Online Manuals RFEM 6 / RSTAB 9 | Concrete Design

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Dipl.-Ing. Juliane Stopper-Akdag

2026-03-12

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Concrete Design Add-on

Theoretical Principles

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Tables for Concrete Design
Graphics for Concrete Design
- Design Checks
  
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Documentation

Confined compression members

By confining the concrete cross-section using transverse reinforcement, the lateral strain of the concrete is limited, thereby increasing its compressive strength and ductility. The effect is schematically illustrated in the following image from [2].

Circular and Rectangular Compression Elements with Confining Reinforcement (Source: [2])

These effects are important for the seismic design of columns, as they ensure the availability of plastic deformation capacities and can improve the overall load-bearing capacity of the structure during an earthquake.

Design Model According to Eurocode 2

An explicit design approach for confined compression members is not specified in DIN EN 1992-1-1.

According to section 3.1.9 of DIN EN 1992-1-1 [1], a multiaxial stress state can be considered in the design by adopting a modified effective stress-strain relationship with increased strengths and enlarged ultimate strains. It is important to note that these increased strength and strain values apply exclusively to the confined concrete core, which is bounded by the centerlines of the confining reinforcement.

The contribution of the concrete cover to the load-bearing capacity (Ultimate Limit State) is generally not considered, as any effective contribution from the concrete cover is usually absent due to spalling.

If no more precise information is available, a parabolic-rectangular diagram according to [1], Figure 3.6, can be used for the confined core concrete. Correspondingly adjusted characteristic strength and strain values should be applied.

Diagram of the stress-strain relation for concrete under multiaxial compressive stress according to EC2.

Stress-Strain Behavior of Concrete Under Multiaxial Compression [1]

The strength of the confined core concrete is described by the following formula.

f_{c k, c} = \{\begin{cases} f_{c k} \cdot (1, 000 + 5, 0 \cdot \frac{σ_{2}}{f_{c k}}) & f ü r σ_{2} \leq 0, 05 \cdot f_{c k} \\ f_{c k} \cdot (1, 125 + 2, 5 \cdot \frac{σ_{2}}{f_{c k}}) & f ü r σ_{2} > 0, 05 \cdot f_{c k} \end{cases}

σ2	Efficient transverse compression stress in the ULS due to transverse strain restriction

Characteristic Strength of Constricted Reinforced Concrete Core According to EC 2, (3.24) & (3.25)

The characteristic strains are determined from the following formulas.

ε_{c 2, c} = ε_{c 2} \cdot {(\frac{f_{c k, c}}{f_{c k}})}^{2}

εc2	Concrete elongation upon reaching f_ck according to EC2, Table 3.1

Concrete Strain Upon Reaching f_ck,c According to EC2, (3.26)

ε_{c u 2, c} = ε_{c u 2} + 0, 2 \cdot \frac{σ_{2}}{f_{c k}}

εcu2	Concrete ultimate strain under uniaxial compressive stress EC2, Table 3.1

Concrete Ultimate Strain Under Multiaxial Compression EN 1992-1-1, (3.27)

Eurocode 2 does not provide a proposal for determining the lateral pressure. According to DAfStb booklet 630 [2], 3.5.4, reference is therefore made to the approaches by Mander et al. The determination equations for the lateral pressure are described in the following section. σ₂ = σ'_l

Calculation Model According to Mander et al.

The model by Mander et al. explicitly describes the stress-strain behavior of confined concrete depending on the effective confinement pressure. From this, an increased effective compressive strength and an enlarged peak strain of the confined core concrete are derived, as well as a ductile, gently descending stress-strain branch. Input variables include the reinforcement content and arrangement of the stirrups/spirals, their steel strength, and the geometry of the enclosed core cross-section.

Comparison of the stress-strain relation of concrete and constricted concrete according to Mander [3], displayed in blue and red.

Stress-Strain Relation for Concrete and Constricted Concrete According to Mander [3]

The stress-strain relationship is described by the following equation, [3] (3), (4), (6), (7) & (8).

σ_{c} = \frac{f_{c c} \cdot x \cdot r}{r - 1 + x^{r}}, m i t : x = \frac{ε_{c}}{ε_{c c}} u n d r = \frac{E_{c}}{E_{c} - E_{s e c}}

E_sec	=f_cc/εcc
E_c	=5,000·fc

Stress Equation According to Mander or Popovics

The associated strain can be described using the following formula, [3] (5).

ε_{c c} = ε_{c} \cdot (1 + 5 \cdot (\frac{f_{c c}}{f_{c}} - 1))

Strain Upon Reaching Compressive Strength of Connstricted Core Concrete According to Mander et. al.

The compressive strength of the confined concrete is determined according to [3] (29).

f_{c c} = f_{c} \cdot (- 1, 254 + 2, 254 \cdot \sqrt{1 + \frac{7, 94 \cdot σ'_{l}}{f_{c}}} - 2 \cdot \frac{σ'_{l}}{f_{c}})

Compressive Strength of Constricted Concrete

The effective lateral pressure stress for this can be determined from the equation below.

σ'_{l} = \frac{1}{2} \cdot ω_{v} \cdot f_{y w} \cdot k_{e}, m i t : ω_{v} = \frac{4 \cdot A_{s w}}{d_{c} \cdot s_{c}}

k_e	Effective Constriction Coefficient
ωv	Volume ratio between confining reinforcement and confined core concrete
f_yw	Yield stress of the transverse reinforcement

Effective Transverse Compression Stress According to Mander et. al.

The confinement effectiveness coefficient is determined according to the following expression.

k_{e} = \frac{A_{e c}}{A'_{c c}}

A_ec	Surface of the efficiently constricted concrete core

Effectiveness Coefficient of Constriction

Where the net area of the core concrete can be determined from:

A'_{c c} = A_{c c} \cdot (1 - ρ_{c c}) = A_{c c} - A_{s l}

ρcc	=A_sl/A_cc longitudinal reinforcement ratio of the constricted concrete core

Cross-Sectional Area of Constricted Concrete Core

The effectively confined concrete area can be determined from

A_{e} = \frac{π}{4} \cdot {d_{c}}^{2} \cdot {(1 - \frac{s'}{2 \cdot d_{c}})}^{2} f ü r K r e i s q u e r s c h n i t t e

A_{e} = (b_{c} \cdot a_{c} - \sum_{i = 1}^{n} \frac{(w'_{i}) ²}{6}) \cdot (1 - \frac{s'}{2 \cdot b_{c}}) \cdot (1 - \frac{s'}{2 \cdot a_{c}}) f ü r R e c h t e c k q u e r s c h n i t t e

d_c	Diameter of the constricted core concrete
a_c, b_c	Horizontal dimensions of the constricted core concrete
s'	Light spacing of the confining reinforcement in the direction of the compressive stress
w'_i	Clear distance between the longitudinal rebars

Efficiently Constricted Concrete Surface According to Mander et al.

Application

The design model according to EC2, 3.1.9 is used for standard-compliant ultimate limit state verifications where an increase in compressive strength due to confinement is permissible.

The Mander model (Mander et al., 1988) is used as a physically based material model when the complete σ_c - ε_c behavior of confined core concrete (increased f_cc, ε_cc, post-peak behavior) should be considered for nonlinear analyses.

References

European Committee for Standardization (CEN). (2010). Eurocode 2: Design of Concrete Structures – Part 1‑1: General Rules and Rules for Buildings, EN 1992‑1‑1:2004 + AC:2010. Brussels, CEN.
German Committee for Structural Concrete e.V. (2018). Heft 630: Bemessung nach DIN EN 1992 in den Grenzzuständen der Tragfähigkeit und der Gebrauchstauglichkeit. Berlin, DAfStb.
Mander, J.B., Priestley, M.J.N. and Park, R. (1988) Theoretical Stress-Strain Model for Confined Concrete. Journal of Structural Engineering, 114, 1804-1825.

Parent Chapter

Design in Seismic Situation