Basic Principles of prestressed concrete

Introduction to prestressed concrete structures

1. 11
UNIVERSITY OF DAR ES SALAAM
SC 442
FUNDAMENTALS OF PRE STRESSED CONCRETE
DESIGN
(c) Dr Daudi S. Augustino
2023

2. References
•Hurst, M.K (1998). Prestressed concrete
design,2
nd
edition.
•Marshall, V & Robberts J.M. Prestressed
concrete design and practice. Concrete
society of Southern Africa pressed concrete
division Midrand, South Africa.
2

3. 33
1.0BASICPRINCIPLES
1.1Introduction
ConceptofPrestressing
(+)
(+)
(-)
+
(+)
(-)
=
P
P
q
Beam loading
Prestress stress profile
Figure1:Prestressprinciple

4. 4
Introduction
The idea of prestressed concrete has been around since the
latter decades of the 19th century, but its use was limited by
the quality of the materials at the time. It took until the 1920s
and ‘30s for its materials development to progress to a level
where prestressed concrete could be used with confidence.
Freyssinet in France, Magnel in Belgium and Hoyer in
Germany were the principle developers

5. 55
Essential Features
-High strength steel
-Loss of prestressing force due for concrete
shrinkage and creep and steel relaxation
-Quality (strength) of concrete
-Strong anchorages

6. 6
Uses of Prestressed Concrete
There are a huge number of uses:
•Railway Sleepers;
•Communications poles;
•Pre-tensioned precast “hollow core” slabs;
•Pre-tensioned Precast Double T units -for very
long spans (e.g., 16 m span for car parks);
•Pre-tensioned precast inverted T beam for
short-span bridges;
•Pre-tensioned precast PSC piles;

7. 7
Uses of Prestressed Concrete (ctd)
•Pre-tensioned precast portal frame units;
•Post-tensioned ribbed slab;
•In-situ balanced cantilever construction -post-
tensioned
PSC; This is “glued segmental” construction;
•Precast segments are joined by post-tensioning;
•PSC tank -precast segments post-tensioned
together on
site. Tendons around circumference of tank;
•Barges;
•Silos,
•And many more.

8. 88
Examples of Ancient Applications of the
Concept of Prestressing:
◊Barrels–woodenstaveskeptinplaceby
metalhoops
◊Cartwheelsprestressedbypressingheated
irontyresaroundawoodenrim.
Application Areas of Prestressed Concrete:
Floorandroofbeams
Longspanconcretebridges
Slabs

9. 99
The idea of prestressing has
also been applied to many
other forms, such as:
•Wagon wheels;
•Riveting;
•Barrels, i.e. the
coopers trade;
In these cases heated metal
is made to just fit an object.
When the metal cools it
contracts inducing prestress
into the object.

10. 1010
Advantages of Prestressed Concrete Construction
FFacilitatesconstructionoflongspanmembers
FFacilitatesconstructionofbridgeswithrestricted
accessbeneath
FDemandslessconcrete(smallerdeadload)
FReducedfoundationcosts
FStructuresmayberenderedcrackfree(important
durabilityconsideration)
FLow/controlleddeflection

11. 1111
Disadvantages of Prestressed Concrete
Long-term creep and relaxation
Highlevelqualitycontrol
Expensivefordevelopingcountries

12. 1212

13. 1313
1.2Methods of Prestressing
There are two methods of prestressing:
Pre-tensioning: Apply prestress to steel strands before casting
concrete;
Post-tensioning: Apply prestress to steel tendons after casting
concrete.
1.2.1 Pre-tensioning
Salient features of the pre-tensioning process:
Tensioned steel tendons (in form of wires) are held between
end anchorages while concrete is placed/cast around them.
Anchorages are released when concrete has hardened and pre-
stress force is then transferred to the concrete through bond.
Protruding tendons at the ends are cut away.
This method is suitable for factory production because of the
large end anchorages demanded.
It is important to ensure freedom of members to move along the
pre-stressing bed.

14. 1414

15. 15

16. 1616
1.2.2Post-tensioning
Process:SalientFeaturesofthePost-tensioning
The prestress force is applied by jacking steel
tendons against an already-cast concrete member.
•This is the common practice for nearly all in-situ pre
stressing.
•Tendons are threaded through ducts cast into the
concrete or outside.
•The jacking force is transferred to the concrete
through especially built-in anchorages.

17. 1717
•The concentrated force applied through the anchorage
sets up a complex state of stress within surrounding
concrete which must be heavily reinforced.
•In most post-tensioned concrete applications the space
between tendon and duct is injected with a cement grout,
for tendon protection and strength improvement.
•Post-tensioning can be done in stages.
•Post-tensioned systems can accommodate curved
tendons while pre-tensioned systems can only
accommodate sharp linear changes of direction.

18. 18

19. 1919

20. 20
Stresses in Prestressed Members
Background
The codes of practice limit the allowable stresses in
prestressed concrete. Most of the work of PSC design
involves ensuring that the stresses in the concrete are
within the permissible limits.
Since we deal with allowable stresses, only service loading
is used, i.e. the SLS case. For the SLS case, at any section
in a member, there are two checks required:
•At Transfer
This is when the concrete first feels the prestress. The
concrete is less strong but the situation is temporary and
the stresses are only due to prestress and self weight.

21. 21
Stresses in Prestressed Members (ctd)
•At Service
The stresses induced by the SLS loading, in addition to
the prestressand self weight, must be checked. At
service stage, the concrete has its full strength but losses
will have occurred and so the prestress
force is reduced.
The ultimate capacity at ULS of the PSC section (as for
RC) must also be checked. If there is insufficient
capacity, you can add non-prestressedreinforcement.
This often does not govern.

22. 22
Allowable Stresses (to BS 8110)
Stresses Class 1Class 2 Class 3
At
tra
nsf
er
Tension:
f
tt
1 N/mm
2
0.45
f
ci
for pre-tensioned members
0.36
f
ci
for post-tensioned members
Compression:
f
tc
0.5 f
ci
*
In
ser
vic
e
Tension:
f
st
0 N/mm
2
0.45
f
ci
(pre)
0.36
f
ci
(post)
See code table
Compression:
f
sc
0.33
f
cu
* there are other requirements for unusual cases –see the code
f
ci = (2/3)
f
cu

23. 23
Notations
y
y
t
b
N. A.
e
We have:
Z
t
Section modulus, top fibre = I/y
t
;
Z
b
Section modulus, bottom fibre = -I /y
b
(taken to be negative);
f
tt
: Allowable tensile stress at transfer;
f
tc
: Allowable compressive stress at
transfer;
f
st
: Allowable tensile stress in service;
f
sc
: Allowable compressive stress in
service;
M
t
: The applied moment at transfer;
M
s
: The applied moment in service
: The ratio of prestress after losses
(service) to prestress before losses,
(transfer).

24. 2424
1.3 Structural Behaviour
(i)
Axial force vis-à-vis axial pre stress forces
illustrated in post–tensioned (bearing plate) and in
pre-tensioning (bond).
Figure2:Axiallyloadedmember

25. 2525
(ii)
Consider the duct not coincident with the
centroidal axis by “e”
Z
b
, Z
t
–Section Moduli (bh
2
/12)
n.a
P
eP

26. 2626
(iii)Addinguniformlydistributedloadtocase(ii)
aboveget
n.a
P
e
P
P
Ac
(+)
(-)
(+)
P.e
Zb
P.e
Zt
+
Ms
Zb
Ms
Zt
(+)
(-)
+ =
(-)
(+)

27. 2727
1.4InternalEquilibrium
Averticalcuttakenalongarectangularpre-
stressedconcretebeamwiththepre-stressing
forceappliedataneccentricityof“e”fromthe
centroidalaxis,maybeseparatedintothefree
bodiesshownin(a)below.
Thefreebodycontainingconcreteonlyisacted
uponbyacompressiveforce Pwhiletheone
containingsteelisacteduponbyatensileforce
T.Inthiscaseequilibriumismaintainedbythe
forcesbeingequalandopposite,andcoincident.

28. 2828
1.4InternalEquilibrium
Fig.Internalequilibrium

29. 2929
If the beam is on simple supports and acted upon by
uniformly distributed load an external bending moment
M
s
is then inflicted at midspan. Thus:
-The resultants of the steel and concrete
stresses at midspan form an internal resisting
moment which balance M
s
;
-The force in the tendons being fixed in position, the
force in the concrete moves to provide an internal
resisting couple, as shown in (b);
-The locus of the concrete force along the
member is referred to as the line of pressure.

30. 3030
Butz=e+y
andyvarieswithx.
•yisthusthelineofpressure,viz.thelocusofthe
concreteforcealongamember.
•y=-ewhenthereisnoexternalforce.

31. 3131
Example1
Asimplysupportedbeamwithsectionshown
belowspans15mandcarriesuniformly
distributedloading(includingselfweight)of50
kN/m.Ifthebeamispre-stressedwithaforceof
2000kNactingataneccentricityof400mm
belowthecentroid,determinethestress
distributionatmidspan.AssumeZ
b
=Z
t
=
70.73x10
6
mm
3
andA
c
=2.9x10
5
mm
2

32. 3232

33. 3333

34. 3434

35. 3535

36. 3636
Notethatthestressconfigurationatthesimple
supports,viz.withzerobendingmomentsindicates
finitetensilestresseswhichismostundesirableasit
isdangerous.Thesolutioniseitherto:
FReduce‘e’atsupportforposttensioned
members;or
FDestroybondbetweenconcreteandtendon
bygreasingorprovidingsleevesroundthem,
informoftubesoranextrudedplasticcoating.

37. 3737

38. 3838
1.5Deflected Tendon
Consider the pre-stressed concrete member
shown below.
Fig. Member with deflected tendons

39. 3939
Fig. Free bodies of concrete and steel

40. 4040

41. 4141
Considerthebeamabovesectionedatathirdpoint
fromtheleftendsupport.Thefreebodyofthe
concreteisasshownbelow
Fig. Free body of concrete near support

42. 4242
Notethefollowing:
□
TheforcePintheconcreteisnothorizontal;
□
Ithasaverticalcomponent,Psinθ,which
counteractstheshearforceV
x
;
□
Theshearstressesatthesectionare
thereforereducedthus,
V
x
=(qx)/2-Psinθ.

43. 4343
1.6IntegralBehaviour
Consideraverticalconcretememberpre-
stressedbyaforcePthroughthecentroidofits
sectionandcompareitwithasimilarvertical
memberloadedwithanexternalloadPapplied
throughitscentroid(Figs(a)and(b)below).

44. 4444
Fig. Axially loaded and prestressed vertical members

45. 4545
AstheforcePisincreased:
-For (a) failure by crushing of concrete will eventually occur;
-For(a)thereisnopossibilityofmemberbucklingwhilefor
(b)failurebybucklingmayoccurbeforecrushingof
concrete,dependingondimensionsofthemember;
-For (a) line of pressure remains coincident with tendon
position while for (b) bending moments are induced if
member is deflected;
-For (a) stress distribution across member remain uniform
while for (b) stress distribution is no longer uniform;

46. 4646
Fig. Curved prestressed member

47. 4747
1.7ForcesExertedbyTendons
•Bydeflectingatendonfromthestraightpositiona
downwardforceisrequiredtomaintainthe
tendoninthedeflectedpositionandthisforceis
transmittedintotheconcreteasupwardforce.

48. 4848
•Inthecaseofacontinuouslycurvedtendon,
theremustbeadistributedforceappliedto
theconcretetomaintainthetendonin
position.
Fig. Free bodies of concrete and curved tendon

49. 4949
Consider a small but finite section of
tendon. The following can be observed:
•Neglecting friction between the tendon and concrete,
the force in tendon at either end of the element Δs is
T.
•If ω is the uniformly distributed load on the tendon
required to keep it in position;
Then, ω. s = 2T.sin(Δθ/2)
for the small element, ω.s = T.Δθ
ω = T.Δθ/s

50. 5050
Fig. 1.24: Small Length of tendon
Fig. 1.25: Sharp change of tendon profile

51. 5151

52. 5252
•Example2
•Asimplysupportedbeamoflength lhasaparabolictendon
profilewithmaximumeccentricity easshownbelow.
Determinetheupwardsforceonthebeamexertedbythe
tendonanddrawtheshearforceandbendingmoment
diagramsduetotheprestressforce,P.

53. 5353

54. 5454
xxx
x
ePMxlxM
x
x
l
M
.)(
2
22
2





55. 5555
•Itwillbeobservedthattheprestressmoment
diagramhasthesameshapeasthetendonprofile
(Ptimesinmagnitude e).Thisistrueforall
staticallydeterminatemembers.
•Considerthetaperedbeamdiagrambelow(witha
straighttendon)

56. 5656
•Thereisnoverticalloadinthiscase,sincethe
tendonisstraight,buttheprestressmoment
diagramcanbedrawnsimplybyconsidering
thedistancebetweenthetendonandlocation
andthecentroidofthememberatanysection
–asillustratedin(b)above.

57. 5757
1.8LossofPrestressForce
Sofarithasbeenassumedthattheforceinthe
tendonisconstant.However,duringtensioningof
post-tensionedmembers,thereisfrictionbetween
tendonsandthesidesoftheductcausedby
changesincurvatureandcontactwiththesides
oftheduct
.

58. 5858
Other causes of loss of pre stress are:

Initial elastic shortening of concrete which results in
shortening of the steel tendon.
Long–term changes in length due to creep and
shrinkage.

59. 5959
Effect of friction on behavior of the prestress member is
illustrated in diagram below.
Fig. Loss of pre stress due to friction

60. 6060
1.9Degree of Pre stressing
Two scenarios are possible pertaining to pre
stressing of concrete, namely, full pre stressing and
partial pre stressing.
-Full pre stressing is achieved when the
whole section is in a permanent state of
compression.
-Partial pre stressing is achieved when there
exist a small amount of tensioned steel to
control service load cracking and larger amount of
un-tensioned reinforcement or vice verse.

61. 6161
There are three classes of pre stressed concrete
as per BS 8110, as follows:
Class1 membersarethoseinwhichthe
minimumstressunderserviceloadiszero ,viz.
fullprestressing.
Class 2 members are those in which some
tensionis allowed provided the tensile strength of
concrete is not exceeded, viz.no cracking is allowed.
Class 3 members are those in which cracking occurs
but the extent is limited by both tensioned and
untensioned steel, viz. may be regarded as normal
reinforced concrete with enough pre stress introduced
to limit service load cracking to 0.1 mm in aggressive
environment and 0.2 mm for allother cases.

62. 6262
Figure: Classes of pre stressed concrete members

63. 6363

64. 6464
1.10SafetyMeasures
•Since high stresses exist in pre stressed concrete
members at both maximum and minimum load
conditions, there must be careful quality control of
materials used.
•Sinceasmallchangeintendoneccentricitycanhave
alargeeffectonthestresses,caremustbetaken
duringconstructiontoensurethatthecorrecttendon
profileismaintained.

65. 6565
SafetyMeasuresContd…..
•Becauseverylargejackingforcesareinvolved,
adequateprovisionmustbemadetoprotectsite
personnelagainstsuddenfailureofasteeltendon
duringtensioning.
•Considering the large amount of energy stored in pre
stressed concrete, demolitions of such structure is
very problematic.