Losses in Prestress | Civil Engineering Optional Notes for UPSC PDF Download

Types of Losses in Prestress

The losses in prestressed concrete are categorized into two main groups: immediate (short term) and time-dependent (long term). Immediate losses occur during the prestressing operation and transfer of prestress to the concrete, while time-dependent losses occur over the service life of the structure. Here are the various types of losses:

Immediate (Short Term) Losses:

1. Friction Losses: Occur due to the resistance encountered by the prestressing steel as it passes through the duct or anchorages.

2. Elastic Shortening of Concrete: Results from the deformation of the concrete under the applied prestressing force, which leads to a reduction in prestress.

3. Anchorage Slip: Refers to the relative movement between the prestressing steel and the anchorage system, causing loss of prestress.

Time-Dependent (Long Term) Losses:

1. Creep of Concrete: Continuous deformation of concrete under sustained load, resulting in a gradual loss of prestress over time.

2. Shrinkage of Concrete: Contraction of concrete due to the loss of moisture, leading to a decrease in prestress.

3. Creep or Relaxation of Steel: Creep is the gradual increase in strain of the prestressing steel under constant stress, while relaxation is the decrease in stress of the steel over time, causing loss of prestress.

Losses in Pre-tensioning:

In pre-tensioning, the prestressing is done before the concrete is cast. The major losses include:

• Elastic Shortening of Concrete
• Creep or Relaxation of Steel
• Shrinkage of Concrete
• Creep of Concrete

Losses in Post-tensioning:

In post-tensioning, the prestressing is applied after the concrete has hardened. The major losses include:

• Friction Losses
• Creep or Relaxation of Steel
• Shrinkage of Concrete
• Creep of Concrete
• Anchorage Slip

Note: In post-tensioning, if all bars are tensioned simultaneously, there are no losses due to elastic shortening, but if the bars are tensioned sequentially, there will be a loss of prestress due to elastic shortening.

Loss in Prestress Due to the Friction

During stretching a curved tendon in a post-tensioned part, friction is formed at the interface of concrete and steel. There is a reduction in prestress along with the member from the stretched end. The stretching must also overcome the tendon’s wobbling in addition to friction. The change in location of the tendon along the duct is referred to as the wobble. Friction and wobbling losses are grouped together under friction. Frictional losses do not arise in pre-tensioned members since the tendon is not concretely tensioned in pre-tensioned members.

Loss of prestress due to the friction (σ_f)= (P₀/A)(K_w X+αμ)

where,

• K_w= wobbles friction loss
• X = L: When jacking from one end
• X = L/2: when jacking from both the ends
• α=Angle of a tendon (Radian)
• μ=Coefficient of friction

Losses in Prestress Due to Anchored Slip

Anchorage is a component that is used to attach the tendons to the concrete while terminating them. When the stressing process is over, the major role of anchorage is to transfer the stressing force to the concrete. Tendons are provided inside the ducts of a precast concrete member in the case of a post-tensioning system. To transfer the stressing force to the concrete, anchoring is supplied at both ends of the tendon. If the anchorage moves from its original position, the tendons loosen, resulting in prestress loss. The loss of stress due to anchorage slip does not occur in the pre-tensioned concrete. The tendons are monolithically implanted in the concrete when pre-tensioning.

The loss due to anchorage slip (σ_a)= (Δl/l)E_s

where,

• Δl = anchorage slip in mm
• l = Length of cable in mm
• E_s= Young’s modulus of steel (N/mm²)

Losses in Prestress Due to Elastic Shortening of Concrete

The loss is only encountered in the Pre-tension member; when the tendons are cut, and the prestressing force is transferred to the member, the concrete undergoes immediate shortening due to the prestress. In addition, the tendon shortens by the same amount. This results in a loss of prestress. Whereas if there is only one tendon, there is no loss because the applied prestress is recorded in the Post-tensioned member after the elastic shortening of the member. When more than one tendon is stretched sequentially, a tendon is lost during the successive stretching of the other tendons.

Loss of prestress due to elastic shortening of concrete (σ_e)= mσ_c

where:

• m = Modular ratio
• σ_c= Stress in the concrete at the level of a steel tendon

Losses in Prestress Due to Creep of Concrete

Creep is the deformation that occurs over time due to a constant force. Prestress is a permanent force in prestressed concrete that causes compressive stress at the steel level. As a result, the member is under stress. Loss of prestress due to concrete creep occurs in both the pretension and post-tension member.

Loss of prestress due to creep of concrete (σ_cr)= θmσ_c

where,

• m = Modular ratio
• σ_c= stress in the concrete at the level of a steel tendon
• θ = Creep coefficient (depends on the age of loading)

Losses in Prestress Due to Creep or Relaxation of Steel

Steel relaxation is described as a decrease in stress over time when under constant tension; due to the relaxation of steel, the pressure in the tendon is reduced with time. The stress loss due to relaxation depends on the types of steel, initial pressure, and temperature. Based on the observation, about 2 per cent loss occurs in pre-tensioned members, whereas about 3 per cent loss of stress occurs in post-tension members.

Losses in Prestress Due to Shrinkage of Concrete

The stress loss is aided by the shortening of tensioned wires caused by concrete shrinkage in prestressed members. In the case of pre-tensioned members, moist curing is usually used to keep them from shrinking until they are transferred. As a result, the total residual shrinkage strain in pre-tensioned members after prestress transfer will be greater than in post-tensioned members, where a portion of shrinkage will have already occurred at the time of stress transfer.

Loss in Pre-tensioned member

Strain due to shrinkage of concrete (ε_sh)= 0.0003

Stress due to shrinkage of concrete (σ_sh)= 0.0003E_s

(σ_sh)= 0.0003*2*10⁵

(σ_sh)= 60 MPa

Loss of Post-tensioned member

Strain due to shrinkage of concrete (ε_sh)= 0.0002/[ln(T+2)]

T= time of prestressing in days (normally 28 days)

Strain due to shrinkage of concrete (ε_sh)= 0.0002/ln(28+2)

(ε_sh)= 5.88 * 10^-5

Stress due to shrinkage of concrete (σ_sh)= 5.88 * 10^-5*(E_s)

(σ_sh)= 5.88 * 10^-5* 2 * 10⁵

(σ_sh)= 12 MPa

Therefore the loss of stress due to shrinkage is more in pre-tension members.

Note: Total Losses in prestressed concrete are listed in the table below.

In pre-tensioned members, the total loss is generally higher compared to post-tensioned members. This difference is primarily due to the fact that pre-tensioning involves applying the prestressing force to the tendons before the concrete has hardened. During this process, the concrete undergoes elastic shortening, which results in a higher total loss compared to post-tensioning, where the tendons are tensioned after the concrete has hardened and thus the elastic shortening is less significant.