PC PRELIMS Flashcards
Reduction in force, addressed as part of the design of a prestressed member.
Partial prestress loss
Prestress losses are divided into two broad categories:
- Initial
- Long-term losses / Time-dependent effects
Occur during stressing operation and include anchor seating, elastic shortening, and friction between prestressing steel and post-tensioning ducts or tendon deviators and harped pretensioned strands.
Initial losses
Occur because of viscoelastic material effects and include concrete shrinkage, creep, and tendon relaxation.
Long-term losses
Recognized as the founder of modern prestressed concrete, was successful because he recognized the value of high-strength prestressing materials and successfully incorporated high-strength materials into his design.
Eugene Freyssinet
All __________ are subject to losses resulting from elastic shortening, shrinkage, creep, and relaxation.
Prestressed members
Are subject to losses resulting from anchor set and friction.
Post-tensioned members
The __________ requires prestress losses to be considered in the calculation of effective tensile stress in the prestressed reinforcement, fse.
ACI Building Code (ACI 318-14)
6 types of prestressing losses
- Prestressed reinforcement seating at transfer (initial)
- Friction loss due to intended or unintended curvature in post-tensioning tendons (initial)
- Elastic shortening of concrete (initial)
- Creep of concrete (long-term)
- Shrinkage of concrete (long-term)
- Relaxation of prestressed reinforcement (long-term)
Are calculated at the tendon centroid and include consideration of the stress and strain in the tendon.
Losses
For _________, the losses are usually calculated at the critical sections, which are typically at midspan and the end of the member.
Precast pretensioned beams
For __________, the critical sections are at the member end, maximum positive moment locations, typically close to midspan, and maximum negative moment locations, usually over the supports.
Post-tensioned members
The ratio of modulus of elasticity of the prestressing reinforcement divided by the modulus of elasticity of concrete.
Modular ratio, n
If the calculated losses are __________, that is higher than actual losses, then more prestressing reinforcement is used and camber increases.
Too high
If the calculated losses are __________, the beam sags and cracks under service load.
Too low
__________ should neither be overly conservative nor ignored.
Loss calculations
3 methods in calculating losses of prestress
- Lump sum
- Detailed
- Time-dependent
The total combined losses in the prestress based on experience or historical data, to select the initial prestress.
Lump sum losses
Initial stress for post-tension
0.80fpu
Maximum initial prestress force for post-tension
0.70fpu
Initial strand stress for pretensioning
0.75fpu
A small amount of movement when a prestressing tendon is released from the jack.
Set
Anchor set of __________ is common for single strand systems and larger values are for some center plug multistrand systems.
1/4 to 3/8 in.
The amount of movement ranges between ____ and ____ depending on the anchorage system.
1/8 in, 1 in
Friction due to misalignment
Wobble friction
Friction due to intentional curvature resulting from the alignment of the duct in the member.
Curvature friction
Maximum sum of wobble and curvature friction
0.30
Reduces the strain in the tendon
Elastic Shortening
Notation:
Modulus of elasticity of the tendon, psi
Eps
Notation:
Modulus of elasticity of the concrete at the time of transfer, psi
Eci
Notation:
Initial prestress force, lbs
Pi
Notation:
Gross area of the section, in²
Ag
Notation:
Eccentricity of the tendon at the critical section, in
ep
Notation:
Gross moment of inertia of the section, in⁴
Ig
Notation:
Dead load moment due to girder weight, lb-in
Mg
Notation:
Unit weight of the concrete, pcf
Wc
Unit weight of precast concrete
160 pcf
Unit weight of cast-in-place concrete
150 pcf
Notation:
Strength of the concrete at the time of transfer, psi
f’ci
NOTATION:
Wobble coefficient
k
Notation:
Curvature coefficient
m (mu)
Transfer of the prestress force from the tendon to the concrete results in
Elastic Shortening
Continued deformation of the concrete under sustained loads.
Creep
Volume reduction of the concrete due to hydration of the cement and loss of water from the concrete as it cures.
Shrinkage
Notation:
Volume-to-surface ratio of the member
V/S
Notation:
Relative humidity
RH
Are induced in a member to counteract the external stresses which are developed due to the external loads or service loads.
Internal stresses
Is basically concrete in which internal stresses of a suitable magnitude and distribution are introduced so that the stresses resulting from the external loads are counteracted to a desired degree
Prestressed concrete
A stretched element used in a concrete member of structure to impart prestress to the concrete.
Tendon
A device generally used to enable the tendon to impart and maintain prestress in concrete.
Anchorage
A method of prestressing concrete in which the tendons are tensioned before the concrete is placed. In this method, the concrete is introduced by bond between steel and concrete.
Pretensioning
A method of prestressing concrete by tensioning the tendons against hardened concrete. In this method, the prestress is imparted concrete by bearing.
Post-tensioning
PRE-TENSION OR POST-TENSION?
Small sections are constructed.
Pre-tension
PRE-TENSION OR POST-TENSION?
Loss of strength is above 17%
Pre-tension
PRE-TENSION OR POST-TENSION?
This method is done due to bonding between concrete and steel.
Pre-tension
PRE-TENSION OR POST-TENSION?
It is cheaper because the cost of sheathing is not involved.
Pre-tension
PRE-TENSION OR POST-TENSION?
It is more durable and reliable.
Pre-tension
PRE-TENSION OR POST-TENSION?
Size of a member is not limited. Heavy long span bridges can be constructed by using this technique.
Post-tension
PRE-TENSION OR POST-TENSION?
Loss of strength is not more than 15%
Post-tension
PRE-TENSION OR POST-TENSION?
This is developed due to bearing.
Post-tension
PRE-TENSION OR POST-TENSION?
It is costlier because the cost of sheathing is required.
Post-tension
PRE-TENSION OR POST-TENSION?
Its durability depends upon the two anchorage.
Post-tension
Minimum grade of concrete for post-tensioned members.
M30
Minimum grade of concrete for pretensioned members.
M40
Requires concrete, which has a high compressive strength reasonably early age with comparatively higher tensile strength than ordinary concrete.
Prestressed concrete
The concrete for the members shall be __________ concrete composed of Portland cement, fine and coarse aggregates, admixtures, and water.
Air-entrained
The air-entraining feature may be obtained by the uses of either __________ or an __________.
Air entraining Portland cement, approved air-entraining admixture.
The entrained air content shall be not less than ___ or more than ___.
4%, 6%
Minimum cement content of __________ is prescribed for the durability requirement.
300 to 360 kg/m³
The water content should be __________.
As low as possible
The prestressing steel used for prestressed concrete can take the form of:
Wires
Strands
Tendon
Cable
Bars
A single unit made of steel.
Wire
Two, three, or seven wires are wound to form a prestressing _____.
Strand
A group of strands or wires are wound to form a prestressing _____.
Tendon
Group of tendons.
Cable
A tendon can be made up of a single steel ___. The diameter of a ___ is much larger than that of a wire.
Bar
High strength steel contains:
0.7% to 0.8% carbon
0.6% manganese
0.1% silica
Cover for pretensioned members.
20mm
Cover for post-tensioned members.
30 mm or size of the cable, whichever is bigger
If the prestress members are exposed to an aggressive environment, cover is increased by another _____.
10 mm
When there is adequate bond between the prestressing tendon and concrete, it is called
Bonded tendon
When there is no bond between the prestressing tendon and concrete, it is called
Unbonded tendon
Pre-tensioned and grouted post-tensioned tendons are example of
Bonded tendons
When grout is not applied after post-tensioning, the tendon is an
Unbonded tendon
This is the simplest type of prestressing, producing large prestressing forces. The hydraulic jack used for the tensioning of tendons, comprises of calibrated pressure gauges which directly indicate the magnitude of force developed during the tensioning.
Hydraulic prestressing
In this type of prestressing, the devices include weights with or without lever transmission, geared transmission in conjunction with pulley blocks, screw jacks with or without gear drives, and wire-winding machines. This type of prestressing is adopted for mass-scale production.
Mechanical prestressing
In this type of prestressing, the steel wires are electrically heated and anchored before placing concrete in the moulds. This type of prestressing is also known as thermoelectric prestressing.
Electrical prestressing
3 sources of prestressing force
Hydraulic prestressing
Mechanical prestressing
Electrical prestressing
PRESTRESSED CONCRETE OR REINFORCED CONCRETE?
Member steel plays active role. The stress in steel prevails whether external load is there or not.
Prestressed concrete
PRESTRESSED CONCRETE OR REINFORCED CONCRETE?
Steel plays a passive role. The stress depends upon the external load. No external load, no stress.
Reinforced concrete
PRESTRESSED CONCRETE OR REINFORCED CONCRETE?
Stresses in steel are almost constant.
Prestressed concrete
PRESTRESSED CONCRETE OR REINFORCED CONCRETE?
The stress in steel is variable with the lever arm.
Reinforced concrete
PRESTRESSED CONCRETE OR REINFORCED CONCRETE?
Has more shear resistance.
PC
PRESTRESSED CONCRETE OR REINFORCED CONCRETE?
Shear resistance is less.
RC
PRESTRESSED CONCRETE OR REINFORCED CONCRETE?
Deflections are less.
PC
PRESTRESSED CONCRETE OR REINFORCED CONCRETE?
Fatigue resistance is higher.
PC
PRESTRESSED CONCRETE OR REINFORCED CONCRETE?
Dimensions are less because external stresses are counterbalanced by the internal stress.
PC
Basic assumption on prestress members:
- Concrete is a homogenous material.
- Within the range of working stress, both concrete and steel behave elastically, notwithstanding the small amount of creep, which occurs in both the materials under the sustained loading.
- A plane section before bending is assumed to remain plane even after bending, which implies a linear strain distribution across the depth of the member.
3 advantages of prestressing
- Section remains uncracked under service loads.
- High span-to-depth ratio.
- Suitable for precast construction.
Span-to-depth ratio of non-prestressed slab
28:1
Span-to-depth ratio of prestressed slab
45:1
7 sections suitable for precast construction
T-section
Double T-section
Hollow core
Piles
L-section
Inverted T-section
I-girders
Limitations of prestressing
- Prestressing needs skilled technology. Not as common as reinforced concrete.
- The use of high-strength materials is costly.
- There is additional cost in auxiliary equipment.
- There is need for quality control and inspection.
Does not remain constant with time.
Prestress
Even during prestressing of tendons and transfer of prestress there is a drop in prestress from the initially applied stress.
True
Reduction of prestress is nothing but the _____.
Loss in prestress
Occur during prestressing of tendons, and transfer of prestress to concrete member.
Immediate losses
Occur during service life of structure.
Time-dependent losses
The losses due to friction and wobble.
Friction Loss
This PC loss does not occur in pretensioned members because there is no concrete during the stretching of the tendons.
Friction Loss
Generated due to the curvature of the tendon and the vertical component of the prestressing force.
Friction
Friction depends on the following variables:
- Coefficient of friction
- Curvature of the tendon
- The amount of prestressing force
The wobble in the tendon is affected by the following variables:
- Rigidity of sheathing
- Diameter of sheathing
- Spacing of sheath supports
- Type of tendon
- Type of construction
The friction due to wobble is assumed to be proportional to the following:
- Length of the tendon
- Prestressing force
Defined as the decrease in stress with time under constant strain.
Relaxation of steel
Due to the __________, the prestress in the tendon is reduced with time.
Relaxation of steel
The ______ depends on the type of steel, initial prestress and the temperature.
Relaxation
NOTATION:
Total area occupied by duct, sheathing, and prestressing reinforcement, mm²
Apd
NOTATION:
Area of prestressed reinforcement in tension zone, mm²
Aps
NOTATION:
Total area of prestressing reinforcement, mm²
Apt
NOTATION:
Area of non-prestressed longitudinal tension reinforcement, mm²
As
NOTATION:
Total area of non-prestressed longitudinal reinforcement bars or steel shapes, and excluding prestressing reinforcement, mm²
Ast
NOTATION:
Area of prestressing reinforcement in a tie, mm²
Atp
NOTATION:
Area of non-prestressed reinforcement in a tie, mm²
Ats
NOTATION:
Nominal diameter of bar, wire, or prestressing strand, mm
db
NOTATION:
Distance from extreme compression fiber to centroid of prestressed reinforcement, mm
dp
NOTATION:
Modulus of elasticity of prestressing reinforcement, MPa
Ep
NOTATION:
Modulus of elasticity of reinforcement and structural steel excluding prestressing reinforcement, MPa
Es
NOTATION:
Specified compressive strength of concrete, MPa
f’c
NOTATION:
Compressive strength of concrete at time of initial prestress, MPa
fci’
NOTATION:
Decompression stress; stress in the zero prestressing steel when stress is zero in the concrete at the same level as the centroid of the prestressing steel, MPa
fdc
NOTATION:
Compressive stress in concrete, after allowance for all prestress losses, at centroid of cross section resisting externally applied loads or at junction of web and flange where the centroid lies within the flange, MPa
fpc
NOTATION:
Compressive stress in concrete due to effective prestress forces, after allowance for all prestress losses, at extreme fiber of section if tensile stress is caused by externally applied loads, MPa.
fpe
NOTATION:
Stress in prestressing steel at nominal flexural strength, MPa
fps
NOTATION:
Specified yield strength of prestressing reinforcement, MPa
fpy
NOTATION:
Modulus of rupture of concrete, MPa
fr
NOTATION:
Tensile stress in reinforcement at service loads, excluding prestressing reinforcement, MPa
fs
NOTATION:
Compressive stress in reinforcement under factored loads, excluding prestressing reinforcement, MPa
f’s
NOTATION:
Effective stress in prestressed reinforcement (after allowance for all prestress losses), MPa
fse
NOTATION:
Specified yield strength of non-prestressed reinforcement, MPa
fy
NOTATION:
Development length in tension of deformed bar, deformed wire, plain and deformed welded wire reinforcement, or pretensioned strand, mm
ld
NOTATION:
Transfer length of prestressed reinforcement, mm
ltr
NOTATION:
Length of prestressing tendon element from jacking end to any point x, mm.
lx
NOTATION:
Modular ratio of elasticity, but not less than 6. Es/Ec
n
NOTATION:
The resultant tensile force acting on the portion of the concrete cross section that is subjected to tensile stresses due to the combined effects of service loads and effective prestress, N
Nc
NOTATION:
Prestressing force at jacking end, N
Ppj
NOTATION:
Prestressing force evaluated at distance lpx from the jacking end, N
Ppx
NOTATION:
Prestressing tendon force at jacking end
Ps
NOTATION:
Factored post-tensioned tendon force at the anchorage device.
Psu
NOTATION:
Vertical component of effective prestress force at section, N
Vp
NOTATION:
Density, unit weight of normal weight concrete or equilibrium density of lightweight concrete, kg/m³
Wc
NOTATION:
Total angular change of prestressing tendon profile in radians from tendon jacking end to any point x
a (alpha)
NOTATION:
Factor for type of prestressing reinforcement.
Yp
NOTATION:
0.55 for fpy/fpu not less than 0.80
0.40 for fpy/fpu not less than 0.85
0.28 for fpy/fpu not less than 0.90
Yp
NOTATION:
Increase in stress in prestressing reinforcement due to factored loads, MPa
∆fv
NOTATION:
Stress in prestressing reinforcement at service loads less decompression stress, MPa
∆fps
NOTATION:
Ratio of prestressed reinforcement
Aps to bdp
rhop
NOTATION:
Ratio of non-prestressed tension reinforcement
rho
