Concrete in compression area

Introduction

Reinforced concrete is a heterogeneous composite material. Its behavior is mainly influenced by the following four components.

• Nonlinear σ-ε relation
• Compression failure
• Crack development under tension
• Strength modification of confined concrete

Concrete in compression area

Material Behavior

Under short-term uniaxial compression, concrete shows the stress-strain behavior shown in the figure below. This can be roughly divided into three areas.

Nonlinear Compression Behavior of Concrete

Range I
In the range up to approximately σ_c ≤ 0.4·f_c, the concrete shows almost linear elastic behavior.

Range II
As the load increases, micro cracks form, leading to a decrease in stiffness and a disproportionate increase in strain until reaching the compressive strength f_c.
Both the stiffness reduction and the achievable strength are strongly dependent on the loading velocity. The fatigue strength is reduced compared to the short-term strength.

Range III
In deformation-controlled tests, stresses in the adjacent area decrease with increasing strain due to progressive destruction of the concrete structure. The curve distribution in the descending zone is the result of the local damage or loosening of the concrete body.
In the case of load-controlled tests, the third area would not show up; brittle failure occurs.

Material Model

To describe the material behavior in the compression zone for uniaxial loading, the following function according to (3.14) was added to EN 1992-1-1.

1. $$\frac{{\sigma }_c}{f_{cm}}=\frac{k·\eta -{\eta }^2}{1+(k-2)·\eta }$$

   η	=εc/εc1
   εc1	Compressive strain for maximum value of concrete compressive stress
   k	1.05·Ecm ·|εc1 |/fcm

   Concrete Stress-Strain Diagram for Nonlinear Method

The following figure shows the resulting curve.

Stress-Strain Behavior of Concrete in Compression Area

According to EC 2, 3.1.5(2), it is permissible to use other idealized stress-strain diagrams if they adequately represent the behavior of the concrete of interest.

Assumptions for SLS

The stress-strain diagram according to EC 2, (3.14) for concrete is calculated for the serviceability limit state design with the mean strengths of the materials.

Assumptions for the ULS

The stress-strain diagram according to EC 2, (3.14) for concrete may be used for the ultimate limit state design. In the equation and in the k-value, f_cm is replaced by the design value of the concrete compressive strength f_cd and E_cm by E_cd = E_cm/γ_CE (5.20).