Eurocode 2. Reinforced concrete structures

1.3 Properties of concrete

In the concrete properties, define the concrete type, concrete class and concrete state diagram. It is possible to set coefficients for concrete strength. By default, the recommended values for the selected normative document are set.

Accidental eccentricities are defined in order to increase the moments, taking into account the second order effects in eccentrically compressed bar elements. The minimum accidental eccentricities are calculated automatically.

Stress-strain diagram

The parabolic-rectangular diagram or the bilinear diagram is chosen as the design diagram for the state of compressed concrete by paragraphs 3.1.7 (1) and 3.1.7 (2) of SP RK EN 1992-1-1:2004/2011. These diagrams show how stresses and relative strains relate to one another.

Relative air humidity

The relative humidity (%) is defined to determine the nominal free shrinkage on drying of concrete with CEM cement of class N by clause 3.1.4 (6) of SP RK EN 1992-1-1:2004/2011.

α_ct - coefficient taking account of long term effects (tension)

According to clause 3.1.6 (2) of SP RK EN 1992-1-1:2004/2011, a coefficient α_ct is defined to take into account the long term effects on the tensile strength and the unfavourable effects resulting from the way the load is applied.

Conversion factor η to reduce γ_c based on testing in a finished structure or element

For concrete strength values that are based on testing in a finished structure or element, the partial safety factor γ_c may be reduced by conversion factor η. See clause A.2.3 (1) of SP RK EN 1992-1-1:2004/2011.

Coefficients which limit the stress

According to clauses 7.2 (2) and 7.2 (3) of SP RK EN 1992-1-1:2004/2011, the coefficients for analysis by serviceability limit states are as follows: k₁, which limits compressive stresses in concrete, and k₂, which limits compressive stresses in concrete during creep (which controls the choice of creep model). The recommended values are 0.3...1.

Creep coefficient

The final value of creep coefficient φ(∞, tn) is defined according to clause 3.1.4 (5) of SP RK EN 1992-1-1:2004/2011.

α_cc - coefficient taking account of long term effects (compression)

According to clause 3.1.6 (1) of SP RK EN 1992-1-1:2004/2011, a coefficient α_cc is defined to take into account the long term effects on the compressive strength and of unfavourable effects resulting from the way the load is applied. By default, α_cc is taken as equal to 0.85, for emergency combinations - as 1.2, for earthquake combinations - as 1. In analysis by serviceability limit states, it is always taken as equal to 1. The recommended values are 0.8...1.

γ_c - safety factor

The partial factor (safety factor) for concrete γ_c for persistent and transient (long-term and short-term) design situations is defined according to clause 2.4.2.4 (1) of SP RK EN 1992-1-1:2004/2011. By default, γ_c is taken as equal to 1.5, for emergency and earthquake combinations - as 1.2, for analysis by serviceability limit states (check for cracks) - as 1. The recommended values are 1...2.

Accidental eccentricities (bar)

Accidental eccentricities in two directions of the section in the X1OZ1 (EY, moment My) and X1OY1 (EZ, moment Mz) planes are defined.

Exact geometrical parameters in design

Option to modify the partial safety factor for materials in case there are accurately measured dimensions; see clause A.2.2 SP RK EN 1992-1-1:2004/2011.

First order effects (Geometric imperfections)

Option to take into account the first order effects (unfavourable effects without taking into account the strain of the structure, but with account of geometric imperfections), see clause 5.2 of the SP RK EN 1992-1-1:2004/2011.

Second order effects

Option to take into account the second order effects (additional unfavourable effects due to strain of the structure), see clause 5.1.4 of the SP RK EN 1992-1-1:2004/2011. In the list, select for which calculations they should be taken into account (Stiffness+Curvature, Stiffness, Curvature).

Table of design parameters

For the selected concrete class, the normative and design parameters are displayed:

• E_cm - modulus of elasticity;
• f_ck - characteristic compressive cylinder strength of concrete at 28 days;
• f_ck_cube - characteristic cube compressive strength of concrete at the age of 28 days;
• f_cm - mean value of concrete cylinder compressive strength;
• f_ctm - mean value of axial tensile strength of concrete;
• f_ctk_005 - characteristic axial tensile strength of concrete;
• (other).

The table may be modified for additional, user-defined classes of concrete.

1.4 Properties of reinforcement

Class, type and strength of longitudinal reinforcement

In the list, select the class of longitudinal reinforcement: A, B, C. The type of longitudinal reinforcement is selected from the list according to t. C.2N of SP RK EN 1992-1-1:2004/2011. The characteristic (normative) yield strength of the longitudinal reinforcement is specified - yield strength f_yk according to t. C.1 SP RK EN 1992-1-1:2004/2011.

Class, type and strength of transverse reinforcement

The class and type of transverse reinforcement are selected from the lists. The characteristic (normative) yield strength of longitudinal reinforcement f_yk is defined.

Ductility characteristics. Tensile strength to yield strength ratio

For longitudinal and transverse reinforcement, define the ratio k=f_tk/f_yk of the tensile strength of the reinforcement to the yield strength, the minimum value, according to t. C.1 SP RK EN 1992-1-1:2004/2011.

Ductility characteristics. Characteristic strain at maximum force

For longitudinal and transverse reinforcement, the characteristic strain (maximum elongation) at maximum force μ_uk, % is specified according to t. C.1 SP RK EN 1992-1-1:2004/2011.

Partial factor

For longitudinal and transverse reinforcement in analysis by ultimate limit state (ULS) for persistent and transient design situations, the partial factor i_s is defined according to clause 2.4.2.4 of SP RK EN 1992-1-1:2004/2011. By default, both coefficients i_s are taken as equal to 1.15, for emergency and earthquake combinations - equal to 1, for serviceability limit states (SLS, check for cracks) - equal to 1. The recommended values are 1...2.

Type of reinforcing cage

The type of reinforcing cage (tied, welded) is selected from the list.

Maximum diameter

For bars, the maximum diameter of longitudinal reinforcement used in strength analysis of reinforcement is defined (6, 8, 10, 12, 14, 16, 18, 18, 20, 22, 25, 28, 32, 36, 40).

Number of rebars in section corners

To select reinforcement with the corner rebar selection algorithm, the number of rebars located in the corners of the section should be defined.

Steel tables

Define the range of diameters that should be applied.

Coefficients which limit the stress

According to clauses 7.2 (5) of SP RK EN 1992-1-1:2004/2011, the coefficients for analysis by serviceability limit states are as follows: k₃, which limits tensile forces in reinforcement, and k₄, which limits tensile forces in reinforcement in forced strain. The recommended values are 0.3...1.

Analysis of transverse reinforcement

To calculate transverse reinforcement by truss model, the angles θ between the concrete compressed diagonal element and the beam axis perpendicular to the transverse force are specified separately for basic (persistent and transient design situations), emergency and earthquake combinations. In the appropriate list, define the method to determine the following data: Analysis (the angle will be computed), Angle (it is necessary to define the angle from 21.8 to 45°), Range (angles in the range of 21.8...45° will be used for analysis). For the ultimate values of the angle θ, see clause 6.2.3 (2) of SP RK EN 1992-1-1:2004/2011. When the certain check box is selected, the value of ctg θ may be 'limited with the length of the StE' (length of the structural element).

Table of design parameters

For reinforcement classes (longitudinal, transverse), the normative and design parameters are displayed:

• f_yk - characteristic (normative) yield strength of longitudinal reinforcement;
• class;
• D - diameter, mm;
• f_yd - design yield strength of longitudinal reinforcement;
• f_tk - characteristic (normative) tensile strength of reinforcement;
• f_ywd - design yield strength of stirrups;
• E_s - modulus of elasticity;
• k (f_tk/f_yk) - ratio of tensile strength of reinforcement to yield strength, minimum value;
• eps_uk - characteristic strain at maximum force.

2. Analysis of reinforcement in bar elements

To analyse reinforcement in bars, the universal iterative optimizing methods are implemented; so using the same method it is possible to analyse sections:
1 - of arbitrary shape (rectangular, cross, T-section, I-section, box, angle, circular, ring);
2 - with arbitrary arrangement of reinforcement;
3 - on arbitrary types of stress strain state, such as flat bending, oblique bending, bending with torsion, flat eccentric compression - tension, simultaneous action of all six types of forces - N, Mx, My, Mz, Qy, Qz.

The fundamental provisions of the building codes are implemented in analysis of reinforcement.

Optimising principles are implemented in the iterative algorithms: reinforcement in the most stressed areas of the section is increased as a priority, and the mutual influence of reinforcement selected according to different DCLs is considered. The realised algorithms meet the requirements of slenderness, as the user could assign the modes of rebar selection:

• select the type for arrangement of reinforcement in the cross-section (symmetric relative to one or two principal axes of the cross-section, uniform arrangement of reinforcement along certain faces, arbitrary arrangement of reinforcement);
• assign the 'corner bars' mode, in which the reinforcement area is increased mainly in the corner zones according to the universal algorithm; in some cases, this strategy can help you use 20-30% less reinforcement than in alternative cross-sectional reinforcement arrangements;
• assign max diameters of rebars when the reinforcement is analysed by serviceability limit state, as the smaller diameters improves the strength of the RC element to cracks and in this case the area of the required reinforcement may be significantly reduced;
• adjust parameters of the iterative process, slightly reducing the accuracy in analysis of reinforcement (in this case the error may be 3-5%), but significantly increasing the speed of the algorithm and vice versa.

3. Analysis of reinforcement in plates

In LIRA-FEM program it is possible to analyse reinforcement area for plate elements according to Wood's theory. There is an algorithm to obtain the area of reinforcement for plate elements by Wood's theory with optimisation of tangential stresses.

When the 'Ductility' option is selected, then in the analysis of RC sections according to SP RK EN 1992-1-1:2004/2011, TKP EN 1992-1-1-2009*, EN 1992-1-1:2004, IDT it is possible to use a modified algorithm to check equilibrium and calculate stresses and strains at arbitrary points of the section. For the Wood-Armer method, this algorithm is used to analyse reinforcement by ultimate and serviceability limit states. This method enables the user to make the analysis faster and to obtain a smoother distribution of reinforcement in the plane of the plate. This algorithm is implemented in the analysis according to SP RK EN 1992-1-1:2004/2011, EN 1992-1-1:2004, DBN B.2.6-98:2009, TKP EN 1992-1-1:2009, DSTU-N B EN 1992-1-1:2010.

After the check of the bearing capacity of sections with a specified reinforcement according to SP RK EN 1992-1-1:2004/2011, TKP EN 1992-1-1-2009 *, EN 1992-1-1:2004, IDT, the reserve factor for load-bearing capacity will be obtained for each plate and in each section of bar.

Strength analysis of the specified longitudinal reinforcement: for bars - in N, My, Mz, for plates - in Mx, My, Mxy, Nx, Ny, Txy. The following checks are also available:
- complete check (including the check for the combined action of torque and shear force and the combined action of torque and bending moment),
- for strength,
- for torque (bars),
- for shear forces,
- for crack propagation.