# Losses In Prestresses

## Table of Contents

## Types of Losses In Prestresses

- Loss of prestress due to elastic deformation of concrete
- Loss due to Shrinkage
- Loss due to creep
- Loss due to relaxation
- Loss due to Anchorage slip
- Loss due to friction

The initial prestress in concrete steadily diminishes from the stage of transfer over time for a variety of reasons. This is commonly known as “Loss of Prestress.”

A reasonably good estimate of the magnitude of the loss of prestress is necessary from the design point of view. The above are some of the causes of loss of prestresses.

## Loss due to Elastic Deformation deformation of Concrete

Concrete’s average stress at the steel level and modular ratio determines how much prestress is lost as a result of elastic deformation.

**In Pretensioned PSC Beam**

Loss of prestress = m.fc (Sometimes the modular ratio is also denoted by <strong> \alpha </strong> )

m = modular ratio = \frac{Es}{Ec}

Es=2\: or \: 2.1*10^5 \: N/mm^2 Ec=5700\sqrt{fck} — **(page. No.16, IS1343)**

Fc= stress in concrete at the level of stress

Fc= \frac{P}{A}+\frac{Pe}{I}.e-\frac{M}{I}\times e**In Post-tensioned PSC Bean**

If the number of cables are pulled “simultaneously” then there is no loss of prestress

### Elastic Shortening

- In pre-tensioned concrete, when the prestress is transferred to concrete, the member shortens and the prestressing steel is also shorter, in it. So there is a loss of prestress
- In the case of post-tensioning, if all the cables are tensioned simultaneously there is no loss since the applied stress is recorded after the elastic shortening has completely occurred.
- If the cables are tensioned by one, there is a loss in a tendon during subsequent stretching of tendons.

If cables are pulled one by one then there is a loss of prestress

**Loss = m.Fc**

## Loss due to Shrinkage

Tensioned wires shorten as a result of concrete shrinkage in prestressed members, which adds to the stress loss.

The type of cement, particles, and curing technique employed all affect how much concrete shrinks.

The use of high-strength concrete with low water-cement ratio results in shrinkage and consequent loss of prestress.

Calculated of Loss due to shrinkage

**Loss = (Shrinkage Strain)*(Es)**

Where Shrinkage Strain = 0.0003 (for Pretension) —**(P.No.16 : IS1343)**

= \frac{0.0002}{\log_{10}{(t+2)}} (For Post tension) —**(P.No.16 : IS1343)**

Where,

t = Age of concrete, transfer in days

## Loss Due To Creep Of Concrete

The concrete of prestressed members experiences continuous prestress, which causes the concrete to creep and so lowers the stress in the high-tensile steel.

The loss of stress in steel due to the creep of concrete can be estimated if the magnitude of the ultimate creep strain or creep coefficient is known.

**(I). Using “Creep Coefficient” **

Where \phi = Creep Co-efficient —**(P.No.17 : IS1343)**

**(II). Using Ultimate Creep Strain **

E_{cs} = ultimate creep strain

## Loss due to relaxation of concrete

The reduction in stress with time at constant strain is called **Relaxation **

- decrease in the stress is due to the fact that some of the initial elastic strain is transformed into inelastic strain under constant strain.
- Stress decreases according to the remaining elastic strain
**Loss = (%) Initial prestress**

Loss of prestress due to relaxation of stress in steel as calculated as % of initial prestress

## Loss due to Anchorage slip of concrete

- Friction wedges in pre-tensioning systems typically slip a short distance as the tendon force is transferred from the jack to the anchoring ends.
- Additionally, anchorage blocks shift before they settle on concrete.
- The ensuing decrease in tendon length is the cause of loss of prestress.
- A certain quantity of prestress is released due to this slip of wise through the anchorages.
- The amount of slip depends on the type of wedge and stress in the wire

Loss Due To anchorage slip is calculated as below

[letex] Loss= \frac{\triangle E_s}{l} \:N/mm^2[/latex]

Where, \triangle = Amount of slip(mm)

l = Beam Span (mm)

\triangle= \frac{Pl}{AE} \: or \: \frac{\sigma l}{E}(This loss is only in the post-tensioned beam)

## Loss due to friction of concrete

In the case of post-tensioned members, the tendons are housed in ducts performed in concrete. The duct is either straight or follows a curved profile based on the specifications of the design, As a result of friction between the curved tendons and the surrounding concrete ducts, tensioning of the curved tendons causes stress loss in the post-tensioned members. The following categories describe the extent of this loss:

- Stress reduction is brought on by the curvature effect, which is dependent on the alignment or form of the tendons, which often follow a curved profile across the length of the beam.
- Stress loss as a result of the wobble effect, which is dependent on local variations in the cable’s alignment. Unintentional or inevitable misalignment occurs when ducts and sheaths cannot be precisely positioned to follow a predefined profile along the whole length of the beam, resulting in the wobble or wave effect.

Loss of prestress due to friction is calculated below

prestress at a section = p_x= P_o e^{-\mu \alpha +Kx} —**(P.No.25 : IS1343)**

P_o = Initial Prestress

\mu = coefficient of friction [0.55- concrete, 0.30- steel, 0.25-lead]

K = Wave effect or Wabble co-efficient ( 15*10^{-4}\: 50*10^{-4} ),

\alpha = cumulative angle

x = distance

### Losses In Prestresses

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