2 PC - Design Guide 2011_v1_apr2011
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Transcript of 2 PC - Design Guide 2011_v1_apr2011
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PRESTRESSED CONCRETE
DESIGN GUIDE
2011
Prepared by:
Prof. CLIPII Tudor, PhDNAGY-GYRGY Tams, Lecturer, PhDFLORUCodru, PhD student
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The numbering of the tables and formulas is according to SR EN 1992-1-1:2004 (EC2).
1. Initial data
- Element type
- Element length
- Support width
- Prestressing stand length
- Number of tendons
- Type of tendons
- Permanent loads (rest)
- Live loads
- Humidity
- Exposure class
- Life cycle
- Type of the technological curve
- Concrete class
- Cement type
- Steel grade- Modulus of elasticity of the tendons
- Steel class
- Relaxation losses
- Slip in anchorage
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1.1 Characteristics of the cross-section
For the element given in the project theme, the following characteristics of the section will
be computed:
Ac area of the concrete section
Ap area of the prestressed reinforcement
Ic second moment of area of concrete section
Wi the modulus of resistance for the bottom fibre;
i
ci
xIW
Ws the modulus of resistance for the top fibre;
s
c
sx
IW
x
X
s
i
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2. Heat curing (Thermal treatment)
Heat curing (thermal treatment) is applied according to the following graph:
3...4 h
Pretensionare
Turnare
Transfer
Transfer la 16...22 h
10
20
30
40
50
60
70
4 h 7 h 5 h3...4 h
Ora 10 14 17 21 04 08 09
timp de relaxare (t )
Ore
C
relaxare
Hours
hour
Pre-stressing
Casting
Release
Force Transfer at
Relaxation time (trelax)
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3. Characteristics of the concrete
fck - Characteristic compressive cylinder strength of concrete at 28 days
C X/Y fck= X MPa (N/mm2)
fcm - mean value of concrete cylinder compressive strength (obtained from table 3.1 infunction of the concrete class)
fctm - mean value of axial tensile strength of concrete (obtained from table 3.1 in functionof the concrete class)
fctm(t) - The compressive strength of concrete at an age t.
In formula (3.1) and (3.2) twill be replaced with tT, computed based on the technologicalgraph using formula (B.10).
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Ecm(t) - Secant modulus of elasticity of concrete at an age t
In formula (3.5) twill be replaced with tT, computed based on the technological graph usingformula (B.10).
3.1. Calculation of the total shrinkage strain
0,, cdhcd k
kh is a coefficient depending on the notional size h0 according to Table 3.3
h0 is the notional size (mm) of the cross-section
h0 = 2Ac/u
where:
Ac is the concrete cross-sectional areau is the perimeter of that part of the cross section which is exposed to drying
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0,cd - Nominal unrestrained drying shrinkage, which may be taken from Table 3.2 or
based on formulas given below (B.11 and B.12 from Annex B)
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)(ca - phenomenon is due to water migration in concrete mass; is given by the formula
(3.12)
3.2 Computation of the creep
),( 0t - is the final creep coefficient, obtained using graphics from Figure 3.1.
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4. Characteristics of the prestressing reinforcement
The 0,1% proof stress (fp0,1k) and the specified value of the tensile strength (fpk) are definedas the characteristic value of the 0,1% proof load and the characteristic maximum load inaxial tension respectively, divided by the nominal cross sectional area. Generally, thesevalues are given by the producers. In this case:
15.11.01.0 kp
s
kppd fff
The characteristic strength of the steel (fp0,1k) is given in the theme of the project.
The relaxation of the reinforcement, given in the project theme, can be assumed:
1000=8% - for Class 11000=2.5% - for Class 2
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1000=4% - for Class 3
Ep - Design value of modulus of elasticity of prestressing steel, given in the projecttheme.
Reinforcement types and their denotations used in this project:0,6 TBP15=75 => Ap=137 mm
2
1/2 TBP12=74 => Ap=88 mm2
3/8 TBP9=73 => Ap=49 mm2
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5. Prestressing force during tensioning
5.1. Maximum stressing force
fp0.1k - characteristic 0,1% proof-stress of prestressing steel. This value is given by theproducer.
In this project, the following formula will be used:
kpkpp ffk 1.01.02max 9.0
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6. Immediate losses of prestress for pre-tensioning
6.1. Losses at the anchorage
Account should be taken of the losses due to wedge draw-in of the anchorage devices,during the operation of anchoring after tensioning, and due to the deformation of theanchorage itself. Values of the wedge draw-in are given in the European Technical
Approval.An average value used in calculation can be 4...6 mm, as given in the theme of the project.
Loss of the prestressing stresses and the prestressing loads, caused by the wedge draw-in(slipping), can be asses according to the following relation:
p
p
sl EL
21
where
sl - loss of prestressing stresses due to anchorage slip.
21; - slipping in the anchorage ends. If the pretensioning is done just from one edge
(side) 2= 0.
In this project is considered, that the pretensioning is done just from one edge (side).
pL - length of the prestressing stand (track)
pE - design value of modulus of elasticity of prestressing steel
slpsl AP
where
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slP - losses due to anchorage slip
pA - cross sectional area of the prestressing tendons
6.2. Relaxation of the prestressing steel
The relaxation of the prestressing steel is producing between the moments from thestressing of steel up to the transfer.
where
slppi max
In the formulas 3.28, 3.29 and 3.30, time t represents time of the prestressing steelrelaxation, from the moment of prestressing to the moment of the transfer.
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The equivalent time (teq) is calculated and it is given in the technological graph theme.
Loss of prestressing force caused by the relaxation of the steel can be evaluated as:
prpr AP
where:
rP - loss of prestressing force caused by the steel relaxation
pA - cross sectional area of the prestressing tendons.
6.3. Heat curing (Thermal treatment)
In order to reach faster the required initial strength for concrete, a heat curing process(thermal treatment) is necessary, usually by using hot steam of hot water.
3.1.3
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7. Elastic deformation of the concrete at the transfer
In the moment of the transfer the value of the prestressing force can be computed as:
PPPPP rslerm maxint
where:
maxP - force applied to prestressing steel
slP - losses due to anchorage slip
rP - loss of prestressing force caused by the steel relaxation
P - loss of prestressing force due to heat curing
x
X
s
i
Ape
cpPinterm
To calculate the unit stress in concrete at the level of prestressing steel (cp) a simplified oran exact procedure can be assumed.
The simplified calculation method
eI
eP
A
P
c
erm
c
erm
cp
intint
where:
Ac - area of the concrete cross sectione - distance between the gravity centres of the prestressing steel and concrete cross
sectionIc - second moment area of the concrete cross section
The exact calculation method
)1(2
2
int
r
eA
A
p
c
e
ermp
cp
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where:
p
erm
ermpA
Pintint
)( 0tE
E
cm
p
e
Ep - modulus of elasticity of the prestressing steelEcm(t0) - secant modulus of elasticity of concrete at an age t0. In the case of this project t0
will be replaced with tT , as was computed before.Ac - area of the concrete cross sectionAp - area of the prestressing steele - distance between the gravity centres of the prestressing steel and concrete cross
sectionr - radius of gyration of the concrete cross section, computed as
cAIcr
Loss of prestressing stress ( el ) and loss of prestressing force ( elP ) caused by the
elastic deformation (shortening) of the concrete at transfer can be evaluated according tofollowing relations:
cpeel
elpelAP
In the moment immediately after the transfer, the stress and force in prestressing steel canbe evaluated using the following relations:
el
p
erm
pmA
P int0
00 pmpm AP
In this stage, the stress in the prestressing steel must satisfy the following conditions:
kppkpm
ff ,1.00 85,0;75,0min
If it is not satisfied, maxp must be reduced.
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8. Static design
2
2
1
1
Combination of actions:
SLS
- characteristic Gk+Qk
- frequent Gk+1Qk
- quasi-permanent Gk+2Qk
ULS
- fundamental 1,35*Gk+1,5Qk
Load Characteristic values Bending moment in section 1-1
Self weigth gself,k8
2
,
,
lgM
kself
kself
Rest of the permanent grest,k8
2
,
,
lgM
krest
krest
1 2
Roof 0,5 0,4
Intermediary slab 0,7 0,4
ldisp
lcalcltransf
lsupp lsupp
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Variable qk
Combination Mod of combination Bending moment in section 1-1
Characteristic Gk+Qk8
)(
2
,, lqggM kkrestkselfEk
Frequent Gk+1Qk8
)( 21,, lqggM
kkrestkself
Ef
Quasi-permanent Gk+2Qk8
)( 22,, lqggM
kkrestkself
EQP
Fundamental 1,35*Gk+1,5Qk8
)5,135,135,1( 2,, lqggM
kkrestkself
Ed
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x
X
s
i
Ape
cpPm0
ct
cb
Mself,k
9. Verification of stresses at transfer
9.1. Design of normal stresses in the section 1-1
i
kselfm
c
m
cbW
MeP
A
P ,00 (bottom)
s
kselfm
c
mct
W
MeP
A
P ,00 (top)
eI
MeP
A
P
c
kselfm
c
m
cp
,00 (at the level of the prestressing steel)
9.2. Design of normal stresses in the section 2-2 (at ldisp)
9.2.1. Determination of the position of the section 2-2 (at ldisp)along the element axis
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x
X
s
i Ap e cpPm0
ct
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s
kselfm
c
mct
W
MeP
A
P22
,00
i
kselfm
c
mcb
W
MeP
A
P22
,00
(1)P Local concrete crushing or splitting at the end of pre- and post-tensioned membersshall be avoided.
(3) The strength of concrete at application of or transfer of prestress should not be lessthan the minimum value defined in the relevant European Technical Approval.
)( 0tfctmct - condition to remain the entire section uncracked
In the case when in section 2-2 the relation )(6,0 0tfckcb is not satisfied, the solution to
decrease the stress in concrete consists in disposal of one or more (plastic) sheets to theone or more tendons. In this way, the wrapped tendon(s) is considered not anchored (nuconlucreaza) in concrete, the section being verified with this new (reduced) stress. If the
relation continues to be unsatisfied (false), another tendon is considered to be wrapped insheet, followed by the re-verification of the section. The procedure is continued up to thestage when the relation is satisfied (becomes true).
In the above formula t0will be replaced with tT, computed based on the technological graphusing formula (B.10).
- condition to avoid longitudinal cracking
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In the case that disposal of one or more sheets is necessary, verification in another cross-
section (2-2), situated at distance ofldisp measured from the sheets end will be done.
ldisp 2
2
2'
2'ldisp
lteaca ldisp
teaca
teaca
123
sheet
sheet
sheet
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10. Final losses of prestress
In the case of this project ezcp .
eI
MM
c
EQPrest
cpQPc
,
eI
MeP
A
P
c
kselfm
c
m
cp
,00
pr - can be evaluated based on the relations 3.28, 3.29 or3.30, considering t
being the life-cycle of the element
and
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QPcepmpi ,0
)( 0tE
E
cm
p
e
where t0 is 28days, thus Ecm(t0) became Ecm.
The final force of prestressing, considering the rheological losses can be determined with:
rscmm PPP 0
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11. Verification of the stresses in service stage in section 1-1
e
ct
cb
Pk=nPm8
M
n=1
11.1. Verifications for ct
For exposure classes XD, XF, XS
ct will be computed considering M = MEkand will be verified the relation
ckct f 6,0
For the rest of the exposure classes
ct will be computed considering M = MEQPand will be verified the relation
ckct f 45,0
11.2. Verifications for cb
For exposure classes X0, XC1, XS
cb will be computed considering M = MEfand will be verified the relation
ctmcb f
For exposure classes XD1, XD2, XD3, XS2, XS3
cb will be computed considering M = MEfand will be verified the relation
0cb
For exposure classes XC2, XC3, XC4
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cb will be computed considering M = MEQPand will be verified the relation
0cb