# Time dependent losses of prestress due to creep, shrinkage and relaxation, Δ`P`_{c+s+r}

_{c+s+r}

## Eurocode 2 part 1-1: Design of concrete structures 5.10.6 (2)

A simplified method to evaluate time dependent losses at location `x` under the permanent loads is given by:

(5.46) |

where:

- Δ
`σ`_{p,c+s+r} - is the absolute value of the variation of stress in the tendons due to creep, shrinkage and relaxation at location
`x`, at time`t` `ε`_{cs}- is the estimated shrinkage strain, in absolute value
`E`_{p}- is the modulus of elasticity for the prestressing steel, see § 3.3.6 (2) and § 3.3.6 (3)
`E`_{cm}- is the modulus of elasticity for the concrete
- Δ
`σ`_{pr} - is the absolute value of the variation of stress in the tendons at location
`x`, at time`t`, due to the relaxation of the prestressing steel. It is determined for a stress of`σ`=_{p}`σ`(_{p}`G`+`P`+_{m0}`ψ`_{2}`Q`) which is the initial stress in the tendons due to initial prestress and quasi-permanent actions `φ(t,t`_{0})- is the creep coefficient at a time
`t`and load application at time`t`_{0} `σ`_{c,QP}- is the stress in the concrete adjacent to the tendons, due to self-weight and initial prestress and other quasi-permanent actions where relevant
`A`_{p}- is the area of all the prestressing tendons at the location
`x` `A`_{c}- is the area of the concrete section
`I`_{c}- is the second moment of area of the concrete section
`z`_{cp}- is the distance between the centre of gravity of the concrete section and the tendons.

Compressive stresses and the corresponding strains should be used with a positive sign.

This application calculates
the time dependent losses Δ`P _{c+s+r}`
from your inputs.