# How to include creep in a concrete slender column in Member

When designing slender reinforced concrete elements, the effects of imperfections, second order, and creep on transverse deformation have to be considered.

For a better understanding of the example on which the problem will be explained go through the tutorial Concrete slender column (EN).

The development of the transverse deformation of the compressed element is shown schematically in the figure above. The total load is composed of a long-term load *F** _{LT}* and a short-term load

*F*

*(variable load). Before loading begins, only the geometric imperfection*

_{V}*e*

*forms the transverse deflection of the element. Once the element is loaded with the*

_{0}*F*

*force, the transverse deformation increases to*

_{LT}*w*

_{LT}*(t*

_{0}*)*. Due to the creep, the transverse deflection will increase to

*w*

_{LT}*(t*

_{∞}*)*in the <t

_{0};t

_{∞}> time interval. The total transverse deflection at the end of the life of the structure (time

*t*

*) after the application of the short-term load*

_{∞}*F*

*is then*

_{V}*w*

_{LT+V}*(t*

_{∞}*)*. The second-order effect caused by this deflection governs the design of a slender compression member.

The individual components of the lateral deflection are shown schematically in the following figure.

Where:

*e*_{0}* * initial geometric imperfection defined by the design standard

*e*_{2,LT}*(t*_{0}*)* second order effect from a permanent *F** _{LT}* load, in time

*t*

*. This deflection also includes the effect*

_{0}of transverse loads or end moments. The value is the result of a GMNIA calculation in the member

(

*U*

*or*

_{x}*U*

*displacement), where the initial imperfection is set to*

_{y}*e*

_{0}*e*_{2,LT}^{CR}*(t*_{∞}*) *the increment to *e*_{2,LT}*(t)* that is caused by concrete creep in the time interval <*t** _{0}*;

*t*

*>.*

_{∞}*e*_{2,LT+V}* *second order effect at time *t** _{∞}* from constant (LT) and variable (V) loads. This value is automatically

taken into account by the program using the GMNIA calculation, where the imperfection is given by

*e*

_{0}*+ e*

_{2,LT}

^{CR}*(t*

_{∞}*).*

For the design of the compressed element, a value of *e*_{2,LT}^{CR}*(t*_{∞}*)* is required. **As deflection ****e**_{2,LT}^{CR}**(t**_{∞}**)**** increases over time, deflection ****e**_{2,LT}**(t)**** will increase simultaneously. **To accurately calculate the final value of *e*_{2,LT}^{CR}*(t*_{∞}*)*, it would be necessary to use a time-dependent analysis (TDA). In the current version, the program does not calculate this automatically and it must be determined manually by an iterative procedure, which is discussed below.

**The calculation steps in the member program are as follows:**

- GMNIA calculation of the response of the member to long-term loads
*F*with specified initial imperfection_{LT}*e*._{0} - Determination of total imperfection e
_{0}+*e*_{2,LT}^{CR}*(t*_{∞}*)* - GMNIA calculation of the response of the member to total load
*F*+_{LT}*F*_{V}_{ ,}with total imperfection e_{0}+*e*_{2,LT}^{CR}*(t*_{∞}*)*specified in the program

**Determination of the deflection ****e**_{2,LT}^{CR}**(t**_{∞}**):**

For the total deflection from permanent *F** _{LT}* loads at the end of life at time

*t*

*:*

_{∞}*w*_{LT}*(t*_{∞}*) = e*_{0}* + e*_{2,LT}^{CR}*(t*_{∞}*) + e*_{2,LT}*(t*_{∞}*)*

Conservatively:

*e*_{2,LT}^{CR}*(t*_{∞}*) = φ(t*_{0}*,t*_{∞}*) * e*_{2,LT}*(t*_{∞}*) *where* φ(t*_{0}*,t*_{∞}*) *is a creep coefficient

**The value of ****e**_{2,LT}**(t**_{∞}**)**** is determined by a GMNIA calculation with the total specified imperfection ****e**_{0}** + e**_{2,LT}^{CR}**(t**_{∞}**) = e**_{0}** + φ(t**_{0}**,t**_{∞}**) * e**_{2,LT}**(t**_{∞}**)****. Clearly, for this simplified and conservative approach, the value of ****e**_{2,LT}**(t**_{∞}**) ****"depends on itself" and has to be determined by iteration.**

You can iterate sequentially as shown below. The four steps of the iteration are shown. The variable labels are slightly different to keep the picture simple.

*φ(t*_{0}*,t*_{∞}*) = φ
e*

_{2,LT}*(t*

_{∞}*) = e*

_{2,LT,i }*w*

_{LT}*(t*

_{∞}*) = w*

_{LT,i}The video tutorial of gradual iteration described above is shown below. The excel file used in this tutorial is also attached.

Note: The load case LE4 contains only **long-term loads** (quasi-permanent combination) and is applied as a ULS load type. This means that the ULS material model is used to calculate the initial imperfection.

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### Attached Downloads

- Member creep (ZIP, 9 kB)