Reinforced Concrete Stress-Strain Diagram
You can obtain the stress–strain diagram of confined and unconfined concrete sections based on the Mander concrete model by defining the section properties using the program above. Additionally, you can download the corresponding stress and strain values for the defined section to your computer in CSV (Excel) format.
The ultimate compressive strain (εcu) for confined concrete is given below:
Mander Concrete Model: Confined and Unconfined Concrete Behavior
In structural engineering, accurately modeling the real behavior of reinforced concrete elements is critical for both the safety of the load-bearing system and long-term durability. Particularly in nonlinear analyses, advanced models are needed to describe the complex stress-strain behavior of concrete. In this context, the Mander Material Model is a reliable behavioral model applicable to both confined and unconfined concrete.
The Mander material model was developed in 1988 by M.P. Mander, M.J.N. Priestley, and P.G. Park (Mander et al., 1988). In this study, the effects of lateral reinforcement pressure on concrete were examined in detail, and a model was proposed that mathematically defines the stress-strain curves for both confined and unconfined concrete.
You can access the related article here.
What is the Mander Concrete Model?
The Mander material model is a mathematical approach based on the stress-strain relationship that expresses the nonlinear behavior of concrete under axial load. The primary objective of the model is to numerically define the softening behavior that concrete exhibits after reaching its peak strength and to quantify the contribution of lateral reinforcement (confined effect) to this process.
This model was developed to more accurately predict the energy dissipation capacity, ductility level, and plastic deformation capability of reinforced concrete elements.
Confined and Unconfined Concrete: Structural Behavior Differences
For effective use of the Mander model, it is essential to understand the differences between confined and unconfined concrete:
Unconfined Concrete: Concrete exposed to axial load without any lateral reinforcement (stirrups, ties, etc.). In this case, concrete’s strength is limited, and after reaching its peak strength, it tends to fail in a brittle manner. Its ductility level is low.
Confined Concrete: Concrete surrounded by lateral reinforcements (e.g., spirals or stirrups) is subjected to internal pressure due to the lateral reinforcement preventing outward expansion. This confinement effect allows the concrete to achieve higher strength and increased deformation capacity. Confined concrete behaves more ductile and has a much higher energy dissipation capacity.
How Does the Mander Model Represent Confinement Effect?
The Mander model represents the confinement effect through the concept of effective lateral pressure. Lateral confinement pressure is calculated using stirrup spacing, reinforcement diameter, yield strength, and the dimensional properties of the concrete. This pressure alters both the peak point and the softening slope of the stress-strain curve.
Unconfined Concrete Curve: Low peak strength, limited deformation, and sharp strength loss.
Confined Concrete Curve: Higher peak strength, wider ductile region, and a more gradual strength reduction until failure.
In this way, the entire behavior spectrum of concrete — from the elastic region to plastic deformation and ultimately to failure — can be modeled more accurately.
(mander confined concrete model excel)
1- Mander, J. B., Priestley, M. J. N., & Park, R. (1988). Theoretical Stress–Strain Model for Confined Concrete. Journal of Structural Engineering, 114(8), 1804–1826.