Reinforced Concrete Stress-Strain Diagram
Mander Concrete Model: Understanding Confined vs. Unconfined Concrete Behavior
In structural engineering, representing the true behavior of reinforced concrete is essential—not only for ensuring the safety of a structure but also for achieving long-term performance and durability. Especially in nonlinear analysis and seismic design, it’s critical to capture the complex stress–strain relationship of concrete. One of the most widely recognized models for this purpose is the Mander Concrete Model, developed in 1988 by Mander, Priestley, and Park.
This model provides a comprehensive framework to simulate both confined and unconfined concrete behavior under axial loads, offering engineers a reliable tool for advanced structural analysis and design.
What is the Mander Concrete Model?
The Mander model mathematically describes the nonlinear stress–strain response of concrete, especially under compression. Its primary advantage is the ability to realistically represent the post-peak softening and increased ductility that occurs due to lateral confinement, such as from ties or spirals in reinforced concrete sections.
Originally proposed by Mander et al. (1988), the model incorporates the influence of transverse reinforcement in enhancing the mechanical properties of concrete, making it particularly suitable for seismic design and ductility-focused evaluations.
Confined vs. Unconfined Concrete: Key Differences
To effectively apply the Mander model, it’s important to distinguish between confined and unconfined concrete:
Unconfined Concrete refers to concrete without lateral reinforcement. This type exhibits lower strength, brittle failure, and limited ductility. Once the peak stress is reached, the material rapidly loses its load-bearing capacity.
Confined Concrete includes concrete that is laterally supported by transverse reinforcement (e.g., stirrups, spirals). This confinement increases the axial strength, strain capacity, and energy dissipation ability of the concrete. The result is a more ductile and resilient structural behavior.
Modeling the Confinement Effect
The Mander model introduces the concept of effective lateral pressure to simulate the confinement provided by transverse reinforcement. This pressure is calculated based on:
The spacing and diameter of stirrups or spirals
The yield strength of the reinforcement
Geometric properties of the confined core
The presence of lateral pressure modifies both the peak stress and the softening slope of the concrete’s stress–strain curve. This results in:
A steeper ascent and gentler descent in the curve for confined concrete
A broader ductile region, representing enhanced deformation capacity
Higher ultimate strain values for confined sections
Why Use the Mander Model?
The Mander model remains a benchmark in reinforced concrete analysis due to its ability to:
Predict failure modes more accurately
Represent both elastic and plastic behavior under load
Quantify the structural benefits of transverse reinforcement
Enhance the accuracy of nonlinear finite element models
Practical Use in Engineering Applications
Modern engineering tools allow users to implement the Mander model to:
Generate stress–strain diagrams for both confined and unconfined concrete sections
Define custom cross-sectional properties
Download data such as stress and strain values in CSV format for further analysis or integration into design software
Reference
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.
