ce 575-lecture-4(partially prestressed concrete beams)
TRANSCRIPT
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LECTURE 5
Part ia l ly Prestressed Concrete Beams
2016CE 407-Prestressed Concrete Structures
1
PRESTRESSED CONCRETE STRUCTURES
(CE 407)
سم ا لرحن لرحيم
By
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Contents
2016CE 407-Prestressed Concrete Structures
2
Objectives of the present lecture
Full Prestressing
Partial Prestressing
Flexural stresses in full prestressed beams
Flexural stresses in partially prestressed beams Problems
Further reading
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Objective of the Present lecture
2016CE 407-Prestressed Concrete Structures
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To define partial prestressing and learn the stepsfor the calculation of flexural stresses in partiallyprestressed beams.
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Full Prestressing
The kind of design, where the limiting tensile stressin the concrete at full service load is zero, is generallyknown as full prestressing.
Full prestressing is required in those cases in whichit is necessary to avoid all risk of cracking.
Such cases include tanks or reservoirs where leaksmust be avoided, submerged structures or those
subject to a highly corrosive environment wheremaximum protection of reinforcement must beinsured.
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Partial Prestressing
The kind of design in which flexural tensionand thus some cracking are permitted in theconcrete at normal service load is called
partial prestressing.
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A Classification
A prestressed concrete structure may be grouped in one of the threeclasses depending on the extent of cracking.
Class 1 Structures: Tensile stresses are not permitted in thesestructures, hence, no cracking under service loads. Such structures
may be referred to as fully prestressed structures.
Class 2 Structures: Limited tensile stresses are permitted but thereshould be no visible cracking under service loads. Tensile stressesshould be less than 3 MPa.
Class 3 Structures: Tensile stresses, and therefore, cracking underservice loads is permitted in these structures. Such members arereferred to as partially prestressed members.
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Partially Prestressed Members
Prestressed concrete members behave well in the post-cracking load range, provided they contain sufficient
bonded reinforcement to control the cracks.
A cracked prestressed concrete section under service
loads is significantly stiffer than a cracked reinforcementconcrete section of similar size and containing similarquantities of bonded reinforcement. Members that aredesigned to crack at the full service loads are calledpartially prestressed.
The width of surface cracks should not exceed 0.1 mm formembers in aggressive environments and 0.2 mm for allother members.
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Elastic Flexural Stresses in full prestressing(Uncracked Beams)
As long as the beam remains uncracked, and both
steel and concrete are stressed only within theirelastic ranges, then concrete stresses can be foundusing equations of mechanics.
CE 407-Prestressed Concrete Structures
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Stress distribution due to initial prestress alone
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Stress distribution due to initial prestress +self-weight
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Stress distribution due to final prestress +full service load
CE 407-Prestressed Concrete Structures
11
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Flexural Stresses in Partially Prestressed Beams
CE 407-Prestressed Concrete Structures
12
21
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Decompression Stage
CE 407-Prestressed Concrete Structures
13
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CE 407-Prestressed Concrete Structures 14
R
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21
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Equivalent concrete
CE 407-Prestressed Concrete Structures
15
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CE 407-Prestressed Concrete Structures 16
Depth of Neutral Axis
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Centroid of Cracked concrete
CE 407-Prestressed Concrete Structures
17
found. be
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CE 407-Prestressed Concrete Structures 18
Contd..
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Final Stresses
CE 407-Prestressed Concrete Structures
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Problem(in US Customary Unit)
CE 407-Prestressed Concrete Structures
20The partially prestressed T beam shown incross section in Fig. below is subjected tosuperimposed dead and service live loadmoments of 38 and 191 ft-kips, in addition to amoment of 83 ft-kips resulting from its own weight. An effective prestress force of 123 kips
is applied using six Grade 250 ½ -inchdiameter strands.Two non-prestressed Grade 60 no. 8 bars arelocated close to the tension face of the beam,The elastic moduli for the concrete, tendonsteel, and bar steel are respectively 3.61 ×106
psi, 27 ×106
psi and 29 ×106
psi.The modulus of rupture of the concrete is 500psi.Find the stresses in the concrete, prestressedsteel, and bar reinforcement at the full serviceload.
Note:1ft-kips = 1.36 kN.mkips=4.45 kN1 ksi = 6.9 MPa1 inch =25.4 mm1 psi = 0.0069 MPa
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Solution
CE 407-Prestressed Concrete Structures
21
22
2
1
3
2
3
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2
in103
in9.16
in1.13
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in1664
in212
aresectioncrossuncrackedtheof Properties
uncracked.ismemebrtheassumingchecked, bewill beam
theof bottomat theconcretein thestresstensiletheFirst,
r
c
c
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Ac
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CE 407-Prestressed Concrete Structures 22
Contd.
beam.d prestresse partiallyfordiscussedasoutcarried bewillanalysisThe
cracked. beenhassectionThe
psi)(500ruptureof modulus psi1186
psi1186
1290
12312000
103
9.169.111
212
123000
1
fiber bottomin thestressestensilederivedhadsection weuncrackedFor
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ec
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e
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Load stage 1
CE 407-Prestressed Concrete Structures
23
; psi143000863.0
123000
istendonin thestressthestage,At thisalone.
prestresseffectiveof napplicatiotoscorrespond(1)stageLoad
1 p
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Decompression stage
CE 407-Prestressed Concrete Structures
24
depth.entirethe
oughstrain thr concretezeroishereat which tconcrete,theof iondecompress
completetoingcorrespond(2)stageloadfictitiousaconsidertousefulisIt
psi108000004.01027Therefore
0004.0103
9.111
1061.3212
1230001
: propertiessectionconcreteuncrackedtheof basison thecalculated becanand
level,at thatconcretein thethatassametheistendonin thestraininchangeThe
622
2
62
2
2
p p p
cc
e p
ε E f
r
e
E A
P ε
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CE 407-Prestressed Concrete Structures 25
in25.16133
9.1113312312
centroid.concreteuncrackedtheabovee
tyeccentriciwithappliedforceresultanta bydrepresente becankips,-ft312
of momenttotalwith thetogetherforce,This.forceoppositeandequalan
applying bycancellednowisforcesingdecompressfictitiousthisof effectThe
kips133)8.10143(863.0)( :forceexternalfictitiousawith pulled
bemusttendontheconcrete,in thestatestresszerothe produceTo
21
R
Fe M e
R
F
f f A F
t
p p p
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Transformed area
CE 407-Prestressed Concrete Structures
26
2
2
6
6
6
6
in61.2157.103.8 barstheof areadTransforme
in6.460.8637.48tendontheof areadTransforme
03.81061.3
1029 and7.481061.3
1027
where,area by thereplacedisentreinforcem bartheand
concretetensileof areaequivalentan byreplacedistendonThe
s s
p p
c
s s
c
p
p
s s
p p
An
An
E E n
E E n
An
An
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Contd..
CE 407-Prestressed Concrete Structures
27
in1.140)15.327(61.1227
)15.325(46.625
15.33
)604(2
-
zero. bemustof actionof
lineabout theforcesinternalallof momentthat theconditionmequilibriu
thefromfound becansurface,topthefromyaxisneutralof depthThe
3
33
y y
y f
y
y f
y y
f
R
c
cc
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Contd..
CE 407-Prestressed Concrete Structures
28
in9347centroidownitsaboutsection,crackedtheof inertiaof momentand
in13561.1246.61.144512
4512areaedtransformEffective
are propertiesSectionsection.theof topthefromin75.7
centroidthelocatessurfacetopabout theareas partialtheof momentsTaking
2
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s s p pct
*
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c
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Contd..
CE 407-Prestressed Concrete Structures
29
in90.1075.71.1325.16
issectionedtransformcrackedthe
of centroidtherespect towithforcetheof tyeccentriciThe
* e
R
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Contd..
CE 407-Prestressed Concrete Structures
30
psi161009347
25.1990.10133000
135
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)(.
psi126009347
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135
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psi-21909347
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Final Stresses
CE 407-Prestressed Concrete Structures
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psi2190: beamtheof surfacetopat thestressConcrete
psi16100entreinforcemBar
psi1664001260010800143000:Tendon
3
3
321
cc
s s
p p p p
f f
f f
f f f f
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Further Reading
2016CE 407-Prestressed Concrete Structures
32
Read more about the partially prestressed concrete beams from:
• Design of Prestressed Concrete by A. H. Nilson, John Wiley and Sons, Second Edition, Singapore.
• Design of Prestressed Concrete by R. I. Gilbert and N. C. Mickleborough, First Edition, 2004, Routledge.
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Thank You
2016CE 407-Prestressed Concrete Structures
33
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