Losses in Prestress: Types of Losses in Prestress

Types of Losses in Prestress

The losses are majorly classified into two groups, immediate (Short term) and time-dependent (Long term). The immediate losses occur when the tendons are prestressed and prestress is transferred to the concrete part, and time-dependent occurs when the prestress members are used or in its service life. The various types of losses are listed below.

Immediate (Short term)

• Losses due to friction.
• Losses due to elastic shortening of concrete.
• Losses due to anchorage slip.

Time-Dependent Losses (Long term)

• Losses due to creep of concrete.
• Losses due to shrinkage of concrete.
• Losses due to creep or relaxation of steel.

Pre-tensioning and post-tensioning are the two procedures for imparting prestressing to a concrete member. Pre-tensioning occurs before the concrete is cast, while post-tensioning occurs after the concrete has hardened. Various forms of losses can occur depending on the prestressing technique.

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Losses in Pre-tensioning

• Losses due to elastic shortening of concrete.
• Losses due to creep or relaxation of steel.
• Losses due to shrinkage of concrete.
• Losses due to creep of concrete.

Losses in Post-tensioning

• Losses due to friction.
• Losses due to creep or relaxation of steel.
• Losses due to shrinkage of concrete.
• Losses due to creep of concrete.
• Losses due to anchorage slip.

When all the bars are tensioned simultaneously, there are no losses owing to elastic shortening in the post-tensioning. However, if the bars are successfully tightened, prestress will be lost owing to elastic shortening.

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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)

Age of loading	Creep Coefficient ()
7 days	2.2
28 days	1.6
1 year	1.1

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.

Types of loss	Pretensioned (Percentage)	Post-tensioned (Percentage)
Elastic shortening of concrete	3	1
Shrinkage of concrete	7	6
Creep of concrete	6	5
Relaxation of steel	2	3
Total Loss	18	15

The total loss in the pre-tensioned member is more than the total loss in the post-tensioned member; it differs mainly due to the elastic shortening of concrete.

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