LOSSES OF PRESTRESS
FRICTION AND
ELASTIC
SHORTENING
BAGAMASBAD, RONNEL B.
MANDANI, VICTOR O.
OAQUIERA, MARK ANTHONY I.
SAPUGAY, JOHN PAUL P.
VILLANUEVA, WALTER R.
BSCE 4C
2023
CONTENTS
01
02
03
INTRODUCTION
•
Losses in
prestress
TYPES OF LOSSES
IN PRESTRESS
• Short Term or
Immediate Losses
• Long Term or Time
Dependent Losses
NOTATIONS/
GEOMETRIC
PROPERTIES
04
05
06
ELASTIC
SHORTENING
•
•
Definition
Formulas
FRICTION
•
•
Definition
Formulas
SAMPLE
PROBLEMS
01
INTRODUCTION
LOSSES OF PRESTRESS
The gradual reduction of
the introduced
compressive stress in a
prestressed member due
to various reasons to
mitigate tensile strains
caused by a load is
called losses of prestress.
LOSSES OF PRESTRESS
LOSSES IN VARIOUS PRESTRESSING SYSTEM
TYPE OF LOSSES
PRETENSIONING
POST-TENSIONING
1. ELASTIC SHORTENING
YES
a.) NO, if all the cables are
simultaneously tensioned.
b.) If the wires are tensioned in
stages loss will exist.
2. FRICTION LOSS
NO
YES
3. ANCHORAGE SLIP
NO
YES
4. CREEP
YES
YES
5. SHRINKAGE
YES
YES
6. RELAXATION OF
STEEL
YES
YES
02
TYPES OF LOSSES IN
PRESTRESS
TYPES LOSSES OF PRESTRESS
Short-Term (Immediate Losses)
- immediate losses occurs
during prestressing of tendons,
and transfer of prestress to
concrete members.
1. Elastic Shortening
2. Friction
3. Anchorage slip
TYPES LOSSES OF PRESTRESS
Long-Term
(Time Dependent Losses)
- time dependent losses
occurs during service life of
prestressed members.
1. Creep
2. Shrinkage
3. Relaxation
TYPES LOSSES OF PRESTRESS
CAUSES OF THE VARIOUS PRESTRESS
03
NOTATIONS /
GEOMETRIC
PROPERTIES
NOTATIONS
NOTATIONS
GEOMETRIC PROPERTIES
NOTATIONS
04
Losses in Prestress due to
ELASTIC
SHORTENING
ELASTIC SHORTENING
Pre-tensioned Members
When the tendons are cut and the
prestressing force is transferred to the
member, the concrete undergoes
immediate shortening due to the
prestress. The tendon also shortens by
the same amount, which leads to the
loss of prestress.
ELASTIC SHORTENING
Post-tensioned Members
If there is only one tendon, there is
no loss because the applied prestress is
recorded after the elastic shortening of
the member. For more than one
tendon, if the tendons are stretched
sequentially, there is loss in a tendon
during subsequent stretching of the
other tendons.
ELASTIC SHORTENING
The elastic shortening loss is quantified
by the drop in prestress (Δfp) in a tendon due
to the change in strain in the tendon (Δεp). It
is assumed that the change in strain in the
tendon is equal to the strain in concrete (εc)
at the level of the tendon due to the
prestressing force. This assumption is
called
strain
compatibility
between
concrete and steel. The strain in concrete at
the level of the tendon is calculated from
the stress in concrete (fc) at the same level
due to the prestressing force. A linear
elastic relationship is used to calculate the
strain from the stress.
ELASTIC SHORTENING
ELASTIC SHORTENING
05
Losses in Prestress due to
FRICTION
FRICTION LOSS
In prestressed concrete, loss of prestress due
to friction refers to the reduction in the amount of
initial prestressing force that is transmitted to
the concrete due to frictional resistance between
the tendons (prestressing steel) and the
surrounding concrete.
The loss of prestress due to friction can occur
during the installation of prestressing tendons,
as well as over time due to various factors such
as the relaxation of the steel and the creep and
shrinkage of the concrete. This can lead to a
reduction in the overall effectiveness of the
prestressing system, affecting the performance
and durability of the structure.
FRICTION LOSS
In post-tensioned members, tendons
in ducts or sheaths.
If the profile of cable is Linear, the loss
will be due to straightening of the cables
called wobble effect.
If the profile is Curved, there will be
loss in stress due to friction between
tendon and the duct or between the
tendons themselves.
FRICTION LOSS
FRICTION LOSS
The magnitude of prestressing force, Px at any distance, x
from the tensioning end follows an exponential function of
the type,
Px = 𝑷𝒐 𝒆−(𝝁𝜶+𝒙𝒙)
Where,
Po = Prestressing force at the jacking end.
μ = Coefficient of friction between cable and the duct.
a = Cumulative angle in radian through which the tangent to
the cable profile has turned b/w any two points under
consideration.
k = Friction Coefficient
Px = Po [1- (μa + kx)]
Px = Po – Po(μa + kx)
Po (μa + kx) = Po - Px
Loss = Po(μa + kx)
FRICTION LOSS
FRICTION LOSS
The calculation of loss in prestress due to
friction can be complex, as it depends on a variety of
factors. However, there is a general formula that can
be used as a starting point for estimating the
amount of loss due to friction:
Lp = μ x fp x Le
where:
Lp = loss of prestress due to friction
μ = coefficient of friction between the tendon and the
surrounding concrete
fp = initial prestress force in the tendon
Le = effective length of the tendon
This formula assumes that the tendon is straight
and the frictional resistance is evenly distributed
along its length. In reality, the frictional resistance
can vary along the length of the tendon depending on
factors such as the curvature of the tendon and the
presence of obstructions.
06
Losses of Prestress due to
SAMPLE
PROBLEMS
in
Elastic Shortening
in
Friction Loss
CONTENT
Thank you.