct and the coefficient of friction between the duct surfaceand the tendon.

For a straight or moderately curved profile, with curved o r straight tendons, thevalue of prestressing fo rcePr at a distance metres from tensioning end andacting in the direction of the tang ent to the curv e of the cable, shall be calculatedas below :

Px = o e p a h

where P = Prestressing force in the prestressed steel at the tensioning end

acting in the direction of the tangent to the curve of the cable,a = Cum ulative angle in radians through which the tangent to the cable

profile has turned between any two points under consideration,

p = Coefficient of friction between tendons and d uct material;p may be taken as 0.55 for steel moving on smooth concrete,

0.30 for steel moving on steel fixed to duct, and0.25 for steel moving on lead), and

k = Coefficient for wave effect varying from 15x to50 x l 0-4per metre.

Frictional losses can be reduced by several methods, such as:

(a) Over-tensioning the tendons by an amou nt equal to the maximumfrictional loss, and

(b) Jacking the tendons from both ends of the beam, generally adoptedwhen the tend ons are long or when the angles of curvature are large.

4 4 LOSS OF PRESTRESS DUE TO NCHOR GE

SLIP

In most of post-tension ing system s, when the cable is tensioned and the jack is

released to transfer prestress to co ncrete, the friction w edges, employed to gripthe wires, slip a small distance before the wires can be firmly held between the


4/10

Prestressed oncrete wedges. The magnitude of slip depends upon the type of wedge and the stress inthe wires. This loss of prestress occurs only in post-tensioned members as noanchorages are used in pre-tensioned members.The loss during anchoring, which occurs with wedge-type grip, is normallyallowed for on the site by over-extending the tendon in the prestressing operationby the amount of the draw in before anchoring.

Loss of prestress due to anchorage slip &L

where s = Modulus of elasticity of steel,

= Anchorage slip, and

L = Length of the cable.

Loss due to slip in anchorage is of special importance with short members andthe necessary additional elongation may be provided at the time of tensioning tocompensate for this loss.

4 5 LOSS OF PRESTRESS DUE TO REEP OFON RETE

Creep of concrete means time dependent deformation of concrete. Its effectdepends upon the interval of time for which the member is loaded. For instance,suppose a concrete member is subjected to an external load which causes adeformation. If the member remains loaded for a long time it is seen that thedeformation increases without any increase of load due to creep.

When the consider creep in regard to loss of prestress, we have to see that theprestressed member is under compressive stresses due to prestresses. Due to

these compressive stresses, compressive strains are produced. The immediateeffect of these compressive strains is considered in the calculation of loss ofprestress due to elastic shortening.

Due to creep of concrete, these compressive strains keep on increasing with time.it means that the length of the member keeps on reducing with time though thislength decrease shall be a of a small magnitude and shall not be visible). Due tothis length decrease, length of tendons also shall decrease by the same amountleading to lowering of stresses in tendons, or in other words, to loss of prestress.

The creep loss due to live load stress, erection stresses and other stresses of shortduration may be ignored. The loss of prestress due to creep of concrete isobtained as the product of the modulus of elasticity of the prestressing steel and

the ultimate creep strain of the concrete fibre integrated along the line of centreof gravity of the prestressing steel over its entire length.

The total creep strain during any specific period shall be assumed, for allpractical purposes, to be the creep strain due to sustained stress equal to theaverage of the stresses at the beginning and end of the period.

The loss of prestress due to creep . f

where = Creep coefficient,

m = Modular ratio, and

f = Original prestress in concrete.

As long as the stress in concrete does not exceed one-third of characteristiccompressive strength, creep may be assumed to be proportional to the stress.


5/10

For calculation of deformation at some stage before the total creep is reached, itmay be assumed that about half the total creep takes place in first month afterloading and that about three-quarters of the total creep takes place in the first sixmonths after loading.

4 6 LOSS OF PRESTRESS DUE TO SHRINK GE OF

CONCRETE

We know that concrete shrinks in volume when it dries up. This volumereduction takes place in the form of reduction of all dimensions. A majorreduction of dimensions in a beam element is expected to take place along thelength as all dimensions proportionally reduce.

The shrinkage of concrete in prestressed members results in a shortening of~ensioned wires and hence contributes to the loss of stress. The shrinkage ofconcrete is influenced by the type of cement, aggregates and the method of curingused.

Shrinkage of concrete depends only on the interval of time and the moistureconditions, but is independent of the stresses in the member due to loads.

The loss of prestress due to shrinkage of concrete shall be the product of themodulus of elasticity of steel and the shrinkage strain of concrete. Theapproximate value of shrinkage strain for design shall be assumed as follows

For pre-tensioning 0.0003

For post-tensioning =0.0002

Log,, t 2

where t =Age of concrete at transfer in days.

For the calculation of deformation of concrete at some stage before the maximumshrinkage is reached, it may be assumed that half of the shrinkage takes placeduring the first month and that about three-quarter of the shrinkage takes place n

first six months after commencement of drying.

4 7 LOSS OF PRESTRESS DUE TO REL X TIONOF STEEL

Relaxation of steel represents the time dependent reduction of stresses in steeleven when the strain remains constant. In a way it may be a phenomenon similarto creep where an increase in strains at a constant stress takes place in a timedependent manner.

The relaxation losses in prestressing steels vary with type of steel, initialprestress, age, and temperature and, therefore, shall e determined fromexperiments. When experimental values are not available, the relaxation lossesmay be assumed as given in Table 4.1.

Table 4 1 Relaxation Losses for Prestressing Steel at 1000 Hours at 27C

Initial Stress

0.580 6 6

0 7 fb

Relaxation LossN/mml)

0

357


6/10

Prestressed Concrete where p is the characteristic strength of prestressing steel.

No reduction in the value of the relaxation losses should be made for a tendonwith a load equal to or greater than the relevant jacking force that has beenapplied for a short time prior to the anchoring of the tendons.

a) List various types of loss of prestress in pretensioned andpost-tensioned members.

b) Describe losses of prestress that occur during the tensioning process.

c) How do you compute the loss of prestress due to elastic deformation?

d) How do you compute the loss of prestress in steel due to shrinkage ofconcrete?

e) How do you compute the loss of prestress in steel due to relaxationof steel?

f) What is relaxation of stress in steel? What do you mean by creep ofconcrete?

Example 4 1

A pre-tensioned concrete beam, 200 mm wide and 300 mm deep, isprestressed by straight wires carrying an initial force of 150 k at aneccentricity of 50 mm. Assume modulus of elasticity of steel as2 lo5 N/mm2 and that of concrete as 0 33 loSN/mm2, respectively.Estimate the percentage loss of stress in steel due to elastic deformation ofconcrete if the area of steel wires is 188 rnrn2

SolutionP I5OkN

Initial Stress in Steel150 x lo3

797 87 800 ~ / m m ~188

Stress in Concrete,


7/10

In the above expression for calculation of stress, e2 comes in the second Losses of Prestress

term on the right hand side as we are calculating stress in concrete fibre at in oncrete

the location of tendon itself. So, y, or y, in is replaced by e .

Loss of stress due to elastic deflection of concrete = m f gp=

6.06 3.33 = 20 N/mm2

Percentage loss of stress in steel = 20 x 100 = 2.5%800

Example 4 2

cylindrical concrete tank, 30 m external diameter, is to beprestressed circumferentially by means of high-strength steel wireE , = 2 lo5 N/mm2) jacked at 4 points, 90 apart. If the minimum stress in

the wire immediately after tensioning is to be 450 N/mm2 and coefficient offriction is 0.5, calculate

(a) The maximum stress to be applied to the wires at the jack, and

(b) The expected extension at the jack.

Take e = 2.7.

Solution

P = stress at the jacked end,

Po = initial stress or force at the jacking end,

Px = Po e-p

or, 450 = Po x e 0.785

ITAs = - radians (i.e. 90 ) and = 0.5

2

Average stress in wire = 981-37 450 = 715.68 ~ ~~~2

Length of wires in one segment = n x 3 4X looO) = 7500

Extension at the jack

- Avegage stress x Length of wires = 715.68 x 7500 n = 84.31 rnmx 2 x 105

In a prestressed concrete beam of cross-section 250 x 350 mm and span6 meter, an initial prestressing force of 350 kN is applied at an eccentricityof 70 rnm, by tendons of area 400 mm2. Assuming modulus of elasticity ofsteel as 2 105 N/rnm2 and that of concrete as 0.33 lo5 N/mm2, slip inanchorage as 1.5 rnm reep coefficient in concrete ( ) as 1, shrinkage

strain of concrete as 0.0002 and relaxation loss in steel as 3%, find the totalpercentage loss of stress in the tendons.


8/10

Prestressed Concrete Solution

A = 400 mm2, e = 70 rn

Initial stress in tendons = 350 lo3 = 875 N/rnrn2400

The losses of prestress due to various causes

(a) Loss of stress due to elastic shortening of concrete :

Initial stress in concrete at the level of the tendons

Loss of stress due to elastic shortening of concrete = m f gp

s(b) Loss of prestress due to anchorage slip =

(c) Loss of stress due to creep of concrete = fc

(d) Loss of stress due to relaxation of steel = 3 of initial stress(given)

3x 875 = 26.25 ~ 1 1 r u n ~

100

(e) Loss of stress due to shrinkage of concrete

= 0.0002 2 lo5 = 40 N/mm2

f) Total loss of stress in the tendons

= 35.875 50 35.875 26.25 40 = 188 N/rnm2

188Percentage loss of stress = 100 = 21.49 .

875


9/10

4 8 TOT L LOSS OF PR STR SSLosses of Prestress

in Concrete

The total amount of losses of prestresses may be accounted for in a prestressedconcrete member by adding different losses which may take place for thatmember.

As the types of construction of pre and post-tensioned concrete members aredifferent, same total loss of prestress does not occur in both of them.

In this connection, we may put various losses in either of two categories losseswhich take place during transfer of prestress and those which take place after thetransfer of prestress have taken place. Los of prestress due to friction andcurvature of ducts and loss of prestress due to slip in anchorage take place only inpost-tensioned construction as there is no scope far them to occur inpre-tensioned construction.

As a general guide, it may be taken that total loss of prestress may be in the rangeof 20 to 25 percent of the initial prestress, the lower and higher values of thisrange generally applying to post-tensioned and pre-tensioned concrete membersrespectively. It may seem natural as prestresses in post-tensioned members aregenerally applied at a later stage by which time concrete is able to have gainedmost of its strength.

(a) A pre-tensioned concrete beam, 250 mm wide and 350 rnm deep, isprestressed by straight wires carrying an initial force of 200 kN at aneccentricity of 50 mm. Assume modulus of elasticity of steel as

2 lo5 N/rnrn2 and that of concrete as 0.33 lo5 N/mm2respectively. Estimate the percentage loss of stress in steel due toelastic deformation of concrete if the area of steel wires is 200 mm2.

(b) A cylindrical concrete tank, 35 m external diameter, is to beprestressed circumferentially by means of high-strength steel wiresE,= 2 lo5 N/rnrn2 jacked at 4 points, 90 apart. If the minimum

stress in the wire immediately after tensioning is to be 400 N/mm2and coefficient of friction is 0.5, calculate

(i) The maximum stress to be applied to the wires by the jack, nd

(ii) The expected extension at the jack location.

(c) In a prestressed concrete beam of cross-section 225 325 mrn andspan 5 m, initial prestressing force of 350 kN is applied at aneccentricity of 60 mm, by tendons of area 400 mm2. Assumingmodulus of elasticity of steel as 2 lo5 N/mm2 and that of concreteas 0.33 lo5 N/mm2, slip in anchorage as 1.5 mm, creep coefficientin concrete as 1, shrinkage strain of concrete as 0.0002 andrelaxation loss in steel as 4%, find the total percentage loss of stressin the tendons.


10/10

Prestressed oncrete4 9 SUMM RY

In this unit we have studied how some of the prestresses in pre and post-tensioned concrete members may be lost. These losses are dependent on type ofthe member pre or post-tensioned) as well as these may occur differentlyentirely in the initial stage or proportionately with time elapsed. These losses inprestresses lower down the initial prestresses introduced and hence thedistribution of stresses in the concrete member shall be subject to changes. Wehave to suitably calculate all such losses taking place and have to takeappropriate steps so that even after the losses of prestress, the required amount ofstresses should remain in the concrete member to take care of the safety of themember. One of the appropriate steps in this respect may be to use better gradesof materials to reduce the losses e.g., losses due to shrinkage and creep.Another way may be to extra stress the tendons by an amount equal to theselosses so that after these losses take place; the required amount of prestressesshall still be available. The use of either pre or post-tensioned concrete memberin a particular case may be dependent on the total amount or mechanism of suchlosses taking place also. For example, due to greater losses anticipated and otherpractical diff~culties, ailway sleepers are manufactured as pre-tensioned concretemembers only.

4 10 NSWERS TO S Qs

SAQ 2

a) 2.575

b) i) 872.33 N/rnm2

ii) 87.4

c) 24.77

Losses in Prestressing Concrete

Documents