INTRODUCTION Prestressed Concrete: - A creation of internal stresses in a structure in order to improve its performance. Such stresses are designed to counter-act stresses induced by external loads. - Concrete is strong and ductile in compression, it is weak and brittle in tension, and hence its response to external loads is improved by pre-compression. - Prestressed concrete is a type of Reinforced Concrete in which steel has been tensioned against the concrete.
Transcript
INTRODUCTION
Prestressed Concrete:
- A creation of internal stresses in a structure in order to improve its
performance. Such stresses are designed to counter-act stresses
induced by external loads.
- Concrete is strong and ductile in compression, it is weak and
brittle in tension, and hence its response to external loads is
improved by pre-compression.
- Prestressed concrete is a type of Reinforced Concrete in which
steel has been tensioned against the concrete.
In this method, the prestressing tendons are initially tensioned between
fixed abutments and anchored.
With the formwork in place, the concrete is cast around the highly
stressed steel tendons and cured.
When the concrete has reached its required strength, the wires are cut or
otherwise released from the abutments.
As the highly stressed steel attempts to contract, the concrete is
compressed.
Prestress is imparted via bond between the steel and the concrete.
Pretensioned concrete members are often precast in pretensioning beds
long enough to accommodate many identical units simultaneously.
Prestressed Methods:
Two different procedures for prestressing concrete were developed:
(a) Pretensioned Concrete
Pretensioning
b- Post-tensioned concrete
In this method, the concrete is cast around hollow ducts which are fixed to any
desired profile.
The steel tendons are usually in place, unstressed in the ducts during the concrete
pour.
When the concrete has reached its required strength, the tendons are tensioned.
Tendons may be stressed from one end with the other end anchored or may be
stressed from both ends.
The tendons are then anchored at each stressing end.
The concrete is compressed during the stressing operation and the prestress is
maintained after the tendons are anchored by bearing of the end anchorage plates
onto the concrete.
After the tendons have been anchored and no further stressing is required, the
ducts containing the tendons are often filled with grout under pressure.
In this way, the tendons are bonded to the concrete and are more efficient in
controlling cracks and providing ultimate strength.
In some situations, however, tendons are not grouted for reasons of economy
and remain permanently unbonded.
Stresses Calculations
P prestressing force
Pj prestressing force at the jack before transfer
Pi prestressing force immediately after transfer
Pe effective prestressing force after time-dependent losses
Stages
a - Initial Stage, Pi, MD (self weight moment)
b- Final Stage, Service, Pe, Mtotal = MD+MSD+ML
MD = Self weight moment
MSD = Super imposed D.L.
ML = Live load moment
Tendon profiles
1- Basic Concept
2- C-line Method
- Line of pressure or thrust concept
- The beam is analyzed as if it were plain concrete
- The prestressing force is assumed as external load
- Use statics to find stresses
Reinforced Concrete Prestressed Concrete
is almost constant aIn Reinforced Concrete
maxvaries from zero to a aIn Prestressed Concrete
3- Load Balancing Method
Example- 1
A pre-tensioned T-beam (8ST24) will carry load WSD + WL = 420 b/ft
AP = Prestressing Area = 12 (1/2″ diameter strands)
fpu = ultimate strength of the prestressing strands = 270 ksi
fpi = 0.7 fpu = 189 ksi
fpe = 150 ksi.
Given the properties of the section 8ST24 are as follows:
AC = 474 in2
r2 = 45.44 in2
ct = 5.94 in
cb = 18.06 in
St = 3626 in3
Sb = 1193 in3
WD = 494 lb/ft
Find the concrete fiber stresses at mid span due to:
a) Initial Conditions
b) Final Conditions
Solution
1. Basic Concept
• Initial Conditions Pi, MD
Pi = fPi x Ap =0.7(270,000)(1.836) = 347,004 lb
Final Service Stage Pe, MT
2- C-Line Method
a) Initial conditions Pi, MD
Pi = 347004 lb.
MD = 3035136 in-lb.
b) Final stage Pe, MT
3- Load Balancing Method
Initial conditions Pi, WD
WD = 494
wub = 494 - 824.59 = - 330.59 lb/ft
lbinl
wM ubub . 4.2031122128
6459.330
8
22
b) Final stage
Pe = 275400 lb.
wT = wD + wSD + wL
= 494 +420 = 914 lb/ft
= 654.3 lb/ft
Example -2
A pretensioned simply supported 10LDT24 double T-beam without topping has
a span of 64 ft and the geometry is shown below.
The beam is subjected to a uniform superimposed gravity dead load (WSD)
and live load (WL) summing to 420 plf. The initial prestress before losses is
fpi = 0.7 fu=189,000 psi, and the effective prestress after losses is fpe=150,000
psi.
Assume that ten ½ in. diameter seven –wire strand tendons with 108-D1
strand pattern are used to prestress the beam. Compute the extreme fiber stresses at the midspan due to:
a- the initial full prestress and no external gravity load. (using the basic
concept method)
b- the final service load conditions when prestress losses have taken place.
(using the three methods)
Solution
Section properties are as follows:
plfW
ininS
inin
ininC
inrinIinA
D
b
b
cc
359
607,3S 264,1
77.7e 77.14e
23.6C 77.17
04.50 469,22 449
3t3
ec
t
2242
a- initial Conditions at Prestressing
lbP
lbfAPinA
e
pipsips
500,229000,15053.1
170,289000,18953.1 53.1153.010 2
The midspan self-weight dead-load moment is
lbinwl
M D 696,205,2128
)64(359
8
22
)( 70607,3
696,205,2)
04.50
23.677.141(
449
170,289)1(
2Cpsi
S
M
r
ec
A
Pf
t
Dt
c
it
)( 277,2264,1
696,205,2)
04.50
77.1777.141(
449
170,289)1(
2Cpsi
S
M
r
ec
A
Pf
b
Db
c
ib
b - Final Conditions at Service Load
Midspan moment due to superimposed dead and live load is
lbinMMomentTotal
lbinMM
T
LSD
. 176,786,4480,580,2696,205,2
. 480,580,2128
)64(420 2
)( 898607,3
176,786,4)
04.50
23.677.141(
449
500,229)1(
2Cpsi
S
M
r
ec
A
Pf
t
Tt
c
et
)( 594264,1
176,786,4)
04.50
77.1777.141(
449
500,229)1(
2Tpsi
S
M
r
ec
A
Pf
b
Tb
c
eb
i- Basic Method
ii- C-line Method
. 08.677.1485.20e . 85.20500,229
176,786,4ineain
P
Ma
e
T
)(594)04.50
77.1708.61(
449
500,229)1(
)(898)04.50
23.608.61(
449
500,229)1(
2
2
Tpsir
ce
A
Pf
Cpsir
ce
A
Pf
b
c
eb
t
c
et
iii- Load Balancing Method
plfl
PaW
fteamidspanat
b
c
552)64(
231.1500,22988
231.177.14 ,
22
lbinlW
MplfW
plfWWWW
ububub
LSDDT
.688,394,1128
)64(227
8 227552779
779420359
22
)(594264,1
688,394,1
449
500,229
)(898607,3
688,394,1
449
500,229
TpsiS
M
A
Pf
CpsiS
M
A
Pf
b
ub
c
b
t
ub
c
t
2 -Example
A T-shaped simply supported beam has the cross-section shown in the given
figure below. It has a span of 36 ft (11m), is loaded with a
gravity live-load unit intensity WL = 2,500 plf (36.5 kN ), and is
prestressed with twelve ½ -in.-dia seven wire stress-relieved strands.
Compute the concrete fiber stresses a service load by each of the following
methods:
(a) Basic concept
(b) C-line
(c) Load balancing
Assuming that the tendon eccentricity at midspan is ec = 9.6 in.
f 'c = 7,000 psi
ft = 12 = 1004 psi (max. allowable tensile stress in concrete)
fc = 0.45 f '́c = 0.45 (7000) = 3150 psi (max. allowable compressive stress)
