Introduction

Table of Content

Last month, we had an interesting and long discussion over the email with the creator of PCTempflow, a widely used software for fire analysis, and others like PCSheetPileWall and Framework: Gerrit Wolsink.

Over the course of the many emails, we have agreed that there is something wrong (or incompatible) in the Eurocodes.

This brief article is our joint effort on clarifying our views on this problem. If you have any input, please feel free to reach out.

Summary

The article might be hard to follow if the reader has not dived in to the same issues before. Therefore, a brief summary is presented here:

• EN-1992-1-2 (Structural Fire Design) recommendations for stress-strain curve at elevated temperatures are not in-line with EN-1992-1-1.
• This inconsistency might results in under-estimation of structural forces during fire, and worse, in case of coupled analysis, both during fire and in statical conditions. (If the software uses the same stress-strain curve at room temperature.)
• There is no direct solution for non-linear analyses aside from tweaking the curves to reach a reasonable stiffness.

For linear analyses, E-modulus degradation recommendations in literature should be taken into account.

• Use of fcm instead of fck in EN-1992-1-2 curves helps, but does not solve the issue. (EN-1992-1-1 uses fcm, EN-1992-1-2 uses fck).

Problem Statement

EN 1991-1-2 clarifies the requirements for structural fire design. For a proper fire analysis, we need at least two of the stress, strain and stiffness of concrete at elevated temperatures. EN 1991-1-2 gives us the strength degredation with increasing temperature as a table and stress-strain relationships at elevated temperatures.

Characteristic Compressive Strength Degradation at Elevated Temperatures

Stress-Strain Relationships of Concrete at Elevated Temperatures

EN 1991-1-2 does not have any recommendation for stiffness and we know that we can calculate the stiffness of the concrete by dividing stress to strain. The problem starts here.

Stiffness using EN-1992-1-2 Approach

All comparisons throught the article will be performed for C40/50 concrete with siliceous aggregates.

The main problem

<aside> <img src="/icons/exclamation-mark_yellow.svg" alt="/icons/exclamation-mark_yellow.svg" width="40px" /> Stiffness at room temperature calculated by EN 1992-1-2 stress-strain diagram is not equal to EN-1992-1-1 recommendation.

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Let’s do this for C40 concrete. As per definition in Eurocode, the stiffness is secant stiffness measured from approximately 40% of the fck. Of course we do not expect to reach the exact E-modulus in Eurocode, but difference is significant.

Compared to 35 GPa at EN-1992-1-1 for C40 concrete, the calculation using EN-1992-1-2 results in 23.7 GPa.